Hi Brian,
I was wondering if you could connect (in the paper) the maths with our 
universe? As an example. What set operations or structures correspond to 
the standard particle model entities, what constitutes a chemical 
reaction or energy, what space is made of... that kind of thing. Maybe 
this is supposed to be obvious... if it is then sorry... but you've lost 
(as an audience) the entire world above mathematical 
physics...especially biofolks.

I am a quintessentially visual/spatial thinker.. math does not speak 
very well to me unless I can 'see' the operations happening. in my mind. 
I don;t manipulate symbols. I manipulate 'stuff' and then retrofit symbols.

I would also like to see how an observer with qualia might be 
constructed of it. In other words...how a universe thus constructed 
might create its own scientist describing it in the way you do....Having 
looked at the paper I hold some hope that it might contain a formalism I 
can use to construct the set theoretic basis of my own model... it might 
be within yours....maybe... not sure.


Brian Tenneson wrote:
> 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.
> >

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