I've complained before about belief in actual infinity as opposed to it being a convenient fiction
that helps us fit our models to reality. The phrase "infinity is infinity" triggered that
homunculus again. Sorry. Infinity is definitely *not* infinity. I guess the simplest way to evoke this
inequivalence is with the reliable old snark "1/∞ ≠ 0. 1/∞ is undefined." Those of you more
math inclined might even rely on the inequivalence of different infinities (e.g. ℵ₁>ℵ₀). But I
don't think that's necessary, here. Another more pedestrian analogy might be the dissimilarities
between household budgets and that of a nation with its own currency. Something like quantitative
easing is simply outside the universe of discourse for households.
I feel this way about space vs time tradeoffs. As much as I enjoy making the parallelism argument (that any time
efficient computaition can be perfectly simulated with a space-efficient computation), when I'm trying to show
good faith, I have to laden it with caveat. And if time really isn't just another spatial dimension, then can
infinite time really be similar to infinite space without squinting? And is there really any way to unify
infinite expanse with infinite density? That seems akin to the claim that 1/∞ = 0 … and hearkening back to the
discussion of consequence operators, "=" ≠ "→". But maybe we can say something like 1/∞ ←→
0? (Aka 1/∞ →₊ 0⁺ ⋀ -1/∞ →₋ 0¯. IDK, though. I don't think approaches from below is really the inverse of
approaches from above. Expansion and contraction just don't seem reversible to me. And is 0⁺ = 0¯, anyway? 0 is
an annihilator, right? Does that mean 0⁺ only annihilates >0 and vice versa? Surely those who think about
things like "white holes" have handled all this, right?)
<story>
A plugin for a discussion platform I'm testing doesn't handle time[zone] well.
If I post a poll and tell it to automatically close the poll at some time (in
PST or UTC). When I mentioned this to one of the participants, he assumed we
had all pretty much decided to always rely on atomic time. UTC includes both
atomic time and solar time, including the leap intervals. That time is socially
constructed in this way further reinforces that time is not time, vapid as that
point may be in the context of the limits of inference from astronomy.
</story>
On 12/28/22 09:30, David Eric Smith wrote:
Citing back to Owen:
Gil is right. The universe could be infinite, and it is at the least big
enough that we have no positive evidence so far that it isn’t infinite.
If it were infinitely large, but only finitely old, then at any given place,
the only photons that could yet have sped past us would be those from a
distance away that is less than the age divided by c. But there would always
be someplace enough further out that you are only now seeing it. Cue lyrics to
“The way we were”, of course....
There is a thing I never learned to understand about cosmological models, which
is how they reconcile finite age with infinite size. Presumably infinity is
infinity, and if your solution is always infinitely extended (flat or negative
spatial curvature), then even if you go back to a Big Bang of infinite density
in the finite past, that infinite density is still infinitely extended. If
there were positive spatial curvature and the universe were closed, one could
just work in the finite-but-large.
(btw, of course, inflation doesn’t solve this; it just changes rates of various
expansions in various eras.)
I guess cosmologists don’t worry about this, because they know there are enough
phase transitions going on in the vacuum going back toward the beginning, that
even if you appear to be negatively curved and open now, the current story may
not extend all the way back.
Another thing that is fun to think about but that I don’t feel comfortable as
having really internalized, is that old parts of the universe are like old
cowboys: they never seem to be traveling away from you at faster than c; they
just fade away in redshift to black. So things can be totally unreachable at
some finite time, yet never seem to have exceeded a finite speed limit to do it.
Eric
On Dec 28, 2022, at 10:56 AM, Gillian Densmore <[email protected]
<mailto:[email protected]>> wrote:
(using a bad analogy) and those photons record what's going on like a on going
WEBB stream? so we now have essentially the ability to see old streams (as it
were) from photons any anything else that can get a snippet of that. and
basically light does take time to show up. it's not exactly instant on the
galatic scale (see also: Relativity). and so by the time WEBB or any other
other telescopes s mirrors cameras and blah blah blah send that to our eyes
those photons are now old reeely old. And the grand expansion is fast enough
to go faster then light? or is it because the universe is stupendously big. so
it takes a while to get to where we can snag some photons?
On Wed, Dec 28, 2022 at 10:49 AM Frank Wimberly <[email protected]
<mailto:[email protected]>> wrote:
My guess: stars, including the Sun, are constantly producing and emitting
new photons. This happens as a result of fusion and other processes.
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
On Wed, Dec 28, 2022, 9:21 AM Owen Densmore <[email protected]
<mailto:[email protected]>> wrote:
In aj NYTimes article:
https://www.nytimes.com/2022/12/27/science/astronomy-webb-telescope.html
<https://www.nytimes.com/2022/12/27/science/astronomy-webb-telescope.html>
..there is the usual discussion on "seeing back to the first several
millennia".
But, and be kind, why haven't these photons already sped past us? I
suppose it is because the exanssion is uniformly everywhere, we just kept ahead
of them? That seems unlikely given the expansion is slower than light.
--
ꙮ Mɥǝu ǝlǝdɥɐuʇs ɟᴉƃɥʇ' ʇɥǝ ƃɹɐss snɟɟǝɹs˙ ꙮ
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