Anonymous at Thu, 7 Mar 2024 03:36:19 UTC No. 16060812

>>16060708
you should look into compactness

Anonymous at Thu, 7 Mar 2024 04:11:14 UTC No. 16060839

>>16060708
Yes, convergence results are key to just about every single kind of mathematics.

Anonymous at Thu, 7 Mar 2024 04:16:58 UTC No. 16060845

>>16060708
Considering even mathematical concepts created as jokes wind up present in physics after the fact, maybe.

Anonymous at Thu, 7 Mar 2024 04:32:51 UTC No. 16060857

>>16060708
Achilles catches up with the tortoise all the time, every place

Anonymous at Thu, 7 Mar 2024 04:39:16 UTC No. 16060866

>>16060857
Space is discrete

Anonymous at Thu, 7 Mar 2024 04:51:14 UTC No. 16060882

>>16060866
prove it

Anonymous at Thu, 7 Mar 2024 04:54:12 UTC No. 16060885

>>16060882
Non-discrete space would take infinite computation power to update the state of, which is obviously bullcrap. Either the universe is full of infinitely many infinitely capable computers working on updating space… Or space is discrete, Occam’s razor.

Anonymous at Thu, 7 Mar 2024 05:08:09 UTC No. 16060904

>>16060885
>Occam’s razor.
Definitely backs up your narrative lmfao

Anonymous at Thu, 7 Mar 2024 05:11:17 UTC No. 16060906

>>16060708
L hopitals rule is basic calc

Anonymous at Thu, 7 Mar 2024 05:11:45 UTC No. 16060908

>>16060885
Why would a continuous state evolution require infinite computation if the computation is done in an analog fashion?

Do you have some reason to believe that the physics of the universe operates via some computational engine? Do you have some reason to believe said engine (supposing it exists in the first place) is discrete in nature rather than continuous?

Anonymous at Thu, 7 Mar 2024 05:23:42 UTC No. 16060916

>>16060908
Ok I got some more arguments.

Likening the universe to a state machine is apt since it follows laws in a seemingly consistent manner. These laws compute the next state based on the previous ones, the computational engine would be the laws of physics and I think it’s more likely that these aren’t infinitely complex.

Non-discrete space gives infinite entropy in even a small volume (infinite possible configurations possible in this volume). If your model predicts an infinity in nature, that is a big sign it is wrong. There are no infinities in nature.

Why is non-discrete space even thought of as the default anyway? Special relativity (which uses non-discrete space) has errors and even Einstein himself thought space would turn out discrete. Special relativity is just useful for macro scale stuff and breaks down at the micro level.

Anonymous at Thu, 7 Mar 2024 05:37:24 UTC No. 16060927

>>16060916
Interesting thoughts, but very counter to my experience and way of looking at the world as an engineer with a background in cyberphysical systems and stochastic modeling.

1) I don't know for certain that we have any reason to believe that the laws of the universe are consistent or deterministic. These are the modeling conventions we use for physics, but it's not possible to tease out how much of the errors in any particular state evolution will be due to process errors and how much will be due to measurement errors. We just make assumptions and find the models that work well enough for our applications with an approach that is more akin to "all models are wrong but some models are useful," than anything like a proper axiomatic theory of physics.

2) Even if the universe were to be something that has consistent laws, why would it necessarily be a state machine? Why wouldn't a signal flow graph with continuous signal flow not also represent said universe well? In fact, it would probably work far better, as any state machine can be exactly represented via a continuous signal flow graph with discretization and zero-order-hold approaches. The same cannot be said in the other direction.

3) Non-discrete space is assumed because most signals in reality appear to be continuous. It gets a little complicated because it is impossible to measure something analog like (as an example) a voltage into a probe, or voltage reading out of an electric thermostat, without interfering with it and introducing measurement errors. However, these errors can be made arbitrarily small if the signal remains consistent by observing over a larger period of time. There does not appear to be any minimum precision within which we can measure realized analog signals like dynamics (position, velocity, acceleration, jerk), temperature distribution on a surface, or voltage.

