Prediction vs Determinism

Dennis Hackethal has a post called “Two Guesses About Creativity” which started out with the following lines:

The problem, in a nutshell, is this: creativity is unpredictable in principle. Computer programs, on the other hand, are completely predictable.

The first part of this comes from Karl Popper who points out that creativity is, by theory, unpredictable. Popper used the example of the invention of a wheel.

Imagine a caveman saying “I predict that in 10 years we’ll invent the wheel.”

Another caveman asks “What’s a wheel?”

The first caveman responds “it’s this circular shaped object that lets you roll things.”

But wait! He didn’t merely predict the wheel, he just invented it! Creativity is therefore, by definition, unpredictable. This simply follows from Popper’s theory.

But prediction is not the same as determinism. Deterministic functions are not, for the most part, predictable. The laws of physics (whether or not we’re talking about GR or QM) are both fully deterministic (for QM across the multiverse) yet they are not predictable. Stephen Wolfram explains why this is. It’s because the only way to determine the outcome of most deterministic computations is to actually perform them. This is the sense in which deterministic functions can be said to be unpredictable.

There are a few computations — very few — where there is a short cut available making prediction possible via the short cut. This is true for, say, predicting the position of the planets. But most deterministic functions have no such shortcut and thus can’t be predicted despite being entirely deterministic.

So in fact there is no contradiction here because creativity can be both deterministic and also unpredictable — as are most deterministic functions. Therefore Dennis’ formation is incorrect in the following way:

Creativity is unpredictable in principle. (True)

Computer programs, on the other hand, are completely predictable. (False)

Thatchapol pointed out to Dennis that if computer programs were predictable (as Dennis originally formulated it) then the halting problem would be solvable, but that isn’t the case. When Thatchapol pointed this out to Dennis, he then changed his formulation to be the following:

The problem, in a nutshell, is this: creativity is not predetermined. Computer programs, on the other hand, are completely deterministic.

Presumably when Dennis says “predetermined” he means merely “determined.” If this isn’t what he meant, then I don’t know what he meant and he’ll need to explain better how ‘predetermined’ differs from ‘determined.’ So I’m reading Dennis like this:

The problem, in a nutshell, is this: creativity is not deterministic. Computer programs, on the other hand, are completely deterministic.

But now we have a new problem, namely that it does not follow from Popper’s theory that creativity is not deterministic. So we replaced one false and one true statement with the following:

Creativity is not determined. (Does not follow from theory, and we have no reason to believe it to be true yet.)

Computer programs, on the other hand, are completely deterministic. (True)

So this formulation won’t work either because it’s simply a statement that doesn’t follow from a currently known good explanation. We have no more reason to assume it is correct then any of an infinite number of possible assertions that happen to not follow from any currently known good explanation. Dennis might as well have asserted “Creativity is a computation that can’t be run on a Turing machine.” And in fact, he’s tacitly saying exactly that whether he realizes it or not.

My challenge to Dennis is to try to reformulate the problem using only assertions that follow from a currently known good explanation. I do not believe it is possible to do so. Or in other words, I believe there is no problem here because I believe the correct formulation is this:

Creativity is a computation that can be modeled on a deterministic turning machine but is also unpredictable.

Computer programs, are completely deterministic because they can all be modeled on a deterministic Turing machine.

But now there is no contradiction at all! So I see no problem in the first place.

Bonus: How to Test My Theory

Dennis can refute my claim by coming up with a formulation that contains the same dilemma he originally intended but contains only statements that follow from currently known good explanations. That is to say, my challenge to Dennis is testable and can in principle be falsified by him (or anyone) by simply reformulating the same problem in a way that uses only statements that follow from good theories. If no one is able to do this, then my view has survived all attempts at criticism and becomes the sole surviving theory. Until someone comes up with such a formulation, this is now the best explanation we have available to us, namely that creativity is a computation that can be computed on a Turing machine and is thus deterministic and there is no contradiction in that.

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