Note:  The first parts of this chapter (in italics) are largely biographical and will not be on the final.  I included them for your interest, but you may skip to "Neurons and Brain Chemistry" if you wish.....

The math department of the University of Nevada, Las Vegas, wasn't a terrible place to be while working out the essential parts of my theory of mind.   I had a good relationship with the students, and the teaching only took me about 20 hours a week, so I was able to spend the rest of my time on my research and thinking.  But the situation was far from ideal.  The administration of the math department didn't care for my research at all, considering it - or so it generally felt -- about 100 times less valuable than even the most insignificant research in pure mathematics.  There was no one to collaborate with intellectually; the few joint research projects I tried to set up progressed at a snail's pace compared to my own solo work.  Also, in spite of being in the middle of a beautiful natural area, Vegas was not the most inspiring city for someone with no interest in gambling.   I wanted to get out.
But the US job market for mathematicians was at an all time low.  With a prolific but offbeat research program, I wasn't the most attractive applicant to the average university math department.  I considered leaving academia for the computer industry, but working 60 hours a week on someone else's ideas did not appeal.  I tried applying for academic computer science jobs, but didn't have a degree in computing, and didn't have that many conventional computer science publications either.   Things seemed bleak, though not hopeless - I kept on trying.
And then in early 1993, Rohan Dalpatadu, a Sri Lankan colleague, told me there were jobs open at the University of Papua New Guinea.  That sounded different, at any rate.  It appealed to my sense of adventure.   I went to the university library to look up the address so I could apply.   While looking through the Commonwealth Universities Yearbook for the address, I found a plethora of other interesting universities to apply to, in Australia, New Zealand, Africa, Asia, etc.  Papua soon seemed like one of the worst options, particularly since the head of the math department there told me on the phone that they generally had a policy of hiring only their own graduates.  Years later, I learned that the university in Papua New Guinea was particularly dangerous, with carjackings in the faculty parking lot not uncommon.
Of the job offers I received, the most appealing was from Waikato University in Hamilton, New Zealand, which in spite of its remote and obscure location had a few faculty members doing top-quality research in machine learning, a variant of artificial intelligence to which I was fairly sympathetic.  And so, on December 26, 1993, my wife Gwen, my two children, and I boarded a plane in the Las Vegas airport, headed for Auckland, New Zealand.  All our possessions were already on their way to New Zealand by boat. We were moving, on a whim, to a country we had never seen, and didn't know much about -- to Hamilton, a rural city of 100,000 smack in the middle of the North Island.
Three days after we arrived in New Zealand, it was New Year's Eve, mid summer in the southern hemisphere.  We rented a car and headed out of town, intent on experiencing some of the famous New Zealand countryside.  But we had been out of Hamilton no more than five minutes when the unthinkable happened: our car collided with another at a rural intersection. After a moment of black, I opened my eyes and was disoriented: somehow I was facing the wrong direction.  The car had skidded thirty feet and spun halfway around, and we hadn't even felt it.
 Immediately Gwen and I reached back to see if the baby was all right.  Zebulon was five months old and safely ensconced in a car seat.  He was looking around absently, a little confused, but not much more so than if, say, the radio had suddenly come on.  We breathed a sigh of relief. But then we saw our four-year-old son Zarathustra.  He was alive, and wasn't bleeding, but he was crying a kind of cry we had never heard before - a sort of quiet, drawn-out wail.  He was sitting by the door the other car had crashed into.
I took him out of the car and asked him where it hurt.  He didn't answer.  I asked him again and he pointed to his head.  The man who had hit us walked over grinning and asked me "Where yer from?"
"Las Vegas."
He winked at me. "Las Vegas -- hot damn!"
It was hard not to punch the guy in the face.
Somebody called an ambulance and it came quickly.  While sitting in the ambulance I felt his head: there was a definite dent in it.  He was quietly moaning but clearly aware; he hadn't been knocked out.  He pointed to his head again.  I told him we'd had a car accident, and he nodded.  I told him he would be all right, and he made no reaction.
By the time we got to the emergency room his mouth had begun to twitch.  He was fully conscious and not at all happy about what his body was doing.  Anesthesia stopped the twitching, and after a few tense hours, a surgeon explained to us what had happened: his skull had impacted into his brain. They would have to reach inside his brain and fish the skull out.  In order to do this, he said, it would be necessary to put him under deep anesthesia, deep enough to stop his lungs; he would have to be on a respirator.  If the brain damage was serious, they would have to keep him under deep anesthesia for a month or two, to give the brain a chance to heal.
 A neurosurgeon was flow in on a helicopter from Auckland; we watched her walk into the operating room in bare feet (a distinctive New Zealand touch).  The nurses showed us a room to sleep in and, after repeatedly overcoming an impulse to throw myself out the window, I fell sound asleep, and slept through the operation, which took several hours.  They knocked on the door of the room to give me the news: it had been an extremely difficult operation, much more difficult than anticipated, but in the end they had managed to get the skull out.  And the brain had not been torn; there was no apparent brain damage.
The intensive care ward was truly frightening, packed full of obviously dying patients ... I sat uncomfortably by our son's bed, while my wife waited outside with the baby.  When he came to from the anesthesia he couldn't speak because of the tube going down his throat, from the respirator to his lungs. His left arm was immobile due to a large IV.  But his right arm was free, and he made full use of it: he pointed to his head, to show his injury ... he pointed to the nurses, to the hospital walls and ceiling ... he pointed to me to show he was happy to have me there ... he pointed to the tube going into his mouth and made a motion indicating he wanted it out.   Something about this pointing struck me oddly, and after a moment I realized what it was -- it was the same exact way he had pointed when he was one year old.
Zar had been a very precocious child in some ways, but his talking had been erratic. Though he had started speaking at nine months, he'd given it up at eleven months and not started again till he was nearly two. For the intervening year, he had communicated mainly by pointing.  To indicate a tree, he would stick his arm out, move it up, then move it down. To indicate a bicycle he would move his hand around and around like a wheel.  Once he had started talking, the intricate pointing language had ceased.  But now that a tube was in his throat and he couldn't talk, it all came back again.  The routines had been sitting in his brain, waiting for a chance to re-emerge.
