Grasshopper – how to train your mind
Or: Mathematics comes to the Shaolin Monastery
Just as the kung fu fighter gains power by studying and emulating the crane, the kung fu thinker can gain power by studying and emulating a variety of creatures… from the fish to the dinosaur to the mouse to the monkey, and only then beyond.
Do you remember those old movies where a student of gung fu at the Shaolin monastery learns to appreciate and imitate the fighting styles of a bird, a preying mantis, a tiger, a monkey and so on? Now, with our new understanding of the brain really works, we can start to do the same kind of thing in training our mind. And since the power of the mind is the most important qi of all (at least on earth), this is serious stuff. But in this case, it’s pretty clear that the animals form a progression… from the least intelligent to the most intelligent, all of them offering important lessons.
At the lowest level is the “vector intelligence,” a level so low we do not see it in real animals. It is actually much higher than what we use in control systems in the world today, but I will not say much more about it now. (Some day I will scan and post an old 1980 paper, from the time when I thought that ordinary mammals only had vector intelligence. We can learn from that level, but now I would want to move higher. Even the simple “perfect vector intelligence” experiences pain and pleasure, and hope and fear. Even the simple vector intelligence may be confused by traumatic and euphoric experiences which he cannot yet explain, and may have all kinds of dreams.)
Next up is “spatial intelligence.” Still not any animal I know of, but maybe the fish might be so low.
The fish does not have grand plans for life, and he does not show much creativity. He does not develop new technologies or build cities. His schools are not really schools. But he does live and survive in a very complex world, full of myriad threats and opportunities. He is assessing these threats and opportunities at every moment of his life.
Can you imagine a fish as a master class player of chess? Actually, it is true in a way. A simple system of spatial intelligence was built by David Fogel in 2005. (It is described in an article in Proceedings of the IEEE, which is the highest ranked journal of the world’s largest engineering society.) Just by learning and paying attention to its simple world, the world of the chessboard, it learned how to beat master class human chess players. Even a fish brain has more neurons and a more sophisticated brain than this simple spatial intelligence which Fogel put together. So how could it beat humans?
This was not like Deep Blue, an ultrafast computer programmed with rules about chess, which beat even the best human chess players. This was only master class. But Fogel’s system was not told any special tricks about chess from human teachers. It had to learn to play all on its own, without so many clues as a human gets form reading chess books. So how could the “baby fish” computer learn better than most of the humans serious about chess?
Its only real advantage was that it PAID ATTENTION. The chessboard was its whole world, and its whole life. The human researcher did work to give this creature good learning experiences, struggling to defeat mirrors of its own self and its own capabilities. Of course it had to work through many experiences of defeat and victory, struggling the whole time. Unlike the simple vector intelligence, it would always pay attention to the symmetries and patterns and connections in its world, just as the fish pays attention to the symmetries and patterns and connections in its own very complex world.
Could a fish then play a master class game of chess, as good as what Fogel’s system could, if properly trained and motivated? Would it require some kind of brain-computer interface to make it pay attention, like what we see in the movie The Matrix? Maybe… maybe not.
Whenever I think of computers playing chess, I think of a strange night at MIT at around 1971. In that year, I went to Harvard graduate school, and had a friend from France. On a lark, for fun, he proposed that we go to visit the MIT Artificial Intelligence center one night. It was then just one part of a floor in a modern building at Kendall Square, where I later worked myself on another floor.
As we entered that mostly dark place, it was an eerie experience indeed. Strange Gothic music imitating Bach suffused the whole place; small white lights gently turned on and off, hundreds of them, near the tops of beautiful baby blue DEC computers which lined most of the walls of this big open area. These computers were mostly implementing a program which was trying to imitate Bach; it was not like real Bach, but the differences only contributed to the sense of unearthly weirdness permeating the whole area.
Off to the right was a special enclave, more brightly lit, where a robot arm was playing with blocks with a baby or very young child. Of course, some computer was implementing a new AI program, “blocks” developed by Richard Winston; it was not a human-like program, but it was entertaining enough for the baby, playing in effect both with the blocks and with the computer. As we stared at this spectacle, the mother rushed up to us, somewhat apologetic and embarrassed, and explained that it was such a nice toy for her child…
And then, off to the left was the chess-player. A magnificently intelligent and serious human face, with a high brow and a countenance a bit like a general of a Roman or Celtic army, was pondering ever so seriously at the well-lit chessboard in front of him, with a computer on the other side. This was not Big Blue; only an older generation hard coded master class computer chessplayer. But as we looked at this master class human, and at the chessboard itself, it was overwhelming to see how the computer slowly and implacably crushed him, despite his best efforts and his obvious intelligence, certainly playing better chess than I or my friend could play (short of some kind of terrible and painful psychic cheating). It reminded me a lot of the Swedish movie, the Seventh Seal, where a human plays chess with the devil.
So whenever I think of a “merely master class” chess machine, I imagine that ponderous scene from the seventh seal, and I also remember the fish. Do not underestimate the fish, and do not underestimate the power of paying attention to the hall of mirrors right in front of you. A fish is not a jellyfish, as any biologist could tell you.
