The Center for American History

The University of Texas at Austin

This is Harry Lucas. Its July 21, 1998 at St. Edmund Hall. Albert Lewis and I are talking with G. M. (Mike) Reed, and were having a very good discussion about his background to the point of being at University of Wisconsin. Okay, go ahead Mike. [break in tape] Its July 21, 1998, and this is a continuation of the Mike Reed interview.

[tape has a lot of background noise and is very difficult to understand]

Mike Reed: I was lucky to get exposure to world-class people doing what
I wanted to do at a very early age, but the topology connection I had was
at Auburn with Ben Fitzpatrick and the other topologists there, especially
Phil Zenor. Ben (Fitzpatrick) was my Moore. What Phil provided me was a
role model of - Phil just came in from Houston as a young assistant professor
who was ambitious and coached me like mad and brought things together.
I learned how to play the game a bit.

Harry Lucas, Jr. Was he a student of Howard Cook?

Reed: Traylor..

Harry Lucas: How do you spell his last name?

Reed: Zenor, Z-E-N-O-R. So, Ben who was the motivating force and got
me started in watching Phil (Zenor) operate, and Phil was very good. That
was before I left Auburn, and at Auburn. I mean we had Kuratowski. I drank
beer with Kuratowski in Auburn. Bing had been there. I couldnt have been
at - the first AMS meeting I went to in Auburn, Alabama, I went to the
national meeting of the American Mathematical Society. I had breakfast
with Bing who was or just had been President of the American Mathematical
Society, and I had tea in his apartment during the meeting with Gayle Young
who at that time was President of the Mathematical Association of America.
I mean, not too many people can come from a southern state university and
walk into a national meeting and have that sort of contact. I first met
Mary Ellen Rudin who came to my talk at that meeting. I spent the night
in her room talking to her and her students. So, Auburn got me that, and
I couldnt have gotten as good at what I wanted to do at Princeton. I couldnt
have gotten into the community to do exactly what I wanted to do any better.
So, I got to Ohio and in 75 I got an AMS Fellowship. There were only three,
and they were open to anybody in the world then. I think now theyre only
open to Americans.

Albert Lewis: AMS or NAS?

Reed: No, NAS was Poland. It was Poland. In fact, I got two more of
those. I went back to Poland again and I was in Czechoslovakia on a NAS,
so I had three NAS while I was still at Ohio. But, in 75-76 I got the
AMS award, and I was the first person in the south to ever get that, and
that gave me a year in England, total funding to go anywhere, so I spent
one term at Pittsburgh with Bob McConnaugh??, Dave Lexer?? That was the
center then of topology and with probably more important for my work was
Poli Schemishinsky who Id met in 74. Poli had been my host, in fact,
in Poland, and he was there on a postdoc and Eric van Douwen was there.
So Eric van Douwen and Poli Schemishinski??and I were there all totally
free to do nothing but mathematics every day and party all night. So this
was again a very influential period, certainly in my mathematics. That
same year Ohio University enrollment dropped from almost 20,000 to almost
10,000 [laughs] over a period of about two years. I think those figures
are roughly right. One reason was that the state had the great idea of
upping their out-of-state tuition by three times and something like two-thirds
of the students at Ohio University were from New York [laughs], so right
away it was during the recession, this was the bad recession. So they cut
all non-tenured staff, every non-tenured person at the university cut across
the board, so I was in Poland when I found this out [chuckles], that Id
have a year when I came back, but that was it. All non-tenured faculty
were given terminal contracts, cut across the board. So I came back to
look for a job. This was when John (Worrell) talked to me about the Institute
for Medicine and Mathematics. So we discussed forming this. In the meantime
I had gotten a job offer, or at least a word of mouth job offer, from the
University of Kansas, which was a good school of mathematics, but I decided
to stay on. I got funding. John and I raised some money. We had lunch with
a guy that wrote a check for half a million dollars, so I had funding,
but what made me stay though First of all, John can be very persuasive
and enthusiastic about how to change the world, but we started a postdoctoral
program, and I got to hire the five best people to work. I chose them.
We had this money. I got Toby Schemishenski, Eric van Douwen. You know
Erics dead now.

Lewis: Oh, I didnt know that.

Reed: Oh, Erics the only person I know that did fifty papers posthumously.
Hes had a great career since he died. He still has a paper every month,
I think, from people who - He really was an author?? Toler?? who is now,
in fact just was, the chairman of the department of computer science at
University of California at Riverside. Peter Nikos who .. worked on ??
South Carolina and Bill Fleishner who is now at Kansas, as professor of
set theory and topology. And Mike Whatley who really is very bright and
went on and got his Ph.D. at Wisconsin from the State Institute for Medicine
and Mathematics and then went to Harvard and got a M.D. and now is a physician
researcher [siren in background] Anyway, that was the group and that was
it. There was not a better place in the world to be in topology during
those years the Institute was running in Athens. We cornered the market,
Dutch, Poland, the States. We captured the best young people at work. We
had conferences. We had the Spring conference and had other conferences.
It was a very exciting time. In fact, I had a conference to solve a normal
Moore-space problem, it had waiting around all these years, and so I just
picked people who could do it. Frank Toll?? and Fleissner, Nikos had never
worked on that, and I think it was either Frank or Judy Woodman?? who talked
about stuff Kunz?? was doing. And theres Nikos just sitting there saw
this axiom could be used to solve this Moore Space problem the other way
and it was done, and then Bill Fleishner, two years later, completed the
thing by showing in fact the problem is equivalent to large cardinals.
It is totally set theory. Its got nothing to do with the Moore space and
topology. It was a theorem about large cardinals. It was one of those horrible
things that ended with a whimper not a bang. The Normal Moore Space Problem
is equivalent to the existence of large cardinals. Everyone thinks its
consistent with set theory that these cardinals exist, but you cant prove
that. Its possible that you can get a counter-example, but no one thinks
thats the case, but theres no model in which you can prove this because
it would take a bigger model. Its one of those Godel sorts of arguments,
so its left with a [laughs] shrug almost. So, the beautiful work that
took forty years of mathematics, but it ended up a most unsatisfactory
solution.

Lucas: Was that the thing you tried to discuss with me at lunch a year
or so ago about n equals e^{n} or something?

Reed: Oh, no, no. This was a problem that F. B. Jones raised in 1937 that Moore spaces werent metrizable Moore plane or tangent disk space was invented by several people, Moore, Hausdorff, Kuratowski. Is a Moore space metrizable? Theres not a ?? metric on this. The question became well, what is it that is lacking to be metrizable and this property called normal? This was the conjecture, that since all the ones they could find that were normal were also metrizable. F. B. Jones was able to prove this using the Continuum Hypothesis in 1937. The Moore Space Conjecture was true, and about 1970 it was ??Frank Hall who had been taking courses from Bing in topology and courses in set theory from Silver saw that there was a connection between this thing called Martins axiom which is a set theoretic axiom thats also consistent with set theory and the denial of the Continuum Hypothesis. Before Frank could do it, he suggested to Silver who was the set theorist who was actually the first person to do it although Frank was the one who was sitting there and saw the connection I think, showed that under that assumption theres a normal Moore Space thats not metrizable. So, in some sense Jones had shown that another condition, separability is a ?? subset. But the actual thing was that Jones in 1937 showed that under the Continuum Hypothesis a normal separable Moore space is metrizable. About 1970 Silvers Hall had shown that under another assumption that is also consistent with set theory there is a normal seperable Moore space that is not metrizable. So, the question of whether normal separable Moore space was metrizable is independent of set theory, meaning their model of set theory was true and the model of set theory was false and you could never prove it absolutely within normal set theory. The question could not be decided. This involves separability, and then the question becomes what about if you dont have separable, can there exist a real one that is not metrizable? This is what turned out to be equivalent to the existence of large cardinals. So, that took another eight to ten years to do that. That had a lot to do with what I did later on. All the things I was interested in became solvable and we pretty much solved them in those ten years of set theory. Thats all I did. I focused on that area, and by the middle eighties it was time for me to look for another area or do something different because I had only been doing that. In the meantime, I stayed at the Institute and became unfortunately more of an administrator and money-getter. I was getting money for all these guys to do this great work, but I was spending my time out talking to little old ladies [laughs] trying to get donations and the Institute wasnt going as well for various reasons on other fronts. We were doing a bunch of things, trying some medicine for research and lots of other things. The university reneged on some promises. It didnt look that favorable. In the meantime, Joy, my wife, (we had been graduate students together at Auburn, and she got her masters from Ben and a Ph.D. from Phil Zenor) was finishing up. She had taken a year out actually as instructor, of course we were at the same level, but she had taken a year out as an instructor while I finished up. Then I took a job at Ohio, and it was more or less a promise or indication that the next job that came up shed get, so this was the thing, but then with this recession there was absolutely nothing, so she was part time teaching and even involved in the institute and was doing some medical. She got some papers on analysis, real analysis of medical application, but there was no future there, and jobs were hard to get in those days. So, she decided to go into computer science, since thats where the jobs were, so she decided that with both of us in topology we were unlikely ever [laughs] to get jobs in the same place. So, she looked around for places to do this and we had to find a way to afford it. Maryland was one of the places that she looked at that had a program that she was interested in the school was in the top ten in computer science.

[break in tape]

Harry Lucas: Were here with Mike Reed on July 21, 1998 Go ahead Mike.

Reed: So I found a way. I became program manager at the National Science
Foundation. I was director of postdoctoral programs and also NATO post
doctoral programs [break in tape] for two years, and it was fun University
of Maryland and I worked in D.C. Joy got her masters and was doing research
and she wanted to stay longer, and [break in tape] I wanted to stay away
from Ohio [laughs] because I was on leave, but I didnt see any hope there.
So, I met at a party at Maryland, Assar Rosenfeld, a World leader in the
field [buzzing on tape] ??head of the international association ?? He had
a lab and he had twenty-five Ph.D.s on research grants working for him.
It was like an industry there, but I talked to him after that meeting and
someone who worked with him and I was a topologist and they had a spot
in topology. They wanted a three-dimensional Jordan curve theorem. They
wanted a theorem that described a surface in three dimensions, something
that ??? outside. At computer stores you look at the screen at a three-dimensional
point. They wanted a definition. If youre ..cat scan looking for a?? they
wanted a mathematical definition and an algorithm essentially that would
come from that definition to give the three-dimensional Jordan curve theorem.
I said, *I would do that. *[laughter] They said if you would do that
well fund you, and I think within a week I quit NSF. I was doing digital
topology.

Lucas: What year was that when you switched?

Reed: Oh, that was 80, 80 or81. So, I was there, and I got it. Again,
one of those cases where thinking in Moore sense was to your advantage.
. Fourier analysisall kinds of mathematics without topology stuff that
I had no ?? [laughs] So, I went home and I worked from home down there
a bit, and ??Id be back ??coat and tie and be able to do mathematics so
it was very challenging, but I went down in the basement; Id bought a
case of wine. I had a grid full of wine boxes so I put this grid down.
My daughter had a Parcheesi board with black and white tokens, so I just
put black and white tokens on the crate in three dimensions, for zeroes
and ones, and just walked around it for days and days, walked around. It
took me two months to write it up, but it was perfect. I didnt use anything
but just sheer brute force, elegant brute force, but it was right. They
had two kinds of notions of connections and I got a counterexample of one
and a proof of the other, and I got a general theory of how ?? I still
get more mileage out of that result. It was one of the least intellectually
satisfying. I mean it was just sheer brute, hard, grinding out cases. For
example, Im on an organizing committee and invited speaker in India in
January for parallel image processing. Only thing Ive ever known in my
life is that Parcheesi board. The only thing Ive ever done in image processing,
but I was invited to Japan last year from that one result. Somehow, I was
the first to do this, so it gets remembered.

Lewis: So this was published?

Reed: It was published in 80.

Lucas: So, you stayed with that deal?

Reed: No, not with that. That was in full computer science and based
on that, again, I wanted to stay around Washington, Rosenfeld was my connection
at the Institute and had insiders knowledge of me. I had been one-time
coordinator of all postdoctoral programs at the agency and NASA had a very
well paying, lucrative postdoc at Goddard Space Flight Center and I happened
to know ?? [laughter] So Rosenfeld had some connections, so I applied,
and with great probability [laughter] got a fellowship at NASA that was
funded, again, to do models. The main problem was they got millions and
millions and millions of* *distorted computer images taken at various
angles by various satellites with different wave bands, and all kinds of
different things, and they wanted to look for a certain object. They were
looking for super novas and they have all kinds of pictures of it, but
they cant find it. I mean the human eye can look through there and see
that this thing is the same; its just rotated and twisted, but to tell
a computer to say its the same thing, but rotated or twisted, but its
a little bit fuzzy so its pattern recognition, recognizing again the
topological geometry and telling a computer how to do it. So, this is what
I did for a year there, and it was great fun. I really enjoyed it. In fact,
I worked only at night because when I took the machine I needed everything.
I needed almost every machine they had, so I only worked at night when
everybody else left because I had to have all the machines running.

Lewis: What location was that?

Reed: It was Goddard Space Flight Center outside of Washington, D.C.
I did that for a year and worked mostly with computer scientists. Realizing
that processing would take hours to run one little picture. I thought aleph1
or C was big, but 2^{125} was a big number. [laughs] You dont
realize how big small numbers; I mean topologists tend to think of things
like that, but my first response when they told me this problem ?? youre
talking about a 5 x 5 x 5 grid with only zeroes and ones, so why dont
you just run a program, and they pointed out that theres not enough time
left in the universe to check all possibilities of zeroes and ones to the
125^{th} [laughs]. Another way to think of it, the way they do
at NASA, one screen is 256 pixels, and each dot has 256 gray levels, and
from about your focusing distance, thats as good as the eye can see, in
other words, thats about as good as youre going to see anything. So,
within that number are all things that you will ever see, 256 x 256 x 256.
They can run random things through there. Everything youll ever be able
to see, anywhere by anybody ever, will eventually appear in that combination,
so thats all the possibilities there are. Theres a revelation of what
you can see. Thats really weird to think about. That somehow brings across
just how big those numbers are. Every face, every scene, every look, its
all there in that 256 x 256 x 256. So, what I got to realizing was that
for what I was trying to do there was no hope, particularly if people are
interested in bodies, where you want a computer to see. I mean if it takes
thirty minutes to figure out one image, then how is this thing going to
work in real time it just seemed impossible. I started reading about
parallel computation where youve got a thousand computers working at the
same time, and now one computer is the size of a dot, so its not just
one computer, now it became possible, but then it was just the beginning
of parallel computing. I started reading about parallel computing just
because I wanted to see what was possible and reading about parallel computers
I found some papers by a guy named Tony Moore?? at Oxford and then I came
to Oxford. Ive been coming to Oxford for years. Peter Collins??, my colleague
the reason Im here. Id been to Poland about ten or fifteen times I
guess, and Id usually stop in Oxford for seminars. ?? computer topologist
at Oxford. So, I was in fact at dinner here and Bill Roscoe, who is computer
science and also a mathematician, also a very bright man, hed just gotten
his degree a couple of years before, and we started talking about the mathematics..
and went back to Ohio. The Institute had closed now so I went back as a
professor of mathematics and computer science. Because of my image processing
I was considered, I guess, computer scientist, so I went back to full professor
in mathematics and computer science.

Lewis: And you were still on leave?

Reed: Id been on leave the whole time under Im not sure, they knew
it, [laughter] but I had a letter. At a certain time after the Institute
closed I pointed out this letter. In fact, Joy was now on the faculty in
computer science, so Joy had a permanent job in computer science, and I
was a full professor in computer science and mathematics. I guess we stayed
in Washington one more year. Joy wanted to stay there because our daughter
had started school and she wanted to finish. Front-page picture on *Washington
*Post that did it. Ill never have anything like that. So, she finished
and I was a professor at the Naval Academy, again one of those fortunate
things in life. You never know how things are going to help. I just wanted
to stay around another year, so I got a visiting professorship at the Naval
Academy. It was fun to be there in Annapolis with the sailboats, and the
pay was very good. The perks were great, the only place in the world where
you can take your faculty ID and check out a sixty-foot yacht for the week
[laughter]. It was great. [buzzing stops] But, because of the Navy I eventually
got a grant from ONR to come to Oxford to study parallel computing. In
fact, I came without the grant. First I decided to come and needed a way
to fund it and was funded by a wonderful woman called Helen Hayes who had
been a student of medicine and mathematics. It was a Texas foundation somewhere
called Future Trends in Dallas or where ever it was, so I mentioned I wanted
to do this and Helen responded to the Institute, *okay, go do it*.
So she funded me that first year. I taught one term at Ohio and then came
here. [tape beeps]

Lucas: This opposite side of the tape is full, Mike Reed

Reed: ?and again it was tax efficient to be a student, because if youre
a student whatever money you get is not taxable. So I came here as an ??
student. I was also a fellow in college; I was a visiting fellow so I had
the high table and all the perks while being a ?? student and working with
John Ford ?? and Bill Rosco?? Roscoe was eventually the supervisor, but
Tony Ober?? was the one that suggested what I work on, and then after that,
I was here two terms I guess. Then in the summer, because of my naval connection,
I arranged a fellowship at the Naval Research Laboratory in computer science
in Washington. I went back to Washington for the summer. Then I left Washington
with a grant from Office of Naval Research that paid me my full professor
salary plus summers, so I came back to Oxford. So, I came back my second
year here as a graduate student earning the highest salary at The University
of Oxford. [laughs], paid through the Oxford payroll. It blew some administrators
minds. So, boy I wish I had that money back, because it was temporary.
I mean this was plenty of money then because after a year we were going
back and I had a job so we rented a manor house across the park. I spent
weekends up here by myself for six months and then again for three months
and Id go to London on weekends and go to the theatres and eat well.

Lucas: What year was that?

Reed: 1985, I guess. 84-85, and then in 85 Joy took leave and came
over and she got a fellowship and so we were both here and intended to
go back to Ohio full-time in 86. But in 86 we also needed a job and so
I took it, giving up two thirds of my salary. And Joy had the research
position at the lab and had to give up her position, and she stayed there
ten years I guess on research positions. But we made virtually the same
amount of money. It was just that if you soft money means you had to continually
apply and you had to switch what you were doing, and this got very old,
not being able to count on the next thing that you would be doing. So she,
I guess about three years ago, took a job at Oxford-Brooks University which
is the other university in town, which is the bigger, Oxford Brooks. I'd
never seen anything but Oxford. In fact, its equivalent to a good state
university. Its ??ed departments, and I think architecture is the best
in England. A bigger computer science department than we have.

Lucas: Was she teaching math?

Reed: No, computer science. So, shes permanent there now, lecturing
there, so we ended up together again finally after all those years. She
was the first one in computer science.

