Shufflebrain

by Paul Pietsch

  ***

  Cyclopes dictated when Carl could start the light-shock training. They began using the top-mounted eye about two weeks after surgery. When we dangled a worm above the water, the denizen would ascend hungrily from the depths, "like a submarine surfacing to salvage a free bargeload of beer," as a pharmacologist colleague of ours characterized it. After the transplanted eye began to work, the Cyclopes preferred sight to all other senses. Vision working again, they seemed compulsive about taking a good look at the worm before making a strike. Often, inspection required acrobatics. If a worm dropped below the plane of the salamander's surfaced-oriented visual field, the animal would duck, twist and pirouette on its snout to aim the eye. It would even poke and thrust at a wriggling red mass, using the eye as a prod and reminding the pharmacologist with the beer of "a rhinoceros chasing one of the Three Stooges around a mimosa tree."

  Carl's instincts told him to wait a couple of extra weeks before launching the light-shock avoidance training. So that he could carefully control temperature and keep the animals in minimal illumination, I turned over my inner sanctum darkroom to him.

  ***

  Over the years Carl and I have observed a rule: no chewing the fat about the data until they've all been retrieved, cleaned up and run through statistical analyses. It isn't just a matter of introducing bias, which is hard enough to control, but to hedge against a potential hell an experimentalists usually learns early on in the career: letting imagination run wild with a false lead. The pure agony in retracting one's brilliant speculations is akin to the Katzenjammer Kid's dachshund having to surrendering a stolen string of succulent sausages. Thus when the big day finally arrived, I had not a hint of what the returns would say about the one-to-one principle of perception and learning. I did think we'd be making big names for ourselves by showing IQ could be raised with the knife.

  Carl came into my lab one day, arms loaded with sheaves of statisticated data. He spread them out on a long high lab bench, then tried to talk. Instead he began to giggle. The giggle turned into a laugh. The laugh became a fit. I feared he might collapse into a tall stack of dirty dishes on the soapstone sink behind him. Finally, he managed to tell me some of what was in the findings.

  One-Eye (the mean avoidances for animals minus a natural eye) had indeed learned more slowly than Two-Eye, which sounded just fine to me. And Triclops (the mean values for animals with the third eye mounted on the head) learned faster than Two-Eye. Well great! I thought. Moreover, the One-Eye versus Two-Eye difference when added back to Two-Eye did equal Triclops, which seemed marvelous to me!

  "What's so funny?" I asked, puzzled. It's swell to be delighted but that shouldn't kick you into a hebephrenic jag. Carl supported himself against the gray steel fume hood next to the sink. "Heee..." Now I'm also chuckling, although I don't know why. "Cyclops...[gasp!]...Cyclops learned faster than all the rest...Heeeeee..." Carl managed one last clause before his puffed eyes closed tight and he became incoherent: the Cyclops data were statistically significant. "Very highly significant..." And then I broke down, too.

  ***

  Why was all this so hilarious to us? One-Eye, Two-Eye and Triclops had behaved according to our a priori expectations. But Cyclops, with one transplanted eye, should have learned at about the same rate as One-Eye ("plus or minus a shkoshi bit to account for the location", as I told our phamacologist). But certainly not faster than Triclops! Our results looked flukey. Mother Nature had played a practical joke on us, it seemed. And she was rubbing it in with statistics--a very high level of statistical significance, at that. It was the statistics that made Carl, and eventually me, come apart. The Cyclops data look preposterous. And statistics turned them into absrudity.

  I'm not saying it's funny when ridiculous results become statistically significant. That happens all the time, really. Indeed, it's tragic when statistics prevent a scientist from recognizing absurdity. This too frequently happens.

  Statistics furnish a rational test for whether or not differences can be accounted for merely from random individual variations within a population. The tests don't guarantee a difference. Also, statistical correlations let an observer decide on formal grounds rather than intuitively, what the random chances are of two sets of events occurring together, given normal variations among the samples. And statistics let us compare results against, say, the honest roulette wheel: they give the odds against winning when we bet on an alleged difference or correlation. There's really no way to conduct quantitative research with "stats."

