At least in the
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? 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
> Time has to begin to travel backwards as things reorganize,
> in which case the final collapse should be a reflection of the initial
> 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.
> "Forever is a long time, especially near the end." -Woody Allen
> ----- Receiving the following content -----
> *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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