 Finally the respirator tube came out. I asked him how old he was; he said "Four."  He knew his name, my name, colors, sounds, everything; there seemed to be nothing wrong with him. It was him again, it was still him, the same old Zar!  I looked at the nurse and said, less than halfheartedly, "Happy New Year."  I asked the doctors how we would know if there had been brain damage; they just shrugged their shoulders.  "You can never really know...."  I asked them what functions would be most likely to be impaired; the response was the same.  I tried to remember what I knew about brain anatomy -- after all, I had written about brain function in my books on mathematical psychology and artificial intelligence and the theory of mind; I was supposed to know this stuff!  But regarding the right parietal lobe, which was the part of his brain that had been hurt, I could remember nothing specific at all, except that it coordinated different types of activity from different areas....  I was drawing a virtual blank.
Within four days he was out of the hospital, with a huge bandage on his head. To him the accident is now ancient history.  He has forgotten it more quickly than his parents -- we left New Zealand for Australia fifteen months afterward, partly to escape continued psychological trauma induced by the car crash.  But Zar remembers the incident vividly, and there are certain psychological after effects.  He maintains an extremely stoic attitude toward injury, he fears general anesthesia with a passion, and he has developed an abiding curiosity about the brain.
"The brain," I explained to him shortly after the accident, "is the worst part of your body to hurt, because it's the part that you think with. It's the part that keeps your 'you' in it, that keeps the part of you that knows who you are. It tells the rest of your body what to do."
He listened carefully -- for at least a year afterwards, whenever he misbehaved, his
excuse was "My brain told me to do it!"  In good scientific fashion, he seemed to have
adopted the idea of the "brain" as an all-purpose explanatory principle -- "the brain made me do it" instead of "the Devil made me do it"....   The following dialogue, which occurred about six months after the accident, was fairly typical:
         "Stop pouring water on your brother, Zar!"
        "I couldn't help it, my brain told me to!"
        "But you are your brain -- that just means you told yourself  to."
        "No, a part of my brain that wasn't being me told the other part of my brain that was being me to. That's what happened, Ben."
        "Well, tell that part of your brain to stop telling the other parts of your brain to pour water on your brother...."
        "No, I do, Ben, but it won't listen. That part of my  brain doesn't remember very well."
        "Well, you'll have to teach it to."
        "No, you can't teach it, because it's not connected to the saving box. The saving box is the part of you that remembers. The saving box isn't in your brain, it's down by your stomach...."
        "There is no saving box in your stomach -- it's your brain that remembers things."
        "That's just for other people.  For me, I have a saving box.  Only I have one of them. That's why I remember things so well!"
Or, another time:
       "Your brain tells you what to do, right?"
       "Yeah."
       "But if you didn't have a brain, you wouldn't be there, so you are your brain really, so your brain can't be telling you what to do because your brain is you."
       "Well ...  you can tell yourself what to do, can't you?"
       "Yes, but you can't tell yourself to do something you don't want to do, because if you don't want to do it, you don't want to tell yourself to do it either...."
       "That's what they say -- you can get what you want, but can you want what you want?"
        "I can."
       "Well, good for you."
Of course, I was pleased by my son's precocious curiosity -- but when he started asking questions like how his brain told his body what to do, or how his brain made him feel like he was there, I was always at a loss for a convincing answer.   And this disturbed me, not because it bruised my fatherly ego, but because I know that, when I can't encapsulate something in a few words that a bright child can understand, I don't fully understand it myself.   In thinking the issue over, my mind always went back to that pointing. His brain had told him to point, but no, it hadn't even been as explicit as that: the preconditions for pointing had been met and so the pointing language had re-emerged.   Then his consciousness, his feeling of "me," had attached itself to the pointing language.  By saying "my brain told me to do it" he was, in his naive, childish way. postulating what the philosophers call a Cartesian dualism -- a split between mind and body. But really there is no split: there is no "me" floating out there in hyperspace waiting for the brain's instructions. There may be an elemental feeling of awareness which is separate from the physical world, but there is absolutely no evidence for a perceiving, acting, knowing agent that exists apart from the remainder of the brain. And in fact, this elemental feeling of awareness may be there in the physical world too -- right down to molecules, atoms, quarks.
 Through the tragic experience of having his skull cracked open, Zar was introduced prematurely to the mysteries how thoughts, feelings and selves work -- and how they come out of the hard, solid reality of the physical world.   Far from just being technical questions in human biology, these questions get at the very soul of the Western, scientific world-view.  We seek to reduce everything to the rational and comprehensible, to encompass everything in linguistic and mathematical formulas.  But studying the brain represents the ultimate challenge for this perspective: for what we are reducing to formulas, in this case, is precisely the collection of cells and molecules that is doing the reduction to formulas.  This reflexivity is what gives brain science its excitement -- to Zar, to me, and to the scientific community at large -- and it is also what makes brain science so difficult, what makes conceptual progress so slow even as the laboratory results pour in.

The Neuron.
Zar's accident made me think hard about how the brain worked, and how the processes inside our heads matched up to my abstract theory of mind.   This was something that I had been studying off and on for quite some time, of course, but from my point of view, as a mathematician obsessed with simplicity and elegance, neurobiology was filled with so many nasty, complicated details that it seemed a potentially endless distraction, a sinkhole for mental effort.  It often seemed to me that neurobiology needed another 50 years of development before it could be really useful for understanding the mind.
 I had begun my serious study of the brain back in 1986, when I was a student at the Courant Institute, a part of New York University.  I found Courant a very exciting place, with an endless series of research seminars on every topic under the sun, and professors who were just as apt to lecture on their own research as on textbook information.  The senior professors seemed to walk around with their heads in the clouds, too busy with their own internal equations to talk to each other, let alone to speak to me. I looked on them with admiration and unease.  It was all a little intimidating, as I was 18 years old and living on my own for the first time -- plunged out of the small, woodsy, 300-student college where I had received my Bachelors degree, into the heart of Lower Manhattan.  I was much younger than all the other students, and accustomed to a relaxed, hippyish environment, rather than the suit-and-tie, serious-business mentality that New Yorkers take for granted.   Socially, I felt more comfortable out in Washington Square Park, talking to street musicians, than walking through the austere, quiet halls of the Institute across the street.  But in spite of my awkwardness, being at the Institute was a tremendous intellectual thrill.  The place was filled with mathematics, it was positively oozing out of the windows.  One got the feeling that the amount of mathematics in the universe was incredible, almost infinite, and this was just the place to set about the task of absorbing it.
