I remember Donald Michie (1923 – 2007)

On July 7, 2007 Dame Anne McLaren and Donald Michie died in a car accident. Last time I had met Anne was in the 1970s when I stayed at their house in Edinburgh. Both were launched on scientific careers that were to lead them to positions rivalling each others’ eminence in their respective fields.

The last time I met Donald (henceforth “DM”) was when my wife and I visited him in Oxford in November 2004. He demo’ed the Sophie chatbot system, asking us what we thought of his choice of accent for the speech-generating software. He was intrigued by the way his current choice, labeled “Southern California Trash”, blended with the other personality attributes of Sophie. The stereo was playing DM’s current favourite, “Harper Valley PTA” sung by Jeannie C. Riley, another sassy American female.

Although excited by his current project, DM was depressed by the gloomy British weather; he would depart shortly to spend the winter in Gibraltar. “Gibraltar??”. “Yes, Gibraltar. I trust it will be sunny, and it is British.” In the following pages I have noted, roughly in chronological order, some experiences with this extraordinary man, one of the great pioneers in Artificial Intelligence.

My first sighting of DM was during an attempted demo of project MiniMAC during the IFIP conference in Edinburgh in 1968. At the time I was a PhD student at the Mathematical Centre in Amsterdam. Rather petulantly I had wanted to test whether I was still loved by the powers that be. I did this by making it known that I wanted to be sent to the conference. A few months earlier I had come across a story in the New Scientist on project MiniMAC, complete with photo of D. Michie, the professor of “Machine Intelligence”. The project was reported to be developing an innovative high-level language named POP-2 to be run on a conversational computing system to rival Project MAC at MIT. It appealed to me that two clever Brits (Rod Burstall and Robin Popplestone) were doing all this at a small fraction of the cost of Project MAC.
I had expected to have to do some sleuthing in Edinburgh to find MiniMAC. It turned out that DM’s PR activities made this unnecessary: out of the IFIP conference materials dropped an invitation to a demo. I showed up at the appointed address, a fashionable downtown location with teletypes supposed to be connected by telephone line. The line did not work, the professor of Machine Intelligence showing up in person at the scene of distress was to no avail, all guests were spirited away, and treated to lunch. Soon, I had forgotten about Michie and MiniMAC.

The following months I was restless at the Mathematical Centre, but couldn’t think of anything to do about it. My wife showed me an announcement for British Council Summer Scholarships. This struck me as singularly unhelpful: this was for people with connections and ideas, neither of which I was endowed with. I continued to mope until I hit upon a crazy idea. The more I thought about it, the less crazy it seemed: I would apply for a six-week visit to Michie’s Experimental Programming Unit in Edinburgh.

The form went off to the British Council; a letter went off to professor Michie, who answered that I would be welcome and, by the way, he was organizing the Fifth Machine Intelligence Workshop — would I have a paper? I didn’t, but wrote an overdue initial sketch of my PhD project, copied out the draft in my best handwriting (in pencil, to hide unsightly corrections), and sent it off.

The afternoon of arrival in Edinburgh faded into one of those long, long evenings of the Northern summer. DM showed me to my office and took me to a performance at the theater club on the Grassmarket, not far from the Unit’s Hope Park Square buildings. After the show it still wasn’t dark. DM walked me across the Meadows to my lodgings. The next day brought an invitation for spaghetti dinner at the Michie home at 4 Dick Place, where I found Alan Robinson and Ira Pohl.

Ira had just finished his PhD at the Stanford Linear Accelerator Centre and Stanford’s Computer Science Department. The obscurity of my institution combined with the uncertainty whether I had even started on a thesis made the contrast with my situation painful. But Ira’s person was not at all intimidating. He had a huge Afro head of hair and kept going on about “Portnoy’s Complaint”, the novel he was reading. As for the other person present, if I had known what Resolution Logic was, I wouldn’t have dared even to enter the room. As it was, I experienced Alan as a pleasant new acquaintance, to me the quintessential American. It turned out that his new employer, Syracuse University, had agreed to have him start employment with a sabbatical year, a year that he was about to start as visitor of DM’s, or affiliated, outfit. Presently DM, in cook’s apron, brought in the spaghetti.

