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.
But this is in the "many worlds" of one world being infinite and
sufficiently homegenous. It is not the Everett, nor the comp
Doppelgangers.
Also, it is not clear why would this be not testable, as we can test
first person indeterminacies on such "Garden of Eden" configuration,
and compare with the observation.
May be *that* can win the 1p-(plural)- measure battle, but I guess
this is today just speculation.
I don't think Tegmark takes the 1p indeterminacy into account, except
in the quantum wave, but not on math in general or in arithmetic.
Bruno
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? 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. 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). 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.
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.
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], [[email protected]]
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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