Stephen P. King (stephenk1@home.com)
Thu, 15 Apr 1999 13:07:37 -0400
Hitoshi,
Some brief remarks :)
Hitoshi Kitada wrote:
>
> Dear Ben,
>
> Just a miscellaneous remark on the parallel between math and Big Bang
> theory... (I hope to understand your paper, but the notion of boundary you
> mention in the paper is difficult for me to understand...)
I too am very intrigued by this, since, for one thing, the definition
of a boundary is a key component of GR - "the boundary of a boundary is
zero" ... ;)
snip
> During lecturing to freshmen about real numbers as Dedekind's cuts today, I
> noticed that mathematics itself starts with nothingness as in your treatment
> of "Standard Model." I.e. in the Peano type construction of natural numbers,
> we assume 0 (zero) is defined as an empty set, and define 1 as {0}, 2 as
> {0,1}, 3 as {0,1,2}, ..., for example. Of course this may be natural because
> you are treating numbers: quaternions, octonions, ... . What I felt
> interesting is that this seems the same spirit as Big Bang theory which starts
> with nothingness in "constructing" the universe. I suspect that here seems to
> be a modern "constructionism" spirit that began in the 19 century along with
> Peano, Frege, Gentzen, Cantor, Hilbert, Zermelo, etc. in mathematics.
>
> If Big Bang can be thought as one of those streams, is it not possible to say
> Big Bang is one of the fashions of the modern age after the 19 century?
>
> Best wishes,
> Hitoshi
The construction of the Reals from the empty set {0} -> {{0}, {0,{0}},
... in traditional mathematical thinking seems to tacitly assume that
such does not require the expenditure of free-energy or, equivalently,
the creation of entropy. It is this assumption that I call into
question! The tacit assuption of a Big Bang similarly assumes that mere
"vacuum fluctuations" can give rise to a non-trivial construction having
a non-zero duration, e.g. having a finite temporal duration. We can
posit the existence of such within an "ensemble of vacuum fluctuations",
but in order to show necessity, we need to show that *any* duration is
possible. The study of the thermodynamics of the ensemble of such finite
Big Bang universes would have to prove that some non-trivial subset of
them has non-invertible dynamics and that such are capable of acting as
computational systems in that they can bisimulate the construction
process itself in some finite way (cf. [time 125]). Thus we can affirm
that it is possible for subsets of U to be considered as observers
having individual subjective experiences.
BTW, the non-Hausdorf property is obvious in this latter remark since
the possibility of communication of observer's subjective experiences
implies that their sets of observables is not completely disjoint!(cf.
[Time 64])
This "nothingness" is not necessarily an ontological *nothing*! It is
merely the totality Universe U in-itself or a proper subset thereof,
since, prior to partitionaing into finite LSs, it has all possible
properties in a pure state superposition, and as such has the properties
of pure white noise, e.g. "everything at once".
The injection of naive realism into physics, I believe, is the cause of
the tacit assumption that the universe of common experience has, like
the human observer, a finite duration... Thus it well could be that the
Big Bang model is merely a "fashion" ... ;)
Onward to the Unknown,
Stephen
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