6 ms·
Does time really flow? New clues from intuitionist math
- deleted 6y ago[deleted]
- jackhalford 6y ago> A real number with infinite digits can’t be physically relevant. but > Popescu objects to the idea that digits of real numbers count as information. I don't know where to stand, what about information encoded in geometry, like pi. If I get a spherical system, in a small enough space - no, in any space - then there's a "cutoff" to the actual number of digits to pi. Because a chunk of spacetime can't contain infinite information? sounds good. > Quantum math bundles energy and other quantities into packets, which are more like whole numbers rather than a continuum. And infinite numbers get truncated inside black holes. Layman here, but AFAIK concepts like black holes aren't consistent with quantum mechanics so I'm not sure it's wise to use concepts from both theories at the same time. (i.e QM predicts that wave functions evolve deterministically but GR predicts information loss in black holes, these two views conflict). It's way beyond my grasp but some theories seems to quantize space, I wonder how those agree with the notion of "thickness". I'm disappointed that the article doesn't point into any mathematical theory that models the "thickness" that comes from removing the empty middle theorem.
- dTal 6y ago>then there's a "cutoff" to the actual number of digits to pi. Because a chunk of spacetime can't contain infinite information? sounds good. It's more subtle than that. The "infinite digits" of pi isn't information, no more so than the endless decimal 1/3 = 0.333... is "infinite information". You can't use it to "store" anything. This is a distinct notion from the practical reality that real spacetime is quantized. An alternate universe with un-quantized spacetime might, or might not, allow you to store infinite information in a chunk - but every digit of pi would be relevant there.
- ineedasername 6y agoWould it be correct to say that, under intuitionist thinking, actually constructing 1/3 = 0.333... (on paper, in a computer, whatever) would take infinite information (not to mention energy and space)? Though if I understand correctly, intuitionist math would also hold that true infinite 0.3333.... also cannot be constructed?
- empath75 6y agoOr 1.000000..... for that matter. Which seems absurd on its face.
- deleted 6y ago[deleted]
- roywiggins 6y agoYou can write down an algorithm to generate the digits of .33..., so that set of digits exists as a "potential infinity". Same with Pi and the square root of two. It is numbers that haven't been constructed that intuitionist mathematics doesn't generally think have been proven to exist.
- paganel 6y ago> exists as a "potential infinity". Not a mathematician nor a physical theorist by any means but some might regard the putting together of "exists" and "potential infinity" (even if using ") as an oxymoron. It's an endless discussion, of course, I personally think it all boils down to Zeno's paradox remaining, well, an unsolved paradox for the foreseeable future.
- shrimpx 6y agoImagine the lazy Fibonacci series. As long as you keep taking a number, the next one in the series is generated. It’s not incorrect to say it’s “potentially infinite”. And it exists, as the live algorithm that keeps cranking as long as you put in energy.
- jeromebaek 6y agoPi is computable. What is computable, can be represented in finite information (the algorithm used to compute the number). Almost all real numbers are not computable.
- Koshkin 6y agoTL;DR A reformulation of physics based on intuitionist mathematics seems to aid human intuition, makes no impact on calculations.
- ineedasername 6y agoIt might make no impact on calculations (I'm not really qualified to say that) but it seems like it would make a big impact on epistemology and determinism. I think?
- madhadron 6y agoNot really. The math is chosen to fit the physics, remember, not the physics chosen to fit the math.
- ineedasername 6y agoI think you're right about that for determinism, but the acceptance of intuitionist math requires a different epistemology. It is literally a different set of assumptions on what is knowable and what is true.
- empath75 6y agoNone of our instruments are infinite precision, nor are very many physical constants, so it sort of makes sense that tossing out real numbers doesn’t make any difference.
- bill_from_tampa 6y ago> If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable. Is this not what Planck's constant implies? We can only know position and/or motion to a certain degree, and not exactly? Does not quantum mechanics already include this idea?
- Koshkin 6y agoHow does discreetness imply imprecision and randomness? If anything, it should indicate some degree of certainty.
- hinoki 6y agoIt depends on your rules for rounding I think.
- akira2501 6y agoI'm an amateur, but I like to think about this: If spacetime is quantized, then the speed of light would be 1 planck length / 1 planck time. Assuming spacetime is actually quantized to that metric, we can then ask: How does something move at 2/3c? Or two discrete planck lenghts in 3 discrete planck times? In one instance it could be: t=0,x=0, t=1,x=0, t=2,x=1, t=3,x=2 It could also do: t=0,x=0, t=1,x=1, t=2,x=1, t=3,x=2. It implies a hidden variable, or at the very least a hidden phase of some sort. All sorts of oddness abounds when you consider all velocities are then quantized fractional values of c.