  But statistics aren't the same thing as truth. They're not the same thing as being right or wrong. And the term significance only refers to how many times in a hundred, thousand, million, etc., you can obtain the same result at an unrigged crap table. People have been known to roll eight or nine sevens in a row, which isn't very likely, statistically. An application of a given statistical test to a body of data may unwittingly violate unknown mathematical conditions. Cross the wrong abstract boundary and you may quickly generate absurdity without knowing it and without being able to control the source of the error. (I've often wondered how many heavy users of statistics have actually examined the theorems and proofs underlying their tests.) Then too, there's the matter of criteria. Much IQ gospel and parapsychology data, for instance, depend on level of significance and coefficients of correlation that would be useless in, say, quantum chemistry or statistical mechanics. On the other extreme, some of the most important discoveries in the history of science are statistically insignificant: Few of Pasteur's experiments were sufficiently replicated or adequately sampled for commonly used statistical tests. None of Koch's were. Nor Galileo's or Newton's.

  Don't get me wrong. Statistics adds a dimension to quantitative analysis that wasn't there before. Nobody denies this. But like any data or body of alleged facts, statistically significant results must be considered within a context of what's happening. If your statistics tell you that a rat learned a maze after it died, something went haywire in the data collection or analysis. If your experimental worms ran the maze 1296 times versus the 1293 for the controls, and your test tells you they are highly significant, maybe the numbers are too large for the type of test you used. (How did the test hold up if you sample ten experimentals and controls? In alternative tests? ) If your results don't make sense or are clearly absurd, you're best off laughing at yourself, canceling your flight to Sweden to pick up your Nobel prize and going on to the next project, which is what Carl and I thought we were doing.

  Carl pitched the data to me. I tossed them up on a dusty shelf above a new computer terminal I recently had installed, and there they moldered for months, where they still might be, except for chance.

  In those days, a computer terminal was a teletype machine, and direct interaction with the computer, instead of feeding in cards, was new. I'd the machine installed ostensibly to assist in an otherwise impossible assays essential to my main line of research. (Actually I wanted to play with the new toy sveral buildings down the block.) The analysis depended on an operation called numerical integration. A brilliant young systems analyst from the Comp Lab had tailored a program to my needs. But the people in the Comp Lab bought a bigger, fancier computer--to the chagrin of us poor dumb slobs out on the user end of the line. The change meant having to relearn new access routines and commands and then recheck the reliability of our canned programs. The changeover cost me two laborious weeks.

  One day, while sitting in front of the terminal, after having convinced myself that I was back in business, I decided on pure impulse to feed my numerical integration program a little absurdity. I'd previously discovered a safety feature that appealed to my empirical predispositions: if I fed the program data from an alleged curve that really wasn't a curve (had jump discontinuities in it), the computer would either balk outright or return utterly impossible results. In went the Cyclops avoidance data. Then I sat, smiling, wondering if the big new computer would simple go into an electronic spasm; or maybe it would tell me that Cycl
ops learned to avoid light forty-eight years before Carl's training sessions had begun.

  It did neither. Back over the teletype came very realistic values. In went more data. Same thing. It went on like this for the test results of every single animal in the entire study.

  I called up a different program and redid the calculations. Same thing.

  Differentiation allows for the back-checking of integration. I back-checked. The results survive. While I had the computer's brain open, I even rechecked Carl's statistical analyses. They held up.

  We were in a genuine ethical jam, I realized. It's one thing to set aside data because they tell you a dog weighs 500 pounds or even because your guts tell you something's fishy. But it's quite another thing to dismiss facts when there's a compelling reason to believe their validity. (If you don't tell the whole truth, you're effectively lying.) And the dancing little ball on the teletype machine had just hammered out very compelling reasons for belief. This was mathematics talking now, the math that builds bridges, runs chemical reactions and propels astronauts to the moon. It was Peirce's mathematics forcing necessary conclusions, even if I didn't understand the implications. I said nothing to Carl. I didn't know what to say, actually. This wasn't funny anymore. And I went into seclusion to think.