Lucas: So essentially the last thirteen years or so since youve been
back, youve been specializing in this CST, or youve focused on that?

Reed: Right, but another attraction for my staying here was that almost
all of my undergraduate teaching is in computer science, but Peter Collins
and I share topology graduate students here equally. So, Ive had Ph.D.
students in topology ever since Ive been here. I think, in fact, that
weve got probably the best over the last ten years, professional group
in the world. We have two or three a year. Peter does half and I do half.
I dont think there is a conference in the world on topology that some
of our students are not giving invited talks. So, what I got here or saw
here I told Mary Ellen and Frank Tol?? That I used to think that you
guys just must be great teachers, and now I understand. You just got great
students [laughs]. You cant go wrong with these people here. You just
have to define a space to them and thats all they need. Theyre just smart
people. But, theyre nice people. So we tell the group we have an Oxford
School of Topology now which Peter and I have done, so Ive had graduate
students in computer science too, but probably more in topology than in
computer science.

Lewis: Could you talk a little bit more about, to what body this School
of Topology is attached. Its not just the college?

Reed: As a matter of fact its the mathematics department. In fact,
Peter is now chair of the math board, so in fact, this is no doubt the
most prestigious school in the world where our kind of point set topology
is still a main

Lewis: Its that particular branch, I mean there are other topologists
here?

Reed: Of course, Phil, Donaldson, Atea. But, theyre all algebraic.

Lucas: James is algebraic too, right?

Reed: James is algebraic but a bit more he was old enough to straddle
both hills. James, at least, practiced ??, but all the others, and they
are the biggest names in the world in topology. Atea, ??,and Donaldson.
There were three Fields Medalists here. And ??, but it isnt ??? its
been Peter and me that ?? by sheer tenacity of it.

Lucas: Who is using mostly say modified Moore method, other than you?
I assume you are.

Reed: I use it. Who where?

Lucas: Here.

Reed: Well, no one. Well, some of our students here have taught their
students that way, and now they have students who are in Auckland, New
Zealand and Canada and elsewhere, but I teach a very modified Moore method.
I normally teach the first year graduate students. I give them a Moore
method course the first term. But, the deal is by the second term theyre
doing research because, first of all, theyve got such a great undergraduate
program. I mean theyre already through prelim levels in the states when
they come here as graduate students.

Lucas: Do you teach any undergraduates?

Reed: I teach undergraduates mostly computer science. I tutor math students,
but Im not responsible we take eight students a year here in some form
of maths or maths computation, and Peter and I manage them. Peters marvelous.
Hes a marvelous tutor; hes one of the best. Hes a topologist, but certainly
not the Moore method, but I think that in the last fifteen years hes had
the highest percentage of firsts in maths in Oxford College. What hes
good at is selecting. We never disagree. We interview separately, but I
listen to Peter because he has proved through his track record of identifying
talent in mathematics.

Lewis: Did he have any acquaintance with Moore before you met him?

Reed: No. Certainly he knew topologists; he knew the topological community.
But no, we have these arguments because he is totally against it, but he
is very supportive of me. Its a good deal. I think weve more or less
converged to a more or less agreement after all these years, but I needle
him on one side and he needles me on the other. But, its a very good humored,
good-natured feeling. In computer science what I did here and what I found
surprising was in the parallel processing ?? initially used the power to
use that processing to actually do particular tasks, ?? analysis, ?? was
in the mathematical reasoning one uses in that theory, something called
semantics, denotational or mathematical semantics. It was in vogue at Oxford
back in the sixties and early seventies to giving mathematical meaning
to computer programs. When you take the syntax for what the computer language
says and you map this on mathematical object and you reason about that
program by reasoning proving theorems in this mathematical structure. You
can write simple programs, but even very, very complex sequential programs
no human being can hold in their mind, but when you get to parallel programs
and youve got a thousand computers each doing a different thing at the
same time on the same data, what in the hell is going on? [laughs] You
may run the same data to that thing ten straight times. You may even get
the same answer. But, it got that answer ten different ways because you
dont know which came first. Things are just happening, so its not just
proving that one sequence of steps work; youve got to prove all possible,
and again, the state explosion is too big. There are too many possible
states to consider, so when you get on that air bus, and its got all those
data processes all working at the same time, there is no way to test the
paperwork. I mean they test, test, test, but I mean these crashes, one
random sequence that no ones ever seen in ten years all of a sudden happens,
and thats the one that causes the thing to lock up or whatever might happen.
So, they will recognize very early in parallel processing that youve got
to have some mathematical way of proving your design is correct. You cant
depend on testing; you cant hope that some program is going to keep this
ones head. Youve got to somehow be able to mathematically get a hold
of these things. So, at Oxford ?? is in the mathematical semantics understanding
of parallel processing, CSP, which is communicating sequential processes
which means parallel. Thats what CSP stands for. So, they had, Hoare had
it down to first semantics I guess in about 1978.

Lucas: How do you spell his last name?

Reed: Hoare, h-o-a-r-e. Then Bill Roscoe and Steve Brooks who is now a professor at Carnegie Mellon head down the full semantics in about 84, and its a really good mathematics program. Its a good mathematical model, and they used I guess the lattice theory. But, of course, you cant just map this thing to objects. You need a structure because youve got infinite programs or recursions have to be limited, in some sense, so you have to have some sort of limiting notion, either least upper bound which you get in lattice theory. Thats one way to do it. And Penscot?? did this. You know who Penscot?? is, the granddaddy of the Domain Theory, which is the name of this kind of mathematics. He was here at Oxford at the time. He was professor of logic at Berkley, of philosophy at Princeton, of mathematics and logic here, and now hes professor of computer science at Carnegie Mellon. Hes had four major universities with a different field every time. Hes into large cardinals and Moore spaces. Hes the one that did the first stuff on large cardinals. Hes done so much. I was just with him about a month ago and worked on his problem. Ill tell you a neat problem. I got this favorite problem. Ive got Dan working on it, and he couldnt get it either. So, when I came in at that point and was trying to find I read some of his papers and was interested in the Domain Theory because it was mathematics. You do embeddings, you build spaces. It was topology. If you look at his lattice theory and look at his topological structure you can put a topology, and you work with one or the other. Its really topology. Think of it as total topology, if you want. And Tony suggested to me that they wanted to handle time. In these programs you could guarantee certain things are true, but you want to guarantee youre going to have a certain amount of time and use a mathematical model that had time? And that was a level of complexity beyond. I mean that was almost a philosophical question: what is time? I mean you really have to mathematically define time in a way that you can treat it with analysis. So, he wanted me to get a timed real time semantic for CSP. So,

[end of tape]

Lucas: July 21, 1998

Reed: I did that over the next, oh, I guess four or five years. That
way I guess the definitive model is just coming out this year. Its sixty
pages, and that doesnt include the proof; thats just the description.
[chuckles] Its one of the most horrendously complex mathematical objects
Ive ever seen in my life.

Lucas: This is essentially what youve been working on the last few
years.

Reed; Yeah, and now I think there have been, I think, seven Ph.D.s
written on this model. I dont know, a hundred papers, a book; its been
used in industries. It was a major I worked Moore spaces for a while,
and then I got into this, and it just got absorbed me in the detail. This
pretty stuff, this beautiful, I mean topology I can usually do in the bath
tub. I mean most theorems Ive gotten, Ive been sitting there and "aah"
because its just "the key turns". Its like that. The difference in this
is that the complexity and detail is so great; youve got to have so much
stuff in your mind at the same time that these flashes of keys turning
happen less regularly. Its more grinding out, putting together these huge
slices and finding some way to reason about the slice without knowing all
the details and then put them together. Its a different sort of thing
and it takes a lot of ?? I outlined the program of what I wanted to do
when I started this thesis, and like I said, its pretty much been accomplished,
but its taken seven Ph.D.s to do all that. It was a horrendous job, but
its now one of the standards. I mean there are other people in the world
who encountered things related and we all pretty much came to the same
general notions of how it should be done, but that problem is considered
solved. But, then that was "the" problem, in the computer sciences area,
to solve timing. And thats what Bill Roscoe and I took on, and we did
it, we and our students. We nailed it. So, thats what I did up until the
mid 90s.

Lucas: What were doing, or what were looking for is now solved, and
weve been asked to ??

Reed: The point was, the difference in this semantics was that it was
based on topology, on pre-measured spaces, using Banachs Fixed Point Theorem
instead of the lattice theory, so this is a topological measuring structure
where topology is in the model because time is a measure. The things are
close if they agree. So, the further they act like the same thing, theyre
the same. So, you can use time as a measure of how things converge over
time, and that was the trick. I thought I was a real genius for thinking
this topology with Bill, but I met someone years later that had talked
to Tony Hoare about this, I guess in the early 80s, and Tony was talking
about doing real time and Tony said, "Yeah, but thats going to be difficult.
I think Ive got to wait for a topologist to come along." [laughs] So he
knew darn well which way it should be done to begin with. I just showed
up and, oh yeah, look at this. It turned out to be ?? Tony, hes won the
Turing Award, which is like the Nobel Prize. I mean hes one who has no
degree in mathematics or computer science. Hes in ??

Lewis: Oh, thats a marvelous British tradition.

Lucas: So, what we have to do while weve got an hour or two left up
here is to get someway or other to find out, and what made me think about
is was this Christopher. This fellow named Christopher Ball up here. Do
you know him or know anything about him? He has something to do with the
education department or the department of mathematical education, is it?

Lewis: No, not particularly in mathematics, no, but he has a linguistics
background.

Lucas: So, we need to look this person up, but I wanted to see if there is anything else that you or Joy had for us on this project. This has been a great background here assuming we picked this up.

[break in tape]

Lucas: This is Mike Reed on the Moore Method telling some of his views
on this.

Reed: Well, Ill give you Joys.

Lucas: All right.

Reed: Joy thinks she was harmed by the Moore Method. I guess her reason
for this is that we left and went to Ohio, and we didnt know as much as
all of those people did, and they were all Damn Yankees anyway and liked
to feel superior. We didnt. They would use terms and use things and they
considered we just didnt have a proper mathematical background.

Lucas: When you left Auburn.

Reed: Of course they were right. But, it bothered her, and it hurt her
confidence and she thinks it was a serious blow, and that she never really
recovered. She feels that if she had gone to a traditional place and been
armed with that sort of knowledge that she would have been better served
to go out into the world to fight. Me it didnt bother at all because I
never felt that. I mean thats the kind of people that do well [laughs]
under the Moore Method. Thats the case. I mean I just didnt care; I mean
lets just take the same problem and a blank sheet of paper and see who
gets it first. Give me your definitions and Ill take you on, if you can
do it that way, but its a personality thing. I think it is true; it was
for her. Mary Ellen Rudin feels she was hurt. I mean I cant speak for
her; she can speak for herself. She thinks that she would have been better
served by traditional mathematics.

Lewis: But, shes still a supporter.

Reed: Shes correct. I just had this discussion in fact in the Tilbilly??
System. She and Walter were both there, and I was sitting with ?? somewhere
and we discussed the Moore Method. Walter had just been to my talk, and
had asked me who I had studied with and I mentioned the Moore Method, and
he said, "Ah, you escaped." I said, "No, I was propelled." [laughs] Walter
Rudin had two years of Moore Method, by the way. Roberts at Duke.

Lewis: Oh, really.

Reed: Yes.

Lucas: And he is against it?

Reed: Oh, yeah, and I guess that Mary Ellen thinks that she just didnt
know enough and it took her an awful long time for her to learn what she
needed to know. She thought Moore was maybe past his prime, maybe not deteriorating
intellectually, but not plugged into world mathematics to the extent that
she wanted to be. But, shes moved in circles of top of the world of mathematics
and I think she's been in defense of herself somewhere along the way
I mean shes the best in the field. Shes my hero. If she thinks she could
have done better, Id be amazed at what would have been, because I cant
imagine better. But, she thinks that she was at a disadvantage not knowing
more about what was going on in world mathematics at that time. You can
ask her, but I think thats fair to say. I guess Mary Ellen and I have
argued for years. We always go back and forth. But, my philosophy now after
all these years is that I think its (Moore Method) the ideal way to start,
but only to start. I think you want to get them to do mathematics on their
own, to get the fun of it, to really get hooked, but you cant continue
it through a whole undergraduate or graduate program and across all fields.
Theres just too much out there. Youve got to let them go and you have
to read, and theyve got to know whats going on. Here, one term is really
all they get. Its not fair because they already know so much and Moore
wouldnt have taught them because they already know too much. But, what
I do is They witness to this. Ive changed their view by going back to
something they dont know and make them start proving for themselves. Thats
when they first start doing. Even if theyve got this huge knowledge, you
can still find something they dont know and teach them Moore Method and
I think you improve them. But, I think you only need to do it one year.
You dont need to spend your life that way. All the Moore students when
I left Auburn, where I taught Moore Method at Ohio, I spent four or five
hours a day, every day, in the library just reading. I had to do that.
I knew I had to do that. A lot of Moore people didnt do that, but I think
all of them who are successful do. You have to find out what the rest of
the world is doing. If youre working on something thats going, I mean,
I tell my students that if theyre working on a hard problem and theyre
getting somewhere, then dont do anything but do that problem. As long
as youre going along, but when you stop, if you dont get any new ideas
go read, go do some reading. Youve got to do both at some point. Joy was
just lacking in confidence about not knowing what all those other people
knew.

Lucas: The emotional and psychological aspect.

Reed: And these people were from Michigan and Wisconsin, Ivy League,
and there was a little bit of status thing there anyway. And, we were Alabama
hicks, so I think it was a combination, but thats happened to a lot of
people, not just Joy. Youve got to be pretty strong to go out there ignorant
and convince people that you know what youre talking about because you
dont. All youve got is tremendous self-confidence. Thats what Moore
Method gives you. In mathematics, you think you can do anything. And, if
you can thats cool [laughs] or if you can do enough of it. On the other
hand, weak students have been some of my best people that Im the most
proud of out of the Moore Method. The weak student who doesnt get anything,
and then all of a sudden they get that one thing, that joy when they do
it. Its just as good as the person who has come in everyday, but again
you cant take a weak student and only give him Moore Method because theyre
going to go out not knowing anything and not able to do a whole lot either.
So, they cant spend their life getting one or two results every year in
whatever job they do. You can make a real change in a weak students life
by introducing the Moore Method and getting him to a point to do that,
but if you only give that person Moore Method hes at a disadvantage. Theyve
got, in the end, to go out there and compete. And, if they arent genius
or they arent brought up ??people ??, so youve go to be fair. Youve
got to give them the Moore Method by all means, but I think youve got
to equip them to be out there in the world. Its a mixture with every student.
The most Moore Method student weve had ?? exam last week I guess he finished
American. He was a student of his father who was a student of Bing. He
just got his Ph.D. thesis solving a Moore space problem, my old problem
of about 25 years. He solved for a Ph.D. thesis. He just left and went
back to the States.

Lucas: Who was his professor?

Reed: He was a student of Bing and Burgess; Im not sure which there
was some combination. A lot of times, like with Moore who was Moores supervisor.
In fact, this guys supervisor is officially Peter, but all his theses
came out of that first term I teach. I gave him that problem. But, particularly
at Oxford, your supervisor is not necessarily the person you happen to
work on the thesis with. And certainly I have students that mostly work
with Peter. So its very hard to get the history. People in the United
States are like that too. David's father was like that. Its not clear.
Bing or Burgess or some combination thereof, yeah, but hes at Brigham
Young.

Lewis: His father?

Reed: His fathers a topologist at Brigham Young.

Lucas: What I suggest is that we come back to this later this year with
a fixed-up video camera and discuss the educational theory a little more
with Albert. Im not sure if I can come back or not, but Albert might be
released in a few more weeks, but somehow or another get into the educational
part further because hes writing some stuff on this now or will be soon.

Reed: I could not have had a better match between

[tape beeps]

Lucas: This is a continuation of a very good interview with Mike Reed,
and we will probably come back and discuss Moore Method and current educational
problems with a video interview, possibly a set of questions.

Reed: People have a bit of a different experience with Moore. When talking
they all have a slightly different view of what happened in that class.
Of course, I think Moore challenged, Bing he just challenged them daily,
you know *try to see if they were good enough to go to the next class*
or whatever, but in some people he would boost their confidence. He was
a psychologist almost, but mainly he loved his subject, and he liked people.
Those are the two things that you have to have: you have to like what youre
doing, and youve got to be able to communicate with people. Ben (Fitzpatrick)
was very good. Ben was the best. Ive seen lots of people do Moore Method
and Ben is the best. I didnt have a class with Moore, but Ben was absolutely
perfect, and I couldnt imagine it being done with more motivation and
talent for getting the most out of each person. He was really good.

Lucas: What were trying to do is just what Albert said, to study Moore
as a teacher, and what he did, and why he did it, and what the results
were. Just get the record and go from there, not so much understanding
the theory behind it because were not sure anybody really can explain
the theory

Lewis: Or those things come and go, and its the famous teachers or
the rare phenomena are rarely recorded and you just know that someone was
a great teacher but thats about all you can say because

Lucas: no one made a study of that.

Lewis: The people were too hard to get hold of, and here there happens
to be an opportunity to get a hold of something thats really major over
the years. You cant say much more than you just said about it openly,
but why not try to lock into it and provide what inspiration he had for
people who were never going to be as close as we were to that, and this
is something that unfortunately some people are not sympathetic toward
because perhaps the scientific evidence was so weak, that why bother? Its
something that can be inspirational

Reed: Well it can. People that were successful adapted it to their own
personality.

Lucas: modified

Reed: yeah, modified. People who tried to be Moore were doomed because
they weren't Moore. People who tried to use that influence, to use themselves,
developed, I think, theMary Ellen, despite what she says, teaches Moore
Method in a fashion. She starts out, but shes too impatient, and she has
to finish. But, what she does is involve people, and her enthusiasm and
some of her students teach Moore Method. Her actions I do things which
would be horrifying to theorists here because competition is something
that is a dirty word almost in England. Having students compete seriously
is just not done. Oh, they do it; theyre cutthroat, but they cant be
seen to be doing it, so its very hard to do this. What I found myself
often doing using the Moore Method, Ill put up some theorems and first
of all, theyre just so bright and they have so much knowledge, that we
just go through them in real time, and somebody will have an idea. Its
a group effort. Sooner or later, youll get one thats so hard that they
have to go home and one person just does it. But, as long as theyre proving
the theorems then somebody puts up an idea, somebody else knocks it down,
and after a while theyre competing. Somebody is trying to get one that
the others cant get, so it develops that way, but if I just go in and
say, *you cant talk to other students about the problems, you have to
come in*I find hostility. But, if I do this and let them do it real
time, then when they get to the hard ones, its what happens naturally.
Again, theyre

Lucas: Thats the thing we ought to explore in your next meeting, the
modified Moore Method as used by Mike Reed on video. No, you said, if one
term or something

Reed: No, I think everybody should

Lucas: Listing specific examples and all that, maybe some names of people
who did some unusual things and a few vignettes maybe, that kind of thing.
But I dont think we can do that this afternoon even if we had the camera
working. But, if you can come back and have a session on that subject I
think that would be really

Reed: Well, Im going to be gone for a long time now.