So it was with great enthusiasm that, in the first semester of my second year at Courant, I signed up for a course from Charles Peskin entitled "The Neuron."   I was very excited about this course because it touched on my long-standing interest in the mathematics of mind.  Right here, at the Courant Institute, a course on the mathematics of neurons, the nerve cells in the brain whose interconnections weave together to form the textures of our mind.  As an undergraduate I had taken courses in philosophy, physics, literature -- all kinds of things -- but in graduate school things were more specialized, it was mathematics, mathematics and mathematics.  I loved mathematics, it was wonderful, but in my heart what interested me was using mathematics to understand things in the world, in particular to understand the mind.  This was why I had gone to Courant instead of one of the other graduate schools I had been accepted into -- Courant had a strong applied mathematics focus.  So far, though, the applied mathematics had been more mathematical than applied; and 99.99% of the applications were to physics.  Finally, I thought, I was going to get the kind of information I really wanted.
 It was an applied math course, not a biology course: after a quick review of neurochemistry, we proceeded to the Hodgkin-Huxley equations which describe the flow of potassium, calcium and sodium through the "ion channel" of the neuron. Using a combination of mathematical calculations and computer algorithms, Peskin showed us how the simple threshold dynamics of the neuron emerge from a much more intricate underlying chemical dynamics.   It was all most fascinating.  For the first time ever, I was seeing some serious equations describing the dynamics of part of the brain!  These partial differential equations written on the board -- they explained what was going on inside my head, they explained the complex dynamical process that, when connected into itself a trillion times, somehow made me me.
The course was thrilling -- but yet, as the semester moved toward the end, the melange of emotions became more complex.   One afternoon, as I walked into the room to hear his lecture, an intense feeling of sadness passed over me, sweeping from the brain down.  With a moment's introspection, I identified it as disappointment.  I realized I was tremendously disappointed with the class -- not with Peskin's lecturing, which was excellent, but with the course content itself.   I had hoped that, in a course on "The Neuron," we would get at least a glimpse of the processes by which neurons come together to form actions, perceptions, feelings and thoughts.  But instead it was all mechanics -- there was not even a little, tiny nod toward the possibility of a higher-level understanding.
Sometime toward the end of the semester I raised my hand and asked the inevitable question: "Okay, so this is what one neuron does. But what happens when you couple a whole bunch of these equations together? Why do you get cooperative behavior? How does it build up to give, you know, thoughts...."
Peskin grinned and raised his finger -- I still remember the whimsical look on his face.  "Aha, of course. That's right -- that's a good question....  Where's the learning?"
"I've read that it may have something to do with synaptic modification...." -- changes in the properties of the connections between neurons.
 He nodded, "It may. At this stage no one really knows."
And that was the end of that.  I approached him after class and tried to pursue the matter further, but he had little interest, deflecting the conversation to the particularities of the Hodgkin-Huxley equation again.  Previously, I had hoped that perhaps I could pursue a Ph.D. on the mathematics of thought, with Peskin as my supervisor, but now I could see that this topic was the furthest thing from his mind.  Above all, this was a lesson in scientific specialization -- Peskin was an expert on  "The Neuron" and not "Neurons Connected Together" or "Learning in Neurons."   That was how science worked -- everyone had their own specialty, their own little cubicle in the endless edifice of information.  Of course, there were some scientists who tried to go beyond the micro level, to ask the big questions, to integrate diverse bodies of information -- but these were few and far between.  By focusing his inquiries tightly, Peskin was doing what he was supposed to do, and making serious scientific progress.
 Upon seeing that the question of learning was of little interest to Dr. Peskin, I foolishly lost interest in his course.  Skipping his class, I spent the next Thursday out in Washington Square Park, fending off drug dealers and reading library books on the brain and thought.  Perusing the research literature, I found that there were indeed many researchers concerned with the problem of learning, albeit not within the discipline of mathematics.  If memory serves, I failed to do my final project for Peskin's course, and received an "Incomplete" for my final grade -- which makes my knowledge of the brain incomplete, I suppose, but does not in this regard distinguish me from anybody else on Earth!   After that semester, I left Courant and transferred to Temple University -- mainly out of a frustration with the difficulties of being an impoverished graduate student in New York City, but also, in the back of my mind, out of a sense of disenchantment with Courant-style applied mathematics.  Mathematics, I felt, had an immense potential to model mind at its most abstract and introspective -- but instead it was being used as an outgrowth of physics and chemistry, as a slave to a simplistic, reductionist view of intelligence.    "The Neuron" was important -- but it had to be possible to say something about "Neurons" too ... about huge bunches of neurons, connected together, and how they gave rise to the mind.

Neurons and Brain Chemistry.
I was, of course, deeply grateful to the surgeons who had repaired Zar's injury.  I appreciate all the researchers who have developed medical and surgical treatments for brain disorders.  Fifty years ago, in the same accident, Zar would have died.  But my goal was different from theirs.  I was not working on repairing human brains, important as that is, I wanted to build an artificial intelligence program loosely modeled on the brain.  Inspired by Zar's questions, I set about to read everything I could find about the structure and function of the human brain.  I wanted to answer the question Peskin had brushed aside: how do neurons produce thoughts?
The existing neuron net computer programs didn't answer the question, because they did not produce the kind of thinking I wanted to produce.  I thought that possibly the problem was that these programs did not simulate the nature of biological neurons closely enough, so I did more comprehensive reading on the biology of the neuron.  My reading reminded me that a neuron is a nerve cell, not fundamentally different from nerve cells elsewhere in the body.  Nerve cells in your skin send information to the brain about what you're touching; nerve cells in your eye send information to the brain about what you're seeing -- and nerve cells in the brain send information to the brain about what the brain is doing.  There was nothing unique about the nerve cells in the brain, as far as I could discover, which explained why they generated intelligence while nerve cells elsewhere in the body did not.
