I was just about to comment this, that's the fastest I've ever heard Matt talk. Any cat you are holding or petting will eventually go apeshit, almost like radioactive decay each cat has its own half-life of calmness.
Cats usually don't like to be held like that or have their bellies rubbed. I know you are incapable of empathy for cats but it would be like a huge violent chimp picking you up and doing that to you with the knowledge that it could rip your guts out at any moment.
Love that the channel doesn’t seem to shy away from more philosophical topics. Didn’t expect you guys to be talking about Neoplatonism but it’s interesting to hear a physicist’s perspective
I am not a fan to be honest. I guess the topics are popular because there is no right or wrong with lots of room for interpretation and opinion. But I'd rather hear about actual science 🤷♂️
@@brunospasta you don’t need to make up new explanations, the philosophical topics are popular because philosophy is interesting to a lot of people. And the reason for that is simply in it’s defining qualities not external reasons, its not exact but has a greater density of thought provoking and novel ideas
This reminds me of a video about a Greek cult that was devoted to numbers and math. Supposedly, their motto was "All is Number" and they believed that Math was the language of everything and that it was always perfect. Then, one day, Hippasus decided to take the square root of 2 and discovered an irrational number. Then, he was either exiled or killed for it. Which taught me an important lesson: don't join any math-based cults.
That is strange.😅 Imagine being that devoted to math. Could you explain to me what an irrational number is. I've heard the word before but I don't get it.
@@avivastudios2311 It’s a number that cannot be represented as a fraction. For example, 0.333333… is a rational number as it can be represented as 1/3. However pi is irrational as it can not be represented by a fraction.
@@avivastudios2311all fractions repeat eventually (or are finite like 0.25), so another way you can think is that it's a number that doesn't repeat. Like square root of 2 = 1.41421367...
That has nothing to do with math and just humans in the past killing each other for going against the common beliefs, like when some guy said the earth isn't flat , a church burned him at the stake .
I feel a great sense of joy at the fact that this video on a mathematical universe is... at time of writing... number 42 on trending. If only we knew what the question was
We live on a mathematical universe that has an undiscovered law which, said law when stated as an equation has a way to put 42 as one side of the equation. This is a fact.
@@Bucephalus84 Its a reference to the comedy-sci-fi book series the Hitchhiker's Guide to the Galaxy, by the late Douglas Adams (an English author). In the story, the answer to the ultimate question of the meaning of life, the universe, and everything is revealed to be "42." They then realize that the answer makes no sense because they don't know what the question was. It's funny if you've read the book.
0:50 To the Editor of this video: The little things you do, like making the text flicker as though it were an old analog television we were watching this on, it's really just the Chef's Kiss of your talents. You add imperceptible quality to these videos, and as thankless as the job is, know you are appreciated. Thank you, mysterious stranger!
Also - It’s obviously apparent why Math works so well. Math is a system of measurement allowing us to measure many aspects. Math works w/ everything not just Space. This conceptual theory is foolery
@@metalgear- you take something to be true without wondering why it is true, as if the miracle of something rather than nothing has already been explained and the fundamental forces are a constant throughout space and time. In short, you’re prey to all your perceptions
@@jazzman7320 - Why it is true? We designed Math to be that way. It’s a very simple numerical value that counts. That’s like asking “How come Math works so well w/ Money Transactions. It’s almost Supernatural”
@@jazzman7320 - My perception is based upon you’re lack of comprehension of why Gravity exists. Why do Stars exist. Why does everything Orbit. My perception is literally flawless while you’re forever stuck on trivial concepts that hold no water like the notion the Universe was built by your Human invention of Math.
@@jazzman7320 Projection: ▪︎ a mental image viewed as reality. ▪︎ the unconscious transfer of one's desires or emotions to another person. You literally just took the appearance that there is 'something _rather_ than nothing' as a miracle, without wondering if and why it would be one, then claimed that thinking 'the fundamental forces are a constant through space and time' is being 'prey to one's perceptions'... Without realising that assuming an event to be a miracle requires someone to perceive said event as extraordinary and inexplicable by some constant behaviour of fundamental forces: in other words, any miracle claim readily assumes said fundamental forces to be constant and unchanging, unless someone able and willing to bend them does so. It seems you're doing precisely what you are projecting unto others, which by your own reasoning implies that you are just prey to your perceptual experience of some powerful agency responsible for what you merely assert to be a miracle. Unless of course, you're not understanding the words you're using and ended up miscommunicating. Either way, the mistake is yours.
One of my favorite channels on all of YT. Accessible (enough lol) yet very intellectually rigorous. Makes me feel like I am just barely keeping up, on the (exhilarating) razor's edge of learning. Great stuff.
OMG, I'm so glad you mentioned it - thought I might be suffering from Dunning-Kruger when your basic description immediately reminded me of incompleteness and the halting problem.
I read Tegmark's "Our Mathematical Universe" for the first time back in 2012 I think. I found it fascinating, if not entirely convincing. Even after re-reading it a few times since then, my views of it are basically the same. It's super interesting and fun to philosophize about, but its biggest weakness is its current lack of any way to falsify it. Still, I continue to enjoy the book (as well as his later book, "Life 3.0", which i've also read several times now). The intersection of philosophy and mathematics is a _very_ interesting field imo. Also, I continue to greatly enjoy (and support) your content 🙂
"... its biggest weakness is its current lack of any way to falsify it. Nor is there any way to test the claim that 'something' is needed to 'act out' the equations. But since the MUH is more parsimonious, the burden of proof surely falls on materialism.
@@jambec144 I agree, it's a parsimony of 1 bit (top-level realness vs. unrealness of entire universes) being discarded because the sense of that is already explained by the fact that we're inside this one, so of course it seems more real _to us,_ but that's not evidence that we're unique, any more than your own internal subjective experience is evidence that everyone else is a philosophical zombie. Our default assumption, that our universe is "real" in some sense that others are not, introduces a _distinction_ we don't have evidence for. To be honest I'm not even sure what is meant by saying a universe is real: if I snap my fingers and make the Peano arithmetic physically real, and snap them again and make them unreal, what am I doing? What has changed? Suppose I do it again, but with a structure that has conscious substructures. When I make it unreal, do they all become philosophical zombies? One possible definition might be: a universe is real if it is possible to find oneself to be an observer-moment within it. We consider ours to be real because we're here, experiencing it. If a universe isn't real, then it means that you can't find yourself to be within it, even if it has some conscious substructure. So realness in this sense would have an effect on anthropic reasoning, and so you could sort of work backward from actual observations to get a sense of evidence for or against the MUH. I don't see what would prevent these structures from finding themselves to be themselves, within their own little self-consistent context, and experiencing qualia and so on, without having to consult our universe first, or what could give our universe that authority. If you think consciousness is basically just a kind of pattern or computation or information processing, and that computation is basically just math, then the MUH is just a short step further in the same direction.
@@Eudaletism MUH is more parsimonious than materialism in that it posits the 'existence' of just the equations, while materialism requires an additional 'substance.' Yes, if one rejects Platonism in the first place, then the MUH amounts to claiming that nothing 'exists' at all. But this would be circular reasoning: you're simply insisting that 'real' things must have 'substance.' (And besides, I suppose that there's nothing more parsimonious than supposing that nothing exists!) But yeah, it's probably more productive to set the whole 'what is real' issue aside and focus instead on what sort of structures allow for an observer. An exploration of the nature and requirements of consciousness might then tell us something about the likely nature of our universe. This would then open the MUH up to empirical testing.
@@jambec144 (The first block of text here was a late addition to my previous comment, rehoming it here because I think I edited it in after you'd replied already; I have a bad habit of doing that.) I'd argue the MUH does have some successful retrodictions. Simple finite structures should be more common on the mathematical landscape, because they occur frequently _as substructures_ of other structures (including infinite ones). Compare finding finite strings of digits within the decimal expansion of some irrational number: every extra bit halves their measure. So the MUH maybe predicts the universe will have simple laws, with lots of symmetry. The MUH predicts a universe with an enormous number of conscious observers (the more observers, the more anthropic chances you have to find yourself to be in that universe), and this is satisfied by Many Worlds (if you like MUH because of parsimony then you probably are already taking MWI as your favored intepretation). There's always the possibility the universe can't be exactly described by math, though. Maybe math can only ever get infinitely close but never touch it, not even with limits or infinite sums or fractals or chaos. Maybe it runs on something fundamentally different from math, and math works well only because math is some kind of universal approximator. I'm not sure what that would mean, though. The issue of consciousness is a sticky one, because it seems that the line between conscious and not-conscious might be blurry, a gradual transition; and then you have to consider that consciousness takes time to compute, but it isn't in discrete steps like a program, but more fluid, so how do we "count" observer-moments, or measure the "amount of conscious observance"? I don't think these are impossible problems, but they require a much more exact understanding of consciousness to approach.
We're getting into theories that are increasingly difficult or impossible to falsify. At least in my lifetime. Knowing that, I am pleased to at least see a theory of the universe that can explain how something can come from nothing.
Yea, it's called metaphysics, all religions also intersect with that. Or... can there be a religion in the platonic world of ideas that has nothing to say about anything at all? Would saying nothing at all be a kind of statement? The Dharma is like this and not like this...
Great episode, only problem I had with it, is that when presenting objections to the universe being mathematical it fell into a very common error of interpretation of the Gödel incompleteness theorems, they are not about limits of math itself, but about limits of the axiomatic method to encompass all of math, a way better objection would be through Ocam´s razor, as the mathematical universe evokes too many ontological assumptions without granting a better or deeper explanation of the subject, my personal opinion about this is that our way of thinking of the universe in terms of physical laws or basic principles which need to be consistent and which underlie all of reality is in itself mathematical, as pretty much is the same as looking for an axiomatization of the universe. Edit: I came to revisit the episode and wanted to mention another thing, I found interesting that this hypothesis requests the different universes to have consisten rules, as in reality it is perfectly possible to work mathematics in the realm of non-classical logics, specifically for this case paraconsistent logics (those in which the principle of the excluded third is assumed as false) so it seems like a fault in the theory that assumes a limitation without a complete justification :)
@@oaktree1383 the equation may well work out, but this is getting into "if a tree(3) falls in the multiverse is anyone around to hear it?" territory, no?
@@oaktree1383 what I mean is that the math itself can be solid, but how do we know the math is anything "more than math"? If I'm understanding what you're saying, we're agreeing.