- tines 6y agoBut then your 2/3c is an average, it's not the real speed of the object at any actual instant.
- Ono-Sendai 6y agoIf you can have real numbers at each spacetime point (as opposed to boolean values) then you can easily get a speed less than c. This is similar to simulating the wave equation on a grid on a computer.
- ffhhj 6y ago> We envision two possible mechanisms that could explain the actualization of the variables: 1. The actualizations happens spontaneously as time passes. This view is compatible with reductionism and it does not necessarily require any effects of top-down causation. Note that this mechanism resembles, in the context of quantum mechanics, objective collapse models such as the “continuous spontaneous localization” (CSL) [23, 25]. 2. The actualization happens when a higher level requires it. This means that when a higher level of description (e.g., the macroscopic measurement apparatus) requires some physical quantity pertaining to the lower-level description to acquire a determined value, then the lower level must get determined. In quantum mechanics a similar explanation is provided by the Copenhagen interpretation and, more explicitly, by the model in Ref. [37]. https://arxiv.org/abs/1909.03697 https://arxiv.org/abs/1909.03697 Seems like a framework for the Simulation Theory.
- empath75 6y agoYeah I did have this idea at one point that if we’re in a simulation, than there is a cost for simulating things at finer and finer detail, which could manifest itself in higher energy requirements that we see in particle accelerators, but that we aren’t actually learning anything new at those levels, maybe we’ll find some new fundamental particles that make up the electron for example, And we’ll find new particles that make up those, none of which even existed until we started poking at them, since they aren’t necessary for the simulation to run.
- ineedasername 6y agoSort of a "turtles all of the way down", but only if you actually go looking for the turtles. This entire article makes my brain hurt in ways I'm really not used to. (I'm used to brain-hurt, you can't be intellectually curious without experiencing that occasional side-effect. It's just this particular flavor of it is... disconcerting)
- Abishek_Muthian 6y agoRegarding the cost of simulation, you might find what Dr. Michio Kaku said during his AMA. >I mentioned that a digital computer cannot simulate even a simple reality, since there are too many molecules to keep track of, far greater than the capabilities of any digital computer. We need a quantum computer to simulate quantum reality, and hence, once again, the weather is the smallest object that can simulate the weather. Therefore, I don’t think we live in a simulation, unless the simulation is the universe itself. -Dr.Michio Kaku
- russellbeattie 6y agoMy key takeaway from the article: Ooooh. That looks like a great chair!
- ineedasername 6y agoMaybe this will help people, maybe just make things worse, but for what it's worth, here's my $0.02: I read the first half (with an early tangent to wikipedia for "intuitionist math") feeling profoundly uncomfortable with the entire premise. Then at the halfway mark, I realized that intuitionist math feels a lot like David Hume's approach to metaphysics and epistemology, which always felt right to me. Intuitionist math still makes me feel uncomfortable, but now at least it also seems consistent with a framework of thought that doesn't. I'm not sure I've ever been quite so profoundly intellectually ambivalent.
- slowmovintarget 6y agoThe first smell for me was the name "intuitionist". The concepts involved make a lot of sense to me, though. This kind of number system follows the rule of "TANSTAAFL" (Robert Heinlein's "there ain't no such thing as a free lunch"), namely that you cannot have zero-cost infinities as real numbers require. As a side note, if this notion pans out... welcome back Free Will.
- naasking 6y agoIntuitionism should be familiar: it's effectively the logic underlying most programming. It's basically what allowed theorem provers like Coq to extract a runnable OCaml program from a logic proof.
- peterburkimsher 6y agoI watched Conway's 6th lecture about Free Will today, and was thinking about the consequences of his theorem. As I understand, he proved that Free Will is mutually exclusive with determinism: "Everything happens for a reason." Then I started thinking about time and causality. Does time really exist? Time dilation really exists, after all. What if there were an elementary particle that has no Free Will? Would that make it eternal? I feel that eternity and infinity are deeply connected, but I'm not mathematically smart enough to prove it. If you'd like to discuss further though, please send me an email! https://www.youtube.com/watch?v=IgvkhgE1Cps&list=PLhsb6tmzSpixUGjmJq6g9iPm73pMWnPnH&index=6 https://www.youtube.com/watch?v=IgvkhgE1Cps&list=PLhsb6tmzSp...
