On 25 Dec 2012, at 19:35, Brian Tenneson wrote:

At least in the video (skip to 43:14), Tegmark estimates that our doppelgangers are 2^10^118 meters away which probably puts it past the range of direct testing and, consequently, makes it not falsifiable.

Regarding (4), I think the disparity between you and Tegmark can be explained by having different definitions of universe and multiverse. Of course, if you have a metauniverse, then you'd have a metametauniverse, ad infinitum. There is only one "totality of all that exists" and I bet that if you were to explain what you mean by the One to him, he would agree that there is only one One. When he uses an aphorism like "multiverse" he may as well be saying "poly mega galaxy cluster" or some such. In other words I don't think Tegmark believes in multiple Ones.

In his mathematical universe paper and ultimate ensemble paper, he posits that there is only one type of existence which would simplify things (a la Occam's razor). Instead of there being mathematical and physical existence, there is an identification between the two so they are seen to be one in the same. This merges the spaces "mathematical objects" with "physical objects". He argues this in those papers (though to me sometimes it seems to be merely a plausibility argument).

Now if ME=PE, then one natural question is which mathematical structure is "the totality of all that exists" isomorphic to? In other words, what is the One?


With comp, any first order logical specification of a Turing universal system will do.

Now if we start from a system having physicalist attribute (like the plane of GOL, for example, or like String Theory), we introduce a pedagogical difficulty in the derivation of the physical laws, and we make harder taking account the difference between the 3p and the 1p, or the quanta and the qualia.





What is the universe? Or to abuse language a bit, what is the multiverse? This is a question that I've been thinking about for a while now and I'm really not sure. The current idea is to take the category of all mathematical structures C (which is large, unfortunately), and embed that into a category of functors defined on that category (a la Yoneda's lemma), in such a way that every mathematical structure is embedded within that category of functors (called a "cocompletion" of C), a sort of "presheaf" category.


Why not take the categories of all categories (besides that Lawyere tried that without to much success, except rediscovering Grothendieck topoi).

But if you assume comp, elementary arithmetic is enough, and it is better to keep the infinities and categories into the universal machine's mind tools.



To have a single mathematical object that all mathematical structures can be embedded would give us an object that, in a sense, contains all structures. If one follows Tegmark's idea that ME=PE, then a definition for universe just might be a mathematical object (which by ME=PE is a physical object) that contains, in a sense, all mathematical objects (i.e., all physical objects).

I think that this is deeply flawed. We cannot identify the physical and the mathematical. We might try theory on the physical, or on the mental, or on the mathematical, which might suggest relation between those thing, but I doubt any non trivial theory would identify them, unless enlarging the sense of the words like mental, physical.

With computationalism, the coupling consciousness/physical is a phenomenon, person perceptible through numbers relations when they (the persons) bet on their relative self-consistency. This explains the appearance of the physical, without going out of the arithmetical. It works thanks to Church thesis and the closure of the comp everything (UD*, sigma_1 completeness).



It's not super clear to me that the cocompletion of the category of all structures C exists though since C is not a small category and thus Yoneda's lemma doesn't apply. I would have to fine-tune the argument to work in the case of the category C I have in mind.

The n-categories might be interesting, but we don't need so rich ontology. If we are machine, the cardinality of the basic TOE is absolutely undecidable from inside. Omega is enough.



If the cocompletion of C is the One, that which all mathematical structures can be embedded, then the parallel universe question would be a matter of logic and category theory; it would depend on how you defined "the visible universe" and "parallel" universe.

You will have to define an observer, its points of view, and to take into account its many distributions in that super-mathematical structure, but you can't do that, as you will need an even bigger structure to define and study the indeterminacy. So you will have to limit your notion of observer and use some "comp" hypothesis (an infinite variant if you want).

With comp, it is easier: you cannot really take more than arithmetic. God created the Natural Numbers, all the rest belong to the (singular and collective) number's imagination. If nature refutes this, it will still remain time to add the infinities needed. I think.

Bruno









On Tuesday, December 25, 2012 6:34:45 AM UTC-8, rclough wrote:
Hi Brian Tenneson

Tegmark has many many good ideas, but I am not a believer in multiverses,
which only a strict mechanistic 19th century type can believe.

Multiverses defy reason. Just off the top of head:

1) For one reason because of Occam's razor: it is a needless complication,
and the universe (or its Creator) does not do needless things,
because IMHO the universe is purposeful.

2) "Purposeful" meaning that Aristotle's end causes are needed for a
final collapse, as they are for life, which is not mechanistic.

3) As in life/mind/consciousness/intelligence, which are also purposeful.

4) In order for there to be multiple universes, there would
have to be multiple platonic Ones. But there can only be one One.

5) Multiverses are mechanistic and so in spacetime, but consciouss life
and all that other good stuff are outside of spacetime.  Would the
minds of multiverses be mashed together ?  And all particular lifes
would have to terminate at the same time.

6) There is no non-Boltzmann physics which is required for a final collapse.
Time has to begin to travel backwards as things reorganize,
in which case the final collapse should be a reflection of the initial creation.
That would be cool.

7) But each universes being differemnt, they would not be expected to
all terminate at the same time.

8) One might conjecture also that the presence of life, consciousness and
intelligence (which are all individual, personal, subjective) are not
mechanical and so cannot be part of a multiverse. It's each man
for himself.  Along these lines, because of natural selection and
different worlds not being all the same, evolution would not occur
in parallel.

9) Besides, there are alternate possibilities for a quantum wave collapse.

10) In a related matter, one of the multiverse sites cited William James
as a proponent. Because of his pragmatism, his multiverses arise
because there is no fixed general in pragmatism for each particular.
There are as many generals (additional universes) as you can think of.
These obviously would not be parallel.

[Roger Clough], [rcl...@verizon.net]
12/25/2012
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content -----
From: Brian Tenneson
Receiver: everything-list
Time: 2012-12-24, 13:11:46
Subject: Re: Fw: the world as mathematical. was pythagoras right after all ?

What do you think of Tegmark's version of a mathematical Platoia?

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