14:05 Slight correction, the halting problem says that there is no general algorithm that can determine whether any arbitrary program/function will finish, not that it’s impossible to determine whether a program will finish at all. There are certainly many specific cases where you can state with certainty that it won’t finish (such as while loops with no exit condition).
Worse than that, he implied that the halting problem was a problem for the Computable Universe Hypothesis. It's like saying that because of the halting problem, computers cannot exist.
@@ethan20minecraft I think you misunderstood. He's saying that if you proposed that only decidable/solvable equations physically exist, then it would have to be known programmatically ahead of time which equations fit this requirement. The halting problem shows how problematic this idea is. Of course, everything about this "theory" is wildly speculative and makes a lot of untestable assumptions so take it all with a grain of salt imo..
Epistemology here. Very interesting ! I have been looking for long about some kind of existing formalisation of this question. You gave me serious clues. I would be interested in the philosophical authors that sustains such position, pro and cons. Anyway, many thanks this excellent work !
Thanks for making the analogy with the cat. I wish you had 2 types of videos. 1 without any simplifications and the other for us people who don't get much because we aren't specialists in the field. Simplified examples really make it much easier to understand, I really enjoyed it
"Simplified examples really make it much easier to understand" - not true. They make you feel good about yourself, but then, so does a cheese burger. It is called the Dr Fox effect. I don't mind Matt doing it.
@@DrWhom ..."not true"? Of course it's true. Isn't that the ultimate goal for any theory? Isn't there a famous quote about this? I don't have the PhD or experience in the field...does that mean I'm not allowed to be interested enough to learn? The "easy examples" make it possible for us idiot's to understand. They plant the seed for hunger of truth and knowledge. That's a good thing. And I love cheeseburgers.
Great video as usual, thanks! I haven't read Tegmark's book, but I did read a summary paper or something by him years ago. I'd just like to comment on the issue of testability. The biggest problem for me with the mathematical hypothesis is the idea that the "baggage" is baggage. The baggage is not basically about how we connect mathematical expressions to human "perspectives," but how we connect them to human _perception_. Without some of that baggage, these strings of symbols clearly don't say anything about the physical world. The empirical content of a fundamental law may come from a higher-level law (or empirical regularity) that supposedly reduces to that fundamental law, but it has to come from _somewhere_, for it to be a statement about the world. So, the mathematical hypothesis is in principle untestable as long as it insists on getting rid of the "baggage." And if it is recognized that we need a translation from the mathematical expressions to outcomes of measurement operations (we need some baggage), then I think that robs the hypothesis of most of its novelty. We're left with some kind of mathematical realism.
the mathematical hypothesis is testable by inventing a better fit symbolic language not intended for use by human minds... Humans being the equations of reality : the universe examining itself.
@@SeaJay_Oceans would that not make it unprovable in reality then? No symbolic representation can be applied that doesn't require the interpretation of an agent of the universe. Every test is an observation of an observer unless the entity exists outside of reality.
@@gregmonks In the original sense of the word, philosophy can include either and often did. "Philosophy" just meant the process of systematically seeking the truth of our world and the findings that come from said process. This made it dynamic, ever evolving and changing because new data/info/understanding is always being encountered. In the modern meaning of "philosophy" it's just a fixed, static, (often arbitrary) framework for viewing things. These "philosophies" are often lifeless, as they're often closed to differing perspectives and data/info/understanding.
Tegmark's "Our Mathematical Universe" is very worth a read, if anyone's interested in this. In my understanding of the hypothesis, it's less that mathematics have a "physical manifestation" as Matt said multiple times, and more that what we "perceive" as a "physical" manifestation is actually simply what it is like to *be* math. To me this theory works really well with the observation that there doesn't really appear to be any actual hard "stuff," if you look closely enough. Atoms are subatomic particles are quarks/gluons are fields, which are simply mathematical descriptions with no obvious "physical" nature, there's no "thing" there. At the bottom, it's just math.
Or perhaps what that 'stuff' is is so far from our intuition that we can't comprehend its true nature. All we can do to understand it is by observing its measurable interactions. In other words, perhaps the reason everything seems to be 'math' is because that's the only means we have to model and understand it.
I really like how this theory really displays the tensions between empiricism and realism. That's counterintuitive, because one would assume the empirical position would be to be a realist. It really takes the realist position (the terms of our scientific theories describe actual physical stuff) to it's ultimate logical consequences: all math is actually real in a physical sense, because all physical things are math. But at the same time, it's not a claim that can be derived from observation but only from abstract reasoning. It's almost like a synthetic a priori theory, for any Kant fans out there
"it's not a claim that can be derived from observation but only from abstract reasoning" Yes!! 100%. Check out my other comment, I'd be curious to hear your thoughts. I can copy and paste it if you can't find it.
@@NestorKYAT Read it down then up like a horseshoe: 0. *God* - - - - - - - - - *Meaning* ▼ ▲ 1. *Philosophy* - - - *Philosophy* ▼ ▲ 2. *Truth* - - - - - - - - *Myth* ▼ ▲ 3. *Logic* - - - - - - - - *Story* ▼ ▲ 4. *Math* - - - - - - - - *Language* ▼ ▲ 5. *Physics* - - - - - - *Symbol* ▼ ▲ 6. *Matter* - - - - - - - *Conveyance* ▼ ▲ 7. *Chemistry* - - - - *Intention* ▼ ▲ 8. *Life* - - - - - - - - - *Thought* \ / 9. *Interest* (as a proto-will which tautologically emerges from the process of survival - ie. the only reason something is alive is because it fulfilled, by whatever means or accident, its interest of not dying) God isn't so much an intentional being as He is a force best understood as the Implicit Observer which naturally substantiates existence. And by substantiate I mean this: Before our universe, suppose there really is total Nothingness. Two things can be said about it for sure - it is singular and uniform. It is my view that Nothingness is inherently accompanied by the nagging question, "Well... isn't this nothing actually sort of a something?" God is the inherent "thing" which "asks" this question. (In this way, Nothingness is actually kind of an impossibility. It is inherently pregnant with infinite potential.) And as soon as it is asked, this singular and uniform Nothingness suddenly becomes the only Something in existence. However, due to the paradox of boundary and scale, it's simultaneously the largest and smallest thing in existence surrounded by an infinity of more implicit Nothingness. This causes the Something to "chase" the Nothingness outward, while the same spacial distinction happens inwards. The relative expansion of the universe and the uncertainty of quantum mechanics is due to the ongoing primal battle between Nothingness and Somethingness which is arbitrated by the God-force CPU, eternally crunching the numbers on the Original Question. I think the infinite difference between the Nothingness and Somethingness (0 and 1) is the source of all the energy in the universe. Also, I suspect gravity and dark matter are emergent consequences of the philosophical force between the two. I think this model which places Truth before Math eliminates the sticky situation of "any viable math has its own universe." I find it far more plausible and evident that the universe rests on the "it just is" principle. 2 + 2 always and only equals 4. There is one seed but infinite branching timelines.
I call this a win - the first Space Time episode where I've understood 100% of the material. And I had all the questions that popped into my head early in the video answered by the end. All ... except maybe, no mention of Gregory Chaitin?
@@kazzz2765 that is, out of dozens of PBS-ST videos, this is the first one I've actually understood LOL. Not to say it's any easier! Just more in line with my background
The halting problem is pretty interesting. I remember it from my "logic" course in University. If I remember correctly, you can actually proof that it's unproofable by using the function itself as an input, thus creating a loop where the functions is input into the function into the function and so on
I've never understood why the halting problem proof is considered so significant. I see no reason why you can't just redefine the question as "is there a general algorithm A for deciding whether another algorithm B halts, not including the special case of B incorporating the output of A?"
@@badlydrawnturtle8484 It's important because it shows there are limits to what a Turing Machine can do. Why is a Turing Machine's limits so important? No idea.
@@bluesillybeard The basic point of a Turing Machine is that it can emulate any computer (provided you aren't concerned with how long it takes to calculate things). Anything you could calculate using a supercomputer, you could also calculate with a Turing Machine. And, unlike actual computers which have intricate details, a Turing Machine is simple enough you can actually prove things about it. So you can use a Turing Machine (or other conceptually simple computer) to prove things about the limitations of all possible computers.
Reminds me of the library of Babel, the idea of an infinite library, a thought experiment until someone realised it could be expressed as a formula and ran on a computer. There is a page in the library of Babel that explains what you did today, and another that explains what you will do tomorrow, if you know what text your looking for you can search for the page reference number. But of course it's infinite, so good luck finding by chance the one that tells you in perfect detail how you will die. But the link is do these pages "exist" before you search for them? They exist in the "math". Hannah fry explains this really well (better than me) in her book Everything* a great read, not at the complexity level of Matt's videos however! (Maybe a future video idea?)
Heh, did it tough? Maths go back as long humans have been civilized. Keep records on how much beer everyone is allowed to drink etc. And in a sense I think a cat also knows it has for example 4 kittens and will deduct that one is missing if it only sees 3.
@@georgelionon9050 IMO life is logic and we discover ourselves and create language to communicate it. I think logic requires values for operation, but a lot of life value from different species seems to be emotions (ranging from negative, neutral to positive) applied to sensory experience in order to make decisions for future survival. Then it's a stored piece of information and if imagination is involved the logic expands to abstract use of the information with other information. maybe...
@@georgelionon9050 That's a very low standard definition for what "discovering math" is. We could take your thoughts even further, given the fact that neurons emerge eventually from mathematical equation, the very first neurons had "discovered" math, because there was math underlying their function, let alone how there is underlying math when a cat looks for a missing kitten. Though it could hardly be defined in precise terms, I'm pretty sure the quote is based on an underlying intuitive notion of *knowing* what math is in some deep sense, rather than just using it.
When it comes to the debate between discovered vs invented in math, I've settled on a middle ground of sorts. What I mean is, the relationships between phenomena in reality exist independently of our perception of them and we have had to invent a way to describe these relationships in a coherent and cohesive way in order to understand them and put them into use. Like a cloud of Starlings, each bird reacting to the one beside it, ignorant of the magnificent shapes we see when seeing them in flight or the atoms of a bridge interacting with one another, ignorant of being a 'bridge'.