- totemandtoken 6y agoI do like the idea of viewing time in the context of physical information. That makes a lot of intuitive* sense to me as a layperson *Intuitive in the colloquial sense of the term, not in the way it's being used in this article
- xelxebar 6y agoHere's what looks like the original paper; it's a mere 3 pages long: https://arxiv.org/abs/2002.01653 https://arxiv.org/abs/2002.01653 It's a lot of prose with hand-wavy analogies. My takeaway is that the author seems to have become enamored with intuitionistic logic but seems to lack much concrete experience working with it. For anyone intrigued by constructive mathematics, there's a nice talk and paper by Andrej Bauer (nice coincidence) called "Five Stages of Accepting Constructive Mathematics." It's a nice mix of prose and rigor of varying levels: http://math.andrej.com/2016/10/10/five-stages-of-accepting-constructive-mathematics/ http://math.andrej.com/2016/10/10/five-stages-of-accepting-c... The metamath[0] proof verifier also has a database of theorems on intuitionistic logic: http://us.metamath.org/ileuni/mmil.html http://us.metamath.org/ileuni/mmil.html It can be neat to compare proofs and theorems there with their counterparts in the classical logic database. [0]:http://us.metamath.org/ http://us.metamath.org/
- mirimir 6y agoThanks. I gave up about 20% in, thinking that whatever it is, it's either BS or over my head. Which is where much cosmology and theoretical physics leaves me. And yes, that probably says more about me than them ;) But whatever, I rather think that subjective time involves movement at the speed of light through some n-dimensional manifold. But maybe that just reflects the SF that I've read. Such as Stephenson and Egan.
- craftinator 6y agoHah, I came here to say much the same thing about the flow of time, much for the same reason (Stephenson, Egan, Asimov).
- johndoe42377 6y agoTime is an abstract concept superimposed by a mind of an intelligent observer (capable of abstract thinking in terms of a language) so it does not exist. There is not a single experiment which demonstrates existence of time as a physical phenomena. Process in the universe do exist, time does not. However it could be "derived" by the mind. The question whether an abstract concept flows contains a type error in it, so all the answers are as good as "does this spell is strong enough" or whether God hears my prayers. Mixing abstract concepts in mathematical equations is the cause of failure of all the theoretical "sciences". Logical type-checkers is what we need. 99% of theoretical bullshit will not survive even a simplest logical type-check.
- mikekchar 6y agoI often think that the flow of time is really just an artifact. At any given point in time, a human has a memory whose state is dependent upon the points in time before it. So at any given point in time, it appears as though we've travelled through time up until that point. However, as long as causality is preserved, I don't really see any necessity at all for movement through time. I mean, the phrase is self-referential - "movement through time". Movement is defined by change in position over time. I think from a practical perspective, the concept of time "flowing" or "moving" is really just saying that causality is preserved. There is an order. That's all. And from an experiential perspective, as long as you have causality and memory, it's going to appear as if time "flows". I'm not sure there is any meaning to be derived beyond that.
- twomoretime 6y agoThat doesn't explain why humans have the concept and sensation of "present".
- jonsen 6y agoThis is due to the (extremely) limited capacity of consciousness. It is only able to handle a window of a few seconds.
- mgamache 6y agoI think the 'frame rate' of the human mind is around 13 milliseconds. We fill in the gaps so our perception is of a continuous reality.
- mgamache 6y agoI can't find the source, but here's a reference: https://www.dailymail.co.uk/sciencetech/article-2542583/Scientists-record-fastest-time-human-image-takes-just-13-milliseconds.html https://www.dailymail.co.uk/sciencetech/article-2542583/Scie...
- posterboy 6y ago
- aunlu 6y ago“Information is destroyed as you go forward in time; it’s not destroyed as you move through space,” Oppenheim said. Strangely, this reminds me Stephen King's "The Langoliers".
- calebm 6y agoDestruction is part of the process of creation.
- posterboy 6y ago> Hilbert and his supporters clearly won that second debate. Hence, time was expulsed from mathematics and mathematical objects came to be seen as existing in some idealized Platonistic world. I guess that was so because the view was common, before. It should be difficult to find and prove that the line had better read "... continued to be seen as ..."
- zone411 6y agoWe know that our experience of physical reality is flawed (thanks to quantum mechanics and relativity). We also know that it's not the only possible way to experience it (thanks to drugs). Does it matter then if physics is formulated in a way that's a closer match to our experience?
- rmdashrfstar 6y agoNot the only possible way to experience it, or is it messing with a functioning motor?
- lonelappde 6y agoArxiv is great, but why it the media writing up non peer reviewed articles?
- DeathArrow 6y agoPretty interesting: >"The dependence of intuitionism on time is essential: statements can become provable in the course of time and therefore might become intuitionistically valid while not having been so before." https://plato.stanford.edu/entries/intuitionism/ https://plato.stanford.edu/entries/intuitionism/
- jeromebaek 6y agoNow tie this with computability theory. Almost all real numbers are uncomputable. It's obvious that they don't "exist" in any sense if by "exist" we mean "computable". Now consider that entropy, is information, is the measure of randomness, or uncomputability, is time. What is uncomputable, coming into existence, is the passage of time.