Anonymous at Thu, 7 Mar 2024 05:42:34 UTC No. 16060931

>>16060708
It has inside the mathematical framework.

Anonymous at Thu, 7 Mar 2024 05:46:26 UTC No. 16060933

>>16060916
>Likening the universe to a state machine is apt since it follows laws in a seemingly consistent manner. These laws compute the next state based on the previous ones, the computational engine would be the laws of physics and I think it’s more likely that these aren’t infinitely complex.
This is cope borne out of our inductive assumptions of doing science. It doesn't say much about how the universe works. Also if reality was discrete why is it difficult to account for the stability of the solar system in n-body dynamics which always become chaotic once we attempt to calculate anything?

Anonymous at Thu, 7 Mar 2024 05:47:27 UTC No. 16060934

>>16060916
As an aside, discrete-space can still give you infinite entropy in a confined volume.

Look at the Shannon entropy of an infinite sequence of IID coin flips. This sequence occupies a "volume" of measure 0 (as it is solely defined at a countable series of isolated points) and yet the entropy of the sequence is infinite. This is the coarsest discretization possible and it still has infinite entropy as you repeat the independent trials in a countable fashion.

Anonymous at Thu, 7 Mar 2024 05:47:36 UTC No. 16060935

>>16060916
because we can't tell if there's a smallest units in space time or not, we don't have the tools yet. It would be highly surprising the timespace is continuous because that could mean a universe exist in every quarks for example

Anonymous at Thu, 7 Mar 2024 05:51:41 UTC No. 16060941

>>16060935
I don't understand your reasoning. Space time being continuous would not mean that "a universe exists in every quark." It would simply mean you could get arbitrarily small in your measurements and you'd never hit a "size" where smaller measurement wouldn't be possible.

It could be possible that there is some smallest possible elementary particle, but there's no guarantee that all of the "space between" any two of these smallest particles would have to be aligned to a grid no finer than the smallest particle of matter.

Anonymous at Thu, 7 Mar 2024 05:53:06 UTC No. 16060943

>>16060916
>Likening the universe to a state machine is apt since it follows laws in a seemingly consistent manner. These laws compute the next state based on the previous ones
You are already presupposing discreteness by referring to "the next state".
>Non-discrete space gives infinite entropy in even a small volume (infinite possible configurations possible in this volume). If your model predicts an infinity in nature, that is a big sign it is wrong. There are no infinities in nature.
Circular reasoning: "space is infinitely divisible, therefore there are infinities in nature" -> "no, because space is discrete" -> "why?" -> "because it implies there are infinities in nature and there aren't"
>Special relativity (which uses non-discrete space) has errors and even Einstein himself thought space would turn out discrete
Einstein was wrong about special relativity but we should trust his random assertion that space is discrete?

Anonymous at Thu, 7 Mar 2024 05:58:01 UTC No. 16060945

>>16060941
`could mean` doesn't not mean `if A then B` it implies a possibility

Anonymous at Thu, 7 Mar 2024 06:02:43 UTC No. 16060948

>>16060945
I get that. I don't get where your justification for the "could mean" part of things comes from.

It seems as vacuous as saying "there could be a galaxy on the tip of every pin," and just leaving it like that. I don't see a reason to believe that the universe being continuous in space or time (or both) allows for the possibility of a "universe in every quark."

Anonymous at Thu, 7 Mar 2024 06:14:12 UTC No. 16060961

>>16060948
Idk what you mean by justification all I was saying is I would find it highly surprising because of that, it's not part of the argumentative it's just a personal observation

Anonymous at Thu, 7 Mar 2024 06:23:13 UTC No. 16060969

>>16060961
I don't mean justification in some formal sense. I mean, can you explain to me how it makes sense to you.

Let me give you another example. Let's say I told you, "If money is printed by the government then everything could be free."

There's a conceptual sense in which one could believe that to be true, but it would also be fair for you to respond to my comment and ask "why do you think that? Can you explain it to me because it doesn't make sense to me?"