I’ve also thought that Gödel’s incompleteness theorems throw a wrench in the mathematical universe. It’s difficult to believe that the universe itself would be incomplete; seems it would be saying that you could run a physical process that just .. doesn’t have a result at all
Perhaps quantum physics is an emergent "remnant" of the incompleteness of the underlying math? What if collapsing wave functions are actually manifestations of certain mathematical statements "deciding" to be true? What if this is what time is in the fundamental level? In the "beginning" all those undecided mathematical statements due to incompleteness are undecided, but as time goes by they choose to be true or false and that affects the construction of true mathematical statements (reality) and hence there is change in the reality with time?
@@pojuantsalo3475 I've thought along very similar lines... except in my version there is a different 'universe' for certain statements being true and for being 'false'. That is, one of the levels of the multiverse is simply a manifestation of undecideability.
If Schrodinger had written his thought experiment using a cobra instead of a cat, today it would have been harder for Matt to shoot the first scene of the episode
It's hilarious watching the cat try to figure out what the heck is going on, while Matt visibly tries not to speak too fast while still getting his intro out before the claws
Dear senior management folks that set the budgets for this series: MORE COWBELL PLEASE (and by cowbell, I mean higher budgets for even more of this much needed and amazing content)
such a good video, the use of the word “baggage” as well as the later explanations of the theories seeing math as a human invention put me firmly in the camp of not finding computational theory compelling but this was such a fascinating video
#TEAMINVENTED I've always felt mathematics to be epiphenomenal, like cutting a jigsaw puzzle, then forgetting you have, and then marveling at the beauty of how it all fits together. Anyone else?
Math is more like imagining a set of jigsaw pieces, any set, and seeing how they could fit together. What you're describing is physics. The universe is a bunch of jigsaw puzzle pieces that have been cut and we're marveling at the beauty of how they fit together, but math has nothing to do with our universe. Math is discovered, physics is invented. All of our current theories of physics are just inventions that approximate reality in a way that is useful for us. And it will stay that way until we DISCOVER the true fundamental Theory of Everything (if ever)
Math with letters... instead you must learn to add random symbols (your choice) to the macro galactic scale of physical interactions and then, work your way back into the the micro, adding integers and whatever until the algebra fits. No much real point applying the letters to numbers into formula until we move beyond this, its a small frame of reference we have so far.. Either end of the rope, is simply ones and zeros.
I started getting the sense that the universe was made of math while studying physics. I heard about Tegmark's ideas a year later, which made me realize I wasn't going nuts.
From Gödel all the way to Stephen Wolfram it is a fun ride. Computational irreducibility, multiway graphs and such things - I hope to see an episode looking deeper into that as well. I want to see where it is heading. However, what is available for my limited brain for now, I vote math to be just a great simulation tool. It is also backed up by my sight through meditation. In spiritual context one can observe the weird way our anthropological viewpoint is all granular and symbolic. Reality has no symbols, no constants and no models.
This video was an absolute gem. I hope you follow up on all of the themes you played with in this video. Very fun, engaging and worth while. Do you have any recommendations about what I should follow up on???
Dunno if "playing with themes" is proper science and should be blown up further. This has been scourge of modern physics and especially "science" communication for a while now.
This feels like a cart before the horse problem. Math works to describe and predict the universe because we formed it to do so, and we also can only think within its form. We apply mathematics to the universe because it’s the only way we have to describe it because it exists at scales we have no real existence in. Emergence is basically pointing out that at our normally observable scale, we have different and more directly experiential ways of describing things.
The only aspect of mathematics that humans invented was the notation to describe it. Mathematics describes pure irreducible logic, and logic simply 'is', requiring no antecedent. Any possible form of 'real' physical reality has to have an immaterial basis; anything else violates the simple rule of cause always preceding effect. It is no coincidence that all observed physical phenomena conform to mathematical principles! MATHEMATICS IS THE HORSE; the physical realm is the cart. Of course this is counterintuitive from our perspective; is the immaterial realm not just a product of our minds, which in turn are a product of physical reality? Yet to relegate logic from basis of mind to its end product is to deny its existence.
@@noyfb4769 Logic isn't inherently real. It's concepts and structure WE created and standardized with our minds. It's a series of fundamental formalizations of our ability to categorize and process incoming data. Logic is simply the formal language structure mathematics is built on. Not part of the inherent nature of reality. It's no more inherently "real" than the arbitrary delineation of Red vs Orange in the visible light spectrum.
@@noyfb4769 This is wrong. Mathematics are designed by humans by accepting and rejecting specific axioms. We can develop a different mathematical system by including a different axiom. For example accepting the fifth postulate leads to Euclidean Geometry but rejecting the fifth postulate gives you Non Euclidean Geometry. Both are self consistent mathematical system but the fifth postulate can't be true and false at the same time so you have to choose one or the other.
"Math works to describe and predict the universe because we formed it to do so..." Alternatively, we have * discovered * the correct description of reality. This debate is several millennia old. You can't settle it by simply declaring one interpretation to be correct.
I have a small but critical correction. Undecidable problems are not "neither true nor false". They are claims that are either true or false but where it can be proven that no algorithm can necessarily determine if the claim is true or false. In the halting problem, for example, it is proven that no algorithm can be written that will always determine if a given program will ever stop. The program in question will stop or never stop, but we can not know which of the cases will happen with by executing an algorithm.
I'd say that math is a language that can describe reality. It is suspiciously good at describing the reality because our minds that created this language are emergent phenomena of the said reality, governed by the same relations and dependencies. In a way, we learn reality in the act of constructing language. However, just like it's possible to write a formally correct sentence that doesn't describe any particular really existing thing (like "pink invisible unicorn"), it's also possible to make formally correct math equations that just doesn't describe anything actually existing.
It wouldn't exist from our point of view. But if these equations described sub structures that were able to observe and model the mathematical environment around them, they would perceive themselves to be living in a real physical universe just like we imagine we do.
This is my view. I have no idea why he wanted to jump all the way to, _Well now EvErYtHiNg_ (computable) _is physical._ It's just easier to say, OK, yeah, our fundamental lowest level of reality is just information, that can be expressed as math. And it makes sense we can find this math as we're in this universe.
It's a relieve for me that at least some people in this world share my interests and take ideas like these seriously. I can rarely discuss stuff like this in real life, so it keeps stuck in my head. Videos like this ease the problem of rarely getting constructive feedback on such ideas.
@@marcosolo6491 No and I've made this point previously, they're definitely running out of material, (lets face it results from the LHC for example, have so far not lived up it's hopes/expectations,) and the question; is a mathematics something that we invent or something that discover is an old one and unlikely to be resolved any time soon.
The book Permutation City by Greg Egan is a really interesting exploration of this idea. I highly recommend it if you're into science fiction (which, given this channel's subject...).
Amazing episode, and one of my favorite theories, along with Conformal Cyclic Cosmology! I think it's very related to the problem of sentience and defining what it "feels" like to exist as any given entity on a subjective level. For example, I have heard theories that sentience is simply what it "feels" like to process large amounts of information, whether or not that sentience results in a single entity that is self aware or not. So in that sense, it must "feel" like something to be a computer, to be the internet, to be a planet even, and the only difference between all that and us is just that our sentience results in the experience of a single consciousness.
Does it feel like anything to be unconscious? If so does something/someone else feel it? Or is it all a series or instantaneous moments or awareness with no memory to provide continuity… and if that’s the case is that what any universal ‘consciousness’ would be like?
@@PatternShift That's something I wonder: if we imagine that planets might have consciousness, then you might also imagine that the universe has a consciousness... but does that mean your arm does as well? Your hair? And if so, which part of reality holds "you"? I mean, I guess it's really not much different to the general hard problem, but it's even more fun to think about in the context of universal consciousness and sand-sized consciousness and the endless matryoshka dolls in between 😊 All simultaneously infinitely separate and one
Look into the attention schema theory of consciousness. I think that theory does the best job of at least describing what “feeling” is in a mechanical and unbiased way. And to me, it’s definitely the most logical working theory of describing consciousness and how it emerges
There are no answers to the “hard problem” to be found in physics, both Penrose and Crick are just wrong about that. Consciousness, as you would think of it (what it means to “be like” something) is not a physical object, it’s a process of the evolution of *abstract* objects. Well beyond the reach of physics just as psychology or sociology are.
Awesome episode as always. This reminds me a thought I had about the mathematical expression zero which can not be found in nature because in reality we can't really work with all the things that do not exist and the universe is fundamentally based on existence and not absence of things. So the questions like why the universe exists might not be applicable since it maybe the the only possible state it can have.
In Computer Science, we have multiple models of computation. The two most popular models are Turing machines and Lambda calculus, both of which are equivalent and can compute anything that is computable. We can use one to prove things about the other. We can use Turing machines to prove things about Lambda calculus, and vice versa. For example, if we use the Turing machine model to prove some problem is undecidable, then that also proves it's undecidable for Lambda calculus. Otherwise, we use known undecidable problems (halting problem) to prove other problems are undecidable. Such a proof is called a Proof by Reduction. This works because the different models of computation are (presumably) consistent. I think the relationship between physics and mathematics is the same Proof by Reduction. We take some physical law and *reduce* it to a mathematical equation, then use mathematics to manipulate these equations, and reduce that back into physical terms. Presumably, both mathematics and physics are consistent, so a proof by reduction usually yields a true statement about the physical world. Something else I don't think was covered in this video, mathematics is essentially founded in the physical world. One of the earliest forms of mathematics is geometry, and geometric shapes are great ways of modeling physical objects. Thousands of years ago, mathematical proofs were largely in terms of geometry, not algebra or similar. So I think the strong relationship between physics and mathematics is no coincidence. I think viewing it as using one consistent system (mathematics) to prove things about another consistent system (physics) via proofs by reduction explains much of the "unreasonable effectiveness of mathematics".
Mathematics is a language that is the most suitable language for describing the physical world, but it is still just a tool. And just as with spoken language, mathematics can get it very close to correct but it can also get it very wrong or it can get a really good prediction for a very specific situation and have ridiculous artifacts along with it. As was mentioned above, this is just a step closer to religion based on philosophical gobbledygook.
Wow, this is exactly the conclusion I had come to years ago about what the universe is... weird to see it verbalised exactly point for point in a Spacetime video! Great to know it has a name and something I can share to help explain it to people, I've struggled with that part!
Yes second Veritasium, it's brilliant I was searching for something like this for years before.. there was never a proper science communication simplification of this. There was only the real thing, Goedels paper that is very hard to read, and there was the book Goedel/Escher/Bach.. but it's a whole book that doesn't get to the point and plays a lot around with recursion.. and there is lots of lots of lots misunderstanding what the theorem says and what people believe it says (including Matt it seams).