In the Mathematical Centre you would run your program by preparing a paper tape on a Flexowriter, which you submitted for processing, with additional tapes for library routines. The turnaround time was measured in hours. The POP-2 system that I played with that first summer was my first experience with interactive computing. It was also my first experience with another programming language. For most people a language coming from Algol 60, the next worse language is a let-down. POP-2 was better. The combination of the language and interactivity was exhilarating. When I returned in the summer of 1970, I gained a better understanding of POP 2: I realized that initially I had just been writing Algol 60 in POP 2.

DM got me to work on memo functions. I had just discovered the tree data structure, which doesn’t come naturally in Algol 60. Appropriately or not, I used for the required storage a tree that adapted its structure in response to use. This absorbed me completely so that I never wondered what memo functions might be good for. We got excited about memo-izing recursive functions, but failed to get anywhere with that. After I got bored with adaptive trees, I dismissed memo functions as a plausible, but not particularly exciting idea, something to be expected from a biologist dabbling in computers. Sixteen years later I read the great book of Abelson and Sussman, where they tell first-year MIT students how memo-izing changes a recursively implemented Fibonacci function from exponential to linear complexity. A near miss in 1970. It hurts to realize the high price of ignorance combined with my stupidity. It also taught me a lesson about “biologists dabbling in computers”.

DM inquired about the possibility of my taking a full-time position in his department. I countered with the observation that I didn’t have my PhD yet. Not so much from conviction behind my PhD project, but from doubts about Artificial Intelligence: it felt messy. My PhD project was inspired by a problem raised by a biologist. Or rather, it was inspired by my revulsion at the messiness of the literature in the area. I was not the kind of programmer itching to get his hands dirty at making the computer crunch the client’s data. My paper in Machine Intelligence 5 was about a nice, clean, fundamental approach to this kind of thing. Still, it was no more than just an idea.

My office mate in Amsterdam was working on the semantics of programming languages. Now, there was the meaty and abstract mathematics that I coveted. I played with the thought of dropping my near-finished thesis and trying to re-start in this glamorous area. This was replaced by the thought of doing that as a PhD, albeit one burdened with a wimpy thesis. But in my biology-inspired MI 5 paper DM had recognized a kind of thinking that he related to. He must have hoped that my lack of further interest was a passing whim.

It turned out to be more than a passing whim. Only in later life did I realize how my instincts were determined by the narrow mind set of mathematics and physics. For example, I did not believe that evolution explained everything that biologists claimed it could. I also rejected the even less plausible alternatives to evolution. I was OK with the idea that there are a lot of things we don’t know, or don’t even know how to begin thinking about. It was only much later, when reading Dawkins on neo-Darwinism, that I got a feel of the kind of thinking that came naturally to DM.

The inquiries from DM “May we call you Doctor yet?” continued, until in 1971 I had to answer in the affirmative. I then weaseled out by pleading a postdoc fellowship at IBM in Yorktown Heights, upon which DM granted me another year’s reprieve. Neither of us was entirely sure of my commitment. The uncertainty may have had something to do with Donald and Jean Michie driving over from Syracuse in July 1972 for a friendly reminder (and a lecture at the T.J. Watson Research Center).

When I arrived in Edinburgh for my research fellowship in the fall of 1972, Jean inquired in a low, ominous voice: “Is your Stack empty?” to which I could only guiltily mumble something. The first weeks I spent finishing a paper on something numeric. The reason for my guilt was not so much this as the knowledge that I was supposed to work on Memo Functions, the title given by DM to the proposal for the grant that was paying my generous salary. In this same meeting I heard Jean say: “What? You haven’t heard of the report by Sir James Lighthill? The man who is trying to abolish us?”

At the time I thought this overly dramatic. However, the Report was soon followed by a heavyweight panel grilling all of those funded by the grants to DM. I had avoided work on Memo Functions, spending all my time on logic programming under the guidance of Bob Kowalski. The panel had me explain what Memo Functions were. Promptly David Park exposed my lack of preparation for such work.

What with the Report and the Panel, by 1974 Science Research Council decided to stop funding most of DM’s projects. Soon after, Edinburgh University Dean of Science decided it was time for a thorough reorganization of Machine Intelligence in Edinburgh. One might think this was just about the worst time for such a move. The Dean of Science thought that, on the contrary, this was a most opportune, even strategic, time for doing so.