Anonymous at Thu, 7 Mar 2024 06:41:17 UTC No. 16060989

>>16060708
My penis is infinitely small, there's that

Anonymous at Thu, 7 Mar 2024 06:47:44 UTC No. 16061001

>>16060969
The reason why I thought about it was simply that if space time is continuous this would mean that there's no identity element (or smallest unit) of space. As there's indefinitely many smaller spaces, and I would assume representation of those space, then there would exist a space representation such that it is the replica of the universe we live in, and that would be true (having a replace representation of the universe) for every element in the universe (whatever that may be).

It's not impossible but it would be suprising to me

Anonymous at Thu, 7 Mar 2024 08:19:46 UTC No. 16061114

>>16060708
nope.

Anonymous at Thu, 7 Mar 2024 23:21:12 UTC No. 16062018

>>16060927
Signal flow graphs are discrete tho. And any continuous such graph is just a discrete one zoomed out sufficiently enough to give that appearance.

Anonymous at Fri, 8 Mar 2024 00:05:12 UTC No. 16062061

>>16062018
Signal flow graphs are not discrete. What are you talking about? They have a discrete number of elements but the signals moving between them are continuous.

Anonymous at Fri, 8 Mar 2024 00:10:36 UTC No. 16062070

>>16062061
>but the signals moving between them are continuous.
Pure fantasy, whatever substrate this graph is run on will render it discrete but finely grained enough so you percieve it as continuous.

Anonymous at Fri, 8 Mar 2024 00:24:41 UTC No. 16062081

>>16062070
I think you don't know how signal flow graphs work. They literally were developed for signal processing of analog continuous voltages using continuous time integration filters via capacitors/inductors.

Have you ever considered actually trying to learn how things work outside of your comp sci bubble instead of just pretending the rest of the world uses the same conventions you do?

Anonymous at Fri, 8 Mar 2024 00:34:13 UTC No. 16062090

The universe is obviously a computer simulation because it just IS okay?

Anonymous at Fri, 8 Mar 2024 01:17:30 UTC No. 16062138

>>16062081
The belief that that graph is continuous is just an abstraction, a thought experiment and not something real. Infinity and infinite detail does not exist in the finite natural universe. Discrete space and time is just a way simpler explanation that introduces less infinites and is therefore probably the more correct out of those 2 options.

Just like the fraction 1/3 = 0.333... does not repeat for infinity. It repeats for as many decimals as you compute it to.

Anonymous at Fri, 8 Mar 2024 01:20:52 UTC No. 16062141

>>16062138
0.333.... is a terrible example, it is "computable" as an infinite object just fine, in that I can tell you what any digit will be

Anonymous at Fri, 8 Mar 2024 01:23:34 UTC No. 16062143

If we take a chunk of any kind of stuff and divide it up as far as we can, we will have to come to a halt at tiny bodies which are indivisible.

We cannot allow matter to be divisible to infinity: for let us suppose that the division has been carried out and then ask: what would ensue if the division was carried out?

If each of the infinite number of parts has any magnitude, then it must be further divisible, which contradicts our hypothesis.

If, on the other hand, the surviving parts have no magnitude, then they can never have amounted to any quantity: for zero multiplied by infinity is still zero.

So we have to conclude that divisibility comes to an end, and the smallest possible fragments must be bodies with sizes and shapes.

These tiny, indivisible bodies were called by Democritus ‘atoms’

Anonymous at Fri, 8 Mar 2024 01:46:20 UTC No. 16062157

That anon is retarded. The strongest evidence that spacetime is discrete are the planck units and energy-mass-charge-spin quantizations in the standard model.
Isn't it kind of obvious? I always thought so.

Anonymous at Fri, 8 Mar 2024 03:50:40 UTC No. 16062261

>>16062138
I don't think you understand what continuity means in the process of continuous signals. You don't need to know that you could measure the signal to an infinite degree of precision to know that its amplitude is continuous. Similarly you don't need to measure the time-clock to an infinite degree of precision to know that it's continuous.

Also, discrete space and time isn't any simpler than it being continuous. In fact, it opens up a whole different can of problems because physical processes which are uncomputable exist in real time (e.g., distributed line delays, which literally cannot be discretized with a finite number of sample delay elements).

