Budding Mathematician

After we moved to Fort Devens my parents started leaving me with the teenage daughter of one of their friends. They'd drop me off at her house. I think her rate was a quarter an hour.

Once again, I had an age-inappropriate crush. I don't know if I had more of them than any other kid my age. But I have the feeling I did, and the rapes had something to do with it. I think I was looking for an attachment that could be a repository for all the uncomfortable feelings.

The baby-sitter's name was something odd. I think it was Sylvania. I remember having to ask what it meant and finding the answer a little hard to believe. Sylvania is a name like that -- who names their daughter "woods?" So let's say she was Syl.

She was a pretty brunette with glasses. She loved math and she was into computers. In 1955! I can't vouch for it, but I was told that for a science project she built some sort of calculator using coat-hangers. I think she was 16 in early 1955. Not having a picture of her, I've substituted Tina Fey, both on this post and in my thoughts.

Syl had a much younger little brother, Fred. He was a couple of years younger than I was. He was what we would call hyperactive today, and he'd be stuffed with Ritalin. To me, he was a super pain in the ass. I wanted him tied and gagged. Not having a picture of Freddy, I've substituted Eddie Munster, both on this post and in my thoughts. During my earliest visits, Syl would put him to bed early, so I'd get to be alone with her for a couple of hours, and she'd use the time to teach me whatever I was interested in. I was interested in math, mostly, and a little science.

At some point I asked her how much you could learn, and she said you could keep learning math forever if you wanted to. I liked the sound of that. She told me about the math she was studying then, called "calculus." I asked her to teach me some calculus, but she said I had to finish learning arithmetic first, and then I'd have to learn geometry, and then I'd have to learn trigo-something, and then I'd have to learn al-something.

I felt like I was close to finishing with arithmetic so I asked for a preview of geometry. She showed me some stuff from Euclid, like the Pythagorean theorem. The square of the hypotenuse of a right triangle equals the sum of the squares of the two sides. It didn't look like anything that could possibly be true, but she said that when you study geometry you learn how to prove things like that.

She didn't show me a proof of the Pythagorean Theorem or any other. It was enough that she just told me there were such things. I started to realize that even in arithmetic I was taking far too much on faith. I should be insisting on proofs. For example, my Mother had often said I could save trouble learning my times table by noticing that the order you multiply two numbers doesn't matter. So if you know 7 times 8, then you also know 8 times 7, because the answer is the same. But how do I really know that the answer is always the same? I would have to see a proof.

I came up with a proof in my head at home while sitting on the floor of the Play Porch. It wasn't rigorous by the standards of a 21st century mathematician, but you have to start somewhere. I just convinced myself that what multiplication did was count the total number of things you got when you arranged first-number rows of second-number things in each row, and that if you switched first-number and second-number the result was the same as turning the arrangement 90 degrees. The turning doesn't add or subtract anything. It was more of a persuasion than a proof, and it was hell making it work for fractions, which I'd just started learning, but, you know what? After getting a Ph.D. in math and picking up a hefty dose of Foundational Theory along the way, I've decided that persuasions are what proofs ought to be, screw overblown rigor.

The new-found need for proofs began to be felt in all matters. I started noticing how often flat statements by even my own parents turned out to be flat wrong. The more I noticed that people could be full of it, the more concerned I was to subject all claims to proof.

I might have decided in the midst of all this to become a mathematician when I grew up, except for one problem: I didn't know that mathematicians existed. I had an idea people could be paid to use mathematics. I certainly did not know that anyone could be paid to discover new mathematics and find new proofs for their discoveries.

I didn't even know at this time that science existed. I assumed that everything that needed to be known about the world was already written down in books somewhere. Probably anything I needed to know was somewhere in our set of Encyclopedia Britannica, and I could find it if I knew the word to look it up under.

The immediate effect of my obsession with proofs was that I pissed Dad off more than ever. "It's true because I say so, Dammit!"

[Below: Chinese-style Pythagorean Persuasion. c-squared = the area of the big square = the area of the four triangles plus that of the center square. The area of each right triangle is half a times b. So c-squared = 4(ab/2) + (b - a)-squared = 2ab + b-squared - 2ab + a-squared = a-squared + b-squared.]

John Cunningham Lilly

At the lunch Wednesday for Robert (Mexican Lunch -- Tahitian Music, posted Feb. 28) the topic of conversation turned, as it often does when you have two hippy-aged old farts like Robert and me in the room, to the question, "What kinds of drugs did you do, or can't you remember?" People are often surprised to learn, especially after reading my writing, but also after looking at me, that I have never done any hallucinogens whatsoever. To excuse myself for that, I always mention the natural auditory and visual hallucinations I had during that little teenage psychotic episode of mine, that convinced me that I shouldn't do those kind of drugs for the same reason I shouldn't smoke while pumping gas.

