Shufflebrain

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 Cyclops 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.