When I look at the wiring diagram of the brain of a fish, I do have some idea of how these circuits work, to give the fish the power to cope with complexity in space. There is a three-layer cortex in the fish, which seems like three of the layers of the cerebral cortex of the human. Three layers are already enough for the fish to learn to predict the complex spatial world it lives in. They allow some circuit properties we call multiplexing and nonlinear state estimation (creating an image of complex reality in its brain). We are very close to building this in computers today.
But beyond the fish lies an impressive animal indeed -- the next level of intelligence, up beyond the spatial intelligence. The level of the dinosaur. The dinosaur is what I use to symbolize this level of intelligence in my slides on the mathematics of intelligence.
In formal terms – the dinosaur level has a brain which can handle multiple time intervals effectively as it decides what it expects and what it will do.
Roughly – look at a big dinosaur and think: “This guy sure knows how to be DECISIVE.
He knows how to make decisions, to set goals and to stick with them over time.”
I look at the dinosaur this week, and I also think of Dick Cheney (recent VP of the US under George Bush) and of Zhou in China (the security guy who worked with Bo Xilai, purged this year). Those people rose very high by being very decisive. Just as the fish and chess player focus so well on space, on a pattern in front of them here and now in space, these more powerful creatures focus on patterns of their own will. When I think of these powerful creatures, I also think of our former President Jimmy Carter, who was so enlightend and intelligent in some ways, but lost power as people concluded that he was simply not decisive enough. Reagan was simpler, but more decisive. And to be honest, I think of my self in some ways. I believe in organisms governed by values and criteria at the highest levels, but I have often been almost a kind of hypocrite… living much of my own life obsessively pursuing a variety of well-defined goals. But deciding to attain a well-defined important goal, and working back how to reach it and visualizing a workable path, is a very important power of the human mind as well. The dinosaur inside us had great powers, if we can keep it under control and not let it serve goals which do not lead to dark outcomes in the end, in the larger picture.
In 1998 and the early years of this century, I published many equations and design details for how to build a dinosaur level of brain in computers. But these were not politically acceptable to the computer scientists, who had more fun playing with simple designs which would not work from their cute old friends. For tough engineers, building a system at the fish level is already a great challenge; so I have mainly talked about that level, and even simple vector intelligence, in recent years. When creatures are not yet ready to stand on two legs, I do not want to just torture them by asking for feats they cannot yet achieve. Yet for us as humans, we can still cultivate and master our inner dinosaur. (Much of the politics of human survival involves trying to master or control the powerful dinosaurs of our world – but we should
not underestimate those dinosaurs as we do so.). But – is a human turtle just a dinosaur with less of an inflated ego? Many emperors of China have identified with the turtle. (Or the snake?)
When I look at the brain of the reptile or the bird, I see another three-layer cortex which helps run the decision making, working with a system called the basal ganglia which executes decisions and learns to perform or lead the variouus kinds of actions or “verbs” which that cortex may ask for.
On my roadmap for mathematical neural networks, the highest step of all, above the dinosaur, is a creature which is even grander and more powerful, the creature with the power to totally defeat and destroy all the dinosaurs of earth, whose fate was sealed but not determined by a great comet in the end – a sign of celestial support to resonate with and accelerate the inevitable defeat of the dinosaur by this more powerful creature.
The more powerful creature, the higher level of intelligence, is the mouse, a high creature worthy of great veneration. (In my mind, I can even imagine Jesus looking at the mouse and the dinosaur and repeating his famous words “the first shall be the last and the last shall be the worst…”).
The basic power of the mouse is the power of creativity.
For many years, I wondered exactly how the mouse achieves the kind of power of creativity which it has. It is easy to build a computer system which, like the dinosaur, easily gets trapped in a rut, a boring cycle of life which is not so great as what a creative creature might learn to discover. How can a mouse possibly be so creative? The mathematics of this problem are very interesting and very challenging. Sometimes I called this “brain-like stochastic search.”
I did not really have the basics figured out until 2009, when I wrote a paper for the journal Neural Networks, stimulated by friends like Dan Levine, Robert Kozma and Frank Lewis. At that time, I thought back to many things, including a paper I read long ago in a classic anthology on neuroscience, called “the Rockefeller series.”
In that book, they explained how the brain of the mouse seems to come from a MERGER of the two older three-level cortex structures. I thought about how this connects to what we now know about the basal ganglia and about spatial complexity… and the explanation flashed immediately to mind:
By COMBINING its power of spatial complexity with the power to make decisions, it is wired up so that it can perform spatial mapping of the space of POSSIBILITIES.
As soon as I understood this, I could make sense of many of my own experiences in finding answers to difficult questions, and in quickly getting a feeling and assessment for complex areas of thought either as an introduction or as a way to get some useful understanding when my time is limited.
