An open problem raised in Tegmark's "ensemble TOE" paper (published in '98, if I recall) is to answer the question that is the subject of this thread.
I believe recent work I have done has the potential to be a step towards that answer. First, a link to the very rough draft (please forgive formatting errors), and second what I think the deficiency is with this document: http://www.universalsight.org/math/9-26-08/01-03-structure_of_all_structures.pdf Abstract: In this document, the author presents a structure with the property that all structures are elementarily embeddable within it. One essen- tial tool is a version of New Foundations set theory, ?first developed by Quine, as presented by Holmes in [1]. The motivation is given by The Mathematical Universe article by Max Tegmark, [2], in which it is hypothesized that physical existence is mathematical existence and, consequently, it is hypothesized that the structure with the aforementioned property could be central in the Math- ematical Universe Hypothesis as being at least keenly connected to the literal universe, if not literally being the universe. The author assumes some knowledge of mathematical logic such as, for ex- ample, the inductive de?finition of a fi?rst-order well-formed formula. The intended audience is primarily Max Tegmark, honestly, but more generally, any physicist interested in Tegmark's self-proclaimed "bananas articles" like the MUH paper, and who have already been exposed to the basics of mathematical logic. Prior to drafting this document, I contacted Prof. Tegmark regarding the core ideas in the draft. I described what I was attempting and if I recall I sent him the abstract. As I will describe shortly, this is incomplete, so I didn't send him this pdf yet. I hope he wouldn't mind my inclusion of his response, which I think many here might find highly debatable (and worthy of discussion), sent by email: <quote> It sounds to me from what you're saying that A would be the Level IV multiverse, i.e., all of physical reality. </quote> Now for the deficiency I see with my document. -If- there aren't any other errors, then something wrong with my ultimate structure is that it is the ultimate structure with respect to just one symbol set. I need a structure that is ultimate with respect to -all- symbol sets. The basic idea I had which I have not yet tried to formalize is encoding all symbol sets into an ultimate symbol set which in human mathematics is a countable set; so something like the set of natural numbers will encode all possible symbols. One simple way to do this would be to say all numbers congruent to 0 mod 3 are encodings of constant symbols, all numbers congruent to 1 mod 3 are encodings of n-ary relation symbols, and all numbers congruent to 2 mod 3 are encodings of n-ary function symbols. So, note that I did not finish what I set out to do in my abstract: "the author presents a structure with the property that all structures are elementarily embeddable within it." I believe what I have done is this: a structure over a fixed symbol set S with the property that all S-structures are elementarily embeddable within it. Now on to the subject of time. If Tegmark is correct and an ultimate structure literally is all of physical reality, what strikes me is that this ultimate structure appears quite static. What then is the source of our perceptions of transition, ie, time? This ultimate structure I presume (safely, I believe) is constant yet we perceive things to change. Why and how? IOW, what is the mechanism that converts the static ultimate structure into a fluid appearance of transition? These questions are still valid even if the ultimate structure I have in mind is wrong; Tegmark still hypothesizes that some math structure is all of physical reality. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