 Much of the research on neurons focused on the mechanisms which made them work. Biologists think of the neuron as a central nucleus surrounded by connections called dendrites.  Each dendrite comes close to another neuron; the gap between the two is called a synapse, and is bridged by chemicals called neurotransmitters.  Neurons' main bodies send electricity out through the dendrites to other neurons, creating a vast web of electrical circuitry that, it is believed, somehow builds up the structures we call mind, perception, self, memory.
The fact that neurons work by electricity never ceases to amaze me.  The same thing you see in the sky during a thunderstorm, the same thing that makes your light bulbs shine and your television light up -- this is the force that makes your own thoughts go around in your head....  We're all running on electric!   Manifestations of our electric nature are not hard to find -- for example, we all know how electroshock therapy affects the brain.  Then there are the strange stories of people who have been struck by lightning.  One man who was struck by lightning was never again able to feel in the slightest bit cold.  He'd go outside in his underwear on a freezing, snowy winter day, and it wouldn't bother him at all.  The incredible jolt of electricity had done something strange to the part of his nervous system that experienced cold.
 By envisioning dendrites and synapses as analogous to wires connecting electrical components, the neuron can be envisioned as an odd sort of electrical machine.  It takes electrical charges in through certain "input connections" and puts charges out through its "output wires."  Some of the wires give positive charge -- these are "excitatory" connections.   Some give negative charge -- these are "inhibitory."   Furthermore, there is a peculiar trick to the neuronal electric switch:  until enough charge has built up in the neuron, it doesn't fire at all.  When the magic "threshold" value of charge is reached, all of a sudden it shoots its load.  What this funny dynamic means, over a longer time scale, is that the more charge you feeds into a neuron, the more frequently it will shoot -- so that, at the crudest level, a neuron may be understood as converting voltage into frequency.  The more charge you feed into the neuron, the faster it puts out its short bursts of charge.  And the charge that is sent out goes into other neurons, through excitatory connections that encourage firing, or inhibitory connections that discourage it.
A great deal of the biological research I read focused on exactly how the neurons accomplish their task.  Much of it focused on the neurotransmitters, the chemicals which help the neurons send signals to each other.  I could see why medical researchers focused on this, because it had a direct payoff in drugs which change the levels of neurotransmitters in the brain.  These drugs help to treat all kinds of diseases including depression, anxiety, schizophrenia, epilepsy and Parkinson's disease.  This knowledge, however, did not help me understand how the neurons generated thought.  Nor was I planning to use biological tissues and neurotransmitters in my artificial brain, I planned to use standard silicon computer chips.  The chemistry of the brain was not directly relevant to my problem.  What I wanted to know is what use the neurons are in building up the mind.
For this question, the best developed theory was one I already knew from my reading of the artificial intelligence literature:  a special kind of neural network AI called the "cell assembly" approach which held that the mind is somehow composed of collections of tightly interlinked neurons called "cell assemblies."   This theory, and the phrase "cell assembly," was first published in Donald Hebb's 1949 book The Organization of Behavior.   Mental entities, in Hebb's view, are patterns of electrical flow among neurons; and collections of tightly interlinked neurons lead to distinct, repeatable patterns of flow.  Furthermore, charge passing through networks is understood to modify the properties of the synaptic connections making up the networks -- so that distinct, repeatable patterns of flow in turn create collections of tightly interlinked neurons.  Everything is patterns of connection, patterns of electrical flow.
 This is a simple, mathematical concept -- mind as network and network dynamics -- which resonates well with modern network computing.  It gives a natural neurobiological substrate for learning, and yields a picture of the brain as being full of "self-supporting circuits," circuits that reverberate and reverberate, keeping themselves going.  Furthermore, it is a vision that has remained basically the same since the 1940's, holding up remarkably well in spite of the tremendous advances in neuroscience that have occurred since then.
There were still some important scientific controversies about neurons.  I found that Stuart Hameroff, an anesthesiologist, believed that the essential thing for intelligence is not the synapses between neurons, but the dynamics of the neural cytoskeleton (a kind of scaffolding of protein "rods and cables" inside the neuron that allows the neuron to hold together its complex shape).  He has allied with the British mathematician and physicist Roger Penrose, who believes that we need a new theory of quantum gravity to explain what's going on in the cytoskeletons of neurons.
I suspected, however, that the best approach for me was not to go more deeply into the structure of the neuron.  I concluded that the neural net people were right: the key question was not how neurons worked internally, but how they interacted with each other in groups.   What I needed was more knowledge about how the neurons the brain are arranged.  The mind, I suspected, would be found in the organizational structure of the brain, not in the characteristics of the individual neurons.

The Structure of the Brain.
 In my ongoing reading about the brain, before and after Zar's accident, I found that biological researchers had compiled a tremendous amount of information about the organizational structure of the brain.  This information was medically useful, it told specialists the consequences of injury to different parts of the brain, and in some cases allowed surgeons to correct problems.  The brain is not just a massive glob of gray matter, nor can one part of the brain easily take over the function of a part which has been damaged.  The brain has something like a hundred major components.  It is tremendously intricate, so much so that two-dimensional diagrams do not do it justice; medical textbooks on the brain are always "pop-up" style, allowing visualization of three-dimensional structure.  Even better models can be viewed on a computer, either on CD-ROM or over the Internet, allowing you to move through the brain, viewing each part of it from different directions.   When I saw all this complexity, I was sure it could not be just an evolutionary accident.  It had to have something to do with Mind, with how we think.
The literature did suggest some answers, although not all experts were agreed, and there are big gaps in the available knowledge.  Experts tended to divide the brain up in different ways, attributing different functions to different parts of the brain.  For example, the brain can be seen to be divided into two hemispheres, the "left brain" and the "right brain."  Often it is found that the right brain deals more with spatial reasoning and artistic intuition, while the left brain deals more with linguistic and logical functions.  This division is less sharp for some people than for others, however, and for some - especially the left handed - it is reversed.