On the ending note, about typical universes - if mathematical structures can get infinitely complex while still supporting life, and at every step up in complexity there's more & more options to choose from that support life, then we should expect to find ourselves in an arbitrarily complex universe. Ie from our perspective, the further we keep digging down to smaller scales to find fundamental laws, the more layers we'll find, & it could well go on arbitrarily (infinitely?) long P.S. thanks for covering my request on this topic 😁 had been super curious about more well-established thinking on this type of multiverse
It seems this theory is fundamentally untestable. Any universe we find ourselves in would be part of this theories multiverse. Unless we somehow discover that the universe does not follow rules at somepoint, it would be impossible to tell if this was true or not.
At least with current physics, we have a difficulty with measurements below the scale of the planck length, given that they would produce a black hole (I cannot remember the exact reason why or if this is 100% the case, remember hearing it from Sean Carroll). I remember thinking about this in my teens though. I think it's plausible, though unlikely testable. How are we to get past the fact that our observations are already collapsing and changing the physical systems we try to measure such that we could even make a deeper measurement? I don't know. Interesting question though.
16:39 This makes me think finding explanations for things we do not currently fully, or at all, understand can be approached from multiple directions. Fascinating. It would be awesome if two groups of scientists worked at a problem from two opposite ways of thinking and came to the same conclusions.
This was a particularly heavy episode, I’m going to have to rewatch it several times before it fully sinks in. Seems my calculator is having trouble with the equations 😂
I'm going to have to rewatch a few (dozen) times as well... General gist from a first casual watch is that this theory would turn gamers into very cruel deities of a sort, as the environment in which they "play" is entirely mathematically derived and self-consistent as well. I had to stop the video there, and ponder my vast sins..
Think you fell into the trap of the Third Man Argument which Plato himself refuted: The Form of 'Circle' isn't itself a circle but the principle of circularity, among which circles are expressions of. Nor would the form of Cat itself be a cat but rather the essence of 'catness'. This becomes obvious when we consider the 'Form of Difference', it's not itself some particular difference but 'difference' and 'differentiation' itself. If it were itself different it would be different to all things including itself. Though, of course, Plato does say this about 'the One' in Parmenides, that it is different from itself...
Recently I had the opportunity to ask Michio Kaku a question and even more recently I had the opportunity to ask ChatGPT a question, obviously, and I asked them both what the implications of being restricted to the rules a formal set would mean if we lived in a universe constructed by mathematics. I got no satisfactory answers. I should have known that Matt and PBS Space Time would eventually save the day with their invaluable content, and I didn't have to wait for long! Thank you so much for this video
Having seen the interview John Michael Godier did with Michio Kaku on his Event Horizon channel a while back I lost any semblance of respect for him as he showed he is no longer capable of thinking off script probably not having had to actually think since he left academia behind for science popularism
Surely the very fact that we as humans can identify and recognise the halting problem(and not get stuck in an infinite loop) goes a long way to proving that the universe is not purely made of math/logic? Is that too reductionist a view, or on point?
I don't believe that everything in the Universe IS math, but can be broken down into a mathematical foundation to be explained. It's truly amazing. Wish I had this kind of drive for knowledge 15 years ago in School
If everything in our Universe can be broken down into and explained by mathematical concepts (and as far as I know, we haven't yet discovered anything that wouldn't be describable using consistent language of rules), then the Universe is isomorphic to a mathematical structure which has the same properties and relationships as the ones we discover in the thing we find ourselves in. What I mean is, there is no difference between our Universe and an abstract mathematical structure which describes our Universe. If two things have exactly the same properties, they are actually the same thing. We tend to intuitively think that there is some special property that the Universe possesses called "physical existence" which makes it "real" as opposed to abstract. In reality, "physical existence" might not even be a meaningful concept, how would you define it? If there is no additional property to our Universe, then it actually is the mathematical structure that its laws define. This to me is truly amazing. There is no reason to even ask why there is something rather than nothing. Mathematical structures just are. That's the only possible option for reality to be free from contradiction.
@@szymskiPL i wouldn't say the universe is math then, but rather like a giant calculator that simulates itself. Besides, there are many theoretical mathematical constructs that don't represent the laws of the universe, otherwise we wouldn't need practical experiments since everything could be derived from math. You can also do mathematical equations at any time while the things that happen in the universe are bound by the laws of physics.
@@SteveAcomb it might just be that the deeper we go the more incomprehensible the universe becomes to the degree that not even math can describe it. Math is something that humans came up with, doesn't mean the universe can be fully described with it. Like for example if the uncertainty in quantum mechanics is truly nom deterministic then math can only make probability predictions but not actually describe what actually will happen. Then there's also no other logic to why it ended up in a certain way in a certain case. Then all physics math is just like statistics with emerging patterns on a bigger scale. It's still super useful but just a simplified model
Sabine Hossenfelder might have a few interesting words to say about this. But hey - on another topic all together, here is an idea I would like to see you pursue in some future episode: Nested black holes. I've seen a lot of vids lately on the "is a the universe a black hole". True or not, it got me thinking about nested black holes. For example it seems like not too big a leap to envision supermassive black holes swallowing stellar mass black holes that would continue to have some existence after crossing the event horizon. But then I started think about what really happens when any black holes merge. Why should we assume the singularities somehow merge. And on that topic .... how close does matter have to be to such a singularity before the density of matter is so high that it would cause black holes to exist. So maybe there are like infinite little black holes surrounding the singularity? Don't know. Needs math I guess.
No lol. Wrong. The earth is actually flat so don't fall off the edge. And there's no such thing as Australia. It's a lie perpetrated by the government.
@@gabor6259 Ys-ish. But infinity is funny, and not usually intuitive. When you have two points of infinite density approaching each other (and I'm not even sure the concept of "approaching" makes sense - these are not "points in space" - these are "space") things might be weird. We have infinite natural numbers. And infinite even numbers. And infinite odd numbers. And they all exist happily together, all equally infinite, none greater than the other. Not intuitive, but mathematically sound. Could there be wormholes hidden in nested blackholes? Even numbers bet "yes". Odd numbers bet "no". Who wins?
I had never think about the relation between Godel theorem and the "mathematical world" 'I feel a sort of disillusion for thinking that with maths were possible fully understand reality. Nice video, I enjoy it and will make me think a lot of things:). Best wishes for the project, greetings from Colombia.
Fair enough, it surprises me so much with these types of theories that reputable scientific figures often just forget about Godel and math being incomplete.
@@teok5665 It's because the PBS guy doesn't understand Godel Incompleteness. Godel incompleteness doesn't say there are statements that are neither true nor false. It's that they are not provable true or false. But instead PBS guy extends that to say that if the universe is math then there are physical laws that are neither true not false. No, no, no: Godel says that for a given set of axioms used to explore the mathematical landscape, there are true mathematical statements that are not provable within that set of axioms. Hence if the universe is math there will always be physical laws that are not provable. But not provable is not saying the law is nether true nor false. It's about our limits of understanding rather than whether the universe is math.
I've been an adherent of this hypothesis for years. It just seems like a natural conclusion that if there is a mathematical structure that can give rise to consciousness, the universe it describes would physically exist from the perspective of that consciousness, even as that universe remains just a hypothetical to us. Existence is relative in this view.
These ideas put forward by Tegmark are not only good, but are the *only* ideas that I know of that are capable of reaching down to and sensibly address the most fundamental question of all - Why is there something rather than nothing?
Indeed, mathematics (or, more fundamentally, logic) is the only thing I wouldn't question the necessity of existence of. Truth doesn't need a universe to be true.
"Something rather than nothing" is a non-question. The only answer is Mu, the answer that un-asks the question. How could there "be" nothing? Nothing doesn't and can't exist, or it wouldn't be nothing. So how long would nothing exist before something existed? It can't, because time isn't nothing. The universe necessarily has always been here, because there was never a time when there was no time.
Yeah it's the closest thing we have to an answer to that question but we still have no explanation of why mathematics has to exist, i mean we can't imagine a world without math, it seems impossible and it probably is, we can't prove it tho, at least for now. A theory of everything (in philosophy) requiers 3 properties : the principle of sufficient reason (every fact t has an explanation t'), comprehensiveness (each facts t are explained by the theory T) and finality (the theory T has no deeper explanation so T explains itself). Tegmark's guess (in his book) is that mathematics, computer science and logic are different ways to look at the same thing, we already know that there is a correspondance between computer programs and mathematical proofs (curry-howard isomorphism) and even a relation between intuitionnistic logic, cartesian close categories and lambda calculus, basically between math, logic and computation (cf : computationnal trilogy), so his guess ain't that crazy.
I've always thought of this. I'm so glad I have a word for it now and also a video to show people whenever it might happen to come up in conversation. Also to now know the phrase "Anthropic Principle" which is another thing I'm always trying to explain to people. I always thought the universe as a whole can be completely explained by a single equation. If you start anything from exactly the same place with exactly the same numbers and exactly the same variables it will always result in the same answer. Now that I've seen this video and some real science behind it, it only makes me think this further. If an equations existence implies it exists physically and can be viewed from outside of itself then that, to me at least, explains everything. Our universe exists everywhere everytime all at once in the same way you can view an equation that will describe a ball dropping and as long as all the variables are the same it will drop the same every time no matter what. You don't need to see the ball physically drop to know that's what it means and it's inevitable outcome. We're simply living inside of the equation so we cannot see it from the outside as a whole, we are the ball dropping at this point incapable of discerning the equation that inevitably lead to the drop. If the equation of the universe is exactly the same in another universe then it will inevitably lead it to create you exactly as you are now, doing exactly what you are right now because at the most fundamental level everything is an equation moving forward through the variable of time. If you rewind time it will always lead to the same place, if you go forward it will always lead to the same place. The atoms that were created in the very beginning will always travel through space in the same way, form the same stars that will then explode in the same way until it inevitably will form the neurons in your brain that are reading this right now. From the outside of the equation it just exists, all the time, everything all at once because just by simply reading the equation and the numbers you can know that it will always end up creating everything as it is, was, and will be. From the beginning to the end.
I’ve never seen a RUclips comment I agree with more! The more I learn about math or science the more I stop believing in free will. Everything in your life was meant to happen and so is everything that will happen. People think they make decisions, but every decision your brain makes could be predicted if you knew all the variables present in the brain at the time the decision is being made. Which just means we think we have free will but all of this is decided anyways. We’re all just part of an equation! I always try to explain this to people and I think no one cares lmao 😔
@@ayoactually5284 your not alone my friend. I’ve been similar thinker. Unfortunately even mentioning the idea of determinism or no free will is like taboo to average closed minded man.