You may think it's simpler because you don't understand what continuous properly means, but it certainly isn't simpler in reality. It's just a different set of problems.

Anonymous at Fri, 8 Mar 2024 03:54:44 UTC No. 16062267

>>16062157
You realize that the Planck units aren't some "source code constants" right? They were specifically chosen for their mathematical convenience based on previous theoretical physics developments. There's no reason to believe that "Planck time" (as an example) is the smallest possible length that time can proceed. It was literally chosen specifically for mathematical convenience in theoretical physics research alone and not some indication that they actually correspond to anything meaningful in meat space.

Anonymous at Fri, 8 Mar 2024 04:34:56 UTC No. 16062301

>>16060708
it has more than you, but admittedly being above than zero is not that high of a bar

Anonymous at Fri, 8 Mar 2024 04:35:58 UTC No. 16062306

>>16060812
hes fairly dense himself, if you catch my drift

Anonymous at Fri, 8 Mar 2024 05:00:34 UTC No. 16062331

>>16062138
Do you believe that, say, a rock just sitting there is repeatedly blinking in and out of existence at planck time intervals? Or that it is continuously present?

Anonymous at Fri, 8 Mar 2024 05:03:45 UTC No. 16062337

>>16062331
The former, not that it would matter to any observer in any meaningful way. Planck time is also not the smallest time, but yeah in the smallest possible time.

Anonymous at Fri, 8 Mar 2024 05:07:27 UTC No. 16062345

>>16062337
> Not that it would matter to an observer in any meaningful way.

You're hiding something important here. When you claim that the universe must be discrete (but discretized to such a fine degree that it appears continuous) you are also making a claim that cannot be meaningful to an observer.

Why do you believe that the rock would be blinking in and out of existence in these intervals? What would lead you to believe that this has to be the case, as opposed to the much simpler idea that it just is sitting still?

Anonymous at Fri, 8 Mar 2024 05:13:02 UTC No. 16062350

>>16062337
This leads to various interesting questions, like where does stuff go (or what happens to it) during that interval, how does it keep vectors of motion/inertia, or if you somehow propulsed matter faster than lightspeed would it just phase through other matter without touching it?

Anonymous at Fri, 8 Mar 2024 05:21:58 UTC No. 16062360

>>16062345
It doesn't really "blink" since there is no time between the smallest units of time. More like it gets updated to a new state, think a new frame in a movie or a game. Now the new state is probably much like the last, so it seems to continiuously stay put. There is no between these smallest units of time (or space) just like there is no 101th molecule in a gas consisting of 100 molecules.

All of our human intuition about "continuous" things have shown to be discrete (gas and liquid are discrete molecules, light and more). Our human cultural concept of "continuous" comes from all of these actually discrete examples while all true continuous examples come from abstract maths concepts without an equivalent in reality (infinites, infinitely repeating decimals, pi and more).

Discreteness therefore seems to be the option more grounded in reality while true continuousness seems to be the more absurd option and it seems to come from a bias that comes from human culture as well as certain maths concepts that have never been observed in reality.

Anonymous at Fri, 8 Mar 2024 05:36:06 UTC No. 16062374

>>16062360
> All of our human intuition about "continuous" things have shown to be discrete.

This just isn't true. It is true for gasses and liquids being made of discrete molecules but it isn't true for energy fields and doesn't appear to be true in general.

As far as I'm aware, there is no discretization of a magnetic field or electric field. As far as I'm aware, there is no discretization of thermal energy as a field. Similarly, gravity and nuclear effects do not seem to be quantized or discretized in any meaningful way.

Similarly, gas and liquid are discrete in the sense that in any particular 3d volume that is perfectly enclosed there is a discrete number of molecules of each substance. However, their kinetic energy does not appear to be discretized. Their electric fields and their charge doesn't appear to be discretized.

What you have done is you have found a few examples where some aspects of what we beleived to be continuous have turned out to be discrete and then extrapolated that everything else must follow what this very small subset has done.