At least as important as the right-left dichotomy is the front-back dichotomy -- the distinction between the forebrain and the hindbrain. In mammals like us, the forebrain is subdivided into three parts: the hypothalamus, the thalamus and the cerebral cortex.  The cortex is divided into several parts, the largest of which are the cerebellum and the cerebrum, but there are also many obscurer regions like the cingulate gyri and so on.
 The cerebellum has a three-layered structure and serves mainly to evaluate data regarding motor functions.  The cerebrum, on the other hand, is the seat of intelligence -- it's the integrative center in which complex thinking, perceiving and planning functions occur.

The cerebellum, incidentally, is familiar to Ramones fans from the immortal song "Teenage Lobotomy":
DDT did a job on me
Now I am a real sickie
Guess it's time to spread the news
That I've got no mind to lose
  Now I guess I'll have to tell 'em
That I've got no cerebellum
All the girls are in love with me --
A TEENAGE LOBOTOMY! ...
However,  the Ramones should have studied harder in school, because they didn't get it quite right!  Their cerebellums, which deal with motor control, must not have been too badly damaged -- they could still play their guitars.  It must've been their cerebrums that the DDT did the job on....  And anyway, everyone knows a lobotomy involves the removal of the frontal lobes, which are part of the cerebrum, not the cerebellum....   ( Of course, if Joey and DeeDee hadn't had those lobotomies in the first place, they might have remembered this stuff from high school biology.)

 The front/back distinction leads into a lot of interesting puzzles.  For example, it is a little-known fact that the entire forebrain evolved to deal with the sense of smell -- a fact which lends Walter Freeman's work on the dynamics of olfaction an importance beyond what is immediately evident.   The structures the brain uses to deal with smell are quite similar to those used to deal with the most abstract thinking.  This sounds odd, but on reflection it is reasonable: after all, smell is not central to our lives today, but it was of paramount importance to our reptile ancestors.  And the neural requirements of smelling, are really quite similar to the requirements of abstract thought.   Vision and hearing aren't nearly so combinatory as smell: two sounds need not combine to make an easily intelligible sound, and two sights superimposed may make a ridiculous blur -- but two smells combined will make a perfectly admissible smell.
Smell leads to neural networks with lots of sprawling combinatory connections, in which each neuron connects to a random assortment of other neurons; vision and hearing, on the other hand, would be expected to lead to more orderly layered connections -- what we call topographic connections, snaking linearly from one neuron to another to another.  Combinatory connections are precisely what is needed for abstract thought.  So it seems we were rather well served by our reptile ancestors' penchant for sniffing; and it seems that Freeman's results, in which classification is carried out by chaotic exploration of multi-lobed attractors, may well be carried beyond the domain of odor identification, and into the domain of intellectual understanding.
 The forebrain is full of complexity.  The simpler hindbrain, on the other hand, is situated right around the top of the neck.  What it does is mostly to regulate the heart and lungs-- and it also controls the sense of taste, a fact which is particularly important, because -- thinking about it in terms of evolution -- the emergence of the forebrain is as a consequence of the move from water to land, for when we moved from water to land, we moved from tasting to smelling.  For a fish, the sense endings in the mouth are indispensable -- they're the main means of exploring reality -- among other things, they're needed to detect the presence of food.  But things that can be tasted when dissolved in the water, can be smelled in the air.  The interior of the nose -- all salty and wet -- is  a sort of simulation of the underwater environment; it's designed to smooth the transition from water-sensing to air-sensing.  And this transition turned out to be a good one -- the sense of smell was the perfect "starting point" for the development of the cortex ... which is the part of the brain that gives us the ability to think, write and read about our own brains in the first place!
And then there's the midbrain, resting on top of the hindbrain; it integrates information from the hindbrain and from the ears and eyes.  Collectively, the hindbrain and midbrain are referred to as the brainstem.  The midbrain seems to play a crucial role in consciousness, and in general in the unification of disparate information into coherent packages....  This function is reflected in its architecture: there's a roof portion called the "tectum," that gets its information from a multilayered hierarchy of neurons.
These divisions are only the coarsest ones; there are plenty of other ways of categorizing the different parts of the brain.  For instance, there's the  "limbic system," first identified by the French neurophysiologist Broca, way back in 1878, defined as a grab-bag of neural subsystems: the hippocampus-fornix, the amygdaloid nucleus, the olfactory areas, the hypothalamus, the mamillo-thalamic tract.  All these regions seem to be collectively responsible for the phenomenon of emotion.  They become activated when a person feels something -- and, often, when a person remembers, suggesting that, as Freud often argued, emotion is necessary for memory.

Einstein's Brain.
A study published in Lancet in June, 1999, suggested that Albert Einstein's genius may have resulted from a brain abnormality.  Apparently, his brain is missing a feature known as the parietal operculum, which allowed the inferior parietal lobe to grow larger than normal.  According to researchers, the inferior parietal lobe is used for mathematical thought, three-dimensional visualization, spatial relationships.  Other researchers may contest this particular finding, but it is altogether possible that many cases of exceptional genius may be found to be associated with differences in brain structure.
 

To really understand the link between brain structure and thought, however, I believe you have to go into the detailed structure of the brain's components.  You have to understand how the neurons in each part of the brain are organized to do that unit's work.  To illustrate this, let us look in detail at the structure of the cortex -- the part of the forebrain that carries the burden of abstract thought and memory.   The cortex is a very thin tissue, about two millimeters thick, folded into the brain in a complicated way, and is generally understood to be structured in two different ways, which we might think of as "vertical" and "horizontal."  First there is a "horizontal" laminar structure, a structure of layers upon layers upon layers -- generally six layers, although in some areas these six can blend with each other, and in others some of them may subdivide into distinct sublayers.   And then, perpendicular to these six layers, there are large neurons called pyramidal neurons, which connect one layer with another, propagating information up and down..