The Dean decreed that there were to be two departments, one of Machine Intelligence, and one of Artificial Intelligence. DM was to head Machine Intelligence. The rest of the re-organization was to be democratically decided: each researcher was to elect the department to be in. Of course, not all of these choices were individual. For example, Meltzer, the head of computational intelligence, elected to be in Artificial Intelligence. This determined Bob Kowalski’s choice. I had been de-facto, if not formally, in that group because of my work with Bob, and I elected Artificial Intelligence. The overall result was that Machine Intelligence ended up with one professor, one secretary, one technician, and a suitably modest share of the offices at Hope Park Square.

As he later said, DM felt this episode as a betrayal he had not imagined possible. Something you read about in Greek dramas, not something that could actually happen to one. For most people it was not a betrayal. Many were in Bob Kowalski’s position, whose allegiance was to Meltzer. But some did have a choice, like Meltzer. And I was another one who did have a choice.

Most of the AI researchers in Edinburgh were happy to be able to work in such pleasant surroundings and to be in one of world’s prime centers of AI research. We were delighted, but also took it for granted, that every summer a significant part of the world’s AI community visited, with several staying for a postdoc or a sabbatical. This way I met Woody Bledsoe, Danny Bobrow, Bob Boyer, Jack Good, Cordell Green, Carl Hewitt, John McCarthy, J Moore, Nils Nilsson, Seymour Papert, Ira Pohl, Bert Raphael, Alan Robinson, Earl Sacerdoti, Aron Sloman, and Gerry Sussman, to mention some that come to mind now.

Some workers resented DM’s entrepreneurial activities. One was furious about DM’s interference with “his” lab. Such a clash was perhaps inevitable: DM saw the lab as part of his creation and regarded the action as necessary guidance. All of us knew DM; knew even where his office was. But many of us did not realize that the very presence of AI in Edinburgh was due to one man, that very English gentleman with the office with the nice view. Just as water vapour cannot condense without a condensation kernel (everyone of the zillions of raindrops in the Earth’s atmosphere has in it a tiny speck of dust or a salt crystal), the glory of AI in Edinburgh had needed one person to condense onto. That man was Donald Michie. By and large, the AI workers in Edinburgh did not want to be reminded of this. Few realized what the outcome of the re-organization meant for DM.

With the trauma of his loss of empire, a golden time started for DM. The meteoric success of the period 1967 – 1970 had come with a heavy burden of managerial and bureaucratic responsibilities. He had handled these confidently and capably, but suffered under the lack of time for research work of his own. DM relished the freedom that now came with his fall from grace. In the years that followed, he and Jean could, and did, accept many of the invitations from abroad. Some were for a whole academic term: two or more in Urbana-Champaign and in Stanford. Some were short visits, including several to us in Waterloo.

Paradoxically, the years I spent in Edinburgh full-time (1972 – 1975) was the period I saw least of DM. But even in this busy and harassed period, he was punctiliously courteous, as evidenced by an Edinburgh-to-Edinburgh telegram soon after the birth of Eva:


During my summer visits in 1969 and 1970 we talked a lot, including memo functions. After 1975 there was also plenty of time to talk. One may well ask whether all this talk came to anything. Maybe not: DM wanted to pick my brain and I enjoyed having my brain picked. Some ex-Edinburghers would indignantly interject at this point: “You were used by DM!”. Sure, and that should be allowed between consenting adults. One such person claimed that so and so had been destroyed by DM. But if life after Edinburgh does not go well, then it’s not clear that DM’s siren calls were to blame; it was, after all, a choice.

DM had a tendency to go into what I called “Testy Mode”, perhaps hurtful to those with tender skins. A nice example is found in the interview with H.J. van den Herik (“Computerschaak, schaakwereld en kunstmatige intelligentie” by H.J. van den Herik, Academic Service, 1983):

vdH: I suppose you know the statement of Dreyfus in this question. Could you give an argument against him?
Michie: He said that no computer could play even amateur chess. Then he played against a computer and he lost. So that seems to answer that particular question. Perhaps you had some other silly remark in mind?

During one dinner, in the 1990’s in the Oak Bay Marina, Donald had been holding forth, resulting in all plates empty, except Donald’s half full of spaghetti. The waiter started clearing the table mumbling something like I presume you’re finished, Sir. “ABSOLUTELY NOT!” was the reply that sent the poor man scampering out of sight.

