Continuous and Discrete

hahaha same I got a lot of what he is saying, but some things I don't quite get, sadly cuz there is still many holes in my knowledge, wish I had more time to study passion subjects like physics and math, but I also gotta focus on my actual field of bioinformatics and I'm already procrastinating by watching this video, but it's ok since the inherent fascination of nature is what is behind my pursuit of science anyway, so we shall keep seeking to understand all things.

Every possible configuration of existence (including chaotic ones) can be described mathematically. So I always find the question of whether reality emerges from math farcical. Mathematics should be treated as our way of describing patterns extracted from all possible existences, including existences that can't practically exist.

You touches on the question wether math is invented or discovered. My own believe is that math more is an language and tool than some underlying reality. So mathematicians invent math system and can then discover stuff within that system. And it's the role of physicists to use math to describe reality and create analogies between mathematical system and physical reality. Natural languages as English has to much ambivalence and can't fully describe complex systems so something like math have to be used. That is contrary to the Platonic believes that the reality is math and beautiful and we are observing an distorted version of it. Stephen firmly believes that the reality is computational, don't know more details on he's philosophy.

@@lubricustheslippery5028 Most working mathematicians, like myself, subscribe to some form of mathematical realism. It seems to me that one can argue about the size of the sandbox, but not about the existence of the sandbox. Moreover, I don't think that mathematics is a "language" that serves as a salad bar for the sciences, any more than a symphony can be reduced to a sheet of music. I believe that Stephen Wolfram, as a friend of the (Turing) Computable Universe Hypothesis (or some ontological form of computationalism), i.e. the claim that nature performs digital computation, would agree with me. The symbolic representation of a given computation and the actual execution of a computation instance are not the same.

If space is discrete, you can relate matter to it through gravity. If space is discrete you can easily explain dark energy as the space between galaxies expanding brick by brick, probably as a swap of matter to space, or energy to space.

"Theory of everything" is for theologians

@@DarkSkay Do you have evidence supporting that anything more than a single theory is required to explain reality? I'm joking with you, but the thing is when it comes to hypothesis creation there are no clear rules. There are some pointers and strategies but nothing strict. Of course nothing should be believed before it has experiments supporting the hypothesis, but how we go about deciding what to test with experiments is up to each person. You can have arguments about if Stephen's way of kinda working backwards from math to reality is productive (I can definitely see arguments against his methods from this pov) but I would say let him keep it up. To me it is an interesting approach to go the generative route when it comes to physical laws and if nothing else we get some interesting math from it (we already have gotten that).

@@Olodus There's a saying that eternity is long, especially towards the end - the set of "everything" can hold quite a lot of elements, especially when the remaining space appears to get smaller. Spinoza and countless others have theory: "Everything is (the) God(s)". With the distinction between singular and plural perhaps insignificant, blurred or transcended in this context of contexts that can hardly be imagined larger.

No, it's not agreed that quantum fields are the base line of the universe. Quantum theory and Relativity contradict each other. That's the whole problem at present . . .

​@@QED_ Like black holes for exemple, both theories dont contradict each other, they just break down and fail to work for different reasons. Can you give me a specific prediction that both theories made that contradicted each other ?

@@TheCrimier Sorry, I'm not a physicist. But as I recall . . . isn't there some issue when tracing each theory back to the big bang (?) About how small Space can get (?)

@@QED_ Nope, both theories dont contradict each other, they just cant contradict each, they are about 2 class of widely different thing, matter and gravity. The issue is merging them together to make predictions about black holes(Big Bang). All attempt to merge them as of today as failed. I will say it again, as we understand Quantum mechanic, baseline reality is quantum fields. I'm not a phisicist either just for the records, I just love physics a lot. *edited some grammar

I think 12:56 (which really got my attention) is the key point here . . .

​@@QED_ Sure but... with any model (simplification of a complex system) this is the case and we (humans) essentially create simplified models to understand.. well, everything (which if I understand what Wolfram is saying, is solely because we are computationally bounded). Dunno, maybe I need to watch this a few more times and think about it some more.