 The pyramidal neurons of the cortex tend to feed into each other with excitatory connections -- so that when one is active, so are the others which connect to it.  They're surrounded by smaller neurons of all different types, mostly very small neurons called interneurons; the connections between pyramidal neurons and interneurons are largely inhibitory.  The pyramidal neurons form the basis for "vertical" structures called cortical columns, which cut through the layers.  They are often rightly considered the "skeleton" of cortical organization.    Each one has two sets of dendrites (connections going out to other neurons): basal dendrites close to the main body of the cell, and apical dendrites distant from the main cell body, connected by a skinny kind of shaft-like membrane formation.  Being large cells, they can each get input from thousands of other neurons, and can transmit signals over centimeters.
The structure of cortical columns is most pronounced and best-understood in the visual  cortex, the part of the brain responsible for building the brain's perceived visual world.   It is pretty well established that, here, all cells lying on a line perpendicular to the cortical layers will respond in a similar way.  A column of, say, 100 microns in width might correspond to line segments of a certain orientation in the visual field.
One lesson learned from studying the visual cortex is that the brain uses redundancy to overcome inaccuracy.  Each neuron is really unreliable -- but the average over 100 or 1000 neurons can still be reliable.  This is a kind of design strategy that we can't very well take with computers.  We have more reliable components, but making the components costs money; we can't just multiply them over and over to compensate for inefficiency.  But a growing system like the brain can make new parts easily.  Improving the reliability of the parts is harder.  In the case of motion detection neurons, for example, each individual neuron may display an error of up to 80% or 90% in estimating the direction of motion -- but the population average may be exquisitely accurate.  We have no problem telling what direction things are moving in, because we detect motion using clusters of similarly functioning cells.
 One fascinating aspect of the visual cortex, and of the cortex in general, is that it combines two fundamental organizational principles which we can call hierarchy and network.  Hierarchical connections are organized into superior and inferior levels, with each level controlling the neurons in the levels below it.  This is the laminar structure of the cortex. Networked connections violate these hierarchal rules, allowing a neuron to reach out to other neurons independently of their position in the hierarchy.  This is the pyramidal structure of the cortex.  In the system of pyramidal cell to pyramidal cell connections, the influence of any single neuron on any other one is really very, very weak.  Very few pairs of pyramidal cells are connected by more than one synapse.  Instead, each pyramidal cell reaches out to nearly as many other pyramidal cells as it has synapses -- thousand and thousands.  These cells can be spread over quite a large distance, so when you add up the figure, you find that no neuron is more than a few synapses away from any other neuron in the cortex.  The cortex "mixes up" information in a most remarkable way, which has to do with the origins of the cortex in the olfactory brain of reptiles -- the sense of smell mixes things up, combines things, in a way that senses like vision and hearing don't.
I believe that all intelligent systems must be organized along both hierarchal and network principles.  In my view, this dual network structure is essential to building a mind, whether that mind is biological or electronic.  In the brain, the laminar structure and the pyramidal, perpendicular structure are important biological facts, but I believe they are of central psychological importance as well.   It is my hypothesis that the multiple layers of the cortex correspond to different levels of reasoning: the lower levels corresponding to simple stimuli, the next level up combinations of stimuli, and so forth, until the highest level, which deals with the most abstract formations.  The network of pyramidal cells based in each level, in this picture, corresponds to the associative, networked structure of the mind, in which  things related to each other, on the same or nearby levels, are connected to each other.
 In this way I believe that the global structure of the brain's neural network, combined with the distribution of neurons of particular types, may be of profound significance for the emergence of mind from brain.  This does not detract from the importance of the idea of the brain as a neural network, but it does suggest that just any neural network will not be good enough to give rise to a mind.  Mind has to do with certain emergent attractor structures, which can be made to come out of neural networks, if the neural networks are structured amenably in the first place.  The cortex would indeed seem to be structured amenably for the emergence of hierarchical/heterarchical mind.  I believed that if I constructed my artificial brain with something like the  laminar/perpendicular structure of the cortex I would have a much better chance of achieving true intelligence.

Closing the Micro/Macro Gap.
This work is accomplishing a very important task: closing the micro/macro gap in brain research.  We know a good deal about the anatomical structure of the brain, the large regions and sub-regions.  And we know a great deal about the neurons and the neurotransmitters.  What we need is more understanding of how the neurons are organized to produce the larger structures.  To really close the gap, however, we have to go beyond a static, cross-sectional approach.  It is not enough to observe the physical structure of the brain, we have to observe how the neurons and groups of neurons relate to each other.  This is very difficult to do in biological research because we do not have the technology to record brain activity in sufficient detail.  Biologists are making great progress, however, and more and more information about the dynamics of brain activity will undoubtedly be published over the next few years.
 I did not want to wait for the biologists, however.  I wanted to go ahead and build my artificial brain now.  This is where chaos theory was a great inspiration.  It suggested that we computer scientists not need to wait for complete details on the dynamics of the brain before replicating its behavior with microchips.  Chaos theory shows that the same emergent behaviors can come out of a lot of different underlying systems.  This means that even if our neural networks are not based on precisely accurate models of the brain, they may still display a lot of the behaviors that real brains do.  This view is supported by research with artificial neural nets.  We find that if we damage or destroy parts of the network, the remaining damaged structure is still able to function, albeit on a reduced level.  Recent experiments with model neural networks that learn to read and pronounce words, for example, show that if you destroy some of the neurons and connections in the network, what you get is a dyslexic neural net -- the same thing you get if you lesion someone's brain in the right area.  You can do the same sort of thing to model epilepsy: by twiddling the parameters of a neural network you can get it to have an epileptic seizure.  But it still works reasonably well between seizures, just as humans with epilepsy function perfectly well most of the time.
This means that we computer scientists don't need to wait for the biologists.  We can simply use the available biological knowledge for guidance, and work on adjusting our own systems to get the results we want.  Even if the systems we develop are different from those in the brain, they may well accomplish the same things.  A number of researchers are working along these lines.   Freeman's above-mentioned work on olfaction is an example.  Another is a fascinating study I read recently of how spirals, tiling patterns, tunnels and other common hallucinations arise out of two-dimensional neural networks similar to those in the visual cortex.  Some researchers are thinking about someday building a meta-neural network out of dozens or hundreds of smaller, specialized neural networks, mimicking the structure and function of individual brain regions.