Lucas: youre leaving when?

Reed: Im leaving Thursday for Greece, and then I probably will come
back, and a couple of weeks later go to the States for a couple or three
weeks.

Lucas: Well, well work it out even if its next summer. Well work
towards that.

Lewis: Are you in the States for a holiday?

Reed: Theres a meeting for this ONR grant that I mentioned. Ive managed
to keep all these years. Its the only way I can afford to live in this
country. So, Im going to Washington. Were having a meeting there at D.C.
in September, and my daughter lives in Philadelphia so well concur.

Lucas: Okay, end of tape.
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?AEIKOThe R. L. Moore Biography Project
The Center for American History
The University of Texas at Austin
This is Harry Lucas. Its July 21, 1998 at St. Edmund Hall. Albert Lewis and I are talking with G. M. (Mike) Reed, and were having a very good discussion about his background to the point of being at University of Wisconsin. Okay, go ahead Mike. [break in tape] Its July 21, 1998, and this is a continuation of the Mike Reed interview.
[tape has a lot of background noise and is very difficult to understand]
Mike Reed: I was lucky to get exposure to world-class people doing what I wanted to do at a very early age, but the topology connection I had was at Auburn with Ben Fitzpatrick and the other topologists there, especially Phil Zenor. Ben (Fitzpatrick) was my Moore. What Phil provided me was a role model of - Phil just came in from Houston as a young assistant professor who was ambitious and coached me like mad and brought things together. I learned how to play the game a bit.
Harry Lucas, Jr. Was he a student of Howard Cook?
Reed: Traylor..
Harry Lucas: How do you spell his last name?
Reed: Zenor, Z-E-N-O-R. So, Ben who was the motivating force and got me started in watching Phil (Zenor) operate, and Phil was very good. That was before I left Auburn, and at Auburn. I mean we had Kuratowski. I drank beer with Kuratowski in Auburn. Bing had been there. I couldnt have been at - the first AMS meeting I went to in Auburn, Alabama, I went to the national meeting of the American Mathematical Society. I had breakfast with Bing who was or just had been President of the American Mathematical Society, and I had tea in his apartment during the meeting with Gayle Young who at that time was President of the Mathematical Association of America. I mean, not too many people can come from a southern state university and walk into a national meeting and have that sort of contact. I first met Mary Ellen Rudin who came to my talk at that meeting. I spent the night in her room talking to her and her students. So, Auburn got me that, and I couldnt have gotten as good at what I wanted to do at Princeton. I couldnt have gotten into the community to do exactly what I wanted to do any better. So, I got to Ohio and in 75 I got an AMS Fellowship. There were only three, and they were open to anybody in the world then. I think now theyre only open to Americans.
Albert Lewis: AMS or NAS?
Reed: No, NAS was Poland. It was Poland. In fact, I got two more of those. I went back to Poland again and I was in Czechoslovakia on a NAS, so I had three NAS while I was still at Ohio. But, in 75-76 I got the AMS award, and I was the first person in the south to ever get that, and that gave me a year in England, total funding to go anywhere, so I spent one term at Pittsburgh with Bob McConnaugh??, Dave Lexer?? That was the center then of topology and with probably more important for my work was Poli Schemishinsky who Id met in 74. Poli had been my host, in fact, in Poland, and he was there on a postdoc and Eric van Douwen was there. So Eric van Douwen and Poli Schemishinski??and I were there all totally free to do nothing but mathematics every day and party all night. So this was again a very influential period, certainly in my mathematics. That same year Ohio University enrollment dropped from almost 20,000 to almost 10,000 [laughs] over a period of about two years. I think those figures are roughly right. One reason was that the state had the great idea of upping their out-of-state tuition by three times and something like two-thirds of the students at Ohio University were from New York [laughs], so right away it was during the recession, this was the bad recession. So they cut all non-tenured staff, every non-tenured person at the university cut across the board, so I was in Poland when I found this out [chuckles], that Id have a year when I came back, but that was it. All non-tenured faculty were given terminal contracts, cut across the board. So I came back to look for a job. This was when John (Worrell) talked to me about the Institute for Medicine and Mathematics. So we discussed forming this. In the meantime I had gotten a job offer, or at least a word of mouth job offer, from the University of Kansas, which was a good school of mathematics, but I decided to stay on. I got funding. John and I raised some money. We had lunch with a guy that wrote a check for half a million dollars, so I had funding, but what made me stay though First of all, John can be very persuasive and enthusiastic about how to change the world, but we started a postdoctoral program, and I got to hire the five best people to work. I chose them. We had this money. I got Toby Schemishenski, Eric van Douwen. You know Erics dead now.
Lewis: Oh, I didnt know that.
Reed: Oh, Erics the only person I know that did fifty papers posthumously. Hes had a great career since he died. He still has a paper every month, I think, from people who - He really was an author?? Toler?? who is now, in fact just was, the chairman of the department of computer science at University of California at Riverside. Peter Nikos who .. worked on ?? South Carolina and Bill Fleishner who is now at Kansas, as professor of set theory and topology. And Mike Whatley who really is very bright and went on and got his Ph.D. at Wisconsin from the State Institute for Medicine and Mathematics and then went to Harvard and got a M.D. and now is a physician researcher [siren in background] Anyway, that was the group and that was it. There was not a better place in the world to be in topology during those years the Institute was running in Athens. We cornered the market, Dutch, Poland, the States. We captured the best young people at work. We had conferences. We had the Spring conference and had other conferences. It was a very exciting time. In fact, I had a conference to solve a normal Moore-space problem, it had waiting around all these years, and so I just picked people who could do it. Frank Toll?? and Fleissner, Nikos had never worked on that, and I think it was either Frank or Judy Woodman?? who talked about stuff Kunz?? was doing. And theres Nikos just sitting there saw this axiom could be used to solve this Moore Space problem the other way and it was done, and then Bill Fleishner, two years later, completed the thing by showing in fact the problem is equivalent to large cardinals. It is totally set theory. Its got nothing to do with the Moore space and topology. It was a theorem about large cardinals. It was one of those horrible things that ended with a whimper not a bang. The Normal Moore Space Problem is equivalent to the existence of large cardinals. Everyone thinks its consistent with set theory that these cardinals exist, but you cant prove that. Its possible that you can get a counter-example, but no one thinks thats the case, but theres no model in which you can prove this because it would take a bigger model. Its one of those Godel sorts of arguments, so its left with a [laughs] shrug almost. So, the beautiful work that took forty years of mathematics, but it ended up a most unsatisfactory solution.
Lucas: Was that the thing you tried to discuss with me at lunch a year or so ago about n equals en or something?
Reed: Oh, no, no. This was a problem that F. B. Jones raised in 1937 that Moore spaces werent metrizable Moore plane or tangent disk space was invented by several people, Moore, Hausdorff, Kuratowski. Is a Moore space metrizable? Theres not a ?? metric on this. The question became well, what is it that is lacking to be metrizable and this property called normal? This was the conjecture, that since all the ones they could find that were normal were also metrizable. F. B. Jones was able to prove this using the Continuum Hypothesis in 1937. The Moore Space Conjecture was true, and about 1970 it was ??Frank Hall who had been taking courses from Bing in topology and courses in set theory from Silver saw that there was a connection between this thing called Martins axiom which is a set theoretic axiom thats also consistent with set theory and the denial of the Continuum Hypothesis. Before Frank could do it, he suggested to Silver who was the set theorist who was actually the first person to do it although Frank was the one who was sitting there and saw the connection I think, showed that under that assumption theres a normal Moore Space thats not metrizable. So, in some sense Jones had shown that another condition, separability is a ?? subset. But the actual thing was that Jones in 1937 showed that under the Continuum Hypothesis a normal separable Moore space is metrizable. About 1970 Silvers Hall had shown that under another assumption that is also consistent with set theory there is a normal seperable Moore space that is not metrizable. So, the question of whether normal separable Moore space was metrizable is independent of set theory, meaning their model of set theory was true and the model of set theory was false and you could never prove it absolutely within normal set theory. The question could not be decided. This involves separability, and then the question becomes what about if you dont have separable, can there exist a real one that is not metrizable? This is what turned out to be equivalent to the existence of large cardinals. So, that took another eight to ten years to do that. That had a lot to do with what I did later on. All the things I was interested in became solvable and we pretty much solved them in those ten years of set theory. Thats all I did. I focused on that area, and by the middle eighties it was time for me to look for another area or do something different because I had only been doing that. In the meantime, I stayed at the Institute and became unfortunately more of an administrator and money-getter. I was getting money for all these guys to do this great work, but I was spending my time out talking to little old ladies [laughs] trying to get donations and the Institute wasnt going as well for various reasons on other fronts. We were doing a bunch of things, trying some medicine for research and lots of other things. The university reneged on some promises. It didnt look that favorable. In the meantime, Joy, my wife, (we had been graduate students together at Auburn, and she got her masters from Ben and a Ph.D. from Phil Zenor) was finishing up. She had taken a year out actually as instructor, of course we were at the same level, but she had taken a year out as an instructor while I finished up. Then I took a job at Ohio, and it was more or less a promise or indication that the next job that came up shed get, so this was the thing, but then with this recession there was absolutely nothing, so she was part time teaching and even involved in the institute and was doing some medical. She got some papers on analysis, real analysis of medical application, but there was no future there, and jobs were hard to get in those days. So, she decided to go into computer science, since thats where the jobs were, so she decided that with both of us in topology we were unlikely ever [laughs] to get jobs in the same place. So, she looked around for places to do this and we had to find a way to afford it. Maryland was one of the places that she looked at that had a program that she was interested in the school was in the top ten in computer science.
[break in tape]
Harry Lucas: Were here with Mike Reed on July 21, 1998 Go ahead Mike.
Reed: So I found a way. I became program manager at the National Science Foundation. I was director of postdoctoral programs and also NATO post doctoral programs [break in tape] for two years, and it was fun University of Maryland and I worked in D.C. Joy got her masters and was doing research and she wanted to stay longer, and [break in tape] I wanted to stay away from Ohio [laughs] because I was on leave, but I didnt see any hope there. So, I met at a party at Maryland, Assar Rosenfeld, a World leader in the field [buzzing on tape] ??head of the international association ?? He had a lab and he had twenty-five Ph.D.s on research grants working for him. It was like an industry there, but I talked to him after that meeting and someone who worked with him and I was a topologist and they had a spot in topology. They wanted a three-dimensional Jordan curve theorem. They wanted a theorem that described a surface in three dimensions, something that ??? outside. At computer stores you look at the screen at a three-dimensional point. They wanted a definition. If youre ..cat scan looking for a?? they wanted a mathematical definition and an algorithm essentially that would come from that definition to give the three-dimensional Jordan curve theorem. I said, I would do that. [laughter] They said if you would do that well fund you, and I think within a week I quit NSF. I was doing digital topology.
Lucas: What year was that when you switched?
Reed: Oh, that was 80, 80 or81. So, I was there, and I got it. Again, one of those cases where thinking in Moore sense was to your advantage. . Fourier analysisall kinds of mathematics without topology stuff that I had no ?? [laughs] So, I went home and I worked from home down there a bit, and ??Id be back ??coat and tie and be able to do mathematics so it was very challenging, but I went down in the basement; Id bought a case of wine. I had a grid full of wine boxes so I put this grid down. My daughter had a Parcheesi board with black and white tokens, so I just put black and white tokens on the crate in three dimensions, for zeroes and ones, and just walked around it for days and days, walked around. It took me two months to write it up, but it was perfect. I didnt use anything but just sheer brute force, elegant brute force, but it was right. They had two kinds of notions of connections and I got a counterexample of one and a proof of the other, and I got a general theory of how ?? I still get more mileage out of that result. It was one of the least intellectually satisfying. I mean it was just sheer brute, hard, grinding out cases. For example, Im on an organizing committee and invited speaker in India in January for parallel image processing. Only thing Ive ever known in my life is that Parcheesi board. The only thing Ive ever done in image processing, but I was invited to Japan last year from that one result. Somehow, I was the first to do this, so it gets remembered.
Lewis: So this was published?
Reed: It was published in 80.
Lucas: So, you stayed with that deal?
Reed: No, not with that. That was in full computer science and based on that, again, I wanted to stay around Washington, Rosenfeld was my connection at the Institute and had insiders knowledge of me. I had been one-time coordinator of all postdoctoral programs at the agency and NASA had a very well paying, lucrative postdoc at Goddard Space Flight Center and I happened to know ?? [laughter] So Rosenfeld had some connections, so I applied, and with great probability [laughter] got a fellowship at NASA that was funded, again, to do models. The main problem was they got millions and millions and millions of distorted computer images taken at various angles by various satellites with different wave bands, and all kinds of different things, and they wanted to look for a certain object. They were looking for super novas and they have all kinds of pictures of it, but they cant find it. I mean the human eye can look through there and see that this thing is the same; its just rotated and twisted, but to tell a computer to say its the same thing, but rotated or twisted, but its a little bit fuzzy so its pattern recognition, recognizing again the topological geometry and telling a computer how to do it. So, this is what I did for a year there, and it was great fun. I really enjoyed it. In fact, I worked only at night because when I took the machine I needed everything. I needed almost every machine they had, so I only worked at night when everybody else left because I had to have all the machines running.
Lewis: What location was that?
Reed: It was Goddard Space Flight Center outside of Washington, D.C. I did that for a year and worked mostly with computer scientists. Realizing that processing would take hours to run one little picture. I thought aleph1 or C was big, but 2125 was a big number. [laughs] You dont realize how big small numbers; I mean topologists tend to think of things like that, but my first response when they told me this problem ?? youre talking about a 5 x 5 x 5 grid with only zeroes and ones, so why dont you just run a program, and they pointed out that theres not enough time left in the universe to check all possibilities of zeroes and ones to the 125th [laughs]. Another way to think of it, the way they do at NASA, one screen is 256 pixels, and each dot has 256 gray levels, and from about your focusing distance, thats as good as the eye can see, in other words, thats about as good as youre going to see anything. So, within that number are all things that you will ever see, 256 x 256 x 256. They can run random things through there. Everything youll ever be able to see, anywhere by anybody ever, will eventually appear in that combination, so thats all the possibilities there are. Theres a revelation of what you can see. Thats really weird to think about. That somehow brings across just how big those numbers are. Every face, every scene, every look, its all there in that 256 x 256 x 256. So, what I got to realizing was that for what I was trying to do there was no hope, particularly if people are interested in bodies, where you want a computer to see. I mean if it takes thirty minutes to figure out one image, then how is this thing going to work in real time it just seemed impossible. I started reading about parallel computation where youve got a thousand computers working at the same time, and now one computer is the size of a dot, so its not just one computer, now it became possible, but then it was just the beginning of parallel computing. I started reading about parallel computing just because I wanted to see what was possible and reading about parallel computers I found some papers by a guy named Tony Moore?? at Oxford and then I came to Oxford. Ive been coming to Oxford for years. Peter Collins??, my colleague the reason Im here. Id been to Poland about ten or fifteen times I guess, and Id usually stop in Oxford for seminars. ?? computer topologist at Oxford. So, I was in fact at dinner here and Bill Roscoe, who is computer science and also a mathematician, also a very bright man, hed just gotten his degree a couple of years before, and we started talking about the mathematics.. and went back to Ohio. The Institute had closed now so I went back as a professor of mathematics and computer science. Because of my image processing I was considered, I guess, computer scientist, so I went back to full professor in mathematics and computer science.
Lewis: And you were still on leave?
Reed: Id been on leave the whole time under Im not sure, they knew it, [laughter] but I had a letter. At a certain time after the Institute closed I pointed out this letter. In fact, Joy was now on the faculty in computer science, so Joy had a permanent job in computer science, and I was a full professor in computer science and mathematics. I guess we stayed in Washington one more year. Joy wanted to stay there because our daughter had started school and she wanted to finish. Front-page picture on Washington Post that did it. Ill never have anything like that. So, she finished and I was a professor at the Naval Academy, again one of those fortunate things in life. You never know how things are going to help. I just wanted to stay around another year, so I got a visiting professorship at the Naval Academy. It was fun to be there in Annapolis with the sailboats, and the pay was very good. The perks were great, the only place in the world where you can take your faculty ID and check out a sixty-foot yacht for the week [laughter]. It was great. [buzzing stops] But, because of the Navy I eventually got a grant from ONR to come to Oxford to study parallel computing. In fact, I came without the grant. First I decided to come and needed a way to fund it and was funded by a wonderful woman called Helen Hayes who had been a student of medicine and mathematics. It was a Texas foundation somewhere called Future Trends in Dallas or where ever it was, so I mentioned I wanted to do this and Helen responded to the Institute, okay, go do it. So she funded me that first year. I taught one term at Ohio and then came here. [tape beeps]
Lucas: This opposite side of the tape is full, Mike Reed
Reed: ?and again it was tax efficient to be a student, because if youre a student whatever money you get is not taxable. So I came here as an ?? student. I was also a fellow in college; I was a visiting fellow so I had the high table and all the perks while being a ?? student and working with John Ford ?? and Bill Rosco?? Roscoe was eventually the supervisor, but Tony Ober?? was the one that suggested what I work on, and then after that, I was here two terms I guess. Then in the summer, because of my naval connection, I arranged a fellowship at the Naval Research Laboratory in computer science in Washington. I went back to Washington for the summer. Then I left Washington with a grant from Office of Naval Research that paid me my full professor salary plus summers, so I came back to Oxford. So, I came back my second year here as a graduate student earning the highest salary at The University of Oxford. [laughs], paid through the Oxford payroll. It blew some administrators minds. So, boy I wish I had that money back, because it was temporary. I mean this was plenty of money then because after a year we were going back and I had a job so we rented a manor house across the park. I spent weekends up here by myself for six months and then again for three months and Id go to London on weekends and go to the theatres and eat well.
Lucas: What year was that?
Reed: 1985, I guess. 84-85, and then in 85 Joy took leave and came over and she got a fellowship and so we were both here and intended to go back to Ohio full-time in 86. But in 86 we also needed a job and so I took it, giving up two thirds of my salary. And Joy had the research position at the lab and had to give up her position, and she stayed there ten years I guess on research positions. But we made virtually the same amount of money. It was just that if you soft money means you had to continually apply and you had to switch what you were doing, and this got very old, not being able to count on the next thing that you would be doing. So she, I guess about three years ago, took a job at Oxford-Brooks University which is the other university in town, which is the bigger, Oxford Brooks. I'd never seen anything but Oxford. In fact, its equivalent to a good state university. Its ??ed departments, and I think architecture is the best in England. A bigger computer science department than we have.
Lucas: Was she teaching math?
Reed: No, computer science. So, shes permanent there now, lecturing there, so we ended up together again finally after all those years. She was the first one in computer science.
Lucas: So essentially the last thirteen years or so since youve been back, youve been specializing in this CST, or youve focused on that?
