From: Lee Corbin (lcorbin@tsoft.com)
Date: Tue Feb 11 2003 - 00:06:48 MST
Last week I was thinking about a quote of Giordano Bruno
whose vision of space was homogeneous, infinite, and
populated by infintely many worlds:
There is a single general space, a single vast immensity which
we may freely call Void: in it are innumerable globes like this
one on which we live and grow; this space declare to be infinite,
since neither reason, convenience, sense-perception nor nature
assign to it a limit.
This is quite wonderful. I think that he is the first person
to announce the complete end of anthropocentrism (in the sense
of there being nothing so special about us or Earth in the
whole cosmos).
As I mentioned earlier, over the last decades it had gradually
dawned on me that despite all the interesting topologies one
hears about for our universe, no one had quite proclaimed that
the whole thing was finite.
Yesterday I did a little calculation: say that there are 10^51
atoms in the Earth, and suppose that morphologically there is
one Earth per galaxy. Then we have, going in a straight line
from here about one Earth every two million light years.
But of course, all those Earth-like planets up to geological
similarity cannot be expected to have people. To complete
Bruno's vision I supposed that any configuration of the 10^51
atoms to be equally probably (and an extremely conservative
bound). There would be about 10^51! (that is, 10^51 factorial)
such configurations. This is fewer than 10^51^51, which is
less than 10^10^53, a number that is so vast that if you
multiply it by a million light-years, you don't change its
value. Thus, amazingly enough (or so I thought), one must
encounter a world exactly like this one in any direction
you go, if you go about 10^10^53 light years.
But Amara suggests
> Astrophysics, abstract
> astro-ph/0302131
> http://it.arXiv.org/abs/astro-ph/0302131
> From: Max Tegmark <max@hep.upenn.edu>
> Date: Fri, 7 Feb 2003 01:39:52 GMT
a new Tegmark essay. Almost in the very first paragraph Tegmark
announces that you will almost surely find an Earth exactly like
this one only 10^10^29 meters from here! A fantastically nice
reduction of my crude estimate. (And, as any mega-mathematician
will tell you, whether you use meters or light-years when dealing
with this kind of magnitude is entirely immaterial.)
Now (unless you were a cryonicist or other immortalist), would
you get at all excited to learn that there was an Earth almost
exactly like this one only 200 ly distant?
You would? Why? What's the practical difference between 200ly
and 10^10^53ly? An erudite off-list correspondent emphasized to
me in an email exchange that anything further away than 10^15
ly is beyond our event horizon, so we can't ever learn anything
about worlds 10^10^53 light years away, and so who cares? Well,
I do. It feels warm and comfy to know that only 10^10^53 ly
away another one of me is pounding out this same email. Gives
me a sense of real community.
Lee
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