I tried to expand on that a little in my last two posts (to Stephen) on
this thread, which somehow got disconnected.  Here it is again:


I wrote the following before you wrote this post, but I think it
addresses it somewhat.

My two cents is again to say that mathematics is about invariance.
Platonia is about invariance.  Invariance is even more fundamental than

number.  Numbers are defined by invariance.  The number 3 is the
invariant attribute of all sets of 3.
I take it that Bruno's existence is just the "interference pattern" of
computations, as I think he sometimes puts it.  According to him, I
think the ether that we swim in (exist in) is computations, an ether of

consistency.  John Barrow in his book "Pi in the Sky" brought up
the possibility that we are part of Platonia, but he concluded that
this didn't make sense.  My opinion is that it doesn't make sense
if Platonia is only numbers, i.e. computation.  This is for the very
reason you bring up, Stephen.  An interference pattern requires a
particular point of view.  But if all points of view are equally
unspecial (modulo consistency), then we are back to the "why
something instead of nothing?" problem ("why this particular point
of view that I am experiencing, rather than another point of view?").
 Something has to break the symmetry of the zero information pool.
"Interference patterns" are not sufficient to break the symmetry.
(Along the same line of reasoning, even an anthropic principle is not
sufficient.)  Summing the interference patterns over all points-of-view

results in zero.  I've taken my answer to this from somewhere outside
myself.  There has to be someone with universal power to say "Let
there be...".

Then we, who are in his image, can recognize that "There is...".  The
purest form of this recognition, I believe, is mathematics.  Of course
I'm a mathematician, so I'm biased.  :)


Stathis Papaioannou wrote:
> Tom Caylor writes:
> > I've been thinking about Platonia lately.  I've just finished reading> John 
> > Barrow's "Pi in the Sky" book, and he seems to have gotten wrapped> around 
> > the axle in regard to mathematics and Platonia.  I think that> mathematics 
> > is not primarily about numbers.  Mathematics is about> invariance.  
> > Invariance is not about any *thing* (existence)> specifically.  Perhaps 
> > this thought can shed light on this somehow?
> What do you mean, "mathematics is about invariance"?
> Stathis Papaioannou

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