Reed: Right, but another attraction for my staying here was that almost all of my undergraduate teaching is in computer science, but Peter Collins and I share topology graduate students here equally. So, Ive had Ph.D. students in topology ever since Ive been here. I think, in fact, that weve got probably the best over the last ten years, professional group in the world. We have two or three a year. Peter does half and I do half. I dont think there is a conference in the world on topology that some of our students are not giving invited talks. So, what I got here or saw here I told Mary Ellen and Frank Tol?? That I used to think that you guys just must be great teachers, and now I understand. You just got great students [laughs]. You cant go wrong with these people here. You just have to define a space to them and thats all they need. Theyre just smart people. But, theyre nice people. So we tell the group we have an Oxford School of Topology now which Peter and I have done, so Ive had graduate students in computer science too, but probably more in topology than in computer science.
Lewis: Could you talk a little bit more about, to what body this School of Topology is attached. Its not just the college?
Reed: As a matter of fact its the mathematics department. In fact, Peter is now chair of the math board, so in fact, this is no doubt the most prestigious school in the world where our kind of point set topology is still a main
Lewis: Its that particular branch, I mean there are other topologists here?
Reed: Of course, Phil, Donaldson, Atea. But, theyre all algebraic.
Lucas: James is algebraic too, right?
Reed: James is algebraic but a bit more he was old enough to straddle both hills. James, at least, practiced ??, but all the others, and they are the biggest names in the world in topology. Atea, ??,and Donaldson. There were three Fields Medalists here. And ??, but it isnt ??? its been Peter and me that ?? by sheer tenacity of it.
Lucas: Who is using mostly say modified Moore method, other than you? I assume you are.
Reed: I use it. Who where?
Lucas: Here.
Reed: Well, no one. Well, some of our students here have taught their students that way, and now they have students who are in Auckland, New Zealand and Canada and elsewhere, but I teach a very modified Moore method. I normally teach the first year graduate students. I give them a Moore method course the first term. But, the deal is by the second term theyre doing research because, first of all, theyve got such a great undergraduate program. I mean theyre already through prelim levels in the states when they come here as graduate students.
Lucas: Do you teach any undergraduates?
Reed: I teach undergraduates mostly computer science. I tutor math students, but Im not responsible we take eight students a year here in some form of maths or maths computation, and Peter and I manage them. Peters marvelous. Hes a marvelous tutor; hes one of the best. Hes a topologist, but certainly not the Moore method, but I think that in the last fifteen years hes had the highest percentage of firsts in maths in Oxford College. What hes good at is selecting. We never disagree. We interview separately, but I listen to Peter because he has proved through his track record of identifying talent in mathematics.
Lewis: Did he have any acquaintance with Moore before you met him?
Reed: No. Certainly he knew topologists; he knew the topological community. But no, we have these arguments because he is totally against it, but he is very supportive of me. Its a good deal. I think weve more or less converged to a more or less agreement after all these years, but I needle him on one side and he needles me on the other. But, its a very good humored, good-natured feeling. In computer science what I did here and what I found surprising was in the parallel processing ?? initially used the power to use that processing to actually do particular tasks, ?? analysis, ?? was in the mathematical reasoning one uses in that theory, something called semantics, denotational or mathematical semantics. It was in vogue at Oxford back in the sixties and early seventies to giving mathematical meaning to computer programs. When you take the syntax for what the computer language says and you map this on mathematical object and you reason about that program by reasoning proving theorems in this mathematical structure. You can write simple programs, but even very, very complex sequential programs no human being can hold in their mind, but when you get to parallel programs and youve got a thousand computers each doing a different thing at the same time on the same data, what in the hell is going on? [laughs] You may run the same data to that thing ten straight times. You may even get the same answer. But, it got that answer ten different ways because you dont know which came first. Things are just happening, so its not just proving that one sequence of steps work; youve got to prove all possible, and again, the state explosion is too big. There are too many possible states to consider, so when you get on that air bus, and its got all those data processes all working at the same time, there is no way to test the paperwork. I mean they test, test, test, but I mean these crashes, one random sequence that no ones ever seen in ten years all of a sudden happens, and thats the one that causes the thing to lock up or whatever might happen. So, they will recognize very early in parallel processing that youve got to have some mathematical way of proving your design is correct. You cant depend on testing; you cant hope that some program is going to keep this ones head. Youve got to somehow be able to mathematically get a hold of these things. So, at Oxford ?? is in the mathematical semantics understanding of parallel processing, CSP, which is communicating sequential processes which means parallel. Thats what CSP stands for. So, they had, Hoare had it down to first semantics I guess in about 1978.
Lucas: How do you spell his last name?
Reed: Hoare, h-o-a-r-e. Then Bill Roscoe and Steve Brooks who is now a professor at Carnegie Mellon head down the full semantics in about 84, and its a really good mathematics program. Its a good mathematical model, and they used I guess the lattice theory. But, of course, you cant just map this thing to objects. You need a structure because youve got infinite programs or recursions have to be limited, in some sense, so you have to have some sort of limiting notion, either least upper bound which you get in lattice theory. Thats one way to do it. And Penscot?? did this. You know who Penscot?? is, the granddaddy of the Domain Theory, which is the name of this kind of mathematics. He was here at Oxford at the time. He was professor of logic at Berkley, of philosophy at Princeton, of mathematics and logic here, and now hes professor of computer science at Carnegie Mellon. Hes had four major universities with a different field every time. Hes into large cardinals and Moore spaces. Hes the one that did the first stuff on large cardinals. Hes done so much. I was just with him about a month ago and worked on his problem. Ill tell you a neat problem. I got this favorite problem. Ive got Dan working on it, and he couldnt get it either. So, when I came in at that point and was trying to find I read some of his papers and was interested in the Domain Theory because it was mathematics. You do embeddings, you build spaces. It was topology. If you look at his lattice theory and look at his topological structure you can put a topology, and you work with one or the other. Its really topology. Think of it as total topology, if you want. And Tony suggested to me that they wanted to handle time. In these programs you could guarantee certain things are true, but you want to guarantee youre going to have a certain amount of time and use a mathematical model that had time? And that was a level of complexity beyond. I mean that was almost a philosophical question: what is time? I mean you really have to mathematically define time in a way that you can treat it with analysis. So, he wanted me to get a timed real time semantic for CSP. So,
[end of tape]
Lucas: July 21, 1998
Reed: I did that over the next, oh, I guess four or five years. That way I guess the definitive model is just coming out this year. Its sixty pages, and that doesnt include the proof; thats just the description. [chuckles] Its one of the most horrendously complex mathematical objects Ive ever seen in my life.
Lucas: This is essentially what youve been working on the last few years.
Reed; Yeah, and now I think there have been, I think, seven Ph.D.s written on this model. I dont know, a hundred papers, a book; its been used in industries. It was a major I worked Moore spaces for a while, and then I got into this, and it just got absorbed me in the detail. This pretty stuff, this beautiful, I mean topology I can usually do in the bath tub. I mean most theorems Ive gotten, Ive been sitting there and aah because its just the key turns. Its like that. The difference in this is that the complexity and detail is so great; youve got to have so much stuff in your mind at the same time that these flashes of keys turning happen less regularly. Its more grinding out, putting together these huge slices and finding some way to reason about the slice without knowing all the details and then put them together. Its a different sort of thing and it takes a lot of ?? I outlined the program of what I wanted to do when I started this thesis, and like I said, its pretty much been accomplished, but its taken seven Ph.D.s to do all that. It was a horrendous job, but its now one of the standards. I mean there are other people in the world who encountered things related and we all pretty much came to the same general notions of how it should be done, but that problem is considered solved. But, then that was the problem, in the computer sciences area, to solve timing. And thats what Bill Roscoe and I took on, and we did it, we and our students. We nailed it. So, thats what I did up until the mid 90s.
Lucas: What were doing, or what were looking for is now solved, and weve been asked to ??
Reed: The point was, the difference in this semantics was that it was based on topology, on pre-measured spaces, using Banachs Fixed Point Theorem instead of the lattice theory, so this is a topological measuring structure where topology is in the model because time is a measure. The things are close if they agree. So, the further they act like the same thing, theyre the same. So, you can use time as a measure of how things converge over time, and that was the trick. I thought I was a real genius for thinking this topology with Bill, but I met someone years later that had talked to Tony Hoare about this, I guess in the early 80s, and Tony was talking about doing real time and Tony said, Yeah, but thats going to be difficult. I think Ive got to wait for a topologist to come along. [laughs] So he knew darn well which way it should be done to begin with. I just showed up and, oh yeah, look at this. It turned out to be ?? Tony, hes won the Turing Award, which is like the Nobel Prize. I mean hes one who has no degree in mathematics or computer science. Hes in ??
Lewis: Oh, thats a marvelous British tradition.
Lucas: So, what we have to do while weve got an hour or two left up here is to get someway or other to find out, and what made me think about is was this Christopher. This fellow named Christopher Ball up here. Do you know him or know anything about him? He has something to do with the education department or the department of mathematical education, is it?
Lewis: No, not particularly in mathematics, no, but he has a linguistics background.
Lucas: So, we need to look this person up, but I wanted to see if there is anything else that you or Joy had for us on this project. This has been a great background here assuming we picked this up.
[break in tape]
Lucas: This is Mike Reed on the Moore Method telling some of his views on this.
Reed: Well, Ill give you Joys.
Lucas: All right.
Reed: Joy thinks she was harmed by the Moore Method. I guess her reason for this is that we left and went to Ohio, and we didnt know as much as all of those people did, and they were all Damn Yankees anyway and liked to feel superior. We didnt. They would use terms and use things and they considered we just didnt have a proper mathematical background.
Lucas: When you left Auburn.
Reed: Of course they were right. But, it bothered her, and it hurt her confidence and she thinks it was a serious blow, and that she never really recovered. She feels that if she had gone to a traditional place and been armed with that sort of knowledge that she would have been better served to go out into the world to fight. Me it didnt bother at all because I never felt that. I mean thats the kind of people that do well [laughs] under the Moore Method. Thats the case. I mean I just didnt care; I mean lets just take the same problem and a blank sheet of paper and see who gets it first. Give me your definitions and Ill take you on, if you can do it that way, but its a personality thing. I think it is true; it was for her. Mary Ellen Rudin feels she was hurt. I mean I cant speak for her; she can speak for herself. She thinks that she would have been better served by traditional mathematics.
Lewis: But, shes still a supporter.
Reed: Shes correct. I just had this discussion in fact in the Tilbilly?? System. She and Walter were both there, and I was sitting with ?? somewhere and we discussed the Moore Method. Walter had just been to my talk, and had asked me who I had studied with and I mentioned the Moore Method, and he said, Ah, you escaped. I said, No, I was propelled. [laughs] Walter Rudin had two years of Moore Method, by the way. Roberts at Duke.
Lewis: Oh, really.
Reed: Yes.
Lucas: And he is against it?
Reed: Oh, yeah, and I guess that Mary Ellen thinks that she just didnt know enough and it took her an awful long time for her to learn what she needed to know. She thought Moore was maybe past his prime, maybe not deteriorating intellectually, but not plugged into world mathematics to the extent that she wanted to be. But, shes moved in circles of top of the world of mathematics and I think she's been in defense of herself somewhere along the way I mean shes the best in the field. Shes my hero. If she thinks she could have done better, Id be amazed at what would have been, because I cant imagine better. But, she thinks that she was at a disadvantage not knowing more about what was going on in world mathematics at that time. You can ask her, but I think thats fair to say. I guess Mary Ellen and I have argued for years. We always go back and forth. But, my philosophy now after all these years is that I think its (Moore Method) the ideal way to start, but only to start. I think you want to get them to do mathematics on their own, to get the fun of it, to really get hooked, but you cant continue it through a whole undergraduate or graduate program and across all fields. Theres just too much out there. Youve got to let them go and you have to read, and theyve got to know whats going on. Here, one term is really all they get. Its not fair because they already know so much and Moore wouldnt have taught them because they already know too much. But, what I do is They witness to this. Ive changed their view by going back to something they dont know and make them start proving for themselves. Thats when they first start doing. Even if theyve got this huge knowledge, you can still find something they dont know and teach them Moore Method and I think you improve them. But, I think you only need to do it one year. You dont need to spend your life that way. All the Moore students when I left Auburn, where I taught Moore Method at Ohio, I spent four or five hours a day, every day, in the library just reading. I had to do that. I knew I had to do that. A lot of Moore people didnt do that, but I think all of them who are successful do. You have to find out what the rest of the world is doing. If youre working on something thats going, I mean, I tell my students that if theyre working on a hard problem and theyre getting somewhere, then dont do anything but do that problem. As long as youre going along, but when you stop, if you dont get any new ideas go read, go do some reading. Youve got to do both at some point. Joy was just lacking in confidence about not knowing what all those other people knew.
Lucas: The emotional and psychological aspect.
Reed: And these people were from Michigan and Wisconsin, Ivy League, and there was a little bit of status thing there anyway. And, we were Alabama hicks, so I think it was a combination, but thats happened to a lot of people, not just Joy. Youve got to be pretty strong to go out there ignorant and convince people that you know what youre talking about because you dont. All youve got is tremendous self-confidence. Thats what Moore Method gives you. In mathematics, you think you can do anything. And, if you can thats cool [laughs] or if you can do enough of it. On the other hand, weak students have been some of my best people that Im the most proud of out of the Moore Method. The weak student who doesnt get anything, and then all of a sudden they get that one thing, that joy when they do it. Its just as good as the person who has come in everyday, but again you cant take a weak student and only give him Moore Method because theyre going to go out not knowing anything and not able to do a whole lot either. So, they cant spend their life getting one or two results every year in whatever job they do. You can make a real change in a weak students life by introducing the Moore Method and getting him to a point to do that, but if you only give that person Moore Method hes at a disadvantage. Theyve got, in the end, to go out there and compete. And, if they arent genius or they arent brought up ??people ??, so youve go to be fair. Youve got to give them the Moore Method by all means, but I think youve got to equip them to be out there in the world. Its a mixture with every student. The most Moore Method student weve had ?? exam last week I guess he finished American. He was a student of his father who was a student of Bing. He just got his Ph.D. thesis solving a Moore space problem, my old problem of about 25 years. He solved for a Ph.D. thesis. He just left and went back to the States.
Lucas: Who was his professor?
Reed: He was a student of Bing and Burgess; Im not sure which there was some combination. A lot of times, like with Moore who was Moores supervisor. In fact, this guys supervisor is officially Peter, but all his theses came out of that first term I teach. I gave him that problem. But, particularly at Oxford, your supervisor is not necessarily the person you happen to work on the thesis with. And certainly I have students that mostly work with Peter. So its very hard to get the history. People in the United States are like that too. David's father was like that. Its not clear. Bing or Burgess or some combination thereof, yeah, but hes at Brigham Young.
Lewis: His father?
Reed: His fathers a topologist at Brigham Young.
Lucas: What I suggest is that we come back to this later this year with a fixed-up video camera and discuss the educational theory a little more with Albert. Im not sure if I can come back or not, but Albert might be released in a few more weeks, but somehow or another get into the educational part further because hes writing some stuff on this now or will be soon.
Reed: I could not have had a better match between
[tape beeps]
Lucas: This is a continuation of a very good interview with Mike Reed, and we will probably come back and discuss Moore Method and current educational problems with a video interview, possibly a set of questions.
Reed: People have a bit of a different experience with Moore. When talking they all have a slightly different view of what happened in that class. Of course, I think Moore challenged, Bing he just challenged them daily, you know try to see if they were good enough to go to the next class or whatever, but in some people he would boost their confidence. He was a psychologist almost, but mainly he loved his subject, and he liked people. Those are the two things that you have to have: you have to like what youre doing, and youve got to be able to communicate with people. Ben (Fitzpatrick) was very good. Ben was the best. Ive seen lots of people do Moore Method and Ben is the best. I didnt have a class with Moore, but Ben was absolutely perfect, and I couldnt imagine it being done with more motivation and talent for getting the most out of each person. He was really good.
Lucas: What were trying to do is just what Albert said, to study Moore as a teacher, and what he did, and why he did it, and what the results were. Just get the record and go from there, not so much understanding the theory behind it because were not sure anybody really can explain the theory
Lewis: Or those things come and go, and its the famous teachers or the rare phenomena are rarely recorded and you just know that someone was a great teacher but thats about all you can say because
Lucas: no one made a study of that.
Lewis: The people were too hard to get hold of, and here there happens to be an opportunity to get a hold of something thats really major over the years. You cant say much more than you just said about it openly, but why not try to lock into it and provide what inspiration he had for people who were never going to be as close as we were to that, and this is something that unfortunately some people are not sympathetic toward because perhaps the scientific evidence was so weak, that why bother? Its something that can be inspirational
Reed: Well it can. People that were successful adapted it to their own personality.
Lucas: modified
Reed: yeah, modified. People who tried to be Moore were doomed because they weren't Moore. People who tried to use that influence, to use themselves, developed, I think, theMary Ellen, despite what she says, teaches Moore Method in a fashion. She starts out, but shes too impatient, and she has to finish. But, what she does is involve people, and her enthusiasm and some of her students teach Moore Method. Her actions I do things which would be horrifying to theorists here because competition is something that is a dirty word almost in England. Having students compete seriously is just not done. Oh, they do it; theyre cutthroat, but they cant be seen to be doing it, so its very hard to do this. What I found myself often doing using the Moore Method, Ill put up some theorems and first of all, theyre just so bright and they have so much knowledge, that we just go through them in real time, and somebody will have an idea. Its a group effort. Sooner or later, youll get one thats so hard that they have to go home and one person just does it. But, as long as theyre proving the theorems then somebody puts up an idea, somebody else knocks it down, and after a while theyre competing. Somebody is trying to get one that the others cant get, so it develops that way, but if I just go in and say, you cant talk to other students about the problems, you have to come inI find hostility. But, if I do this and let them do it real time, then when they get to the hard ones, its what happens naturally. Again, theyre
Lucas: Thats the thing we ought to explore in your next meeting, the modified Moore Method as used by Mike Reed on video. No, you said, if one term or something
Reed: No, I think everybody should
Lucas: Listing specific examples and all that, maybe some names of people who did some unusual things and a few vignettes maybe, that kind of thing. But I dont think we can do that this afternoon even if we had the camera working. But, if you can come back and have a session on that subject I think that would be really
Reed: Well, Im going to be gone for a long time now.
Lucas: youre leaving when?
Reed: Im leaving Thursday for Greece, and then I probably will come back, and a couple of weeks later go to the States for a couple or three weeks.
Lucas: Well, well work it out even if its next summer. Well work towards that.