Anonymous at Fri, 8 Mar 2024 05:51:01 UTC No. 16062389

>>16062374
I think those examples you give are also discrete. Because, like I said before, infinite detail is more absurd than limited detail. Any notion of infinity in nature is absurd and should be discarded.

And when you add point like particles with no volume together with infinitely detailed space and time, you get some funky potential configurations.

Anonymous at Fri, 8 Mar 2024 06:07:50 UTC No. 16062396

>>16062389
Can you point me to any meaningful discrete theory of electric fields? What is the discrete quantity? What would it even mean for, as an example, the momentum of a group of water molecules in a volume to be discrete?

It seems like your whole thought process is based around misunderstanding what it would actually mean for the universe to be discrete in the way you believe. It wouldn't just require that we see "sufficient sampling" to appear continuous. It would fundamentally rewrite how we handle physics at every level from moments to electromechanical to fields and waves to heat transfer. None of which work well for your discretized model.

Discretization works well for counting and discrete sets of poses. That's just about it. If you aren't talking about something that lends itself we'll to quantization or has a physically meaningful sense in which it is quantized, you are making a useless arbitrary decision because you personally don't feel comfortable with the notion of continuity or unboundedness.

Anonymous at Fri, 8 Mar 2024 06:14:13 UTC No. 16062398

>>16062396
>It would fundamentally rewrite how we handle physics at every level from moments to electromechanical to fields and waves to heat transfer.
The current models (QM and relativity) already have holes that prove that they are not some sort of truth of the universe, but merely approximations to be used for engineering purposes. There is no issue in discarding them, but future models will have to be able to handle the predictions that they did get right.

I can't provide alternatives myself. My sole line of reasoning is infinities can't exist in reality.

Anonymous at Fri, 8 Mar 2024 06:17:46 UTC No. 16062404

>>16062398
Okay, so you essentially have an axiomatic commitment to the concept that "unboundedness" can't happen in reality and then have inductively generated the rest of your world view from this apriori belief.

All of QM could get rewritten tomorrow (and I don't see a reason to believe that our current theoretical physics will prove to be the final one, unless of course we blow ourselves up before we make more progress). It getting rewritten tomorrow doesn't give you any reason to believe that your particular finitist discretization of reality view is any more likely to be the one that prevails. In fact every bit that I've seen seems to indicate the opposite.

It appears more and more that it isn't possible to discretize concepts like thermal energy or EM field intensity without losing information no matter how finely partitioned the space is.

Anonymous at Fri, 8 Mar 2024 06:28:04 UTC No. 16062411

>>16062404
How would you even prove continuousness of space? The only evidence for it is the absence of evidence for discreteness. Discreteness can be proven if it is the case, but the belief in continuousness will always only be the default when we don't find the space atom that is 10^-100cm cubed or whatever.

We can call it functionally continuous for all engineering purposes, but can there ever be hard proof for it? I don't think so.

Anonymous at Fri, 8 Mar 2024 06:49:31 UTC No. 16062423

>>16062138
>repeats for as many decimals as you compute it to.
Then it wouldn't equal 1/3.
It would just be an approximation.
To equal 1/3, there must be infinite 3s.

Anonymous at Fri, 8 Mar 2024 06:51:22 UTC No. 16062424

>>16062423
In fantasy alone, an exact 1/3 does not exist in nature.

Anonymous at Fri, 8 Mar 2024 06:54:53 UTC No. 16062427

>>16062157
Planck length limits how close you can compute ,for example, the field strength of an electron.
However, you can move the electron itself half of a Planck to the side. Space isn't made of 'space-pixels'.

Anonymous at Fri, 8 Mar 2024 06:56:36 UTC No. 16062430

>>16062424
there is a reason this board is called "/sci/ - Science & Math"

Anonymous at Fri, 8 Mar 2024 07:00:45 UTC No. 16062431

>>16062411
All it means for something to be continuous is that you can't discretize it without losing information. Every single attempt to discretize continuous physics has consistently shown you cannot do so for real analog signals without losing information. The information you lose becomes more marginal as your discretization gets better, but barely so.