In many difficult areas, there is a key stage in the beginning when I do a kind of thrashing around in thinking, considering many different points of view. The possible ways of thinking seem to curve around and connect in a very strange kind of space, repeating and revisiting or contradicting, forming areas where people cannot escape unless they explore a certain other direction. What happens in that very important time of thrashing? It seems… this is how one engages the natural ability to map out the space of possibilities of ways of thinking. And that thrashing is absolutely essential to the highest levels of creativity we humans are capable of. Of course, there must also be a motivation – like the big question or goal we are thinking about… but we need to do this cognitive mapping.
Many people become famous dinosaurs, but actually hold back progress, because they do not ever do this kind of thrashing around in thinking. Maybe they thrash just once or twice, and settle down to some comforting ideology, and never thrash enough to have a good map of the territory.
But for real creativity of real humans, there is another factor -- the social factor.
Some very lucky people have free and flexible friends they can trust, who are just as advanced as they are in probing the limits of the questions they are working on. They can have deep “brainstorming sessions,” where they thrash freely through the space of possibilities, without ideological or conventional limitations, without reinventing simple issues, and each do the cognitive mapping of this space. Because of the way we humans are – with the social aspect of our motivational systems and our natural tendency to feel that things are “real” when other people also feel they are real – this is extremely important in mobilizing the full power of the human mind. In my own life, I have only really experienced this twice – once in 1979, when I worked with a guy named Joe Firestone at Census Use Research (a research organization which no longer exists) and now with my wife Ludmila.
But with these kinds of brainstorming sessions, there are two dangers which we also must remember. First, they always have some degree of limitation. It is especially dangerous to creativity when they become brainstorming sessions of like-minded people, who exclude other points of view which a true creative thinker of high integrity would not ignore; it can reinforce irrational “groupthink,” a major threat to creativity. Second, they are never quite as free or as fast as what a powerful thinker can do on his/her own, at times of peak clarity and focus. For myself, my ability to answer really difficult questions which others have mostly give up on has depended a lot on being able to drive myself despite lack of social reinforcement to keep thrashing through questions which others mainly hide from. Of course, exploring the space of possibilities means exploring the space of possible strategies to answer the question; strategic thinking, both in words and in images, is a central part of this thrashing.
After I wrote this, and expressed my thanks to my wife again for the unique importance of our relationship, I suddenly realized: of course the mouse too is a very social animal, much more than any reptile. Mice do not have the deep empathy and mirror neurons that a monkey has, but they do have strong families, and some kind of communication abilities. I wonder: how much do “smiles” and petting influence the ability of some mice to boldly explore their environment, and find new paths to cheese or even to dinosaur eggs? I do not know. I have even seen a baby mouse “smile” at a cat, who then carried it away to a safe place in the forest behind our house.
I can even imagine someone saying: “How can you have so much reverence for the mouse? What’s next? Will you be telling us that Mickey Mouse and Walt Disney deserve more serious reverence than the Bible?” Actually, when my son was small, I remember a time when came home and asked: “Daddy and mommy, the kids at school said they believe in Adam and Eve, and asked whether we believe in Adam and Eve too?” My immediate response: “Well, I believe more in Lilo and Stitch than in Adam and Eve. And if they say Santa Claus is on the north Pole… I think he would be all wet by now, and I really think it is more true that Big Bird lives on the South Pole.” (Side note: NSF runs the biggest base on the South Pole, and also funded the development of Sesame Street.) In actuality, I do believe it would be a great mistake to underestimate the depth and validity of many of things which Walt Disney tried to portray. And certainly, many adults would be more creative if they could remember some basic aspects of reality which are clear to children.
But then, even higher than the great mouse is the great monkey…
All of the above was written in Shenyang, China, where I saw thousands of people
in the morning, 4:30AM to 6:30 AM, doing morning exercises in Bei Lin Park, next to the conference hotel where I was staying --- some of them wu shu of various kinds,
including tai qi.
The monkey is revered in China, but really this leads to more advanced stages
discussed in my paper "Neural Networks and the Experience and Cultivation of Mind,"
in the journal Neural Networks, August 2012. With a brief extension under submission elsewhere...
Of course, one cannot mention the Great Mouse without paying some respects to Walt Disney. I meant to say more of the serious respect we should have for Disney... but
time ran out in Shenyang for this kind of thing, and I am not ready right now to fill in that gap.
Regarding the neuroanatomy ... I resolved to go back and reread the sources on comparative neurology and comparative neuroscience of the vertebrates, to nail down all of this. Last night, I reread the first part of the Neurosciences Rockefeller book, second study series... mainly the first half of Nauta's piece... and it seems
I should properly review a whole lot of other stuff, some which I read and some not,
to nail down some of this.
In Nauta's version, he refers to "external striatum" for what I saw described
as "another 2 or 3 layer cortex", perhaps in Bitterman. So instead of merger
of two cortices, in the mouse, I should have said merger of 3-level cortex with
external striatum, to follow Nauta's way of describing things.
Do we have fish, say, with all the spatial stuff but not the external striatum?
Nauta leaves that open; when he wrote, apparently people did not know as much
about the fish as we do now. Certainly the external striatum appeared at SOME
point in the evolution of the vertebrate brain... even if the modern fish should have an external striatum, it would have to have an aquatic ancestor who did not.
Best of luck....