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? 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