Lewis: Are you in the States for a holiday?
Reed: Theres a meeting for this ONR grant that I mentioned. Ive managed to keep all these years. Its the only way I can afford to live in this country. So, Im going to Washington. Were having a meeting there at D.C. in September, and my daughter lives in Philadelphia so well concur.
Lucas: Okay, end of tape.
July 21, 1998 Mike Reed
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The Center for American History
The University of Texas at Austin
This is Harry Lucas. Its July 21, 1998 at St. Edmund Hall. Albert Lewis and I are talking with G. M. (Mike) Reed, and were having a very good discussion about his background to the point of being at University of Wisconsin. Okay, go ahead Mike. [break in tape] Its July 21, 1998, and this is a continuation of the Mike Reed interview.
[tape has a lot of background noise and is very difficult to understand]
Mike Reed: I was lucky to get exposure to world-class people doing what I wanted to do at a very early age, but the topology connection I had was at Auburn with Ben Fitzpatrick and the other topologists there, especially Phil Zenor. Ben (Fitzpatrick) was my Moore. What Phil provided me was a role model of - Phil just came in from Houston as a young assistant professor who was ambitious and coached me like mad and brought things together. I learned how to play the game a bit.
Harry Lucas, Jr. Was he a student of Howard Cook?
Reed: Traylor..
Harry Lucas: How do you spell his last name?
Reed: Zenor, Z-E-N-O-R. So, Ben who was the motivating force and got me started in watching Phil (Zenor) operate, and Phil was very good. That was before I left Auburn, and at Auburn. I mean we had Kuratowski. I drank beer with Kuratowski in Auburn. Bing had been there. I couldnt have been at - the first AMS meeting I went to in Auburn, Alabama, I went to the national meeting of the American Mathematical Society. I had breakfast with Bing who was or just had been President of the American Mathematical Society, and I had tea in his apartment during the meeting with Gayle Young who at that time was President of the Mathematical Association of America. I mean, not too many people can come from a southern state university and walk into a national meeting and have that sort of contact. I first met Mary Ellen Rudin who came to my talk at that meeting. I spent the night in her room talking to her and her students. So, Auburn got me that, and I couldnt have gotten as good at what I wanted to do at Princeton. I couldnt have gotten into the community to do exactly what I wanted to do any better. So, I got to Ohio and in 75 I got an AMS Fellowship. There were only three, and they were open to anybody in the world then. I think now theyre only open to Americans.
Albert Lewis: AMS or NAS?
Reed: No, NAS was Poland. It was Poland. In fact, I got two more of those. I went back to Poland again and I was in Czechoslovakia on a NAS, so I had three NAS while I was still at Ohio. But, in 75-76 I got the AMS award, and I was the first person in the south to ever get that, and that gave me a year in England, total funding to go anywhere, so I spent one term at Pittsburgh with Bob McConnaugh??, Dave Lexer?? That was the center then of topology and with probably more important for my work was Poli Schemishinsky who Id met in 74. Poli had been my host, in fact, in Poland, and he was there on a postdoc and Eric van Douwen was there. So Eric van Douwen and Poli Schemishinski??and I were there all totally free to do nothing but mathematics every day and party all night. So this was again a very influential period, certainly in my mathematics. That same year Ohio University enrollment dropped from almost 20,000 to almost 10,000 [laughs] over a period of about two years. I think those figures are roughly right. One reason was that the state had the great idea of upping their out-of-state tuition by three times and something like two-thirds of the students at Ohio University were from New York [laughs], so right away it was during the recession, this was the bad recession. So they cut all non-tenured staff, every non-tenured person at the university cut across the board, so I was in Poland when I found this out [chuckles], that Id have a year when I came back, but that was it. All non-tenured faculty were given terminal contracts, cut across the board. So I came back to look for a job. This was when John (Worrell) talked to me about the Institute for Medicine and Mathematics. So we discussed forming this. In the meantime I had gotten a job offer, or at least a word of mouth job offer, from the University of Kansas, which was a good school of mathematics, but I decided to stay on. I got funding. John and I raised some money. We had lunch with a guy that wrote a check for half a million dollars, so I had funding, but what made me stay though First of all, John can be very persuasive and enthusiastic about how to change the world, but we started a postdoctoral program, and I got to hire the five best people to work. I chose them. We had this money. I got Toby Schemishenski, Eric van Douwen. You know Erics dead now.
Lewis: Oh, I didnt know that.
Reed: Oh, Erics the only person I know that did fifty papers posthumously. Hes had a great career since he died. He still has a paper every month, I think, from people who - He really was an author?? Toler?? who is now, in fact just was, the chairman of the department of computer science at University of California at Riverside. Peter Nikos who .. worked on ?? South Carolina and Bill Fleishner who is now at Kansas, as professor of set theory and topology. And Mike Whatley who really is very bright and went on and got his Ph.D. at Wisconsin from the State Institute for Medicine and Mathematics and then went to Harvard and got a M.D. and now is a physician researcher [siren in background] Anyway, that was the group and that was it. There was not a better place in the world to be in topology during those years the Institute was running in Athens. We cornered the market, Dutch, Poland, the States. We captured the best young people at work. We had conferences. We had the Spring conference and had other conferences. It was a very exciting time. In fact, I had a conference to solve a normal Moore-space problem, it had waiting around all these years, and so I just picked people who could do it. Frank Toll?? and Fleissner, Nikos had never worked on that, and I think it was either Frank or Judy Woodman?? who talked about stuff Kunz?? was doing. And theres Nikos just sitting there saw this axiom could be used to solve this Moore Space problem the other way and it was done, and then Bill Fleishner, two years later, completed the thing by showing in fact the problem is equivalent to large cardinals. It is totally set theory. Its got nothing to do with the Moore space and topology. It was a theorem about large cardinals. It was one of those horrible things that ended with a whimper not a bang. The Normal Moore Space Problem is equivalent to the existence of large cardinals. Everyone thinks its consistent with set theory that these cardinals exist, but you cant prove that. Its possible that you can get a counter-example, but no one thinks thats the case, but theres no model in which you can prove this because it would take a bigger model. Its one of those Godel sorts of arguments, so its left with a [laughs] shrug almost. So, the beautiful work that took forty years of mathematics, but it ended up a most unsatisfactory solution.
Lucas: Was that the thing you tried to discuss with me at lunch a year or so ago about n equals en or something?
Reed: Oh, no, no. This was a problem that F. B. Jones raised in 1937 that Moore spaces werent metrizable Moore plane or tangent disk space was invented by several people, Moore, Hausdorff, Kuratowski. Is a Moore space metrizable? Theres not a ?? metric on this. The question became well, what is it that is lacking to be metrizable and this property called normal? This was the conjecture, that since all the ones they could find that were normal were also metrizable. F. B. Jones was able to prove this using the Continuum Hypothesis in 1937. The Moore Space Conjecture was true, and about 1970 it was ??Frank Hall who had been taking courses from Bing in topology and courses in set theory from Silver saw that there was a connection between this thing called Martins axiom which is a set theoretic axiom thats also consistent with set theory and the denial of the Continuum Hypothesis. Before Frank could do it, he suggested to Silver who was the set theorist who was actually the first person to do it although Frank was the one who was sitting there and saw the connection I think, showed that under that assumption theres a normal Moore Space thats not metrizable. So, in some sense Jones had shown that another condition, separability is a ?? subset. But the actual thing was that Jones in 1937 showed that under the Continuum Hypothesis a normal separable Moore space is metrizable. About 1970 Silvers Hall had shown that under another assumption that is also consistent with set theory there is a normal seperable Moore space that is not metrizable. So, the question of whether normal separable Moore space was metrizable is independent of set theory, meaning their model of set theory was true and the model of set theory was false and you could never prove it absolutely within normal set theory. The question could not be decided. This involves separability, and then the question becomes what about if you dont have separable, can there exist a real one that is not metrizable? This is what turned out to be equivalent to the existence of large cardinals. So, that took another eight to ten years to do that. That had a lot to do with what I did later on. All the things I was interested in became solvable and we pretty much solved them in those ten years of set theory. Thats all I did. I focused on that area, and by the middle eighties it was time for me to look for another area or do something different because I had only been doing that. In the meantime, I stayed at the Institute and became unfortunately more of an administrator and money-getter. I was getting money for all these guys to do this great work, but I was spending my time out talking to little old ladies [laughs] trying to get donations and the Institute wasnt going as well for various reasons on other fronts. We were doing a bunch of things, trying some medicine for research and lots of other things. The university reneged on some promises. It didnt look that favorable. In the meantime, Joy, my wife, (we had been graduate students together at Auburn, and she got her masters from Ben and a Ph.D. from Phil Zenor) was finishing up. She had taken a year out actually as instructor, of course we were at the same level, but she had taken a year out as an instructor while I finished up. Then I took a job at Ohio, and it was more or less a promise or indication that the next job that came up shed get, so this was the thing, but then with this recession there was absolutely nothing, so she was part time teaching and even involved in the institute and was doing some medical. She got some papers on analysis, real analysis of medical application, but there was no future there, and jobs were hard to get in those days. So, she decided to go into computer science, since thats where the jobs were, so she decided that with both of us in topology we were unlikely ever [laughs] to get jobs in the same place. So, she looked around for places to do this and we had to find a way to afford it. Maryland was one of the places that she looked at that had a program that she was interested in the school was in the top ten in computer science.
[break in tape]
Harry Lucas: Were here with Mike Reed on July 21, 1998 Go ahead Mike.
Reed: So I found a way. I became program manager at the National Science Foundation. I was director of postdoctoral programs and also NATO post doctoral programs [break in tape] for two years, and it was fun University of Maryland and I worked in D.C. Joy got her masters and was doing research and she wanted to stay longer, and [break in tape] I wanted to stay away from Ohio [laughs] because I was on leave, but I didnt see any hope there. So, I met at a party at Maryland, Assar Rosenfeld, a World leader in the field [buzzing on tape] ??head of the international association ?? He had a lab and he had twenty-five Ph.D.s on research grants working for him. It was like an industry there, but I talked to him after that meeting and someone who worked with him and I was a topologist and they had a spot in topology. They wanted a three-dimensional Jordan curve theorem. They wanted a theorem that described a surface in three dimensions, something that ??? outside. At computer stores you look at the screen at a three-dimensional point. They wanted a definition. If youre ..cat scan looking for a?? they wanted a mathematical definition and an algorithm essentially that would come from that definition to give the three-dimensional Jordan curve theorem. I said, I would do that. [laughter] They said if you would do that well fund you, and I think within a week I quit NSF. I was doing digital topology.
Lucas: What year was that when you switched?
Reed: Oh, that was 80, 80 or81. So, I was there, and I got it. Again, one of those cases where thinking in Moore sense was to your advantage. . Fourier analysisall kinds of mathematics without topology stuff that I had no ?? [laughs] So, I went home and I worked from home down there a bit, and ??Id be back ??coat and tie and be able to do mathematics so it was very challenging, but I went down in the basement; Id bought a case of wine. I had a grid full of wine boxes so I put this grid down. My daughter had a Parcheesi board with black and white tokens, so I just put black and white tokens on the crate in three dimensions, for zeroes and ones, and just walked around it for days and days, walked around. It took me two months to write it up, but it was perfect. I didnt use anything but just sheer brute force, elegant brute force, but it was right. They had two kinds of notions of connections and I got a counterexample of one and a proof of the other, and I got a general theory of how ?? I still get more mileage out of that result. It was one of the least intellectually satisfying. I mean it was just sheer brute, hard, grinding out cases. For example, Im on an organizing committee and invited speaker in India in January for parallel image processing. Only thing Ive ever known in my life is that Parcheesi board. The only thing Ive ever done in image processing, but I was invited to Japan last year from that one result. Somehow, I was the first to do this, so it gets remembered.
Lewis: So this was published?
Reed: It was published in 80.
Lucas: So, you stayed with that deal?
Reed: No, not with that. That was in full computer science and based on that, again, I wanted to stay around Washington, Rosenfeld was my connection at the Institute and had insiders knowledge of me. I had been one-time coordinator of all postdoctoral programs at the agency and NASA had a very well paying, lucrative postdoc at Goddard Space Flight Center and I happened to know ?? [laughter] So Rosenfeld had some connections, so I applied, and with great probability [laughter] got a fellowship at NASA that was funded, again, to do models. The main problem was they got millions and millions and millions of distorted computer images taken at various angles by various satellites with different wave bands, and all kinds of different things, and they wanted to look for a certain object. They were looking for super novas and they have all kinds of pictures of it, but they cant find it. I mean the human eye can look through there and see that this thing is the same; its just rotated and twisted, but to tell a computer to say its the same thing, but rotated or twisted, but its a little bit fuzzy so its pattern recognition, recognizing again the topological geometry and telling a computer how to do it. So, this is what I did for a year there, and it was great fun. I really enjoyed it. In fact, I worked only at night because when I took the machine I needed everything. I needed almost every machine they had, so I only worked at night when everybody else left because I had to have all the machines running.
Lewis: What location was that?
Reed: It was Goddard Space Flight Center outside of Washington, D.C. I did that for a year and worked mostly with computer scientists. Realizing that processing would take hours to run one little picture. I thought aleph1 or C was big, but 2125 was a big number. [laughs] You dont realize how big small numbers; I mean topologists tend to think of things like that, but my first response when they told me this problem ?? youre talking about a 5 x 5 x 5 grid with only zeroes and ones, so why dont you just run a program, and they pointed out that theres not enough time left in the universe to check all possibilities of zeroes and ones to the 125th [laughs]. Another way to think of it, the way they do at NASA, one screen is 256 pixels, and each dot has 256 gray levels, and from about your focusing distance, thats as good as the eye can see, in other words, thats about as good as youre going to see anything. So, within that number are all things that you will ever see, 256 x 256 x 256. They can run random things through there. Everything youll ever be able to see, anywhere by anybody ever, will eventually appear in that combination, so thats all the possibilities there are. Theres a revelation of what you can see. Thats really weird to think about. That somehow brings across just how big those numbers are. Every face, every scene, every look, its all there in that 256 x 256 x 256. So, what I got to realizing was that for what I was trying to do there was no hope, particularly if people are interested in bodies, where you want a computer to see. I mean if it takes thirty minutes to figure out one image, then how is this thing going to work in real time it just seemed impossible. I started reading about parallel computation where youve got a thousand computers working at the same time, and now one computer is the size of a dot, so its not just one computer, now it became possible, but then it was just the beginning of parallel computing. I started reading about parallel computing just because I wanted to see what was possible and reading about parallel computers I found some papers by a guy named Tony Moore?? at Oxford and then I came to Oxford. Ive been coming to Oxford for years. Peter Collins??, my colleague the reason Im here. Id been to Poland about ten or fifteen times I guess, and Id usually stop in Oxford for seminars. ?? computer topologist at Oxford. So, I was in fact at dinner here and Bill Roscoe, who is computer science and also a mathematician, also a very bright man, hed just gotten his degree a couple of years before, and we started talking about the mathematics.. and went back to Ohio. The Institute had closed now so I went back as a professor of mathematics and computer science. Because of my image processing I was considered, I guess, computer scientist, so I went back to full professor in mathematics and computer science.
Lewis: And you were still on leave?
Reed: Id been on leave the whole time under Im not sure, they knew it, [laughter] but I had a letter. At a certain time after the Institute closed I pointed out this letter. In fact, Joy was now on the faculty in computer science, so Joy had a permanent job in computer science, and I was a full professor in computer science and mathematics. I guess we stayed in Washington one more year. Joy wanted to stay there because our daughter had started school and she wanted to finish. Front-page picture on Washington Post that did it. Ill never have anything like that. So, she finished and I was a professor at the Naval Academy, again one of those fortunate things in life. You never know how things are going to help. I just wanted to stay around another year, so I got a visiting professorship at the Naval Academy. It was fun to be there in Annapolis with the sailboats, and the pay was very good. The perks were great, the only place in the world where you can take your faculty ID and check out a sixty-foot yacht for the week [laughter]. It was great. [buzzing stops] But, because of the Navy I eventually got a grant from ONR to come to Oxford to study parallel computing. In fact, I came without the grant. First I decided to come and needed a way to fund it and was funded by a wonderful woman called Helen Hayes who had been a student of medicine and mathematics. It was a Texas foundation somewhere called Future Trends in Dallas or where ever it was, so I mentioned I wanted to do this and Helen responded to the Institute, okay, go do it. So she funded me that first year. I taught one term at Ohio and then came here. [tape beeps]
Lucas: This opposite side of the tape is full, Mike Reed
Reed: ?and again it was tax efficient to be a student, because if youre a student whatever money you get is not taxable. So I came here as an ?? student. I was also a fellow in college; I was a visiting fellow so I had the high table and all the perks while being a ?? student and working with John Ford ?? and Bill Rosco?? Roscoe was eventually the supervisor, but Tony Ober?? was the one that suggested what I work on, and then after that, I was here two terms I guess. Then in the summer, because of my naval connection, I arranged a fellowship at the Naval Research Laboratory in computer science in Washington. I went back to Washington for the summer. Then I left Washington with a grant from Office of Naval Research that paid me my full professor salary plus summers, so I came back to Oxford. So, I came back my second year here as a graduate student earning the highest salary at The University of Oxford. [laughs], paid through the Oxford payroll. It blew some administrators minds. So, boy I wish I had that money back, because it was temporary. I mean this was plenty of money then because after a year we were going back and I had a job so we rented a manor house across the park. I spent weekends up here by myself for six months and then again for three months and Id go to London on weekends and go to the theatres and eat well.
Lucas: What year was that?
Reed: 1985, I guess. 84-85, and then in 85 Joy took leave and came over and she got a fellowship and so we were both here and intended to go back to Ohio full-time in 86. But in 86 we also needed a job and so I took it, giving up two thirds of my salary. And Joy had the research position at the lab and had to give up her position, and she stayed there ten years I guess on research positions. But we made virtually the same amount of money. It was just that if you soft money means you had to continually apply and you had to switch what you were doing, and this got very old, not being able to count on the next thing that you would be doing. So she, I guess about three years ago, took a job at Oxford-Brooks University which is the other university in town, which is the bigger, Oxford Brooks. I'd never seen anything but Oxford. In fact, its equivalent to a good state university. Its ??ed departments, and I think architecture is the best in England. A bigger computer science department than we have.
Lucas: Was she teaching math?
Reed: No, computer science. So, shes permanent there now, lecturing there, so we ended up together again finally after all those years. She was the first one in computer science.
Lucas: So essentially the last thirteen years or so since youve been back, youve been specializing in this CST, or youve focused on that?