  ***

  One thing the calculations did yield, besides a bad headache, was a body of nice data to work with. Differentiation permits a close estimate of the instantaneous rate of change at a given moment. Thus at any point along the curve, I could tell precisely how fast an animals was learning the task. By carrying out a second differentiation, one can make a close estimate of acceleration. Acceleration is an excellent measure of how a moving body's past affects its rate at the moment you took the measurement. Acceleration in avoidance gave us a very precise measure of how an animal's previous learning influenced its learning in progress--something the raw empirical data, or even rates, could never have revealed. Integration (the sum of all the minute changes) let us look at total learning, both as a whole and between any given periods.[7]

  Yet when polished up, organized into crisp, clean tables and spread out on the lab bench, the data were even more baffling than before.

  Triclops hadn't merely learned faster than the normal Two-Eye. Triclops's test scores were exactly on the mathematical mark: were precisely as the one-to-one principle predicted, a priori. Let me convert the values to the scale used with IQ to show you exactly what I mean.

  Let Two-Eye's IQ (normal) be 100. One-Eye's IQ turned out to be 80. Now if we take the 20-point difference--our increment of change from an extra eye-- and add it back to the 100 points for Two-Eye, we get 120 as the predicted IQ for Triclops. What did we actually find? The tricloptic animals had a mean IQ of 117, plus or minus enough standard deviation to make the score the same as 120!

  By themselves, these data seemingly made a perfect case for the one-to-one principle, which Triclops obeyed to the letter, and which we would have convincingly asserted in the scientific literature, but for Cyclops, originally the source of mirth but now of consternation.

  Light-Shock Avoidance in Salamander Larvae*

  EXPERIMENT

  AVOIDANCES

  IQ

  Rate

  Per Trial

  Acceleration

  Per Trial

  One-Eye

  0.085

  0.2364

  80

  Two-Eye (normal)

  0.112

  0.3044

  100

  Triclops

  0.126

  0.3504

  117

  Cyclops

  0.188

  0.5228

  173

  *From Schneider, C.W. and P. Pietsch,

  Brain Research

  , volume 8, pp. 271-280, 1968.

  We had envisaged Cyclops as Triclops minus two natural eyes. And what was the mean cycloptic IQ? It turned out to be 173! It wasn't just that Cyclops IQ was much higher than Triclops's (which in itself was wacky). What was so utterly baffling was this. To make an accurate prediction of Triclops's IQ, we should have taken the normal 100 and added the 173 points (now the increment of change) to it. Triclops IQ should have been 273 points, not the measly 117 we actually observed.

  ***

  I began to put an explanation together over a bottle of Chianti late one night at the kitchen table after my wife and kids had gone to bed. Ironically, the epiphany struck while I mused over a picture of a Riemann surface in a book I'd borrowed from a friend.[8]

  Just consider what 273 visual IQ points would mean . That's 2.7 times normal-- practically triple the normal IQ! Suppose we shift from the visual to the auditory system. Ask yourself what it might mean to have a mind's ear three times more alert and discriminating than yours is now. Suppose, suddenly, the crackle of the corn flakes takes away your appetite. And what if the cat's meow summoned with the authority of the roar of the lion? And what, now, of the previously unnoticed pat of the rat? Pondering questions like these, I couldn't help but think of a line of graffiti on a wall in an Ann Arbor john:

  "Every blip a blop

  "And me a flop!"

