Nello Cristianini:  

A Kind of Anthropic Principle


An old epistemological problem, at the basis of induction theory, is: why do we live in a learnable world? Of the many theoretically imaginable environments, very few would have this property, the inherent regularity that makes them learnable and hence predictable.

John Barrow formulated the question in this way: why is the world mathematical?

"The surprising fact that the world is cognizable tells a lot, not only about our capacities, but also about our universe. (...) Given the limitless variety of ways in which matter and energy can arrange themselves, almost all of which would be `random`, the fact that the physical world is a coherent collection of mutually tolerant, quasi stable entities is surely a key scientific fact in need of explanation. (...). We could also describe it by saying: why is the world algorithmically compressible? (...) The fact that there is Cosmos rather than Chaos is the starting point of science" (Davies, 1990).

So on one side we see that it is improbable to find a regular world, and on the other side - by being able to learn or do science - we verify that our world is regular.

One way to look at it is to invoke a kind of anthropic principle. Let's observe that the structure of an organism embodies knowledge about the environment which it is adapted to. In is possible to regard evolution as a learning process. This process is subject to the same rules indicated by Popper for the growth of scientific knowledge: casual conjectures (mutations) and successive refutations (extinction). (This isomorphism between evolution and acquisition of scientific knowledge is at the basis of Popper's "Evolutionary Epistemology".)

Not only life and cognition have this somehow similar aspect. They also have the same prerequisites. They both require a certain kind of universe, very peculiar, to be possible. This leads to the following situation, akin to an anthropic principle: it is possible to make science (and epistemological questions) only in the few worlds satisfying the minimum requisites for life. And among them, we have seen, there is predictability.

Nobody could wonder that his world is not learnable: in that world, as a matter of fact, there could be nobody!

6 July 2000

[more detailed argument]