Reed: Right, but another attraction for my staying here was that almost all of my undergraduate teaching is in computer science, but Peter Collins and I share topology graduate students here equally. So, Ive had Ph.D. students in topology ever since Ive been here. I think, in fact, that weve got probably the best over the last ten years, professional group in the world. We have two or three a year. Peter does half and I do half. I dont think there is a conference in the world on topology that some of our students are not giving invited talks. So, what I got here or saw here I told Mary Ellen and Frank Tol?? That I used to think that you guys just must be great teachers, and now I understand. You just got great students [laughs]. You cant go wrong with these people here. You just have to define a space to them and thats all they need. Theyre just smart people. But, theyre nice people. So we tell the group we have an Oxford School of Topology now which Peter and I have done, so Ive had graduate students in computer science too, but probably more in topology than in computer science.
Lewis: Could you talk a little bit more about, to what body this School of Topology is attached. Its not just the college?
Reed: As a matter of fact its the mathematics department. In fact, Peter is now chair of the math board, so in fact, this is no doubt the most prestigious school in the world where our kind of point set topology is still a main
Lewis: Its that particular branch, I mean there are other topologists here?
Reed: Of course, Phil, Donaldson, Atea. But, theyre all algebraic.
Lucas: James is algebraic too, right?
Reed: James is algebraic but a bit more he was old enough to straddle both hills. James, at least, practiced ??, but all the others, and they are the biggest names in the world in topology. Atea, ??,and Donaldson. There were three Fields Medalists here. And ??, but it isnt ??? its been Peter and me that ?? by sheer tenacity of it.
Lucas: Who is using mostly say modified Moore method, other than you? I assume you are.
Reed: I use it. Who where?
Lucas: Here.
Reed: Well, no one. Well, some of our students here have taught their students that way, and now they have students who are in Auckland, New Zealand and Canada and elsewhere, but I teach a very modified Moore method. I normally teach the first year graduate students. I give them a Moore method course the first term. But, the deal is by the second term theyre doing research because, first of all, theyve got such a great undergraduate program. I mean theyre already through prelim levels in the states when they come here as graduate students.
Lucas: Do you teach any undergraduates?
Reed: I teach undergraduates mostly computer science. I tutor math students, but Im not responsible we take eight students a year here in some form of maths or maths computation, and Peter and I manage them. Peters marvelous. Hes a marvelous tutor; hes one of the best. Hes a topologist, but certainly not the Moore method, but I think that in the last fifteen years hes had the highest percentage of firsts in maths in Oxford College. What hes good at is selecting. We never disagree. We interview separately, but I listen to Peter because he has proved through his track record of identifying talent in mathematics.
Lewis: Did he have any acquaintance with Moore before you met him?
Reed: No. Certainly he knew topologists; he knew the topological community. But no, we have these arguments because he is totally against it, but he is very supportive of me. Its a good deal. I think weve more or less converged to a more or less agreement after all these years, but I needle him on one side and he needles me on the other. But, its a very good humored, good-natured feeling. In computer science what I did here and what I found surprising was in the parallel processing ?? initially used the power to use that processing to actually do particular tasks, ?? analysis, ?? was in the mathematical reasoning one uses in that theory, something called semantics, denotational or mathematical semantics. It was in vogue at Oxford back in the sixties and early seventies to giving mathematical meaning to computer programs. When you take the syntax for what the computer language says and you map this on mathematical object and you reason about that program by reasoning proving theorems in this mathematical structure. You can write simple programs, but even very, very complex sequential programs no human being can hold in their mind, but when you get to parallel programs and youve got a thousand computers each doing a different thing at the same time on the same data, what in the hell is going on? [laughs] You may run the same data to that thing ten straight times. You may even get the same answer. But, it got that answer ten different ways because you dont know which came first. Things are just happening, so its not just proving that one sequence of steps work; youve got to prove all possible, and again, the state explosion is too big. There are too many possible states to consider, so when you get on that air bus, and its got all those data processes all working at the same time, there is no way to test the paperwork. I mean they test, test, test, but I mean these crashes, one random sequence that no ones ever seen in ten years all of a sudden happens, and thats the one that causes the thing to lock up or whatever might happen. So, they will recognize very early in parallel processing that youve got to have some mathematical way of proving your design is correct. You cant depend on testing; you cant hope that some program is going to keep this ones head. Youve got to somehow be able to mathematically get a hold of these things. So, at Oxford ?? is in the mathematical semantics understanding of parallel processing, CSP, which is communicating sequential processes which means parallel. Thats what CSP stands for. So, they had, Hoare had it down to first semantics I guess in about 1978.
Lucas: How do you spell his last name?
Reed: Hoare, h-o-a-r-e. Then Bill Roscoe and Steve Brooks who is now a professor at Carnegie Mellon head down the full semantics in about 84, and its a really good mathematics program. Its a good mathematical model, and they used I guess the lattice theory. But, of course, you cant just map this thing to objects. You need a structure because youve got infinite programs or recursions have to be limited, in some sense, so you have to have some sort of limiting notion, either least upper bound which you get in lattice theory. Thats one way to do it. And Penscot?? did this. You know who Penscot?? is, the granddaddy of the Domain Theory, which is the name of this kind of mathematics. He was here at Oxford at the time. He was professor of logic at Berkley, of philosophy at Princeton, of mathematics and logic here, and now hes professor of computer science at Carnegie Mellon. Hes had four major universities with a different field every time. Hes into large cardinals and Moore spaces. Hes the one that did the first stuff on large cardinals. Hes done so much. I was just with him about a month ago and worked on his problem. Ill tell you a neat problem. I got this favorite problem. Ive got Dan working on it, and he couldnt get it either. So, when I came in at that point and was trying to find I read some of his papers and was interested in the Domain Theory because it was mathematics. You do embeddings, you build spaces. It was topology. If you look at his lattice theory and look at his topological structure you can put a topology, and you work with one or the other. Its really topology. Think of it as total topology, if you want. And Tony suggested to me that they wanted to handle time. In these programs you could guarantee certain things are true, but you want to guarantee youre going to have a certain amount of time and use a mathematical model that had time? And that was a level of complexity beyond. I mean that was almost a philosophical question: what is time? I mean you really have to mathematically define time in a way that you can treat it with analysis. So, he wanted me to get a timed real time semantic for CSP. So,
[end of tape]
Lucas: July 21, 1998
Reed: I did that over the next, oh, I guess four or five years. That way I guess the definitive model is just coming out this year. Its sixty pages, and that doesnt include the proof; thats just the description. [chuckles] Its one of the most horrendously complex mathematical objects Ive ever seen in my life.
Lucas: This is essentially what youve been working on the last few years.
Reed; Yeah, and now I think there have been, I think, seven Ph.D.s written on this model. I dont know, a hundred papers, a book; its been used in industries. It was a major I worked Moore spaces for a while, and then I got into this, and it just got absorbed me in the detail. This pretty stuff, this beautiful, I mean topology I can usually do in the bath tub. I mean most theorems Ive gotten, Ive been sitting there and aah because its just the key turns. Its like that. The difference in this is that the complexity and detail is so great; youve got to have so much stuff in your mind at the same time that these flashes of keys turning happen less regularly. Its more grinding out, putting together these huge slices and finding some way to reason about the slice without knowing all the details and then put them together. Its a different sort of thing and it takes a lot of ?? I outlined the program of what I wanted to do when I started this thesis, and like I said, its pretty much been accomplished, but its taken seven Ph.D.s to do all that. It was a horrendous job, but its now one of the standards. I mean there are other people in the world who encountered things related and we all pretty much came to the same general notions of how it should be done, but that problem is considered solved. But, then that was the problem, in the computer sciences area, to solve timing. And thats what Bill Roscoe and I took on, and we did it, we and our students. We nailed it. So, thats what I did up until the mid 90s.
Lucas: What were doing, or what were looking for is now solved, and weve been asked to ??
Reed: The point was, the difference in this semantics was that it was based on topology, on pre-measured spaces, using Banachs Fixed Point Theorem instead of the lattice theory, so this is a topological measuring structure where topology is in the model because time is a measure. The things are close if they agree. So, the further they act like the same thing, theyre the same. So, you can use time as a measure of how things converge over time, and that was the trick. I thought I was a real genius for thinking this topology with Bill, but I met someone years later that had talked to Tony Hoare about this, I guess in the early 80s, and Tony was talking about doing real time and Tony said, Yeah, but thats going to be difficult. I think Ive got to wait for a topologist to come along. [laughs] So he knew darn well which way it should be done to begin with. I just showed up and, oh yeah, look at this. It turned out to be ?? Tony, hes won the Turing Award, which is like the Nobel Prize. I mean hes one who has no degree in mathematics or computer science. Hes in ??
Lewis: Oh, thats a marvelous British tradition.
Lucas: So, what we have to do while weve got an hour or two left up here is to get someway or other to find out, and what made me think about is was this Christopher. This fellow named Christopher Ball up here. Do you know him or know anything about him? He has something to do with the education department or the department of mathematical education, is it?
Lewis: No, not particularly in mathematics, no, but he has a linguistics background.
Lucas: So, we need to look this person up, but I wanted to see if there is anything else that you or Joy had for us on this project. This has been a great background here assuming we picked this up.
[break in tape]
Lucas: This is Mike Reed on the Moore Method telling some of his views on this.
Reed: Well, Ill give you Joys.
Lucas: All right.
Reed: Joy thinks she was harmed by the Moore Method. I guess her reason for this is that we left and went to Ohio, and we didnt know as much as all of those people did, and they were all Damn Yankees anyway and liked to feel superior. We didnt. They would use terms and use things and they considered we just didnt have a proper mathematical background.
Lucas: When you left Auburn.
Reed: Of course they were right. But, it bothered her, and it hurt her confidence and she thinks it was a serious blow, and that she never really recovered. She feels that if she had gone to a traditional place and been armed with that sort of knowledge that she would have been better served to go out into the world to fight. Me it didnt bother at all because I never felt that. I mean thats the kind of people that do well [laughs] under the Moore Method. Thats the case. I mean I just didnt care; I mean lets just take the same problem and a blank sheet of paper and see who gets it first. Give me your definitions and Ill take you on, if you can do it that way, but its a personality thing. I think it is true; it was for her. Mary Ellen Rudin feels she was hurt. I mean I cant speak for her; she can speak for herself. She thinks that she would have been better served by traditional mathematics.
Lewis: But, shes still a supporter.
Reed: Shes correct. I just had this discussion in fact in the Tilbilly?? System. She and Walter were both there, and I was sitting with ?? somewhere and we discussed the Moore Method. Walter had just been to my talk, and had asked me who I had studied with and I mentioned the Moore Method, and he said, Ah, you escaped. I said, No, I was propelled. [laughs] Walter Rudin had two years of Moore Method, by the way. Roberts at Duke.
Lewis: Oh, really.
Reed: Yes.
Lucas: And he is against it?
Reed: Oh, yeah, and I guess that Mary Ellen thinks that she just didnt know enough and it took her an awful long time for her to learn what she needed to know. She thought Moore was maybe past his prime, maybe not deteriorating intellectually, but not plugged into world mathematics to the extent that she wanted to be. But, shes moved in circles of top of the world of mathematics and I think she's been in defense of herself somewhere along the way I mean shes the best in the field. Shes my hero. If she thinks she could have done better, Id be amazed at what would have been, because I cant imagine better. But, she thinks that she was at a disadvantage not knowing more about what was going on in world mathematics at that time. You can ask her, but I think thats fair to say. I guess Mary Ellen and I have argued for years. We always go back and forth. But, my philosophy now after all these years is that I think its (Moore Method) the ideal way to start, but only to start. I think you want to get them to do mathematics on their own, to get the fun of it, to really get hooked, but you cant continue it through a whole undergraduate or graduate program and across all fields. Theres just too much out there. Youve got to let them go and you have to read, and theyve got to know whats going on. Here, one term is really all they get. Its not fair because they already know so much and Moore wouldnt have taught them because they already know too much. But, what I do is They witness to this. Ive changed their view by going back to something they dont know and make them start proving for themselves. Thats when they first start doing. Even if theyve got this huge knowledge, you can still find something they dont know and teach them Moore Method and I think you improve them. But, I think you only need to do it one year. You dont need to spend your life that way. All the Moore students when I left Auburn, where I taught Moore Method at Ohio, I spent four or five hours a day, every day, in the library just reading. I had to do that. I knew I had to do that. A lot of Moore people didnt do that, but I think all of them who are successful do. You have to find out what the rest of the world is doing. If youre working on something thats going, I mean, I tell my students that if theyre working on a hard problem and theyre getting somewhere, then dont do anything but do that problem. As long as youre going along, but when you stop, if you dont get any new ideas go read, go do some reading. Youve got to do both at some point. Joy was just lacking in confidence about not knowing what all those other people knew.
Lucas: The emotional and psychological aspect.
Reed: And these people were from Michigan and Wisconsin, Ivy League, and there was a little bit of status thing there anyway. And, we were Alabama hicks, so I think it was a combination, but thats happened to a lot of people, not just Joy. Youve got to be pretty strong to go out there ignorant and convince people that you know what youre talking about because you dont. All youve got is tremendous self-confidence. Thats what Moore Method gives you. In mathematics, you think you can do anything. And, if you can thats cool [laughs] or if you can do enough of it. On the other hand, weak students have been some of my best people that Im the most proud of out of the Moore Method. The weak student who doesnt get anything, and then all of a sudden they get that one thing, that joy when they do it. Its just as good as the person who has come in everyday, but again you cant take a weak student and only give him Moore Method because theyre going to go out not knowing anything and not able to do a whole lot either. So, they cant spend their life getting one or two results every year in whatever job they do. You can make a real change in a weak students life by introducing the Moore Method and getting him to a point to do that, but if you only give that person Moore Method hes at a disadvantage. Theyve got, in the end, to go out there and compete. And, if they arent genius or they arent brought up ??people ??, so youve go to be fair. Youve got to give them the Moore Method by all means, but I think youve got to equip them to be out there in the world. Its a mixture with every student. The most Moore Method student weve had ?? exam last week I guess he finished American. He was a student of his father who was a student of Bing. He just got his Ph.D. thesis solving a Moore space problem, my old problem of about 25 years. He solved for a Ph.D. thesis. He just left and went back to the States.
Lucas: Who was his professor?
Reed: He was a student of Bing and Burgess; Im not sure which there was some combination. A lot of times, like with Moore who was Moores supervisor. In fact, this guys supervisor is officially Peter, but all his theses came out of that first term I teach. I gave him that problem. But, particularly at Oxford, your supervisor is not necessarily the person you happen to work on the thesis with. And certainly I have students that mostly work with Peter. So its very hard to get the history. People in the United States are like that too. David's father was like that. Its not clear. Bing or Burgess or some combination thereof, yeah, but hes at Brigham Young.
Lewis: His father?
Reed: His fathers a topologist at Brigham Young.
Lucas: What I suggest is that we come back to this later this year with a fixed-up video camera and discuss the educational theory a little more with Albert. Im not sure if I can come back or not, but Albert might be released in a few more weeks, but somehow or another get into the educational part further because hes writing some stuff on this now or will be soon.
Reed: I could not have had a better match between
[tape beeps]
Lucas: This is a continuation of a very good interview with Mike Reed, and we will probably come back and discuss Moore Method and current educational problems with a video interview, possibly a set of questions.
Reed: People have a bit of a different experience with Moore. When talking they all have a slightly different view of what happened in that class. Of course, I think Moore challenged, Bing he just challenged them daily, you know try to see if they were good enough to go to the next class or whatever, but in some people he would boost their confidence. He was a psychologist almost, but mainly he loved his subject, and he liked people. Those are the two things that you have to have: you have to like what youre doing, and youve got to be able to communicate with people. Ben (Fitzpatrick) was very good. Ben was the best. Ive seen lots of people do Moore Method and Ben is the best. I didnt have a class with Moore, but Ben was absolutely perfect, and I couldnt imagine it being done with more motivation and talent for getting the most out of each person. He was really good.
Lucas: What were trying to do is just what Albert said, to study Moore as a teacher, and what he did, and why he did it, and what the results were. Just get the record and go from there, not so much understanding the theory behind it because were not sure anybody really can explain the theory
Lewis: Or those things come and go, and its the famous teachers or the rare phenomena are rarely recorded and you just know that someone was a great teacher but thats about all you can say because
Lucas: no one made a study of that.
Lewis: The people were too hard to get hold of, and here there happens to be an opportunity to get a hold of something thats really major over the years. You cant say much more than you just said about it openly, but why not try to lock into it and provide what inspiration he had for people who were never going to be as close as we were to that, and this is something that unfortunately some people are not sympathetic toward because perhaps the scientific evidence was so weak, that why bother? Its something that can be inspirational
Reed: Well it can. People that were successful adapted it to their own personality.
Lucas: modified
Reed: yeah, modified. People who tried to be Moore were doomed because they weren't Moore. People who tried to use that influence, to use themselves, developed, I think, theMary Ellen, despite what she says, teaches Moore Method in a fashion. She starts out, but shes too impatient, and she has to finish. But, what she does is involve people, and her enthusiasm and some of her students teach Moore Method. Her actions I do things which would be horrifying to theorists here because competition is something that is a dirty word almost in England. Having students compete seriously is just not done. Oh, they do it; theyre cutthroat, but they cant be seen to be doing it, so its very hard to do this. What I found myself often doing using the Moore Method, Ill put up some theorems and first of all, theyre just so bright and they have so much knowledge, that we just go through them in real time, and somebody will have an idea. Its a group effort. Sooner or later, youll get one thats so hard that they have to go home and one person just does it. But, as long as theyre proving the theorems then somebody puts up an idea, somebody else knocks it down, and after a while theyre competing. Somebody is trying to get one that the others cant get, so it develops that way, but if I just go in and say, you cant talk to other students about the problems, you have to come inI find hostility. But, if I do this and let them do it real time, then when they get to the hard ones, its what happens naturally. Again, theyre
Lucas: Thats the thing we ought to explore in your next meeting, the modified Moore Method as used by Mike Reed on video. No, you said, if one term or something
Reed: No, I think everybody should
Lucas: Listing specific examples and all that, maybe some names of people who did some unusual things and a few vignettes maybe, that kind of thing. But I dont think we can do that this afternoon even if we had the camera working. But, if you can come back and have a session on that subject I think that would be really
Reed: Well, Im going to be gone for a long time now.
Lucas: youre leaving when?
Reed: Im leaving Thursday for Greece, and then I probably will come back, and a couple of weeks later go to the States for a couple or three weeks.
Lucas: Well, well work it out even if its next summer. Well work towards that.
Lewis: Are you in the States for a holiday?
Reed: Theres a meeting for this ONR grant that I mentioned. Ive managed to keep all these years. Its the only way I can afford to live in this country. So, Im going to Washington. Were having a meeting there at D.C. in September, and my daughter lives in Philadelphia so well concur.