@@jackroman8821 Me too . . . for sure.

computational equivalence is the definition that a system is operating at a complexity equivalent to a Turing machine (turing universality) and computational irreducibility is that because of this feature, what the system does is therefor undecidable. Wolframs main contribution to us, is that principle of computational equivalence...where we think about systems in nature have essentially have this property...where It's like trying to answer the halting problem. we can't know exactly what is going to happen because what the system might do is infinitely complex. He showed in his book New Kind of Science, that the ability to reach turing universality...is trivial and ubiquitous (that it happens in practically all systems, with practically any rules) Everything else, like the Wolfram Model and all that, stems from these building blocks. Like the idea that perfect prediction doesn't exist because if you could perfectly predict a system it means you could solve the halting problem. Mathematics has effectively avoided this conclusion because most of the problems dealt with in mathematics are reducible problems...that have decidable answers. Systems in nature DONT OPERATE under just these MATHEMATICAL constraints...they follow ALL POSSIBLE RULES...the capital letters being the major difference between Things like the "Mathematical universe" and the "Wolfram Model" Hope this information helps you out. Just some background I have been studying the the wolfram model for 2.5 years now. I recommend watching his book series on YT, New Kind of Science.

@@NightmareCourtPictures Props.

Not a professor!!! Just a remarkable student :)

At least both of them are attributing dark matter/energy to our lack of understanding of space or time, rather than the conventional and extremely unparsimonious idea that there's a whole other table of 'dark' standard model particles or whatever. I for one think it's kind of silly to believe we have any authority at all to declare what's twisting distant galaxies millions of light years away, based off of ancient light and not even a century of observations. It's like a grains of sand in Antarctica in 1 billion B.C. declaring the laws of physics for a grain of sand in Pasadena in 2023 lol.

@epencil I'm not aware of any suggestions they contributed for dark energy, do educate me. When I studied I decided to derive an analogue to schrodinger's eq but with 2 time dimensions and one space ... got an interesting result but I was no theorist. When you say ancient light I assume you mean from our perception because light itself carries no information about time. They experience no time between events and are not conserved being bosons with integer spin. I consider them to be solely the energetic carrier of electronic transition levels - but I haven't studied widely or deeply enough to strongly validate if that is right/wrong or even obvious/not obvious. But just remember it's not really about declaring or validation, but about falsification (Popper's construction of the scientific method ... and I had to stay quiet when the teachers training me to be a teacher thought they were being clever to weaken 'the' scientific method to 'a' scientific method, but really they were missing the bigger [philosophical] picture).

@epencil However if you are skeptical about the assumption physical laws haven't changed over time you would be interested to know that has also been an interest of mine, inspired by the rabbit hole in Web of Stories with Freeman Dyson. I think I did enough digging to write off that it wasn't the case for electron magnetic forces (at least not testable / measurable) but can't remember if I even wrote it off for the gravitational case , it was a suggestion from Dirac based solely on mathematical aesthetics and makes the case that the rate that the gravitational force has got weaker (if it did) compared to the other forces , would roughly correspond to the age of the Universe. And i don't know why I'm blanking on the conclusion that I came to about that , so I mustn't have closed the question sufficiently enough. I did have another 'not a theorist' idea about the origin of dark energy and Universe expansion (or rather contraction of 'stuff' between space) inspired by a method of energy extraction from blackholes.... and I later learnt Herman Weyl had a similar suggestion but it was apparently falsified by the observed size of Hydrogen (bigger or smaller can't remember). But my argument and open question is , IF everything is getting smaller so that space in between is getting larger / expanding, then how would we be confidently measuring that, assuming the 'rulers' are also getting smaller by the same rate. (In Wolfram's project the atoms of space are x^-100 Meters, where does that come from, are they assumed to have always been that ratio to e.g. the electron r ~ 10^-18 m). Just thinking aloud here.