 Of course, one could take the chaos theory argument one step further, and posit that there could be systems that aren't rigged up to look anything like the brain, systems that don't contain simulated "neurons" and "synapses," which do many of the same things the brain does.  This is very possibly true.  There may be very different ways of organizing to achieve brainlike dynamics.  However, the brain is the best working model we have, so it seems to make sense to begin by mimicking its structure and dynamics.
Neural Darwinism.
One more piece to the puzzle is provided by the notion of neural evolution -- meaning, not the evolution of brains over history, but the "evolution" of appropriate structures within a given brain, as a consequence of experience.  This theory is important because our goal is not just to understand the static structure of the brain, but how it operates - its dynamics.  Evolutionary theory addresses precisely this question.  Evolutionary theory was developed by nineteenth century thinkers such as Herbert Spencer. Friedrich Nietzsche and Charles Darwin, whose goal was not just to describe the species which existed, but to explain the origins of those species.  Not just what they were, but where the came from, how they developed.  This is what we need to know about the brain, not just what the structures are, but how they work, how they develop thoughts.
The idea that thoughts evolve was first brought to the attention of the neuroscience community by Gerald Edelman in his book Neural Darwinism.   The key idea here is that, when we come up with an idea or a percept or an action, we're actually evolving this entity from among a population of neural networks representing different possibilities, by a process not all that different from the evolution of species in an ecosystem.
This is just a variant on the basic cell assembly framework proposed by Hebb in the 1940's, but it's an interesting variant.  Hebb talked about coherent assemblies of neurons coming about through spontaneous interaction, and the modification of synapses.  Edelman proposed that the brain contains a huge number of similar neural networks, networks which are slight variations on the same theme, and that much of the process of originating useful neural assemblies is a process of selecting the best ones from among ensembles of similar networks.
 We then have two processes governing brain dynamics: Hebb's self-organization, according to which networks pull themselves together, and Edelman's evolution, according to which networks are selected from ensembles based on usefulness.   Of course, "usefulness" need not be defined relative to the external environment -- it can be defined internally relative to other networks.  The evolution of perceptual-motor "maps," neural meta-networks telling how the organism should respond to various situations -- e.g. telling how a cat should respond to seeing a mouse in front of it -- involves selecting among candidate networks based on their usefulness at solving a real-world problem: catching the mouse.  On the other hand, the evolution of neural networks dealing with mathematical reasoning or language processing may be governed by how well these networks fit in with other networks in the brain -- just as, in the evolution of species, the fitness of an evolving species depends not only on how well it fits in with the external environment, but also on how well it fits in with the other species around it.
This neural evolutionary process is important throughout life, but it seems to be the most intense during the pre-natal stage, when the brain is still developing its connection structure.  In fact, the notions of neuronal evolution and brain chaos provide a new answer to the perennial question of "heredity versus environment."   Basically, the answer seems to be -- some of both, but a lot of neither.   DNA, it would seem, sets up the initial conditions of the fetal brain, and then the brain itself determines the rest of its structure, by its own processes of self-organization and evolution -- processes which are highly complex and which appear to display at least one of the hallmarks of chaos: sensitivity to initial conditions or deterministic unpredictability.
 As the fetal brain grows, it iteratively determines its own structure: its structure now helps to determine its structure an hour later.  But if these dynamics are chaotic, then their overall course is sensitively dependent on slight environmental fluctuations.  Thus the motions of the mother and the noises outside the womb may play a role in the development of the fetal brain -- but not entirely a predictable role, to some extent an "arbitrary" role of pushing self-organizing neural dynamics one way or the other at a bifurcation point.
Edelman analyzes neural development in terms of special molecules called cell adhesion molecules.  The way to think about these molecules is as special glues-- they serve to stick things together.  But the complexity of their behavior puts Elmer's Glue to shame.  They come in several different types: for instance, there are L-CAM's and M-CAM's.  If something has L-CAM on it, it will only stick so something else with L-CAM on it; it won't stick to something with M-CAM on it.  So, envision a brain full of growing neurons, each doused with a certain type of CAM.  The neurons will grow out and out, but because of the weird CAM dynamics, they won't necessarily stick to the first other neuron they come across.  They'll keep on snaking and snaking until they find another neuron with the right kind of CAM, the right kind of glue.  Thus the tortuous, nonlocal neural connections of the brain.   The growth process is self-organizing, because the path of a growing neuron depends on the paths of the other neurons which it finds in its way.  Edelman argues that, eventually, the result of the process is a brain divided into neuronal groups-- clusters of neurons, each one full of neurons that connect more richly to one another than to neurons outside the cluster.  Originally, a cluster may have formed from a group of neurons all coated with L-CAM.  But in the long run, all that matters is the cluster structure.
 And it's these clusters that are, in Edelman's view, the building blocks of thought.  Each cluster realizes a certain function, and it is quite possible, perhaps even common, for internally different clusters to realize the exact same function.  Instead of networks of neurons, one winds up thinking about networks of neuronal groups, interacting with one another, and being selected from ensembles of similar groups based on usefulness for external or internal functions.  Neural network models, dating back to Hebb, are based on the idea we think by changing interneuronal connections.  Neural Darwinism suggests that we should instead think of the modification of inter-group connections, from among populations of connections to similar groups, as the basic dynamic of thought.  The selection of useful connections, and the weakening of useless connections -- this is the "Darwinism" that gives Edelman's theory its name.
Neuronal groups are still too primitive to have any direct relation with experienced mind.  But Edelman says that the fundamental element of mind is the "neural map" -- the network of interconnected neuronal groups.  The most commonly studied neural maps are the ones which connect perception with action-- sense neurons with motor neurons.  This sort of neural map behaves in a very direct way: it takes a certain input and turns it into a certain output ... as in the example given above, of a map that tells a cat what actions to take when its eyes perceive a mouse.  But these low-level, perceptual and motor oriented neural maps are only the beginning....  There are also higher-level maps -- neural maps whose input and output consist largely or entirely of other neural maps.  These maps resolve conflicts among low-level maps, and they also help to create new low-level maps, by reinforcing certain inter-group connections based on their own criteria.