I believe that, the universe is deterministic, or at least that free will is nothing more than a mental tool to keep us actionable. I also find this thought quite fascinating, but at the same time I don’t really care. After coming to that conclusion nothing really changes. It has no practical implication. I think that is, why many people don’t care in the first place. It’s just completely irrelevant for our lives apart from being fun to think about.
The current state of physics doesn't provide much support for a deterministic universe, because no one knows how quantum mechanics decides where a particle is going to be. It's considered random, which really means we just don't know. I suspect that we will never know whether the universe is truly deterministic, because it would be impossible to test.
Levels 1,2 and 3 are the multiverses in our level 4 mathematical structure, however according to tegmark in other mathematical structures may contain none of those, but completely new and different types of multiverses we can't imagine. This was all in tegmarks book it blew my mind.
Tegmarkian baggage is just a generalization of how we conceptualize emergence; in computer science terms, the layers of abstraction a system has. The dichotomy between observation and absolute reality also reminds me of constructor theory and the participatory universe concept.
Ive always said maths is a fundamental element of the universe PS: im glad no one even notices his Australian accent, they’re so used to it. This folks is the real Aussie accent...its stunning in its normalness.
@@PeterKnagge the only nonsense about "math"is that anyone says "maths" It's not plural, and it's an abbreviation of mathematics, also not a plural. So why would you cut out the middle and leave the s at the end!?
Would love to see you talk about the Nov 30 2022 Nature paper by Jafferis et al "Traversable wormhole dynamics on a quantum processor". Some of the pop sci articles are touting it as "confirming the holographic principle". Curious if it's all hype. Sounds like extremely fascinating research being done on the Google Sycamore processor but I don't fully understand it myself.
This video made me think that maybe I should give Tegmark’s book another chance. I got it several years ago and while I have started reading it twice I haven’t gotten past the first few chapters. Also, my aunt was in the same high school class as Tegmark for about a year.
"If there's nothing else to an electron but a set of numbers describing its position, momentum, and charge, can we say that the electron is simply that set of numbers?" It seems to me that if you have to describe the numbers as having particular meanings, then you've already answered your own question.
Well charge, momentum, and position are all mathematical quantities. Math in this case isn’t just numbers, geometry is part of mathematics, the math in this case is things like vectors, wave functions, spaces and fields. What do you think energy is? Is it some “spirit of motion” or some undefined thing like that? No, it’s a mathematical quantity that causes changes in the structures of other mathematical structures like space, fields, and strings. The concept of “matter” is also similarly undefined as that example, a lot of people think “well matter is made of mass and charge” and other properties, but when you go down to it things like spin, mass, charge, and any other property in physics, they’re all mathematical quantities. The RUclips channel ScienceClic has a video on quantum field theory that describes the conserved quantities and things I’m talking about if you want to look into that more, though there are other channels too, that one just describes it really well. Basically it goes down to that if you’re saying “well the universe is made of matter” and that the mathematical descriptions are just tools used to describe some mysterious substance, then that mysterious substance is just some undefined thing that somehow is not the sum of the mathematical properties like energy, charge, spin, etc. which we know are mathematical in nature. You’d basically be saying the world is made of the essence of god or magic or any other undefined thing. Now, what is a mathematical structure is a tougher one to explain, from the stuff I’ve thought about myself, a mathematical structure is just an element, some thing, that’s described by logic, the idea came from how there is an equation that describes lines, basically the line is the information contained in that description, or if you want to call it, logical arrangement. That’s probably not the best explanation I could write but it’d be a lot of work to write more than that and keep it from being a pain to read. (Also sorry for writing this super long damn comment in your replies, I just wanted to talk about this and I found it very hard to make this a comment by itself, so apologies)
why? if you mean words like "position, momentum, and charge" then those are just convenient labels used to talk about these concepts. if you mean the actual concepts to which these labels refer, they're described by laws of physics which would themselves also be a part of the computable mathematical structures Tegmark describes. the "meanings" of space, momentum, and charge are all mathematical in nature so certainly no question has been answered
I'd highly recommend Permutation City by Greg Egan! To those who enjoy these ideas and entertaining what these mathematical universes might look like. He takes this idea in a sci-fi future, and explores what would happen if one man decides to *really* test out this hypothesis by simulating himself inside one
I completely agree with you. If its possible to derive mathematical constants like e from just the concept of numbers, which themselves can be derived from just boolean logic it seems very plausible that the physical universe we know is also a direct consequence of logic itself, just like another constant and exists simply because it can.
What paradox? Something definitely comes out of nothing. Think of sound: what do you really hear? Especially with low pitched sounds, there's some sort of graininess to it, because sound is a wave and every wave is intermittent with a through of silence. There can only be sound when before there was silence. Otherwise, how could you tell sounds apart at all? Non-existence IMPLIES existence, and the other way around as well. I don't like tegmark's hypothesis for two simple reasons, it lacks predictive power (which is the whole reason we do science) and is ill-defined. What do you mean that something is made of math? How does consciousness come into play?
@@FunkyDexter I don't think you grasp what is meant by "nothing". Before there was sound, there was air for the new sound to take place in. There's space for the air that's teaming with particles and time. There's physical laws governing the spacetime. Hardly "nothing".
@@Quarkburger Then what is it that you mean by "nothing"? In that sense not even empty space is nothing, spacetime has elastic properties that respond to the energy in it. I don't think you can even really grasp what nothing truly is, because as soon as you try thinking about it you immediately end up assigning it some properties, like"black emptiness" or similar. The only possible way you can define true nothingness is by defining what it isn't, and work like a sculptor by removing stone piece by piece, except you'll always end up with some stone in your definition. The crux of the problem is that there is no way to define a lack of something without referencing that something. You need existence to define non existence, so in that sense sound DOES come from nothing, because the only way to tell it apart from other air motions are specific attributes that air lacked before. It's not about cause and effect, which is simply a linear sequence of events that always happen in succession. A natural cause is also very rarely linear: the universe is a closed system only as a whole, but if we trace back the "cause" of every event we always end up encompassing the whole visible universe, as interactions tend to spread over time. You'll find that tracing the causes of a phenomenon back in time is not that useful to understand the full nature of the phenomenon; for that you need a description of what the phenomenon is doing that it wasn't doing before. Only after you cleared that up you can safely investigate a bit further back.
@@FunkyDexter True Nothingness is extremely hard to grasp. Anything other than Nothingness needs to have an explanation, and this is where cause and effect and the paradox comes in. You can't trace causes and effects back to true Nothingness. So either you start with something, which has no explanation, or you trace causes and effects back to Nothingness. I don't see how either one is possible.
![Seungmin "그렇게, 천천히, 우리(As we are)" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/kAzmhLHePqU/mqdefault.jpg)
That cat was like, "you've got 30 seconds, make it count".
I have it on good authority all cats are into superstring theory
Pause
@@jopmens6960 Anything but quantum mechanics, they really hate Schrodinger!
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Video discussing complex philosophical hypothesis of the nature of reality.
Top comment: "LOL CAT!"
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I love how Matt rushes through the intro, waiting - like a ticking countdown - for the cat to be getting out of there.
I was just about to comment this, that's the fastest I've ever heard Matt talk. Any cat you are holding or petting will eventually go apeshit, almost like radioactive decay each cat has its own half-life of calmness.
He was almost talking as fast as that motor mouth guy from 80's commercials lol
@@barretprivateer8768 So basically a Half-Life cat meme (look it up on RUclips for some laughter)
Cats usually don't like to be held like that or have their bellies rubbed. I know you are incapable of empathy for cats but it would be like a huge violent chimp picking you up and doing that to you with the knowledge that it could rip your guts out at any moment.
Tthe cat seems uncomfortable from the start. They tend not to like being held in a particular way or at all.
Love that the channel doesn’t seem to shy away from more philosophical topics. Didn’t expect you guys to be talking about Neoplatonism but it’s interesting to hear a physicist’s perspective
I am not a fan to be honest. I guess the topics are popular because there is no right or wrong with lots of room for interpretation and opinion. But I'd rather hear about actual science 🤷♂️
@@brunospasta you don’t need to make up new explanations, the philosophical topics are popular because philosophy is interesting to a lot of people. And the reason for that is simply in it’s defining qualities not external reasons, its not exact but has a greater density of thought provoking and novel ideas
@@brunospasta 🤓
@@brunospasta 🤓🤓
@Repent and believe in Jesus Christ stfu
This reminds me of a video about a Greek cult that was devoted to numbers and math. Supposedly, their motto was "All is Number" and they believed that Math was the language of everything and that it was always perfect.
Then, one day, Hippasus decided to take the square root of 2 and discovered an irrational number. Then, he was either exiled or killed for it. Which taught me an important lesson: don't join any math-based cults.
That is strange.😅 Imagine being that devoted to math.
Could you explain to me what an irrational number is. I've heard the word before but I don't get it.
@@avivastudios2311 It’s a number that cannot be represented as a fraction. For example, 0.333333… is a rational number as it can be represented as 1/3. However pi is irrational as it can not be represented by a fraction.
@@avivastudios2311all fractions repeat eventually (or are finite like 0.25), so another way you can think is that it's a number that doesn't repeat. Like square root of 2 = 1.41421367...
That has nothing to do with math and just humans in the past killing each other for going against the common beliefs, like when some guy said the earth isn't flat , a church burned him at the stake .
@@netdreamr You can also word it differently if you want
I feel a great sense of joy at the fact that this video on a mathematical universe is... at time of writing... number 42 on trending. If only we knew what the question was
It's probably an equation.
We live on a mathematical universe that has an undiscovered law which, said law when stated as an equation has a way to put 42 as one side of the equation. This is a fact.
@@vohemiq please explain further. What significance does 42 have?
@@Bucephalus84 Its a reference to the comedy-sci-fi book series the Hitchhiker's Guide to the Galaxy, by the late Douglas Adams (an English author). In the story, the answer to the ultimate question of the meaning of life, the universe, and everything is revealed to be "42." They then realize that the answer makes no sense because they don't know what the question was. It's funny if you've read the book.
@mchevre So long and thanks for all the fish!
0:50
To the Editor of this video: The little things you do, like making the text flicker as though it were an old analog television we were watching this on, it's really just the Chef's Kiss of your talents. You add imperceptible quality to these videos, and as thankless as the job is, know you are appreciated. Thank you, mysterious stranger!