Conversations are not the only way to commune; another is to browse each other’s book shelves. In Hope Park Square offices were not locked; I felt free to roam when nobody was around. During an early visit I found on one of DM’s bookshelves “The Estimation of Probabilities” a slim book by I.J. Good (was this the “Jack Good”, I wondered, who kept popping up in conversations with DM). I had been schooled in a strictly frequentist doctrine according to which probabilities only start to make sense for events that occur sufficiently frequently. Given this background, it was mind-boggling to find someone seriously proposing, coherently, to estimate probabilities of events that have never occurred.

I found another mind-boggling book, this one edited by that same I.J. Good, The Scientist Speculates. The subtitle is An Anthology of Partly-Baked Ideas. The novel phenomenon here was famous scientists being less than serious on serious topics. Many of the pieces in The Scientist Speculates are more whimsy than science. They are in the spirit of table talk among scientists and convey a quality essential to scientific discovery (as opposed to plodding routine science). The exceptional thing of this volume is that the whimsy got recorded. The volume, published in 1961, contains a contribution by DM (“Puzzle-learning versus Game-Learning in Studies of Behaviour”), a non-whimsical piece befitting the junior person that he was in presence of so many luminaries: Isaac Asimov, J.D. Bernal, David Bohm, Sir Cyril Burt, Arthur Clarke, Bruno de Finetti, Dennis Gabor, Arthur Koestler, J.E. Littlewood, N.W. Pirie,
Michael Polanyi, George Pólya, Oliver Selfridge, Harlow Shapley, John Maynard Smith, C.H. Waddington, Eugene Wigner; truly an all-star cast assembled by Good. When I read Turing’s 1950 paper “Computing machinery and intelligence”, the famous one that proposed what has become known as the Turing Test, I get the feeling of a Partly-Baked Idea avant la lettre. I suspect that submitting it to Mind, a serious journal of The Other Culture, was a bit of a lark, worthy of the pranks in The Scientist Speculates.

My refuge after Edinburgh was the Computer Science department of the University of Waterloo. This was a big department, yet there was no AI, as far as I could tell. That I felt comfortable there, was witness to my ambiguous attitude to the enterprise. Yet within a year of our arrival there, Donald paid his first visit, and we could talk some more.

On one of the Waterloo visits by Donald and Jean we had as an additional guest Saba, the pedigree Birmese of the Pietrzykowskis, who, as usual in the summer, were in a Buddhist retreat. Jean was fond of Saba, having been a cat breeder herself. Jean had holed herself up in my little den for her unremitting editorial labours. Presently, Saba was seen to be forcefully evicted. We all knew the offense: incorrigible walking, sitting, or lying down on the very page of one’s current attention.

DM inquired after a suitable present for Eva, by now six years old. After due deliberation, a fish was decided upon, preferably of an algaevore type. I dropped DM off at a pet store. After I came back from a quick errand nearby, I found DM in conversation with another customer, who was showing him photographs. On the way back DM explained: he had met a rat-fancier who always carried around photos of his favourites. DM could understand because as a schoolboy he had been a mouse fancier. It is no co-incidence that I’m counting twenty-five papers on mice among his early research papers.

On such a visit Donald and Jean would insist on cooking dinner for one of the evenings. Accordingly, Jos was banished from the kitchen, and they went shopping. The catering included sherry; peanuts were provided. (There is a contradiction here: Alan Robinson reports being comforted by the knowledge that, whatever happens, somewhere in the world, at 5:30 pm Donald Michie is fixing Dry Martinis. It is true that the Waterloo visits also included afternoons with Dry Martinis.)

On a later visit Donald went exploring in the huge Mathematics building, and returned with the report of having found Jonathan Schaeffer. I had no idea who he was, but Donald knew from the computer chess grapevine that the author of TreeFrog, a contender for the world computer chess championship, had to be somewhere in Waterloo. Donald also unearthed Larry Rendell, who worked on solving problems like the fifteen-puzzle. In the official absence of AI in Waterloo at the time, students like these had trouble finding supervisors. Typical supervisors expect their students to be yoked to their research waggons. To accommodate a driven student with his own project requires a supervisor who is not one of those lowly beavers. In the case of Schaeffer it was Morven Gentleman; for Rendell it was Tomasz Pietzrykowski. When Gentleman left, the nearly finished Schaeffer was transferred to Randy Goebel and myself. As a result, he is, pro forma, my most famous student.

