Saturday, December 8, 2012

Computers vs. human higher thought

The mind-body problem and Piaget on

correspondence vs. interdependence

We can use Jean Piaget's distinction between correspondence and interdependence to help make better sense of the mind-body problem. My soul and my physical body (to use old-fashioned language) form a two-layer system. My conscious thoughts form a layer of reality which is in correspondence with, but is not interdependent with, its biochemical substrate.

That is every time a thought in my mind changes, there will be a corresponding change in the minute electrical impulses and tiny biochemical balances in my brain cells and their interconnections. But one cannot mechanically deduce all of our higher human thought structures simply by detailing all the causal connections between the electrical and biochemical changes which occur as part of that process.

Let me give a simple example to illustrate this point. Douglas Hofstadter, the computer scientist at Indiana University's Bloomington campus, has recently published a book called I Am a Strange Loop, in which he describes a simple computer setup for determining whether a given integer is a prime number. I am going to modify his story a little bit, but I want to give credit to him for posing the issue in this interesting fashion.

When I was in high school, I won a minor prize at a science fair with a small computer which I built, using mechanical electromagnetic relays salvaged from old pinball machines. Each relay consisted of a steel lever which would be pulled down to close a circuit if an electrical impulse traveled through an electromagnet made of coiled wire. A mechanical catch then held the lever down, so that the current continued to flow through the wire attached to it, even after the original electrical impulse was no longer being applied. But there was a second electromagnet which would, if an electrical impulse passed through it, pull the catch back so that the lever would flip up, at which point the relay would no longer be sending current down a wire to the next relay. So the relay basically consisted of an on-off switch, which would transmit a continuous electrical current if one magnet was activated even momentarily, but would turn that current off again if the other magnet was activated even for just a second or so.

Although the computer I built was designed to solve a different kind of problem (it was designed to carry out the basic computations involved in solving syllogisms in elementary Aristotelian logic), it could easily have been rebuilt to solve Hofstadter's prime number problem. It could have been set up so that when a number like 19 was entered, it would first divide the number by 2 to see if there was remainder. And in this case, 19 divided by 2 would give us 9 plus a remainder. The computer would then work its way down stepwise from 9, dividing 19 next by 8, then 7, then 6, and so on, all the way down to 3, checking each time to see whether there was a remainder, or whether 19 was evenly divisible by one of those numbers. By salvaging a few more parts from old pinball machines, the computer could have been constructed so that a red light would start blinking the first time the number which was input was evenly divisible by some smaller number (indicating that the number was not a prime number) and that a bell would start ringing if the process carried through to completion with no even divisor being found (which meant that we had successfully found a prime number).

No matter what number we entered -- a prime number like 17, 19, or 23, or a non-prime number like 18, 20, 21, or 22 -- we could "explain" what happened by simply describing the way in which each electromagnetic relay was activated by its predecessor in the series, and then transmitted an impulse to its successor in the series. But would that in fact be a real explanation? No matter how the relays were connected to one another, one could "explain" which relays were triggered (or de-triggered) and how by this kind of explanation, but one would come nowhere near explaining what the idea of a prime number meant. The most important thing going on would be left totally unexplained by this kind of analysis.

The fundamental idea of what a prime number is, and the way we would have to structure our ideas and thought in order to determine whether a given number was a prime number, were in correspondence with but NOT interdependent with the clicking and clacking of the mechanical electromagnetic relays as they opened and closed.

Taken from Glenn F. Chesnut, God and Spirituality: Philosophical Essays, Hindsfoot Foundation Series on Spirituality and Theology (Bloomington, Indiana: iUniverse, 2010), Chapter 21, "Self-Transcendence," pp. 418-420. The entire chapter can be read online at . For more on the book, and to read other chapters, see .

Douglas Hofstadter, I Am a Strange Loop (New York: Basic Books, 2007).

For an excellent explanation of Jean Piaget's distinction between correspondence and interdependence, see John H. Flavell, The Developmental Psychology of Jean Piaget (Princeton, New Jersey: D. Van Nostrand, 1963).

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