Also - It’s obviously apparent why Math works so well. Math is a system of measurement allowing us to measure many aspects. Math works w/ everything not just Space. This conceptual theory is foolery
@@metalgear- you take something to be true without wondering why it is true, as if the miracle of something rather than nothing has already been explained and the fundamental forces are a constant throughout space and time. In short, you’re prey to all your perceptions
@@jazzman7320 - Why it is true? We designed Math to be that way. It’s a very simple numerical value that counts. That’s like asking “How come Math works so well w/ Money Transactions. It’s almost Supernatural”
@@jazzman7320 - My perception is based upon you’re lack of comprehension of why Gravity exists. Why do Stars exist. Why does everything Orbit. My perception is literally flawless while you’re forever stuck on trivial concepts that hold no water like the notion the Universe was built by your Human invention of Math.
@@jazzman7320 Projection:
▪︎ a mental image viewed as reality.
▪︎ the unconscious transfer of one's desires or emotions to another person.
You literally just took the appearance that there is 'something _rather_ than nothing' as a miracle, without wondering if and why it would be one, then claimed that thinking 'the fundamental forces are a constant through space and time' is being 'prey to one's perceptions'... Without realising that assuming an event to be a miracle requires someone to perceive said event as extraordinary and inexplicable by some constant behaviour of fundamental forces: in other words, any miracle claim readily assumes said fundamental forces to be constant and unchanging, unless someone able and willing to bend them does so.
It seems you're doing precisely what you are projecting unto others, which by your own reasoning implies that you are just prey to your perceptual experience of some powerful agency responsible for what you merely assert to be a miracle.
Unless of course, you're not understanding the words you're using and ended up miscommunicating. Either way, the mistake is yours.
This channel consistently puts out some of the best science content on RUclips. Gotta love PBS.
why am i hearing "meth" all the time? if only the universe was meth...
Peanut Butter Spread?
This was not science
Nathan Oakley sent me ✌😃
ruclips.net/user/live9HqcaDQ_Fc0?feature=share
Much love❤
@@bpscast right, it was metaphysics, which is more fun than science :)
One of my favorite channels on all of YT. Accessible (enough lol) yet very intellectually rigorous. Makes me feel like I am just barely keeping up, on the (exhilarating) razor's edge of learning. Great stuff.
Mathematically nothing or zero is more than possible.
But we can't find nothingness in our Universe
0:26 I love how the cat kind of freaks out when realizes his body could be made entirely of equations
I want the bloopers of this one!
it knows.
It's a scary thing to imagine some phenomena in the Universe that mathematics would never be able to explain.... Like cats.
@@redneckshaman3099 Classy.
ye funny how it starts to spin reality around itself so the floor matches the orientation of its feet
I love that when the cat is confronted with being a mathematical object, it immediately tries to escape Matt.
It failed math class and doesn’t want to hear or talk about maths
Who wouldn't
It realised that matt was getting too close to the truth and decided to escape 😂
It felt the gig was up!
Matt: Does that mean that the cat is made of math?
Cat: Do not want!
That would explain why I seem to be so bad at dealing with it. Very compelling.
😂
I came to make this exact joke but you got here first. Hats off to you, sir or madam. :)
Even if it's dumbed down to something as insignificant as a human life?
🤣🤣🤣👍👍👍
Best comment I've seen all week
OMG, I'm so glad you mentioned it - thought I might be suffering from Dunning-Kruger when your basic description immediately reminded me of incompleteness and the halting problem.
I read Tegmark's "Our Mathematical Universe" for the first time back in 2012 I think. I found it fascinating, if not entirely convincing. Even after re-reading it a few times since then, my views of it are basically the same. It's super interesting and fun to philosophize about, but its biggest weakness is its current lack of any way to falsify it. Still, I continue to enjoy the book (as well as his later book, "Life 3.0", which i've also read several times now). The intersection of philosophy and mathematics is a _very_ interesting field imo.
Also, I continue to greatly enjoy (and support) your content 🙂
"... its biggest weakness is its current lack of any way to falsify it.
Nor is there any way to test the claim that 'something' is needed to 'act out' the equations. But since the MUH is more parsimonious, the burden of proof surely falls on materialism.
@@jambec144 I agree, it's a parsimony of 1 bit (top-level realness vs. unrealness of entire universes) being discarded because the sense of that is already explained by the fact that we're inside this one, so of course it seems more real _to us,_ but that's not evidence that we're unique, any more than your own internal subjective experience is evidence that everyone else is a philosophical zombie. Our default assumption, that our universe is "real" in some sense that others are not, introduces a _distinction_ we don't have evidence for. To be honest I'm not even sure what is meant by saying a universe is real: if I snap my fingers and make the Peano arithmetic physically real, and snap them again and make them unreal, what am I doing? What has changed? Suppose I do it again, but with a structure that has conscious substructures. When I make it unreal, do they all become philosophical zombies?
One possible definition might be: a universe is real if it is possible to find oneself to be an observer-moment within it. We consider ours to be real because we're here, experiencing it. If a universe isn't real, then it means that you can't find yourself to be within it, even if it has some conscious substructure. So realness in this sense would have an effect on anthropic reasoning, and so you could sort of work backward from actual observations to get a sense of evidence for or against the MUH. I don't see what would prevent these structures from finding themselves to be themselves, within their own little self-consistent context, and experiencing qualia and so on, without having to consult our universe first, or what could give our universe that authority. If you think consciousness is basically just a kind of pattern or computation or information processing, and that computation is basically just math, then the MUH is just a short step further in the same direction.
@@Eudaletism MUH is more parsimonious than materialism in that it posits the 'existence' of just the equations, while materialism requires an additional 'substance.' Yes, if one rejects Platonism in the first place, then the MUH amounts to claiming that nothing 'exists' at all. But this would be circular reasoning: you're simply insisting that 'real' things must have 'substance.' (And besides, I suppose that there's nothing more parsimonious than supposing that nothing exists!)
But yeah, it's probably more productive to set the whole 'what is real' issue aside and focus instead on what sort of structures allow for an observer. An exploration of the nature and requirements of consciousness might then tell us something about the likely nature of our universe. This would then open the MUH up to empirical testing.
@@jambec144 (The first block of text here was a late addition to my previous comment, rehoming it here because I think I edited it in after you'd replied already; I have a bad habit of doing that.)
I'd argue the MUH does have some successful retrodictions. Simple finite structures should be more common on the mathematical landscape, because they occur frequently _as substructures_ of other structures (including infinite ones). Compare finding finite strings of digits within the decimal expansion of some irrational number: every extra bit halves their measure. So the MUH maybe predicts the universe will have simple laws, with lots of symmetry. The MUH predicts a universe with an enormous number of conscious observers (the more observers, the more anthropic chances you have to find yourself to be in that universe), and this is satisfied by Many Worlds (if you like MUH because of parsimony then you probably are already taking MWI as your favored intepretation).
There's always the possibility the universe can't be exactly described by math, though. Maybe math can only ever get infinitely close but never touch it, not even with limits or infinite sums or fractals or chaos. Maybe it runs on something fundamentally different from math, and math works well only because math is some kind of universal approximator. I'm not sure what that would mean, though.
The issue of consciousness is a sticky one, because it seems that the line between conscious and not-conscious might be blurry, a gradual transition; and then you have to consider that consciousness takes time to compute, but it isn't in discrete steps like a program, but more fluid, so how do we "count" observer-moments, or measure the "amount of conscious observance"? I don't think these are impossible problems, but they require a much more exact understanding of consciousness to approach.
We're getting into theories that are increasingly difficult or impossible to falsify. At least in my lifetime. Knowing that, I am pleased to at least see a theory of the universe that can explain how something can come from nothing.
The level of reality where physics and philosophy intersect is fascinating to me. Always happy to see more videos like this.
Philosophy intersects with everything, everywhere, all the time, since the foundations of philosophy. That's what makes it so fundamental.
Yea, it's called metaphysics, all religions also intersect with that. Or... can there be a religion in the platonic world of ideas that has nothing to say about anything at all? Would saying nothing at all be a kind of statement? The Dharma is like this and not like this...
@@BitcoinIsGoingToZero Lol philosohpy isnt fundamental, philosophy is just applied logic, logic is fundamental, which is a part of mathematics.
Philosophy is just wankers smelling their own farts.
The wikipedia game proves that everything leads to philosophy
The pace in this episode, the progressive dive into the details step-by-step, and the final editing of the video are superb! Great work!
Agree, having read Max Tegmarks book, the baggage in that compared to this episode is evident.
Kudos to the graphics team for convincingly recreating the TI calculator from my childhood.
I've been here for about 5 or 6 years.
I think this is one of my favourite videos yet.
Very grateful thanks for the content.
Great episode, only problem I had with it, is that when presenting objections to the universe being mathematical it fell into a very common error of interpretation of the Gödel incompleteness theorems, they are not about limits of math itself, but about limits of the axiomatic method to encompass all of math, a way better objection would be through Ocam´s razor, as the mathematical universe evokes too many ontological assumptions without granting a better or deeper explanation of the subject, my personal opinion about this is that our way of thinking of the universe in terms of physical laws or basic principles which need to be consistent and which underlie all of reality is in itself mathematical, as pretty much is the same as looking for an axiomatization of the universe.
Edit: I came to revisit the episode and wanted to mention another thing, I found interesting that this hypothesis requests the different universes to have consisten rules, as in reality it is perfectly possible to work mathematics in the realm of non-classical logics, specifically for this case paraconsistent logics (those in which the principle of the excluded third is assumed as false) so it seems like a fault in the theory that assumes a limitation without a complete justification :)
@@oaktree1383 the equation may well work out, but this is getting into "if a tree(3) falls in the multiverse is anyone around to hear it?" territory, no?
@@oaktree1383 what I mean is that the math itself can be solid, but how do we know the math is anything "more than math"? If I'm understanding what you're saying, we're agreeing.
14:05 Slight correction, the halting problem says that there is no general algorithm that can determine whether any arbitrary program/function will finish, not that it’s impossible to determine whether a program will finish at all. There are certainly many specific cases where you can state with certainty that it won’t finish (such as while loops with no exit condition).
Physicists != Computer Scientists
Or one with no branches at all
Worse than that, he implied that the halting problem was a problem for the Computable Universe Hypothesis. It's like saying that because of the halting problem, computers cannot exist.