 This is where Edelman's theory becomes fuzzy: his biological data and his computer simulations operate on the level of perception and action, and they give very few precise ideas regarding the operation of these more abstract maps, these maps mapping maps to maps.  By this point, however, Edelman's constructs have become sufficiently abstract that they can be analyzed mathematically with systems theory.  What we have is a large number of neural maps, combinations of neural networks, which are linked to other maps.  Some maps are inputs into other maps.  As these neuronal maps interact with each other, stable patterns or "attractors" emerge.  According to this theory, this is how mind develops:  it is an attractor of this interacting network of neural maps.
This theory also helps to explain the ubiquity of the numerical archetypes which we discussed in the last chapter.  They are attractors which emerge the dynamics of the system of neural maps.  But they also emerge from the dynamics of other complex systems, including those of the early universe which created the chemical elements.  That is why the numerical archetypes are so pervasive, why they are found both in the mind and in nature.  Evolution is a pervasive process, and certain attractors are likely to be emerge wherever it takes place.
In the specific case of the brain, the structure of neural connections which we observe in anatomical studies evolves while the brain is still in the fetus.  This structure is "modularized" into neuronal groups, so that the important interactions are between groups of neurons rather than individual neurons.  The networks of neuronal groups called maps are the essential components of thought, perception and action.  And, while some of these maps connect perceptual neurons to motor neurons, others just connect maps to maps.  The network of maps mapping maps to maps is itself a complex self-organizing system -- and mind is built from the strange attractors of this system.  Or, at least, this is the theory that made the most sense to me, and which I used as the inspiration for WebmindTM.
The Dual Network in the Brain.
I stayed at Waikato University only a year - although the university was a great place to work, and New Zealand was incomparably beautiful, the car crash had traumatized my wife and for that among other reasons she badly wanted to leave New Zealand.    I found an even better job, as a Research Fellow in Cognitive Science at the University of Western Australia, in Perth, an idyllic city on the far west coast of the Land of Oz.   This job required almost no teaching - maybe an hour a week, on average - and had basically no duties.  My direct boss was the dean of the Faculty of Science, to whom I was never once introduced.  I had free rein to follow the meanderings of my mind.   I spent some time helping to organize an interdisciplinary Cognitive Science degree program, an effort that had been going on there for a while, but that was aided by my ability to speak the languages of the different university departments involved, such as psychology, computer science, linguistics, and mathematics.  During this time I began thinking about Internet intelligence and moving toward the zero'th approximation for a Webmind design.   And  I also realized that the "dual network structure of mind" could clearly be seen in the structure of the cortex.
My reasoning was simple.  Parts of the cortex, particularly the visual cortex, could clearly be seen to be divided into 6 layers.  Large, pyramidal neurons shot out perpendicular to these layers, piercing them, carrying charge from one level to the other.  Interneurons and other small neurons carried charge along individual layers, without moving up or down.  There it was: a simple but beautiful illustration of the principle of hierarchical/heterarchal  interpenetration.  The layers of cortical sheet were clearly one of the brain's tools for giving rise to the hierarchy of mind.  The lateral connections within each sheet were clearly part of the brain's associative heterarchy.  The integration of the two into a single functioning neural network with its own complex dynamics was the emergence of dual network!   Of course, this physical mapping from brain structure onto mind structure was not complete, and clearly there was a lot more to the emergence of the dual network from the human brain.  But, the parallel was remarkable.   Edelman's neuronal groups were not just strewn about in a pool inside the brain, they were organized along hierarchal and networking principles.
 To me, this was all came together beautifully!  It was a Eureka experience.  I was confident I finally understood how the brain created thoughts.  I wrote a brief article on the dual network and the cortex, which was published in the journal Complexity.  More than ever, I was convinced that I had found a level of abstraction on which the structure and dynamics of the brain and the structure and dynamics of computer programs could be compared and interanalyzed.
I briefly considered whether I could use this insight to "prove" my theory of mind correct in a neuroscience sense.  Some people at UWA were working on analyzing brain structure using PET and MRI scanners, hi-tech machines that study the flow of blood in the brain, and can identify which parts of the brain are used to carry out various processes.   For instance, PET scans were used to show that Peirce was right about the brain having no "central cell" controlling consciousness - conscious awareness seems to be correlated with activity across at least 7 different areas of the brain, and slightly different ones for each different conscious experience.
But unfortunately, I soon concluded that the technology was not yet there to explore my ideas about brain dynamics.  You could take a snapshot of the brain's activity at any given time, but you couldn't watch it changing over time; you could only get a snapshot every few seconds at fastest. This wasn't rapid enough to watch the mind in action.  Only by watching the dynamics of the brain could you really tell what was going on.  I briefly distracted myself by trying to learn enough engineering to build a better brain scanner, but quickly thought the better of it!   The empirical study of the dynamics of thought would have to wait until brain scan technology was a little further along.
 But, the goal of building a thinking machine was more plausible.  Computer technology was more nearly "there" than brain scan technology.  It still had its problems - not enough memory, not enough parallelism - but it seemed that these were being solved at a feverish pace.  It seemed clear to me then, in 1995 and 1996, that within 10 years at most, the computing power to build a desktop computer intelligence would be available.  And there wasn't really any need to wait.  There was more than enough power available on the Net - if one only knew how to harness it.
The study of the brain was inspirational, but, I decided to put it aside, and at this point I must admit I have forgotten much of the neurobiology I used to know.   Sometimes, to achieve what you want, you have to put aside your diverse interests and develop a single focus.  As a Research Fellow I was allowed to move in all directions at once, letting my brain pull me where it might.  But I realized that if I was going to really succeed in doing what no one had done before, building a thinking machine, I would have to concentrate with all my might.  Even with all the thinking I had put into it over the last 7 years, and my confidence in my ideas, I knew this was going to be the challenge of a lifetime.