Then, to explain why I didn't change my mind and try some acid or mescaline in graduate school, say, when the psychosis would have been far enough behind me as to encourage my native recklessness, I mention the caution inspired by the story of John Lilly, the great dolphin scientist and famed acid-neuronaut . When I did this at our lunch only Anitra, who is exactly eight days younger than myself, knew of whom I was speaking. I expected Robert wouldn't know, even though, as I've said, he's about my age, because Robert isn't that into the details of the Persian Carpet of Life, so to speak. Except for Tim Harris, our Director, I thought youth and 9-11 excused the rest of the party for not knowing who Lilly was. Most of his celebrity was achieved before they were born, and the fact that he picked 19 days after 9-11 to die meant there wasn't the usual national 5 minutes of obituary for the old guy that might have clued the younger generation in.

But when Tim didn't know I have to say I was a little surprised. Here's a guy whose blog (Apesma's Lament) is named for a Captain Beefheart lyric. He's posted a medical illustration of an extended hemorrhoid on said site, as well as a 5-7-6 Haiku. So he NEEDS to know who John Cunningham Lilly was and still is. Therefore I am talking about that.


















In this picture, found on a web page titled "John C. Lilly Community of One Love" we see, from left to right, Allen Ginsberg, Timothy Leary, and John C. Lilly, hanging out in 1991. This gives you one idea who he was.


Another way you can get an idea of him is to read the fourth book of the Hitchhiker's Guide to the Galaxy trilogy. Chapter 31 of So Long, and Thanks for All the Fish introduces a character called Wonko the Sane, and named John Watson, who lives in the outside part of an inside-out house called Outside the Asylum (the inside part being the part the rest of us are living in.) The Wonko character is obviously an amalgam of about 80% John C. Lilly with about 20% James Watson (of Watson and Crick.) John C. Lilly was the dolphin scientist of the two. But both had interests in neurology.

Lilly was the one guy most responsible for the popular notion that if Cetaceans aren't really really smart, they're at least like, really sensitive, and wise. One of the things he worked hard on, besides attempting to learn how dolphins talk to one another so we could join in their conversations, was at understanding how dolphins see with sonar. Lilly came to the think that dolphins and whales have the neurological capacity and the sensory equipment necessary to see in sonar not only in stereo (like we do with our eyes) but in true 3-D. The difference between stereo and true 3-D is the difference between seeing the surfaces of your surroundings and seeing the insides as well. John Lilly arrived at the tentative conclusion that dolphins could see the workings of each others internal organs and so could read moods and feelings off internal states. He realized that if true this could make understanding a dolphin language beyond all human capacity because we could never grasp its context. We don't have any way to relate to that kind of continuous unrelenting intimacy.

These ideas spawned the best Star Trek movie with the original cast ever, IV, The Voyage Home, with humpback whales in place of dolphins. We also got Day of the Dolphins, sadly.

Before trying to understand the different ways another species might conceptualize reality as a context for communication, Lilly thought of going back to square one and seeing what happens when you remove the context altogether. That was the gist of the idea of sensory-deprivation tanks. Lilly may not have been the first to think of exploring sensory-deprivation, but he made it work. He solved the engineering problems and he wrote about his experiments and fired the public up about it. That got us Altered States and at least one Simpson episode.

Lilly's involvement with LSD was big-time. Like Timothy Leary, John Lilly's career was begun in league with the CIA and the Military-Industrial Complex. The military probably funded his earliest research, which involved mapping brain activity on cathode ray tubes. The sensory deprivation research began in 1954. By the early sixties Lilly was incorporating LSD in his sensory-deprivation experiments. The LSD was provided by the CIA as part of a project called MK-ULTRA.

In MK-ULTRA, also called MKULTRA, and later MKSEARCH, the MK apparently stood for Mind Kontrol. Maybe they wanted to avoid MCULTRA for fear their acronym would end up on a fast-food menu. Anyway MK-ULTRA was all about the CIA's attempt to discover cool new ways to manipulate people's minds. MK-ULTRA research included sensory-deprivation studies from the outset, and they may have funded all of Lilly's 1950s experiments on that. But by the sixties they were definitely supporting Lilly.

I don't think Lilly took part in it himself, but some of the other research involving sensory-deprivation for the CIA explored its use as a means of enhancing the impact of psychological torture.

I read about Lilly's work with dolphins before I got to graduate school. By the time I got to grad school, Lilly had written Centre of the Cyclone, which documents his LSD experimentation, both official and personal. One of his stories details a singularly bad trip in which he saw his wife as a hairy ape and freaked out. That was enough to convince me that I didn't want the stuff, because I was looking to get laid, and didn't need those sorts of complications. Reading the book I got the impression that Lilly was pretty scared by the whole thing.

It must not have scared him too much though, because not much later he was back at it, this time with ketamines. He is reported to have tried to warn President Ford at one point that computers were trying to take over the world.

By the end of his life Lilly had his own website, so he must have decided to stop fearing the computers and learn to communicate with them from within their own frameworks. Lilly lives on at that website.