Lucas: Okay, end of tape.
PAGE 12
PAGE 36
July 21, 1998 Mike Reed
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?AEIKOThe R. L. Moore Biography Project
The Center for American History
The University of Texas at Austin
This is Harry Lucas. Its July 21, 1998 at St. Edmund Hall. Albert Lewis and I are talking with G. M. (Mike) Reed, and were having a very good discussion about his background to the point of being at University of Wisconsin. Okay, go ahead Mike. [break in tape] Its July 21, 1998, and this is a continuation of the Mike Reed interview.
[tape has a lot of background noise and is very difficult to understand]
Mike Reed: I was lucky to get exposure to world-class people doing what I wanted to do at a very early age, but the topology connection I had was at Auburn with Ben Fitzpatrick and the other topologists there, especially Phil Zenor. Ben (Fitzpatrick) was my Moore. What Phil provided me was a role model of - Phil just came in from Houston as a young assistant professor who was ambitious and coached me like mad and brought things together. I learned how to play the game a bit.
Harry Lucas, Jr. Was he a student of Howard Cook?
Reed: Traylor..
Harry Lucas: How do you spell his last name?
Reed: Zenor, Z-E-N-O-R. So, Ben who was the motivating force and got me started in watching Phil (Zenor) operate, and Phil was very good. That was before I left Auburn, and at Auburn. I mean we had Kuratowski. I drank beer with Kuratowski in Auburn. Bing had been there. I couldnt have been at - the first AMS meeting I went to in Auburn, Alabama, I went to the national meeting of the American Mathematical Society. I had breakfast with Bing who was or just had been President of the American Mathematical Society, and I had tea in his apartment during the meeting with Gayle Young who at that time was President of the Mathematical Association of America. I mean, not too many people can come from a southern state university and walk into a national meeting and have that sort of contact. I first met Mary Ellen Rudin who came to my talk at that meeting. I spent the night in her room talking to her and her students. So, Auburn got me that, and I couldnt have gotten as good at what I wanted to do at Princeton. I couldnt have gotten into the community to do exactly what I wanted to do any better. So, I got to Ohio and in 75 I got an AMS Fellowship. There were only three, and they were open to anybody in the world then. I think now theyre only open to Americans.
Albert Lewis: AMS or NAS?
Reed: No, NAS was Poland. It was Poland. In fact, I got two more of those. I went back to Poland again and I was in Czechoslovakia on a NAS, so I had three NAS while I was still at Ohio. But, in 75-76 I got the AMS award, and I was the first person in the south to ever get that, and that gave me a year in England, total funding to go anywhere, so I spent one term at Pittsburgh with Bob McConnaugh??, Dave Lexer?? That was the center then of topology and with probably more important for my work was Poli Schemishinsky who Id met in 74. Poli had been my host, in fact, in Poland, and he was there on a postdoc and Eric van Douwen was there. So Eric van Douwen and Poli Schemishinski??and I were there all totally free to do nothing but mathematics every day and party all night. So this was again a very influential period, certainly in my mathematics. That same year Ohio University enrollment dropped from almost 20,000 to almost 10,000 [laughs] over a period of about two years. I think those figures are roughly right. One reason was that the state had the great idea of upping their out-of-state tuition by three times and something like two-thirds of the students at Ohio University were from New York [laughs], so right away it was during the recession, this was the bad recession. So they cut all non-tenured staff, every non-tenured person at the university cut across the board, so I was in Poland when I found this out [chuckles], that Id have a year when I came back, but that was it. All non-tenured faculty were given terminal contracts, cut across the board. So I came back to look for a job. This was when John (Worrell) talked to me about the Institute for Medicine and Mathematics. So we discussed forming this. In the meantime I had gotten a job offer, or at least a word of mouth job offer, from the University of Kansas, which was a good school of mathematics, but I decided to stay on. I got funding. John and I raised some money. We had lunch with a guy that wrote a check for half a million dollars, so I had funding, but what made me stay though First of all, John can be very persuasive and enthusiastic about how to change the world, but we started a postdoctoral program, and I got to hire the five best people to work. I chose them. We had this money. I got Toby Schemishenski, Eric van Douwen. You know Erics dead now.
Lewis: Oh, I didnt know that.
Reed: Oh, Erics the only person I know that did fifty papers posthumously. Hes had a great career since he died. He still has a paper every month, I think, from people who - He really was an author?? Toler?? who is now, in fact just was, the chairman of the department of computer science at University of California at Riverside. Peter Nikos who .. worked on ?? South Carolina and Bill Fleishner who is now at Kansas, as professor of set theory and topology. And Mike Whatley who really is very bright and went on and got his Ph.D. at Wisconsin from the State Institute for Medicine and Mathematics and then went to Harvard and got a M.D. and now is a physician researcher [siren in background] Anyway, that was the group and that was it. There was not a better place in the world to be in topology during those years the Institute was running in Athens. We cornered the market, Dutch, Poland, the States. We captured the best young people at work. We had conferences. We had the Spring conference and had other conferences. It was a very exciting time. In fact, I had a conference to solve a normal Moore-space problem, it had waiting around all these years, and so I just picked people who could do it. Frank Toll?? and Fleissner, Nikos had never worked on that, and I think it was either Frank or Judy Woodman?? who talked about stuff Kunz?? was doing. And theres Nikos just sitting there saw this axiom could be used to solve this Moore Space problem the other way and it was done, and then Bill Fleishner, two years later, completed the thing by showing in fact the problem is equivalent to large cardinals. It is totally set theory. Its got nothing to do with the Moore space and topology. It was a theorem about large cardinals. It was one of those horrible things that ended with a whimper not a bang. The Normal Moore Space Problem is equivalent to the existence of large cardinals. Everyone thinks its consistent with set theory that these cardinals exist, but you cant prove that. Its possible that you can get a counter-example, but no one thinks thats the case, but theres no model in which you can prove this because it would take a bigger model. Its one of those Godel sorts of arguments, so its left with a [laughs] shrug almost. So, the beautiful work that took forty years of mathematics, but it ended up a most unsatisfactory solution.
Lucas: Was that the thing you tried to discuss with me at lunch a year or so ago about n equals en or something?
Reed: Oh, no, no. This was a problem that F. B. Jones raised in 1937 that Moore spaces werent metrizable Moore plane or tangent disk space was invented by several people, Moore, Hausdorff, Kuratowski. Is a Moore space metrizable? Theres not a ?? metric on this. The question became well, what is it that is lacking to be metrizable and this property called normal? This was the conjecture, that since all the ones they could find that were normal were also metrizable. F. B. Jones was able to prove this using the Continuum Hypothesis in 1937. The Moore Space Conjecture was true, and about 1970 it was ??Frank Hall who had been taking courses from Bing in topology and courses in set theory from Silver saw that there was a connection between this thing called Martins axiom which is a set theoretic axiom thats also consistent with set theory and the denial of the Continuum Hypothesis. Before Frank could do it, he suggested to Silver who was the set theorist who was actually the first person to do it although Frank was the one who was sitting there and saw the connection I think, showed that under that assumption theres a normal Moore Space thats not metrizable. So, in some sense Jones had shown that another condition, separability is a ?? subset. But the actual thing was that Jones in 1937 showed that under the Continuum Hypothesis a normal separable Moore space is metrizable. About 1970 Silvers Hall had shown that under another assumption that is also consistent with set theory there is a normal seperable Moore space that is not metrizable. So, the question of whether normal separable Moore space was metrizable is independent of set theory, meaning their model of set theory was true and the model of set theory was false and you could never prove it absolutely within normal set theory. The question could not be decided. This involves separability, and then the question becomes what about if you dont have separable, can there exist a real one that is not metrizable? This is what turned out to be equivalent to the existence of large cardinals. So, that took another eight to ten years to do that. That had a lot to do with what I did later on. All the things I was interested in became solvable and we pretty much solved them in those ten years of set theory. Thats all I did. I focused on that area, and by the middle eighties it was time for me to look for another area or do something different because I had only been doing that. In the meantime, I stayed at the Institute and became unfortunately more of an administrator and money-getter. I was getting money for all these guys to do this great work, but I was spending my time out talking to little old ladies [laughs] trying to get donations and the Institute wasnt going as well for various reasons on other fronts. We were doing a bunch of things, trying some medicine for research and lots of other things. The university reneged on some promises. It didnt look that favorable. In the meantime, Joy, my wife, (we had been graduate students together at Auburn, and she got her masters from Ben and a Ph.D. from Phil Zenor) was finishing up. She had taken a year out actually as instructor, of course we were at the same level, but she had taken a year out as an instructor while I finished up. Then I took a job at Ohio, and it was more or less a promise or indication that the next job that came up shed get, so this was the thing, but then with this recession there was absolutely nothing, so she was part time teaching and even involved in the institute and was doing some medical. She got some papers on analysis, real analysis of medical application, but there was no future there, and jobs were hard to get in those days. So, she decided to go into computer science, since thats where the jobs were, so she decided that with both of us in topology we were unlikely ever [laughs] to get jobs in the same place. So, she looked around for places to do this and we had to find a way to afford it. Maryland was one of the places that she looked at that had a program that she was interested in the school was in the top ten in computer science.
[break in tape]
Harry Lucas: Were here with Mike Reed on July 21, 1998 Go ahead Mike.
Reed: So I found a way. I became program manager at the National Science Foundation. I was director of postdoctoral programs and also NATO post doctoral programs [break in tape] for two years, and it was fun University of Maryland and I worked in D.C. Joy got her masters and was doing research and she wanted to stay longer, and [break in tape] I wanted to stay away from Ohio [laughs] because I was on leave, but I didnt see any hope there. So, I met at a party at Maryland, Assar Rosenfeld, a World leader in the field [buzzing on tape] ??head of the international association ?? He had a lab and he had twenty-five Ph.D.s on research grants working for him. It was like an industry there, but I talked to him after that meeting and someone who worked with him and I was a topologist and they had a spot in topology. They wanted a three-dimensional Jordan curve theorem. They wanted a theorem that described a surface in three dimensions, something that ??? outside. At computer stores you look at the screen at a three-dimensional point. They wanted a definition. If youre ..cat scan looking for a?? they wanted a mathematical definition and an algorithm essentially that would come from that definition to give the three-dimensional Jordan curve theorem. I said, I would do that. [laughter] They said if you would do that well fund you, and I think within a week I quit NSF. I was doing digital topology.
Lucas: What year was that when you switched?
Reed: Oh, that was 80, 80 or81. So, I was there, and I got it. Again, one of those cases where thinking in Moore sense was to your advantage. . Fourier analysisall kinds of mathematics without topology stuff that I had no ?? [laughs] So, I went home and I worked from home down there a bit, and ??Id be back ??coat and tie and be able to do mathematics so it was very challenging, but I went down in the basement; Id bought a case of wine. I had a grid full of wine boxes so I put this grid down. My daughter had a Parcheesi board with black and white tokens, so I just put black and white tokens on the crate in three dimensions, for zeroes and ones, and just walked around it for days and days, walked around. It took me two months to write it up, but it was perfect. I didnt use anything but just sheer brute force, elegant brute force, but it was right. They had two kinds of notions of connections and I got a counterexample of one and a proof of the other, and I got a general theory of how ?? I still get more mileage out of that result. It was one of the least intellectually satisfying. I mean it was just sheer brute, hard, grinding out cases. For example, Im on an organizing committee and invited speaker in India in January for parallel image processing. Only thing Ive ever known in my life is that Parcheesi board. The only thing Ive ever done in image processing, but I was invited to Japan last year from that one result. Somehow, I was the first to do this, so it gets remembered.
Lewis: So this was published?
Reed: It was published in 80.
Lucas: So, you stayed with that deal?
Reed: No, not with that. That was in full computer science and based on that, again, I wanted to stay around Washington, Rosenfeld was my connection at the Institute and had insiders knowledge of me. I had been one-time coordinator of all postdoctoral programs at the agency and NASA had a very well paying, lucrative postdoc at Goddard Space Flight Center and I happened to know ?? [laughter] So Rosenfeld had some connections, so I applied, and with great probability [laughter] got a fellowship at NASA that was funded, again, to do models. The main problem was they got millions and millions and millions of distorted computer images taken at various angles by various satellites with different wave bands, and all kinds of different things, and they wanted to look for a certain object. They were looking for super novas and they have all kinds of pictures of it, but they cant find it. I mean the human eye can look through there and see that this thing is the same; its just rotated and twisted, but to tell a computer to say its the same thing, but rotated or twisted, but its a little bit fuzzy so its pattern recognition, recognizing again the topological geometry and telling a computer how to do it. So, this is what I did for a year there, and it was great fun. I really enjoyed it. In fact, I worked only at night because when I took the machine I needed everything. I needed almost every machine they had, so I only worked at night when everybody else left because I had to have all the machines running.
Lewis: What location was that?
Reed: It was Goddard Space Flight Center outside of Washington, D.C. I did that for a year and worked mostly with computer scientists. Realizing that processing would take hours to run one little picture. I thought aleph1 or C was big, but 2125 was a big number. [laughs] You dont realize how big small numbers; I mean topologists tend to think of things like that, but my first response when they told me this problem ?? youre talking about a 5 x 5 x 5 grid with only zeroes and ones, so why dont you just run a program, and they pointed out that theres not enough time left in the universe to check all possibilities of zeroes and ones to the 125th [laughs]. Another way to think of it, the way they do at NASA, one screen is 256 pixels, and each dot has 256 gray levels, and from about your focusing distance, thats as good as the eye can see, in other words, thats about as good as youre going to see anything. So, within that number are all things that you will ever see, 256 x 256 x 256. They can run random things through there. Everything youll ever be able to see, anywhere by anybody ever, will eventually appear in that combination, so thats all the possibilities there are. Theres a revelation of what you can see. Thats really weird to think about. That somehow brings across just how big those numbers are. Every face, every scene, every look, its all there in that 256 x 256 x 256. So, what I got to realizing was that for what I was trying to do there was no hope, particularly if people are interested in bodies, where you want a computer to see. I mean if it takes thirty minutes to figure out one image, then how is this thing going to work in real time it just seemed impossible. I started reading about parallel computation where youve got a thousand computers working at the same time, and now one computer is the size of a dot, so its not just one computer, now it became possible, but then it was just the beginning of parallel computing. I started reading about parallel computing just because I wanted to see what was possible and reading about parallel computers I found some papers by a guy named Tony Moore?? at Oxford and then I came to Oxford. Ive been coming to Oxford for years. Peter Collins??, my colleague the reason Im here. Id been to Poland about ten or fifteen times I guess, and Id usually stop in Oxford for seminars. ?? computer topologist at Oxford. So, I was in fact at dinner here and Bill Roscoe, who is computer science and also a mathematician, also a very bright man, hed just gotten his degree a couple of years before, and we started talking about the mathematics.. and went back to Ohio. The Institute had closed now so I went back as a professor of mathematics and computer science. Because of my image processing I was considered, I guess, computer scientist, so I went back to full professor in mathematics and computer science.
Lewis: And you were still on leave?
Reed: Id been on leave the whole time under Im not sure, they knew it, [laughter] but I had a letter. At a certain time after the Institute closed I pointed out this letter. In fact, Joy was now on the faculty in computer science, so Joy had a permanent job in computer science, and I was a full professor in computer science and mathematics. I guess we stayed in Washington one more year. Joy wanted to stay there because our daughter had started school and she wanted to finish. Front-page picture on Washington Post that did it. Ill never have anything like that. So, she finished and I was a professor at the Naval Academy, again one of those fortunate things in life. You never know how things are going to help. I just wanted to stay around another year, so I got a visiting professorship at the Naval Academy. It was fun to be there in Annapolis with the sailboats, and the pay was very good. The perks were great, the only place in the world where you can take your faculty ID and check out a sixty-foot yacht for the week [laughter]. It was great. [buzzing stops] But, because of the Navy I eventually got a grant from ONR to come to Oxford to study parallel computing. In fact, I came without the grant. First I decided to come and needed a way to fund it and was funded by a wonderful woman called Helen Hayes who had been a student of medicine and mathematics. It was a Texas foundation somewhere called Future Trends in Dallas or where ever it was, so I mentioned I wanted to do this and Helen responded to the Institute, okay, go do it. So she funded me that first year. I taught one term at Ohio and then came here. [tape beeps]
Lucas: This opposite side of the tape is full, Mike Reed
Reed: ?and again it was tax efficient to be a student, because if youre a student whatever money you get is not taxable. So I came here as an ?? student. I was also a fellow in college; I was a visiting fellow so I had the high table and all the perks while being a ?? student and working with John Ford ?? and Bill Rosco?? Roscoe was eventually the supervisor, but Tony Ober?? was the one that suggested what I work on, and then after that, I was here two terms I guess. Then in the summer, because of my naval connection, I arranged a fellowship at the Naval Research Laboratory in computer science in Washington. I went back to Washington for the summer. Then I left Washington with a grant from Office of Naval Research that paid me my full professor salary plus summers, so I came back to Oxford. So, I came back my second year here as a graduate student earning the highest salary at The University of Oxford. [laughs], paid through the Oxford payroll. It blew some administrators minds. So, boy I wish I had that money back, because it was temporary. I mean this was plenty of money then because after a year we were going back and I had a job so we rented a manor house across the park. I spent weekends up here by myself for six months and then again for three months and Id go to London on weekends and go to the theatres and eat well.
Lucas: What year was that?
Reed: 1985, I guess. 84-85, and then in 85 Joy took leave and came over and she got a fellowship and so we were both here and intended to go back to Ohio full-time in 86. But in 86 we also needed a job and so I took it, giving up two thirds of my salary. And Joy had the research position at the lab and had to give up her position, and she stayed there ten years I guess on research positions. But we made virtually the same amount of money. It was just that if you soft money means you had to continually apply and you had to switch what you were doing, and this got very old, not being able to count on the next thing that you would be doing. So she, I guess about three years ago, took a job at Oxford-Brooks University which is the other university in town, which is the bigger, Oxford Brooks. I'd never seen anything but Oxford. In fact, its equivalent to a good state university. Its ??ed departments, and I think architecture is the best in England. A bigger computer science department than we have.
Lucas: Was she teaching math?
Reed: No, computer science. So, shes permanent there now, lecturing there, so we ended up together again finally after all those years. She was the first one in computer science.
Lucas: So essentially the last thirteen years or so since youve been back, youve been specializing in this CST, or youve focused on that?
Reed: Right, but another attraction for my staying here was that almost all of my undergraduate teaching is in computer science, but Peter Collins and I share topology graduate students here equally. So, Ive had Ph.D. students in topology ever since Ive been here. I think, in fact, that weve got probably the best over the last ten years, professional group in the world. We have two or three a year. Peter does half and I do half. I dont think there is a conference in the world on topology that some of our students are not giving invited talks. So, what I got here or saw here I told Mary Ellen and Frank Tol?? That I used to think that you guys just must be great teachers, and now I understand. You just got great students [laughs]. You cant go wrong with these people here. You just have to define a space to them and thats all they need. Theyre just smart people. But, theyre nice people. So we tell the group we have an Oxford School of Topology now which Peter and I have done, so Ive had graduate students in computer science too, but probably more in topology than in computer science.
