At 6:09 PM +0100 3/28/02, Juergen Schmidhuber wrote: > >Predictive power is measurable by standard concepts of probability theory >and complexity theory.
Agreed. > 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 have. >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 >it. 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 getting annoyed. Bill
