At 6:09 PM +0100 3/28/02, Juergen Schmidhuber wrote:
>Predictive power is measurable by standard concepts of probability theory
>and complexity theory.
> You may choose to ignore this, but don't include
>all those who don't among "the rest of us".
>Write down all assumptions, derive the consequences, and observe that
>the AP _by itself_ cannot predict anything nontrivial.
If your point is that it cannot predict anything _by itself_ then I
agree. There is always background information, and one is required
(as you say) to make use of whatever background information you may
>Fortunately Hoyle was more careful than some who cite him - he just
>wrote: "the results...were obtained subject to certain assumptions
>...have not been demonstrated in a manner free from all doubt.
>Nevertheless, the number of assumptions made was much less
>than the number of results obtained."
>Thus he informally invoked Occam's razor: find short descriptions that
>explain a lot. Occam's razor is not the AP. It is formally treated by
>the theory of inductive inference. Although this theory is at the heart
>of what physicists are doing, some of them are not yet fully aware of
Ockham's razor is a consequence of probability theory, if you look at
things from a Bayesian POV, as I do.
I regard Hoyle's prediction as a genuine prediction of the
AP+background information that Hoyle had. Do you disagree with that?
I've put you back on my reading list, and I apologize to you for