So there’s a “reply” (or whatever) that I have had an impulse to post for two
weeks now, but had to forbid myself the frivolity of writing.
Also, having seen the recent posts, I think it is already resident in
everything Glen takes for granted as having settled from our years of
conversation on this list.
OTOH, I appear to be a strong believer in priming. On 12/27/22 I wrote the
tangent about the Edmundson critique of Rorty, and out of the many things that
could have been triggered by reference to Peirce, Glen replied with things
related to infinity and fixed points, which were actually what was on my mind
too.
Then, on 12/29/22 there was the exchange in response to Gil’s questions about
Big Bang, and infinity became the center of Glen’s and my back-and-forth,
though more as a feature of another discussion than as the main topic.
Then there was Nick on 01/07/23 and my rejoinder about sample estimators and
whatever central tendency they might converge to if they are unbiased.
That is my lead-in for making some things related to infinity the main point in
this post, and not merely features of some other application.
A thing that has been a sort of nuisance to me, on which I would like to have
an opinion, is a cloud around several of these topics. I listen to the
contemplatives talk about the way they actually understand “reality” and
everyone else is benighted, and I can’t tell if they actually understand
something or are fetishists for a certain form (this is not directed at DaveW,
but at a different collection of people). I don’t mean this antagonistically,
but just as a statement that if there is substance behind their language, I
have no ability to tell, or what it might be.
Then there is the cluster of questions about Truth a la Peirce, and various
questions about mathematical Platonism. Constructivism, and formalist vs.
intuitionist schools, where again I find myself having difficulty understanding
what it is they are willing to fight to the death about, when what I can see on
the outside is a bunch of conventional behaviors, at most, which seemingly one
could “feel” about quite many ways.
So, to boil it down to too-few tokens, here is what I try to content myself
with as an explanation.
1. A lot of this is about getting at the nature and characteristics of thought.
To say that, I do not accept being committed to either the
“philistine-the-world-is-out-there” camp or the dreamy
“world-is-contained-in-mind” camp. We haven’t said enough of anything definite
to have meant anything yet. I am still at the level of the crudest descriptive
empiricism, and _NO_ profundity.
2. Some things seem to be pretty tractable as literals, which we might call
“states of knowledge”. Finite counts of things, the numerical quantities of
sample estimators, nouns that are only used to point at things, in the sense of
directing attention, or whatever.
3. But we also have rules, and a lot of the rules can be applied recursively
without limit. We seem to need, as part of “the structure of thought”
(whatever that should mean), to treat those things we have constructed to be
unattainable as having been attained. Chuck Norris has counted to infinity.
Twice.
4. What shall we do with point 3? Well, we can’t attain them, so we will put
up placeholders to stand for a kind of poetic fiction of “attaining them” —
meant in the sense of Jerry Sussman’s aphorism that “math is poetry” — and then
propose finite syntactic constructions to manipulate the fixed points.
Frequently we want to define the syntax to manipulate the fixed points from
properties of the rules whose recursion the fixed points are supposed to fix.
But maybe we have to just invent, out of imagination, other properties we want
the fixed points to have, which are not constructible directly from the rules
and their recursions.
5. My claim to Nick is that these placeholders for the fixed points of rule
recursions are clearly understandable as filling a different mental or
cognitive role than the states of knowledge that we are aware correspond to
only finite orders of rule use.
6. The conjecture (by me) is that what we can see of our own thought structure
from ways of handling infinities is not a bad model, not only for “Truth” a la
Peirce, but also for tokens like “Reality”. I don’t generally imagine I have
any idea what someone else thinks he means when he talks “about reality” or
“about what is real”. But I am willing to cast an opinion about what he is
doing cognitively with such a term, which is treating a thing he has
constructed as unattainable, as if it had been attained.
7. Of course, there are differences. For sample estimators and underlying
properties, we don’t worry about “whether both of these, or only one of them,
exists”, since we are in a domain where the equivalent status of both as
existing (whatever status that is) is a starting point of the framing. Only
our access to their values differs between the two. When we get to “Truth” or
“Reality”, what we can probably say with some confidence is that we are using
them the way the mind needs to use certain tokens. But our need to use them no
longer follows from any good basis for thinking that the tokens do have
antecedents, the way we take it as a prior given that the number representing
the fairness of a coin has an antecedent in properties of the coin that we can
triangulate other ways. That procedure too, though, has an analogue within
sample estimation: if a sample estimator is biased but we don’t realize that,
the values can converge to something wrong, which only gets corrected by
correcting the estimator to something unbiased. None of the cognitive roles
have to be re-thought to add a role for debiasing.
8. Point 7 would be my antidote to naive pigeonholing of Point 1 above as
either “realist” or “idealist”, when both of those positions seem like
unresolved tokens to me. It seems enough to say that recognizing the role that
tokens like “Reality” have for us simply gives no starting point for saying
anything that isn’t tautological about the status of antecedents to them. To
do better than tautology, we would need other ways of triangulating that aren’t
simply embedded within the language of the “Reality” tokens we were trying to
better understand. In practice, we mostly talk about properties of sample
estimators, and judge what seems to be reproducible. It is very much like
Cosma’s paper that, since there is no such thing as Objective Bayesianism, the
modeler is always obligated to recognize the prior as just one more dimension
of the modeling frame, to be tested for its performance, just like the
likelihood.
9. If all my maundering above ever becomes interesting for anything, the place
I would look is people’s discomfort with quantum mechanics’s states. This is
the thing that came up in one of my tangential replies to DaveW’s post that
included an incidental comment on what QM is or isn’t a theory for. Sean
Carroll, who I am becoming quite impressed with as being solidly reliable, even
when he isn’t saying anything that invents outside what we already have
(already much better than the norm; a praise I also often give to Scott
Aaronson), has a short segment somewhere on why we should feel compelled by
anyone’s objections that some “interpretation” is needed of QM (we shouldn’t).
Sean’s position seems to be the same as mine: QM is what it is, what do you
find deficient? And here, I mean “what” as a request for real analysis of your
use of the tools and your response to that use. Since, if “Reality” as we got
used to it in classical mechanics was just a set of syntactic rules for
handling a placeholder (“syntactic” in the extremely extended sense, of all our
habits of perception and response), and since that rule-set was distilled
without the input of QM, why would we think it anything other than a project of
rebuilding, to find that in a QM-informed epistemology, we needed a different
set of habits for manipulating the various “Reality” tokens. By this I don’t
mean the deliberately snide “shut up and calculate”, which would be a Bohr-ish
admonition to just juggle the sample estimators and stay busy. It is meant to
acknowledge the role that such fixed points (as “Reality”) seem to play in our
cognition, at the same time as recognizing their very provisional status, the
odd way they are completely created (“fictive” in that sense), even as the
stable ones can have relations to sources that we have no reason to see as
coming from us.
Anyway, I guess that’s my piece. That and USD6,50 will get you a cup of coffee.
Eric
On Dec 29, 2022, at 1:05 PM, glen <[email protected]> wrote:
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.