Think about 5 GHz wifi for a second. If all of this 5 GHz bandwidth were to be occupied (which would be super power inefficient but is theoretically possible) you'd need to sample 10 billion times per second to reconstruct the analog signal with no potential for aliasing and that's assuming that there's no additive noise in your detection process.

There's absolutely no reason to believe that this same process suddenly stops at some order of magnitude. If we already are taking about analog signals with frequency content in the billions of oscillations per second and this isn't even the upper end of realizable EM (it's just the upper end of what is cheaply and easily controllable currently) what makes you believe that there's some barrier at which point this process stops? What is the finite number that restricts the upper bound of oscillation frequency for an EM wave, and why would it be that bound necessarily exist?

If you can not discretize at any level without losing information, then your system is analog. That information you lose may become more and more marginal as your partition becomes refined, but if it's never 0, then your system can't be discrete and must be continuous.

P !JWbtblGP2U at Fri, 8 Mar 2024 07:01:49 UTC No. 16062435

>>16060708

Anonymous at Fri, 8 Mar 2024 07:02:54 UTC No. 16062438

>>16062430
Yes, the "science" part deals in nature while the "maths" part deals in abstraction. Some of this abstraction has no realized equivalent in nature and is only a novelty for people to toy around with.

Anonymous at Fri, 8 Mar 2024 07:04:27 UTC No. 16062441

Yes, the concept of infinity does have uses. If you took calc I & II you should know this. Convergence of infinite series, limits of horizontal asymptotes as x->infinity, and improper integrals all utilize the concept of infinity. Probability Theory makes plenty use of infinity. The Gaussian, or Normal distribution, goes to positive and negative infinity. But if you take the definite integral from negative to positive infinity, the value is 1. Interest Rate Theory uses infinity a lot. Perpetuities are present values of cash flow streams that go forever, which is the sum of an infinite amount of cash flows, but it converges to a value. Also if you have an accumulation function a(t) = (1+r/n)^(nt), where t is time in years, n is number of compounding periods in a year, and r is the nominal interest rate compounded every period, then you can take the limit as n approaches infinity to get a(t) =exp{rt}. Infinity is a beautiful concept because it is used in many facets of life and of mathematics.

Anonymous at Fri, 8 Mar 2024 07:04:55 UTC No. 16062443

>>16062438
So your line of "abstraction" is that you can't cut a pie into three equal slices? That's where the line is for you? Of all notions to get filtered by, you got filtered by fractions?!

Anonymous at Fri, 8 Mar 2024 07:11:15 UTC No. 16062454

>>16062441
Something increasing without limit is not an infinity. It would be apt to call those things unlimiteds.

Anonymous at Fri, 8 Mar 2024 08:02:32 UTC No. 16062513

>>16060885
>infinite computation power
i miss the clockwork concept of how reality worked, now not only do i have to endure retards comparing reality to computers,, but due to the advent of "AI", i will soon endure even further shit in the form of "reality from AI" in the form of a Boltzmann's CPU

Anonymous at Fri, 8 Mar 2024 19:12:20 UTC No. 16063311

>>16060708
literally calculus?
you wanna know the future speed/trajectory of something? yes? then get comfortable with limit calculations

also the notion of the "infinite horizon" forms the basis of model predictive control(controller theory)

Anonymous at Fri, 8 Mar 2024 19:26:24 UTC No. 16063336

>>16062513
Likening the universe to a state machine is very fitting tho.

Anonymous at Fri, 8 Mar 2024 21:26:14 UTC No. 16063590

>>16063336
fitting=/=is, my guy, this dick sure fitting your mom's mouth, but it sure as hell ain't

Anonymous at Fri, 8 Mar 2024 21:27:58 UTC No. 16063594

>>16063590
It's a type of state machine for sure. A turing complete one at that, so yea it's a computer.

Anonymous at Fri, 8 Mar 2024 22:05:28 UTC No. 16063662

>>16060885
Or you know. Space is not a simulation that has to be computed discretely.