Donald and Jean reciprocated by inviting me to whatever their current visiting place was, Urbana-Champaign or Stanford. DM had considerable tolerance for America. In fact, he rather liked being there. One of my visits to Stanford, c/o The Michies, started with them picking me up from the airport and proceeding to lunch at “The British Bankers’ Club”, a restaurant in Menlo Park. Nobody could be more acutely aware than DM of the phoniness of the place: one of his own brothers was a real British Banker, and DM was a member of two real Clubs, one in Edinburgh and one in London. But he was proud to have found “The British Bankers’ Club”, with better and less expensive lunches than the real bankers’ clubs.

Donald and Jean stoically endured the downside of the itinerant life, which lasted from 1975 until well into the 1990s: the ever-returning chores of leasing a car, renting a house, lugging the extra suitcase(s) with books and papers (there was always an MI volume to be edited).

In 1980 I spent another summer in Edinburgh as a guest of DM. Since the low point of 1975, thanks to assiduous and inventive joint pursuit of funding possibilities by Donald and Jean, the Machine Intelligence Research Unit was alive with work focused on chess endgames. There were students, including Andrew Blake, Tim Niblett, and Alen Shapiro. Danny Kopec was there, perhaps formally as a student, but de facto as the resident chess consultant. Ivan Bratko visited frequently. Alen was the administrator of the dream computing environment of that time: a small PDP-11 running Unix.

In the 1970s DM was fond of proclaiming “Chess, the Drosophila Melanogaster of Artificial Intelligence”. A public pronouncement of his point of view can be found in an interview with H.J. van den Herik held in 1981 (Computerschaak, schaakwereld en kunstmatige intelligentie by H.J. van den Herik, Academic Service, 1983). It is a long interview, from which I quote DM’s answer to the question: “What do you think about the applicability of the research done in computer chess?”

The applicability is I think enormous and quite critical. Scientific study of computer chess, which includes the technological work, but goes far beyond that, is the most important scientific study that is going in the world at present. In the same sense, if I were asked what was the most important study in process during the first world war, I would say the genetic breeding experiments on the drosophila fruit fly by Morgan and his colleagues. The analogy is very good. The final impact of the early work in laying down the basic theoretical framework for the subject was just enormous, unimaginable. We see now the industrial take-off of genetic engineering which is the delayed final outcome for human society of the fly-breeding work. The use of chess now as a preliminary to the knowledge engineering and cognitive engineering of the future is exactly similar, in my opinion, to the work on drosophila. It should be encouraged in a very intense way, for these reasons.

What does not come out in the interview is DM’s observation on research strategy. At one stage, the genetics of Drosophila received more research attention than all other organisms combined. This discrepancy, frequently criticized, was valued by DM as a fruitful research strategy: to find a suitable microcosm and exploit its accessibility to gain knowledge about the entire field.

It may well be that this insight about chess stems from the war-time conversations with Turing. These are well-known, but give rise to some amusing misunderstandings, as in the obituary in the Daily Telegraph: “Michie was one of the few at Bletchley Park who could match Turing at chess.” This may be literally true, but not in the suggested way. The way DM used to tell it was that Turing was obsessed by chess and wanted to play anyone he could get hold of. Unfortunately, he was so much worse at the game than just about everyone else that he had difficulty finding a partner. Good was a county champion and half the British chess team was in Turing’s group (Stuart Milner-Barry, Harry Golombek, and Hugh Alexander). DM was the only one whose chess was weak enough to be able to stand playing Turing.

Though I had missed the significance of memo functions, I was immediately impressed by DM’s idea of the “Human Window”, described in his “New Face of AI”, a departmental report of 1977. He considers curves characterizing the trade-off between memory and processing requirement between various implementations of computing tasks. The implementations that can be understood by humans happen to be those that strike a balance between the two extremes. Thus, if we are to avoid being helpless in the malfunctioning of software in safety-critical tasks such a control of air traffic or of a nuclear reactor, the software has to fit in the “Human Window”. But this is not the easiest or most natural for the software engineer.

DM demonstrated the Human Window phenomenon with chess end games. He proposed a form of describing end-game knowledge that he called “advice” and described a formal language, Advice Language One, for expressing such advice. The language could be translated into a form that guided a computer to play the end-game at the level of skill of a chess expert. Soei Tan, Ivan Bratko and Danny Kopec were chess experts who used this framework to implement specific end games.

