Tuesday, December 20, 2005

The Uncarved Block

Taoists speak of the ``uncarved block'' that contains within itself all of the forms into which it can be carved, which somehow reminds me of Michelangelo's claim that he saw the figure in an uncarved block of marble and carved away at it until the figure was set free.

I have recently realized that a general purpose digital computer is like the uncarved block, for such a computer contains within itself everything that can be computed, just waiting, as it were, to be set free by the appropriate computer program.

If that realization is too romantic for your taste, then here is another way of formulating the same idea: Each general purpose digital computer contains the answer to every answerable mathematical question.

Now I suspect that most people reading this who are not familiar with the internal workings of computers, and some who are, will consider these claims to be ridiculous.

On the other hand, computer scientists, almost universally, accept the truth of the Church-Turing thesis that:

any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available.
Wikipedia, Church-Turing Thesis

The ``algorithm'' here is a set of instructions telling the computer what to do. In other words, it is what we know more informally as a ``computer program.'' I should also note that a human computer, given paper and pencils enough and time, can also carry out---at least in theory---instructions to calculate anything that that can be calculated.

This matter is not only of philosophical, or mathematical, interest; it also, I submit, goes a long way toward explaining why the Supreme Court of the United States in Gottschalk v. Benson 409 U.S. 63 (1972) held that algorithms---instructions to a computer setting out a process for solving a mathematical problem---are not patentable, even though processes in general are, provided that they are useful, novel, and not obvious.

As I see it, algorithms correspond to questions such as: ``what is two and two?'' and questions are not patentable. The answer to the question---the solution to the mathematical problem---, on the other hand, is not novel and is in a very meaningful sense obvious, for all one has to do is ask a computer---instruct a computer---to answer the question and, if the question is answerable, the computer will answer it.

For those who are not that familiar with the workings of a computer, try asking Google ``What is pi times e times i squared?''---a question that conceivably is novel.

Google will reply ``pi times e times (i squared) = -8.53973422'' which is---approximately---true. That answer is not novel. It is a fact. It is something that is universally true. And universal truths are not patentable. The answer is, and always has been, lurking inside the computer---or computers---we call Google---and inside all other computers---the way that the image of Michelangelo's Pieta was once lurking unseen inside an uncarved block of stone.


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