Incorrect
@@ethan20minecraft I think you misunderstood. He's saying that if you proposed that only decidable/solvable equations physically exist, then it would have to be known programmatically ahead of time which equations fit this requirement. The halting problem shows how problematic this idea is. Of course, everything about this "theory" is wildly speculative and makes a lot of untestable assumptions so take it all with a grain of salt imo..
Epistemology here. Very interesting ! I have been looking for long about some kind of existing formalisation of this question. You gave me serious clues. I would be interested in the philosophical authors that sustains such position, pro and cons. Anyway, many thanks this excellent work !
I'm not thrilled with the concept of life being a mathematical construct, but I am really bad at math so it checks out.
Thanks for making the analogy with the cat. I wish you had 2 types of videos. 1 without any simplifications and the other for us people who don't get much because we aren't specialists in the field. Simplified examples really make it much easier to understand, I really enjoyed it
"Simplified examples really make it much easier to understand" - not true. They make you feel good about yourself, but then, so does a cheese burger. It is called the Dr Fox effect. I don't mind Matt doing it.
@@DrWhom ..."not true"? Of course it's true. Isn't that the ultimate goal for any theory? Isn't there a famous quote about this?
I don't have the PhD or experience in the field...does that mean I'm not allowed to be interested enough to learn? The "easy examples" make it possible for us idiot's to understand. They plant the seed for hunger of truth and knowledge. That's a good thing.
And I love cheeseburgers.
I love the appearance of the "TI-∞" calculator at 8:34 that calculates the universe. Texas Instruments really outdid themselves with that one.
They invented the transistor after all ;-)
Great video as usual, thanks! I haven't read Tegmark's book, but I did read a summary paper or something by him years ago. I'd just like to comment on the issue of testability. The biggest problem for me with the mathematical hypothesis is the idea that the "baggage" is baggage. The baggage is not basically about how we connect mathematical expressions to human "perspectives," but how we connect them to human _perception_. Without some of that baggage, these strings of symbols clearly don't say anything about the physical world. The empirical content of a fundamental law may come from a higher-level law (or empirical regularity) that supposedly reduces to that fundamental law, but it has to come from _somewhere_, for it to be a statement about the world. So, the mathematical hypothesis is in principle untestable as long as it insists on getting rid of the "baggage." And if it is recognized that we need a translation from the mathematical expressions to outcomes of measurement operations (we need some baggage), then I think that robs the hypothesis of most of its novelty. We're left with some kind of mathematical realism.
Any suggestions on where one could find this summary paper of tegmarks book?
@Citius60 It is you who say that I am.
the mathematical hypothesis is testable by inventing a better fit symbolic language not intended for use by human minds... Humans being the equations of reality : the universe examining itself.
Nathan Oakley sent me ✌😃
ruclips.net/user/live9HqcaDQ_Fc0?feature=share
Much love❤
@@SeaJay_Oceans would that not make it unprovable in reality then? No symbolic representation can be applied that doesn't require the interpretation of an agent of the universe. Every test is an observation of an observer unless the entity exists outside of reality.
Amazing.
This is my favourite kind of math...
Philosophy.
Nathan Oakley sent me ✌😃
ruclips.net/user/live9HqcaDQ_Fc0?feature=share
Much love❤
Philosophy is neither science nor math.
@@gregmonks In the original sense of the word, philosophy can include either and often did. "Philosophy" just meant the process of systematically seeking the truth of our world and the findings that come from said process. This made it dynamic, ever evolving and changing because new data/info/understanding is always being encountered.
In the modern meaning of "philosophy" it's just a fixed, static, (often arbitrary) framework for viewing things. These "philosophies" are often lifeless, as they're often closed to differing perspectives and data/info/understanding.
Fillawfasees
As a matter of fact (and assuming I'm remembering correctly), "Natural Philosophy" was what they used to call the sciences.
Tegmark's "Our Mathematical Universe" is very worth a read, if anyone's interested in this.
In my understanding of the hypothesis, it's less that mathematics have a "physical manifestation" as Matt said multiple times, and more that what we "perceive" as a "physical" manifestation is actually simply what it is like to *be* math.
To me this theory works really well with the observation that there doesn't really appear to be any actual hard "stuff," if you look closely enough. Atoms are subatomic particles are quarks/gluons are fields, which are simply mathematical descriptions with no obvious "physical" nature, there's no "thing" there.
At the bottom, it's just math.
That helps ! I can't get round the 'stuff' problem.
"what it is like to *be* math." that's a way better way of saying it than anything ive ever tried
you're saying the exact same thing as Matt is though? "there's no "thing" there.
At the bottom, it's just math."
Or perhaps what that 'stuff' is is so far from our intuition that we can't comprehend its true nature. All we can do to understand it is by observing its measurable interactions. In other words, perhaps the reason everything seems to be 'math' is because that's the only means we have to model and understand it.
Amazingly put
I really like how this theory really displays the tensions between empiricism and realism. That's counterintuitive, because one would assume the empirical position would be to be a realist. It really takes the realist position (the terms of our scientific theories describe actual physical stuff) to it's ultimate logical consequences: all math is actually real in a physical sense, because all physical things are math. But at the same time, it's not a claim that can be derived from observation but only from abstract reasoning. It's almost like a synthetic a priori theory, for any Kant fans out there
More physics/philosophy of science crossovers, please
"it's not a claim that can be derived from observation but only from abstract reasoning" Yes!! 100%. Check out my other comment, I'd be curious to hear your thoughts. I can copy and paste it if you can't find it.
@@markwincek6688 i think that might be a good idea, there's way too many comments now 😅
@@NestorKYAT Read it down then up like a horseshoe:
0. *God* - - - - - - - - - *Meaning*
▼ ▲
1. *Philosophy* - - - *Philosophy*
▼ ▲
2. *Truth* - - - - - - - - *Myth*
▼ ▲
3. *Logic* - - - - - - - - *Story*
▼ ▲
4. *Math* - - - - - - - - *Language*
▼ ▲
5. *Physics* - - - - - - *Symbol*
▼ ▲
6. *Matter* - - - - - - - *Conveyance*
▼ ▲
7. *Chemistry* - - - - *Intention*
▼ ▲
8. *Life* - - - - - - - - - *Thought*
\ /
9. *Interest* (as a proto-will which
tautologically emerges from the process
of survival - ie. the only reason something
is alive is because it fulfilled, by whatever
means or accident, its interest of not dying)
God isn't so much an intentional being as He is a force best understood as the Implicit Observer which naturally substantiates existence.
And by substantiate I mean this: Before our universe, suppose there really is total Nothingness. Two things can be said about it for sure - it is singular and uniform. It is my view that Nothingness is inherently accompanied by the nagging question, "Well... isn't this nothing actually sort of a something?" God is the inherent "thing" which "asks" this question. (In this way, Nothingness is actually kind of an impossibility. It is inherently pregnant with infinite potential.)
And as soon as it is asked, this singular and uniform Nothingness suddenly becomes the only Something in existence. However, due to the paradox of boundary and scale, it's simultaneously the largest and smallest thing in existence surrounded by an infinity of more implicit Nothingness. This causes the Something to "chase" the Nothingness outward, while the same spacial distinction happens inwards. The relative expansion of the universe and the uncertainty of quantum mechanics is due to the ongoing primal battle between Nothingness and Somethingness which is arbitrated by the God-force CPU, eternally crunching the numbers on the Original Question.
I think the infinite difference between the Nothingness and Somethingness (0 and 1) is the source of all the energy in the universe. Also, I suspect gravity and dark matter are emergent consequences of the philosophical force between the two.
I think this model which places Truth before Math eliminates the sticky situation of "any viable math has its own universe." I find it far more plausible and evident that the universe rests on the "it just is" principle. 2 + 2 always and only equals 4. There is one seed but infinite branching timelines.
Ok this particular video really made me be in awe of how often we get these videos :0
I call this a win - the first Space Time episode where I've understood 100% of the material. And I had all the questions that popped into my head early in the video answered by the end. All ... except maybe, no mention of Gregory Chaitin?
Damn, maybe i should reconsider my subscription to the channel if this is an easier video
@@kazzz2765 that is, out of dozens of PBS-ST videos, this is the first one I've actually understood LOL. Not to say it's any easier! Just more in line with my background
The halting problem is pretty interesting. I remember it from my "logic" course in University. If I remember correctly, you can actually proof that it's unproofable by using the function itself as an input, thus creating a loop where the functions is input into the function into the function and so on
For anyone curious about a good explanation for people who don't know about programming: ruclips.net/video/92WHN-pAFCs/видео.html
I've never understood why the halting problem proof is considered so significant. I see no reason why you can't just redefine the question as "is there a general algorithm A for deciding whether another algorithm B halts, not including the special case of B incorporating the output of A?"
yes, in the end its the possibility of self reference that foils everything.
@@badlydrawnturtle8484 It's important because it shows there are limits to what a Turing Machine can do.
Why is a Turing Machine's limits so important? No idea.
@@bluesillybeard The basic point of a Turing Machine is that it can emulate any computer (provided you aren't concerned with how long it takes to calculate things). Anything you could calculate using a supercomputer, you could also calculate with a Turing Machine.
And, unlike actual computers which have intricate details, a Turing Machine is simple enough you can actually prove things about it. So you can use a Turing Machine (or other conceptually simple computer) to prove things about the limitations of all possible computers.
it's amazing how I'll sit here listening enthusiastically while my brain is literally melting.
"...my brain is *literally* melting."
You should maybe have a doctor look at that.
@@jambec144 in due time, for now we ponder our existance within the cosmos.
That doesn't sound good.. I'd get to a doctor while you're still coherent... But you're probably dead now
PONDER
9:11 this video.
9:12 my brain.
It was rather fun seeing all the ideas from my Computer Science Degree again.
Well done. This is the most tech-jargon I have even seen in PBS and Matt explain it's beautifully
Reminds me of the library of Babel, the idea of an infinite library, a thought experiment until someone realised it could be expressed as a formula and ran on a computer. There is a page in the library of Babel that explains what you did today, and another that explains what you will do tomorrow, if you know what text your looking for you can search for the page reference number. But of course it's infinite, so good luck finding by chance the one that tells you in perfect detail how you will die.
But the link is do these pages "exist" before you search for them? They exist in the "math".
Hannah fry explains this really well (better than me) in her book Everything* a great read, not at the complexity level of Matt's videos however! (Maybe a future video idea?)
