If there is a "TOE," I would expect it to be pretty lengthy and complicated. The "TOE" would basically be a conjunction of all answers to all questions.
But can this even be done in human terms? Wouldn't there be infinitely many questions (e.g., what is 1+1, what is 1+2, what is 1+3)? That would mean that "TOE" is infinite in length. So then the question becomes can this infinite set of answers can be abridged into a finite, yet equivalent, document? And finally, can we find a particular document with all the answers and be able to prove that is the most succinct those answers could possibly be? (IOW, can we find the shortest document that contain all answers to all questions?) Well the subject of questions and answers related to all this is given here: http://arxiv.org/abs/0708.1362 That which answers questions is called an inference device. It appears that there might be some interesting results concerning strong inference devices. It would vastly simplify things if something is considered an answer only if that answer has a finite proof. Then the question would become "how many finite proofs are there?" There are infinitely many different finitely long proofs. That leads me to the conclusion that "TOE" is not expressible in a finite document. However, if there are finitely many "categories of proofs" then the document would just be a summary of the categories of proofs which would make the "TOE" document finite. Two proofs are in the same category if their conclusions are equivalent and not in the same category if their conclusions are not equivalent, meaning that they are not merely restatements of one another. Thus, there are finitely many categories of proof if and only if "TOE" is a finite document. There being finitely many categories of proof implies that "TOE" is a finite document. There being infinitely many categories implies that "TOE" is an infinite document. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