@@Nick_Tag I think two time dimensions is where the answer may be at. You probably know about Itzhak Bars' ideas. Yes the lack of information carried in ancient light is a good way of putting it; it's so presumptuous from mainstream physics to infer the state of the universe, including constants of nature, over time back billions of years and billions of light years away, with only fifty years of astronomy behind it. The fine structure constant, which no one even knows what it really is, could change slightly with space or time and all the laws of physics would go out the window. There's an apparent paradox at the foundation of reality and it's something like backwards-going time. That doesn't mean it's a free-for-all, there is some conformal structure in how information behaves with change, but hard-nosed objectivism or reductionism isn't going to cut it anymore.

You meaning working over rings which mathematicians have also been doing for hundreds of years?

i dont think these are mutually exclusive. i think a pretty important detail is that time with which computation can continue for a undecidable problem, is infinite and might never halt. That's pretty important detail for Wolframs Model. If everything was finite, then the halting problem has a solution, and then everything would not be computationally equivalent...it is that property that turing machines approximate to a ruliad object that makes them equivelent constructs. I also believe with very good reason that discrete and continuous are not mutually exclusive either...that we can't be separated from a continuous reality even when it is discrete because of how we are embedded in that reality...so even when it is an illusion, it can be considered as real as the discrete structure that underlies the continuous features of it (and this is what effective theories are) Cheers,

@@NightmareCourtPictures Good stuff thanks for sharing! 👍 I found the ideas about the inextricability of consciousness from some form of continuousness especially intriguing.

@@dinobotpwnz Maybe, I've never heard that term before. I'll check it out thanks for the tip!

​@@elindauer no problem. If you took an interest to that, I can explain a couple things in a bit more in depth. There's a thought experiment I use to help conceptualize the union between discrete and continuous with respect to the Wolfram model in the following manner: Alice and Bob exist in a room where its only them, each with a button that can "freeze time" or more precisely stop the reception of input about the other. So Alice when she presses her button, can freeze bob in time, so that he receives no input from Alice. She hits the button Bob freezes. Alice hits the button again and bob unfreezes. So Alice mashes this button intermittently. You could ask what Bobs experience of the world would be like in this room. Would Bob ever notice that Alice had pushed the button or for how long? And the answer is that no he wouldn't. He would actually perceive the continuity of time, as continuous, as if she hadn't pressed the button at all. Because it is the act of receiving input that informs his perception of the universe. You can then pull the thought experiment out into N elements, each with K buttons that "stop time" like a game of hot potato. (and more importantly how a Turing machine would compute some computation one bit at a time) How would each element in N perceive the universe every time any button in K is pressed... So if you are some observer inside a Turing machine, and time worked discretely as it does in the wolfram model, you as an observer inside that universe would not experience time in reality as discrete...you would experience it continuously, since input is what casually informs every observer in n about the state of n. Further more, one can make a deeper statement about time. That if the universe behaved like a turing machine computing one bit at a time, and the observers that exist inside this construct perceive time as happening continuously like in this thought experiment with Alice and Bob... then does it matter how long it takes the turing machine to compute the universe? Like in the thought experiment, the answer is that it doesn't matter. It could be 10 second intervals or 10 million year intervals where the button is pressed...we as observers inside the construct perceive time exactly the same, that this experience would be continuous. This conclusion puts into question about whether time even abstractly exists in the Ruliad object at all...and it's likely (and wolfram reasonably concludes) that it has no objective meaning there, to us. The Ruliad simply exists...both instantaneously and at infinite time as if the two were the same thing. So ya. I find this inseparable union of the two concepts quiet beautiful, when thee universe is viewed from the perspective of a computation. It's this kind of elegance (the ability to make unified two deeply opposing concepts) that continues to sell me on the wolfram model as being a true theory of physics.

Explain?

What about space itself

He doesn’t want to talk about that apparently. I’m happy to see one guy with his head on his shoulders here. Thanks!

It was not about the unit calories. It was about the theory that heat is something like an fluid that was called caloric.

discrete strictures can be infinite.