  No, we wouldn't survive if we awoke one morning with perception tuned up anywhere near the level equivalent to Triclop's calculated IQ. Nor would the salamander make it out in the woods with 273 visual IQ points. Not where too fast a response to a glint from the belly of a hungry trout might draw the egg-heavy female away from her lover before she had insured next season's crop of new salamanders. Maybe even 173 points would be too much to bear in a world where reward and punishment come in the form of life and death. Some amphibians once did sport a functional third eye atop the head. They've most vanished. Maybe they weren't gifted with Triclops's talent for making perception fit the one-to-one principle. Maybe the three-eyed beasts of our past failed Nature's test of intelligence, the price of which is not as a mild electric goose in the ass, but the demise of the species.

  Triclops wasn't dumber than Cyclops, I concluded. His normal eyes had let him do with extra visual perception what my knife had taken away from poor old Cyclops: normal visual field data which Triclops could use to impose minus signs in calculating the final behavioral outcome. Cyclops's 173 IQ points represented a more primitive response than Triclops's 117. Higher IQ wasn't smarter. It was just higher. To borrow a metaphor from Hemingway's Snows of Kilamanjaro Cyclops's lofty IQ was like

  "fat on the soul."

  I tried to make a quick interpolation from 273 to 117 to see just what kind of math Triclop's mind would have to mimic. I couldn't even come close to an answer with pencil and paper. Carl and I would eventually write that the Triclops had toned down his response, with "integrative precision."[9] His IQ had algebra in it--complex tensor algebra. Poor old Cyclops, reminiscent of Bitterman's hammering goldfish, had performed simple arithmetic.

  I reasoned that an "active-negative" component must be operative in the salamander's intelligence. What Triclops didn't do was as important as what he did. But manifested as non-response, indistinguishable from no reaction, hidden on a completely invisible hyperplane[10], the active-negative mode would, of course, go undetected in conventional paradigm, which is what light-shock was. An attempt to determine intelligence from IQ is like being in a fight with an opponent who has an invisible arm. You never know when a thunderbolt will come flying out of Kant's realm of noumena to lay you flat. No, I concluded, the conventional tests don't measure intelligence. They measure IQ.

  ***

  I also concluded that one-to-one is a valid principle and becomes useful providing we understand its epistemological nature. Like the active-negative mode, one-to-one is not simple arithmetic, but algebraic in character. And one-to-one is not an a priori principle of sensation-perception-learning. It is a by-product of intelligence. The mind imposes one-to-one, not the other way around. It is an effect not a cause, a consequence, not an antecedent.

  I spent the next few days translating the main argument into scientese,
drafted a manuscript and give it to Carl. He corrected my spelling, made a few minor changes and we shipped it off to Brain Research, which accepted it without changes, and published it in 1968. And Carl and I went on to other things.

  ***

  What did Triclops's two normal eyes do for him? I ponder the question, even today. But it was several years before even a clue surfaced. The main obstacle was the test itself, which, after Triclops and Cyclops, looked to me like the sure route to dysinformation. But then I found a vision-dependent response that reopened the whole issue. As with the Looking-up reaction, the discovery was an outcome of making do.

  I had some students working in the lab and we happened to have a larger number of larvae than of glass finger bowls. As a substitute, I bought polystyrene Dixie cups, which were inert and, by the gross, cost less than a half cent a piece. (I still owe my wife for them.) The cups were a brilliant bride's white. Against this background, the normal animals blanched to a very bright coloration, which they maintained, I found, even when the illumination was drastically curtailed (to moonlight levels). Transferred to a black pan, the normal animals darken until you can hardly find them; in clear cups or bowls, they assume a tawny color. In marked contrast, eyeless animals when illuminated assumed dark coloration in recepticles of any color, including the white cups.

  Over the years, I'd become vaguely aware of the larva's ability to alter skin coloration, and I knew there was a literature on what is their camouflage reactions (the technical term is metachrosis) out in the wilds. It isn't anything like the chameleon, not dramatic or quick, and is not rwith the animals in clear crystal. But in the white cups, the reactions were conspicuous and they caught my immediate attention.