Lewis: Could you talk a little bit more about, to what body this School of Topology is attached. Its not just the college?
Reed: As a matter of fact its the mathematics department. In fact, Peter is now chair of the math board, so in fact, this is no doubt the most prestigious school in the world where our kind of point set topology is still a main
Lewis: Its that particular branch, I mean there are other topologists here?
Reed: Of course, Phil, Donaldson, Atea. But, theyre all algebraic.
Lucas: James is algebraic too, right?
Reed: James is algebraic but a bit more he was old enough to straddle both hills. James, at least, practiced ??, but all the others, and they are the biggest names in the world in topology. Atea, ??,and Donaldson. There were three Fields Medalists here. And ??, but it isnt ??? its been Peter and me that ?? by sheer tenacity of it.
Lucas: Who is using mostly say modified Moore method, other than you? I assume you are.
Reed: I use it. Who where?
Lucas: Here.
Reed: Well, no one. Well, some of our students here have taught their students that way, and now they have students who are in Auckland, New Zealand and Canada and elsewhere, but I teach a very modified Moore method. I normally teach the first year graduate students. I give them a Moore method course the first term. But, the deal is by the second term theyre doing research because, first of all, theyve got such a great undergraduate program. I mean theyre already through prelim levels in the states when they come here as graduate students.
Lucas: Do you teach any undergraduates?
Reed: I teach undergraduates mostly computer science. I tutor math students, but Im not responsible we take eight students a year here in some form of maths or maths computation, and Peter and I manage them. Peters marvelous. Hes a marvelous tutor; hes one of the best. Hes a topologist, but certainly not the Moore method, but I think that in the last fifteen years hes had the highest percentage of firsts in maths in Oxford College. What hes good at is selecting. We never disagree. We interview separately, but I listen to Peter because he has proved through his track record of identifying talent in mathematics.
Lewis: Did he have any acquaintance with Moore before you met him?
Reed: No. Certainly he knew topologists; he knew the topological community. But no, we have these arguments because he is totally against it, but he is very supportive of me. Its a good deal. I think weve more or less converged to a more or less agreement after all these years, but I needle him on one side and he needles me on the other. But, its a very good humored, good-natured feeling. In computer science what I did here and what I found surprising was in the parallel processing ?? initially used the power to use that processing to actually do particular tasks, ?? analysis, ?? was in the mathematical reasoning one uses in that theory, something called semantics, denotational or mathematical semantics. It was in vogue at Oxford back in the sixties and early seventies to giving mathematical meaning to computer programs. When you take the syntax for what the computer language says and you map this on mathematical object and you reason about that program by reasoning proving theorems in this mathematical structure. You can write simple programs, but even very, very complex sequential programs no human being can hold in their mind, but when you get to parallel programs and youve got a thousand computers each doing a different thing at the same time on the same data, what in the hell is going on? [laughs] You may run the same data to that thing ten straight times. You may even get the same answer. But, it got that answer ten different ways because you dont know which came first. Things are just happening, so its not just proving that one sequence of steps work; youve got to prove all possible, and again, the state explosion is too big. There are too many possible states to consider, so when you get on that air bus, and its got all those data processes all working at the same time, there is no way to test the paperwork. I mean they test, test, test, but I mean these crashes, one random sequence that no ones ever seen in ten years all of a sudden happens, and thats the one that causes the thing to lock up or whatever might happen. So, they will recognize very early in parallel processing that youve got to have some mathematical way of proving your design is correct. You cant depend on testing; you cant hope that some program is going to keep this ones head. Youve got to somehow be able to mathematically get a hold of these things. So, at Oxford ?? is in the mathematical semantics understanding of parallel processing, CSP, which is communicating sequential processes which means parallel. Thats what CSP stands for. So, they had, Hoare had it down to first semantics I guess in about 1978.
Lucas: How do you spell his last name?
Reed: Hoare, h-o-a-r-e. Then Bill Roscoe and Steve Brooks who is now a professor at Carnegie Mellon head down the full semantics in about 84, and its a really good mathematics program. Its a good mathematical model, and they used I guess the lattice theory. But, of course, you cant just map this thing to objects. You need a structure because youve got infinite programs or recursions have to be limited, in some sense, so you have to have some sort of limiting notion, either least upper bound which you get in lattice theory. Thats one way to do it. And Penscot?? did this. You know who Penscot?? is, the granddaddy of the Domain Theory, which is the name of this kind of mathematics. He was here at Oxford at the time. He was professor of logic at Berkley, of philosophy at Princeton, of mathematics and logic here, and now hes professor of computer science at Carnegie Mellon. Hes had four major universities with a different field every time. Hes into large cardinals and Moore spaces. Hes the one that did the first stuff on large cardinals. Hes done so much. I was just with him about a month ago and worked on his problem. Ill tell you a neat problem. I got this favorite problem. Ive got Dan working on it, and he couldnt get it either. So, when I came in at that point and was trying to find I read some of his papers and was interested in the Domain Theory because it was mathematics. You do embeddings, you build spaces. It was topology. If you look at his lattice theory and look at his topological structure you can put a topology, and you work with one or the other. Its really topology. Think of it as total topology, if you want. And Tony suggested to me that they wanted to handle time. In these programs you could guarantee certain things are true, but you want to guarantee youre going to have a certain amount of time and use a mathematical model that had time? And that was a level of complexity beyond. I mean that was almost a philosophical question: what is time? I mean you really have to mathematically define time in a way that you can treat it with analysis. So, he wanted me to get a timed real time semantic for CSP. So,
[end of tape]
Lucas: July 21, 1998
Reed: I did that over the next, oh, I guess four or five years. That way I guess the definitive model is just coming out this year. Its sixty pages, and that doesnt include the proof; thats just the description. [chuckles] Its one of the most horrendously complex mathematical objects Ive ever seen in my life.
Lucas: This is essentially what youve been working on the last few years.
Reed; Yeah, and now I think there have been, I think, seven Ph.D.s written on this model. I dont know, a hundred papers, a book; its been used in industries. It was a major I worked Moore spaces for a while, and then I got into this, and it just got absorbed me in the detail. This pretty stuff, this beautiful, I mean topology I can usually do in the bath tub. I mean most theorems Ive gotten, Ive been sitting there and aah because its just the key turns. Its like that. The difference in this is that the complexity and detail is so great; youve got to have so much stuff in your mind at the same time that these flashes of keys turning happen less regularly. Its more grinding out, putting together these huge slices and finding some way to reason about the slice without knowing all the details and then put them together. Its a different sort of thing and it takes a lot of ?? I outlined the program of what I wanted to do when I started this thesis, and like I said, its pretty much been accomplished, but its taken seven Ph.D.s to do all that. It was a horrendous job, but its now one of the standards. I mean there are other people in the world who encountered things related and we all pretty much came to the same general notions of how it should be done, but that problem is considered solved. But, then that was the problem, in the computer sciences area, to solve timing. And thats what Bill Roscoe and I took on, and we did it, we and our students. We nailed it. So, thats what I did up until the mid 90s.
Lucas: What were doing, or what were looking for is now solved, and weve been asked to ??
Reed: The point was, the difference in this semantics was that it was based on topology, on pre-measured spaces, using Banachs Fixed Point Theorem instead of the lattice theory, so this is a topological measuring structure where topology is in the model because time is a measure. The things are close if they agree. So, the further they act like the same thing, theyre the same. So, you can use time as a measure of how things converge over time, and that was the trick. I thought I was a real genius for thinking this topology with Bill, but I met someone years later that had talked to Tony Hoare about this, I guess in the early 80s, and Tony was talking about doing real time and Tony said, Yeah, but thats going to be difficult. I think Ive got to wait for a topologist to come along. [laughs] So he knew darn well which way it should be done to begin with. I just showed up and, oh yeah, look at this. It turned out to be ?? Tony, hes won the Turing Award, which is like the Nobel Prize. I mean hes one who has no degree in mathematics or computer science. Hes in ??
Lewis: Oh, thats a marvelous British tradition.
Lucas: So, what we have to do while weve got an hour or two left up here is to get someway or other to find out, and what made me think about is was this Christopher. This fellow named Christopher Ball up here. Do you know him or know anything about him? He has something to do with the education department or the department of mathematical education, is it?
Lewis: No, not particularly in mathematics, no, but he has a linguistics background.
Lucas: So, we need to look this person up, but I wanted to see if there is anything else that you or Joy had for us on this project. This has been a great background here assuming we picked this up.
[break in tape]
Lucas: This is Mike Reed on the Moore Method telling some of his views on this.
Reed: Well, Ill give you Joys.
Lucas: All right.
Reed: Joy thinks she was harmed by the Moore Method. I guess her reason for this is that we left and went to Ohio, and we didnt know as much as all of those people did, and they were all Damn Yankees anyway and liked to feel superior. We didnt. They would use terms and use things and they considered we just didnt have a proper mathematical background.
Lucas: When you left Auburn.
Reed: Of course they were right. But, it bothered her, and it hurt her confidence and she thinks it was a serious blow, and that she never really recovered. She feels that if she had gone to a traditional place and been armed with that sort of knowledge that she would have been better served to go out into the world to fight. Me it didnt bother at all because I never felt that. I mean thats the kind of people that do well [laughs] under the Moore Method. Thats the case. I mean I just didnt care; I mean lets just take the same problem and a blank sheet of paper and see who gets it first. Give me your definitions and Ill take you on, if you can do it that way, but its a personality thing. I think it is true; it was for her. Mary Ellen Rudin feels she was hurt. I mean I cant speak for her; she can speak for herself. She thinks that she would have been better served by traditional mathematics.
Lewis: But, shes still a supporter.
Reed: Shes correct. I just had this discussion in fact in the Tilbilly?? System. She and Walter were both there, and I was sitting with ?? somewhere and we discussed the Moore Method. Walter had just been to my talk, and had asked me who I had studied with and I mentioned the Moore Method, and he said, Ah, you escaped. I said, No, I was propelled. [laughs] Walter Rudin had two years of Moore Method, by the way. Roberts at Duke.
Lewis: Oh, really.
Reed: Yes.
Lucas: And he is against it?
Reed: Oh, yeah, and I guess that Mary Ellen thinks that she just didnt know enough and it took her an awful long time for her to learn what she needed to know. She thought Moore was maybe past his prime, maybe not deteriorating intellectually, but not plugged into world mathematics to the extent that she wanted to be. But, shes moved in circles of top of the world of mathematics and I think she's been in defense of herself somewhere along the way I mean shes the best in the field. Shes my hero. If she thinks she could have done better, Id be amazed at what would have been, because I cant imagine better. But, she thinks that she was at a disadvantage not knowing more about what was going on in world mathematics at that time. You can ask her, but I think thats fair to say. I guess Mary Ellen and I have argued for years. We always go back and forth. But, my philosophy now after all these years is that I think its (Moore Method) the ideal way to start, but only to start. I think you want to get them to do mathematics on their own, to get the fun of it, to really get hooked, but you cant continue it through a whole undergraduate or graduate program and across all fields. Theres just too much out there. Youve got to let them go and you have to read, and theyve got to know whats going on. Here, one term is really all they get. Its not fair because they already know so much and Moore wouldnt have taught them because they already know too much. But, what I do is They witness to this. Ive changed their view by going back to something they dont know and make them start proving for themselves. Thats when they first start doing. Even if theyve got this huge knowledge, you can still find something they dont know and teach them Moore Method and I think you improve them. But, I think you only need to do it one year. You dont need to spend your life that way. All the Moore students when I left Auburn, where I taught Moore Method at Ohio, I spent four or five hours a day, every day, in the library just reading. I had to do that. I knew I had to do that. A lot of Moore people didnt do that, but I think all of them who are successful do. You have to find out what the rest of the world is doing. If youre working on something thats going, I mean, I tell my students that if theyre working on a hard problem and theyre getting somewhere, then dont do anything but do that problem. As long as youre going along, but when you stop, if you dont get any new ideas go read, go do some reading. Youve got to do both at some point. Joy was just lacking in confidence about not knowing what all those other people knew.
Lucas: The emotional and psychological aspect.
Reed: And these people were from Michigan and Wisconsin, Ivy League, and there was a little bit of status thing there anyway. And, we were Alabama hicks, so I think it was a combination, but thats happened to a lot of people, not just Joy. Youve got to be pretty strong to go out there ignorant and convince people that you know what youre talking about because you dont. All youve got is tremendous self-confidence. Thats what Moore Method gives you. In mathematics, you think you can do anything. And, if you can thats cool [laughs] or if you can do enough of it. On the other hand, weak students have been some of my best people that Im the most proud of out of the Moore Method. The weak student who doesnt get anything, and then all of a sudden they get that one thing, that joy when they do it. Its just as good as the person who has come in everyday, but again you cant take a weak student and only give him Moore Method because theyre going to go out not knowing anything and not able to do a whole lot either. So, they cant spend their life getting one or two results every year in whatever job they do. You can make a real change in a weak students life by introducing the Moore Method and getting him to a point to do that, but if you only give that person Moore Method hes at a disadvantage. Theyve got, in the end, to go out there and compete. And, if they arent genius or they arent brought up ??people ??, so youve go to be fair. Youve got to give them the Moore Method by all means, but I think youve got to equip them to be out there in the world. Its a mixture with every student. The most Moore Method student weve had ?? exam last week I guess he finished American. He was a student of his father who was a student of Bing. He just got his Ph.D. thesis solving a Moore space problem, my old problem of about 25 years. He solved for a Ph.D. thesis. He just left and went back to the States.
Lucas: Who was his professor?
Reed: He was a student of Bing and Burgess; Im not sure which there was some combination. A lot of times, like with Moore who was Moores supervisor. In fact, this guys supervisor is officially Peter, but all his theses came out of that first term I teach. I gave him that problem. But, particularly at Oxford, your supervisor is not necessarily the person you happen to work on the thesis with. And certainly I have students that mostly work with Peter. So its very hard to get the history. People in the United States are like that too. David's father was like that. Its not clear. Bing or Burgess or some combination thereof, yeah, but hes at Brigham Young.
Lewis: His father?
Reed: His fathers a topologist at Brigham Young.
Lucas: What I suggest is that we come back to this later this year with a fixed-up video camera and discuss the educational theory a little more with Albert. Im not sure if I can come back or not, but Albert might be released in a few more weeks, but somehow or another get into the educational part further because hes writing some stuff on this now or will be soon.
Reed: I could not have had a better match between
[tape beeps]
Lucas: This is a continuation of a very good interview with Mike Reed, and we will probably come back and discuss Moore Method and current educational problems with a video interview, possibly a set of questions.
Reed: People have a bit of a different experience with Moore. When talking they all have a slightly different view of what happened in that class. Of course, I think Moore challenged, Bing he just challenged them daily, you know try to see if they were good enough to go to the next class or whatever, but in some people he would boost their confidence. He was a psychologist almost, but mainly he loved his subject, and he liked people. Those are the two things that you have to have: you have to like what youre doing, and youve got to be able to communicate with people. Ben (Fitzpatrick) was very good. Ben was the best. Ive seen lots of people do Moore Method and Ben is the best. I didnt have a class with Moore, but Ben was absolutely perfect, and I couldnt imagine it being done with more motivation and talent for getting the most out of each person. He was really good.
Lucas: What were trying to do is just what Albert said, to study Moore as a teacher, and what he did, and why he did it, and what the results were. Just get the record and go from there, not so much understanding the theory behind it because were not sure anybody really can explain the theory
Lewis: Or those things come and go, and its the famous teachers or the rare phenomena are rarely recorded and you just know that someone was a great teacher but thats about all you can say because
Lucas: no one made a study of that.
Lewis: The people were too hard to get hold of, and here there happens to be an opportunity to get a hold of something thats really major over the years. You cant say much more than you just said about it openly, but why not try to lock into it and provide what inspiration he had for people who were never going to be as close as we were to that, and this is something that unfortunately some people are not sympathetic toward because perhaps the scientific evidence was so weak, that why bother? Its something that can be inspirational
Reed: Well it can. People that were successful adapted it to their own personality.
Lucas: modified
Reed: yeah, modified. People who tried to be Moore were doomed because they weren't Moore. People who tried to use that influence, to use themselves, developed, I think, theMary Ellen, despite what she says, teaches Moore Method in a fashion. She starts out, but shes too impatient, and she has to finish. But, what she does is involve people, and her enthusiasm and some of her students teach Moore Method. Her actions I do things which would be horrifying to theorists here because competition is something that is a dirty word almost in England. Having students compete seriously is just not done. Oh, they do it; theyre cutthroat, but they cant be seen to be doing it, so its very hard to do this. What I found myself often doing using the Moore Method, Ill put up some theorems and first of all, theyre just so bright and they have so much knowledge, that we just go through them in real time, and somebody will have an idea. Its a group effort. Sooner or later, youll get one thats so hard that they have to go home and one person just does it. But, as long as theyre proving the theorems then somebody puts up an idea, somebody else knocks it down, and after a while theyre competing. Somebody is trying to get one that the others cant get, so it develops that way, but if I just go in and say, you cant talk to other students about the problems, you have to come inI find hostility. But, if I do this and let them do it real time, then when they get to the hard ones, its what happens naturally. Again, theyre
Lucas: Thats the thing we ought to explore in your next meeting, the modified Moore Method as used by Mike Reed on video. No, you said, if one term or something
Reed: No, I think everybody should
Lucas: Listing specific examples and all that, maybe some names of people who did some unusual things and a few vignettes maybe, that kind of thing. But I dont think we can do that this afternoon even if we had the camera working. But, if you can come back and have a session on that subject I think that would be really
Reed: Well, Im going to be gone for a long time now.
Lucas: youre leaving when?
Reed: Im leaving Thursday for Greece, and then I probably will come back, and a couple of weeks later go to the States for a couple or three weeks.
Lucas: Well, well work it out even if its next summer. Well work towards that.
Lewis: Are you in the States for a holiday?
Reed: Theres a meeting for this ONR grant that I mentioned. Ive managed to keep all these years. Its the only way I can afford to live in this country. So, Im going to Washington. Were having a meeting there at D.C. in September, and my daughter lives in Philadelphia so well concur.
Lucas: Okay, end of tape.
July 21, 1998 Mike Reed
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