@@mishikookropiridze Yes, and that is what I believe leads to continuity.

@@imjustadev not necessarly bu definition you still have gaps between points.

In this context it means that there is some sort of fundamental building block. Essentially, he's arguing that space is not perfectly continuously smooth. You can't infinitely reduce it up into smaller and smaller pieces, because at some point you'll get to the fundamental object from which space is constructed. Pretty trippy, and currently theoretical.

@@My_Personal_KZfaq thank you. Better explained than what I found elsewhere!

It’s to do with division. Continuous means you can keep dividing/cutting something into smaller pieces, forever with no smallest piece. Discrete means there would be eventually a fundamental building block. It would hell to have done discrete and continuous math functions to have a grasp on this.

I think you were thinking of "discreet" - a different word altogether

@@EbrahimLPatel most definitely

Neither.

When lights need to be rendered it is a particle

I would say that reality makes it to seem or appear discrete because a conscious observer reality is about making and dealing with discreteness (to survive, gather knowledge or whatever)

Its quite paradoxical that Wolfram says "we as computationally bounded observers conclude definite things happen". Yeah, but that would also include the conclusion of space being discrete haha.

I think Wolfram wont be able to prove that space is made of discrete elements, he may find things that suggest the conclusion, but that doesnt mean proving. I think that if observer is computationally bounded then hes also bounded by premises he makes about the world he perceives, and this may suggest that nature of reality is ultimately up to interpretation.

@@maziusclavo8021 Interestingly, three replies for three different aspects. Reminds me of this quote: "And on the magical path of discovery - like an inexhaustible love to always come with friends - each single answer attempted or found, brings three new questions."

If space is discrete, you can relate matter to it through gravity. If space is discrete you can easily explain dark energy as the space between galaxies expanding brick by brick, probably as a swap of matter to space, or energy to space.

Instead of a pull, Einstein saw gravity as the result of curved space. He said that all objects in the universe sit in a smooth, four-dimensional fabric called space-time.

Brilliant lol

Cement? Thats conk-creet baybee

Try to be a little more discreet

Reality is a shared perspective that can be independently tested.

Reality is a shared perspective that can be independently tested.

Reality is a shared perspective that can be independently tested.

You are using multiple technologies to write that comment that rely on the same principles you are questioning. Stupidly hilarious and sad at the same time. Science is all wrong but somehow all these technologies work despite that. Lmao.

@@williambrandondavis6897 the rocket is the proof? Wittgenstein does not agree.

I don't think it tells you anything about whether Space is continuous . . .

He's assuming all of these continuous equations we like are approximations to some as yet undiscovered discrete thing. His evidence is very thin though.

@@dinobotpwnz Well, "assuming" can just be "hypothesizing" . . . which seems fair enough. But leaving aside the whole of the evidence (to which I can't speak), I'm interested in what kind of personality factors would otherwise go into someone gravitating to one or the other of the two hypotheses: discrete or continuous. I'd gladly read a book that tried to explain Schrodinger's (continuous ?) and Einstein's (discrete ?) choices . . . based on their personality traits.

Explain please? Lol

Agreed. Reality is neither discrete nor continuous as I have explained.

Jonathan Gorard is doing work with connecting it with known physics. I think it's actually mostly Jonathan that is behind most of Wolfram physics projects theory.

​@@lubricustheslippery5028 My point is that Stephen shows zero interest in the work of other physicists (e.g. on quantum gravity) but, at the same time, does expect them to be interested in his work. Regarding connections with known physics: He's making huge claims (saying that he has derived QM and GR) but he has delivered nothing substantial. That's the main reason why I watch this guy; as a case study of a delusional narcissist.

he knows quantum theory he just didnt know the backstory of the thinkers :)

@@hhandle who?

The guy that wrote the math program that all physicist use (Mathematica)! He is not big as an scientist but far from just some random crackpot.

Sabine Hosenfelder's video is interesting, she talks about discrete space and quantum computers, that nature is not algorithmic. Tell me what you think after watching it