Once again, I did not get it. I could not help acting in my then usual role of Prolog evangelist and wanted to demonstrate that the beauty of Prolog was that it rendered superfluous things like Advice Language One. Accordingly I wrote a Prolog program that played an end game using Advice in DM’s sense. DM generously allowed me my say in a paper in the Tenth Machine Intelligence workshop. It’s a nice paper, but it does not get it.

What is “it”? Paul Graham calls it “bottom-up programming”. At the time I was only aware of the virtues of “top-down programming”. Here is how Graham (in his book On Lisp, page 3)
explains the complementary concept:

Experienced Lisp programmers divide up their programs differently. As well as top-down design, they follow a principle which could be called bottom-up design — changing the language to suit the problem. In Lisp, you don’t just write your program down toward the language, you also build the language up toward your program. As you’re writing a program you may think “I wish Lisp had such-and-such an operator”. So you go and write it. Afterward you realize that using the new operator would simplify the design of another part of the program, and so on. Language and program evolve together. Like the border between two warring states, the boundary between language and program is drawn and redrawn, until eventually it comes to rest along the mountains and rivers, the natural frontiers of your problem. In the end your program will look as if the language had been designed for it. And when language and program fit one another well, you end up with code which is clear, small, and efficient.

One of the things that make Lisp powerful is the macro facility that allows one to define the ad-hoc language in this way. It so happens that Prolog is one of the very few other standardized languages with a macro facility of comparable power. But I had not learned enough of Prolog to realize that a better way to write my end-game program was to first discover the language that makes the problem trivial (DM had done this with Advice Language One), implement that, and then write the trivial program.

In the 1990s I heard DM mostly about Machine Learning. Jean and he were scouting for a congenial retirement location. With this in mind DM accepted an invitation to visit the University of Victoria. Jean was working with human subjects to study the learning of control tasks. A tool for this was software written under DM’s direction for control of a simulated inverted pendulum. Of course something that looks like an inverted pendulum (“pole and cart”) is only one possible iconification of that particular dynamic system. DM’s software had another one, one that looked like a mandala turning inside a compass rose. Controlling pole and cart was hard enough; the mandala was maddening. The student subjects felt they deserved a hardship premium in addition to the regular hourly stipend. However, rebelliousness turned to awe on the few occasions when DM took the controls. The mandala’s motions would then take on a mysterious elegance that, in combination with DM’s palpable concentration, was awe-inspiring.

The stay in Victoria was scheduled on purpose in winter. DM knew he would like the summers, but worried about winter in Victoria. It did not take long for him to come to his verdict: “Too much like Scotland”. Next winter we visited Donald and Jean in Palm Desert, California, where they had bought a condo. Jean had found suitable subjects in the local college and completed her PhD in psychology not long after that. We dined out, except for a risotto put on by my wife. Jean could cook delicious dinners, but, as she said: “What I need is a housewife.”

It was in machine learning that my inadequacy as an intellectual partner to DM became most obvious. The subject felt “messy” to me. Indeed, I felt an aversion to the other biology-inspired computing paradigms such as neural networks and genetic algorithms. It is only in the past decade, when the communication channel with DM started to become erratic and finally fell still, that I realized the gap not between Two Cultures, but between Two Temperaments. The one temperament only feels at home with the clean, with the abstract. It likes to work, metaphorically speaking, with crystals. The other temperament is comfortable with blobs of protoplasm. The one Temperament is exemplified by Plato, the other by Aristotle.

The one Temperament is exemplified by the eminent physicist who descended from his mountain top with the judgment: “As a physicist, I can state that it is impossible for the eye to have evolved by natural selection”. It is only recently that I have learned to look at the question from the other end, imagining the gene pool of an interbreeding population. The key observation is that it will not stay the way it is. What will happen to it? I like to imagine the gene pool as a swarm of objects in an abstract space (the phase space), like the way a gas is modeled in statistical mechanics. How will this gas of genes behave? In the absence of a container, it will spread out over the phase space. But in an ecological system there is the equivalent of a container, the walls of which are determined by the physical environment and by the gene pools of species that compete, predate, serve as food, serve as shelter, and so on. This causes the containers of all the species the assume intricate shapes, an intricacy unimaginable by us already in four dimensions, and a fortiori so in hundreds of dimensions. The exquisitely engineered eagle’s eye and gull’s wing are manifestations of these intricately shaped containers in gene space.

Few minds were able to straddle the Two Temperaments. Norbert Wiener was one; Donald Michie another. Donald deserved a better conversational partner. I would be a better one now, but that comes too late.

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