One of my favourite quotes, can't remember who said it:
"Mathematics is a wonderful thing. Pity it discovered us so late."
Heh, did it tough? Maths go back as long humans have been civilized. Keep records on how much beer everyone is allowed to drink etc.
And in a sense I think a cat also knows it has for example 4 kittens and will deduct that one is missing if it only sees 3.
@@georgelionon9050 IMO life is logic and we discover ourselves and create language to communicate it.
I think logic requires values for operation, but a lot of life value from different species seems to be emotions (ranging from negative, neutral to positive) applied to sensory experience in order to make decisions for future survival. Then it's a stored piece of information and if imagination is involved the logic expands to abstract use of the information with other information.
maybe...
@@Mike1Lawless There is not much logic out there in the world...
@@georgelionon9050 That's a very low standard definition for what "discovering math" is. We could take your thoughts even further, given the fact that neurons emerge eventually from mathematical equation, the very first neurons had "discovered" math, because there was math underlying their function, let alone how there is underlying math when a cat looks for a missing kitten. Though it could hardly be defined in precise terms, I'm pretty sure the quote is based on an underlying intuitive notion of *knowing* what math is in some deep sense, rather than just using it.
When it comes to the debate between discovered vs invented in math, I've settled on a middle ground of sorts. What I mean is, the relationships between phenomena in reality exist independently of our perception of them and we have had to invent a way to describe these relationships in a coherent and cohesive way in order to understand them and put them into use.
Like a cloud of Starlings, each bird reacting to the one beside it, ignorant of the magnificent shapes we see when seeing them in flight or the atoms of a bridge interacting with one another, ignorant of being a 'bridge'.
I’ve also thought that Gödel’s incompleteness theorems throw a wrench in the mathematical universe. It’s difficult to believe that the universe itself would be incomplete; seems it would be saying that you could run a physical process that just .. doesn’t have a result at all
Perhaps quantum physics is an emergent "remnant" of the incompleteness of the underlying math? What if collapsing wave functions are actually manifestations of certain mathematical statements "deciding" to be true? What if this is what time is in the fundamental level? In the "beginning" all those undecided mathematical statements due to incompleteness are undecided, but as time goes by they choose to be true or false and that affects the construction of true mathematical statements (reality) and hence there is change in the reality with time?
What about the center of a black hole? Sounds like a great candidate location for where a "physical process has no (meaningful) result."
@@pojuantsalo3475 I've thought along very similar lines... except in my version there is a different 'universe' for certain statements being true and for being 'false'. That is, one of the levels of the multiverse is simply a manifestation of undecideability.
@@Flavia1989 Volition (aka Karma, Free Will) alone is causality.
Incompleteness relates to uncertainty - inevitable with choices involved, and hence a complete theory can't possibly be derived (chosen).
I have waited for this topic with high expectations, and you have done a great work. Thanks, Matt and PBS for this awesome video!
How machines enslaved humanity 👉 The Connections (2021) [short documentary] 🔥
If Schrodinger had written his thought experiment using a cobra instead of a cat, today it would have been harder for Matt to shoot the first scene of the episode
It's hilarious watching the cat try to figure out what the heck is going on, while Matt visibly tries not to speak too fast while still getting his intro out before the claws
Years watching Space Time, Matt being a cat person finally puts everything in perspective
Cat not being a Matt person 😅was funny too haha 😂
Of course he was AND wasn't a cat person until you watched this.
Love the cameow from our mathematically purrfect co-host at the beginning of this episode!
The editing on this episode was beautiful! This is also a topic Im really interested in
I found the background music too loud, and very irritating.
Dear senior management folks that set the budgets for this series:
MORE COWBELL PLEASE
(and by cowbell, I mean higher budgets for even more of this much needed and amazing content)
The new co host in the opening needs more screen time and I’d like to hear it’s theory
he fears Schroedingers name may popup during the show
Here is the full clip : ruclips.net/video/DIyI8_1RUEQ/видео.html
Cats are really into string theory.
@@timjohnson979 Brilliant !!!!!
The cat felt half dead after this.
Matt and/or the editor seemed to have left longer and more pauses between sentences. I enjoyed that. It let me absorb the content better.
such a good video, the use of the word “baggage” as well as the later explanations of the theories seeing math as a human invention put me firmly in the camp of not finding computational theory compelling but this was such a fascinating video
This show is so good. Great job explaining the different points of view and their consequences.
#TEAMINVENTED I've always felt mathematics to be epiphenomenal, like cutting a jigsaw puzzle, then forgetting you have, and then marveling at the beauty of how it all fits together. Anyone else?
Math is more like imagining a set of jigsaw pieces, any set, and seeing how they could fit together.
What you're describing is physics.
The universe is a bunch of jigsaw puzzle pieces that have been cut and we're marveling at the beauty of how they fit together, but math has nothing to do with our universe.
Math is discovered, physics is invented.
All of our current theories of physics are just inventions that approximate reality in a way that is useful for us.
And it will stay that way until we DISCOVER the true fundamental Theory of Everything (if ever)
Yep, I was just talking about this recently under another channel.
No.
@@viliml2763 yours is the best comment under this video!
Math with letters... instead you must learn to add random symbols (your choice) to the macro galactic scale of physical interactions and then, work your way back into the the micro, adding integers and whatever until the algebra fits.
No much real point applying the letters to numbers into formula until we move beyond this, its a small frame of reference we have so far..
Either end of the rope, is simply ones and zeros.
THIS episode was absolutely fan-freaking-tastic! Thank you!
I still have questions about the moon episode though.
I started getting the sense that the universe was made of math while studying physics. I heard about Tegmark's ideas a year later, which made me realize I wasn't going nuts.
Yes, you are going nuts. You have just found another nut like yourself. Go get a room. ;-)
From Gödel all the way to Stephen Wolfram it is a fun ride. Computational irreducibility, multiway graphs and such things - I hope to see an episode looking deeper into that as well. I want to see where it is heading. However, what is available for my limited brain for now, I vote math to be just a great simulation tool. It is also backed up by my sight through meditation. In spiritual context one can observe the weird way our anthropological viewpoint is all granular and symbolic. Reality has no symbols, no constants and no models.
It's heading nowhere. It marks the very end, the limit of what can be known.
How machines enslaved humanity 👉 The Connections (2021) [short documentary] 🔥
This video was an absolute gem. I hope you follow up on all of the themes you played with in this video. Very fun, engaging and worth while. Do you have any recommendations about what I should follow up on???
Agree! Joscha Bach is very good at distilling many of these concepts in useful ways, check him out if you haven't already.
ruclips.net/video/HeQX2HjkcNo/видео.html if you havent seen this, it really shakes up if math is even good.
Dunno if "playing with themes" is proper science and should be blown up further. This has been scourge of modern physics and especially "science" communication for a while now.
This feels like a cart before the horse problem. Math works to describe and predict the universe because we formed it to do so, and we also can only think within its form.
We apply mathematics to the universe because it’s the only way we have to describe it because it exists at scales we have no real existence in. Emergence is basically pointing out that at our normally observable scale, we have different and more directly experiential ways of describing things.
The only aspect of mathematics that humans invented was the notation to describe it. Mathematics describes pure irreducible logic, and logic simply 'is', requiring no antecedent. Any possible form of 'real' physical reality has to have an immaterial basis; anything else violates the simple rule of cause always preceding effect. It is no coincidence that all observed physical phenomena conform to mathematical principles! MATHEMATICS IS THE HORSE; the physical realm is the cart. Of course this is counterintuitive from our perspective; is the immaterial realm not just a product of our minds, which in turn are a product of physical reality? Yet to relegate logic from basis of mind to its end product is to deny its existence.
@@noyfb4769 Logic isn't inherently real. It's concepts and structure WE created and standardized with our minds. It's a series of fundamental formalizations of our ability to categorize and process incoming data. Logic is simply the formal language structure mathematics is built on. Not part of the inherent nature of reality.
It's no more inherently "real" than the arbitrary delineation of Red vs Orange in the visible light spectrum.
Interesting.
@@noyfb4769 This is wrong. Mathematics are designed by humans by accepting and rejecting specific axioms. We can develop a different mathematical system by including a different axiom. For example accepting the fifth postulate leads to Euclidean Geometry but rejecting the fifth postulate gives you Non Euclidean Geometry. Both are self consistent mathematical system but the fifth postulate can't be true and false at the same time so you have to choose one or the other.
"Math works to describe and predict the universe because we formed it to do so..." Alternatively, we have * discovered * the correct description of reality. This debate is several millennia old. You can't settle it by simply declaring one interpretation to be correct.
I have a small but critical correction. Undecidable problems are not "neither true nor false". They are claims that are either true or false but where it can be proven that no algorithm can necessarily determine if the claim is true or false. In the halting problem, for example, it is proven that no algorithm can be written that will always determine if a given program will ever stop. The program in question will stop or never stop, but we can not know which of the cases will happen with by executing an algorithm.
I'd say that math is a language that can describe reality. It is suspiciously good at describing the reality because our minds that created this language are emergent phenomena of the said reality, governed by the same relations and dependencies. In a way, we learn reality in the act of constructing language.
However, just like it's possible to write a formally correct sentence that doesn't describe any particular really existing thing (like "pink invisible unicorn"), it's also possible to make formally correct math equations that just doesn't describe anything actually existing.
It wouldn't exist from our point of view. But if these equations described sub structures that were able to observe and model the mathematical environment around them, they would perceive themselves to be living in a real physical universe just like we imagine we do.
This is my view. I have no idea why he wanted to jump all the way to, _Well now EvErYtHiNg_ (computable) _is physical._ It's just easier to say, OK, yeah, our fundamental lowest level of reality is just information, that can be expressed as math. And it makes sense we can find this math as we're in this universe.
If the universe is math, then I am math, and that would mean I am math that is bad at math.
Just hit the math gym
Cats were once worshipped as gods. They have never forgotten this.
Glad you mentioned incompleteness, before you did I was thinking that it throws a pretty big wrench in the whole idea.
That was a magnificent video. I have struggled with these very ideas for many years!
It's a relieve for me that at least some people in this world share my interests and take ideas like these seriously. I can rarely discuss stuff like this in real life, so it keeps stuck in my head. Videos like this ease the problem of rarely getting constructive feedback on such ideas.
@@markusschluter7488 so plato forms ideas are already debunked or not?
Yes I have also been thinking about this a bit and had these ideas as well over the past few years.
My favorite thing about this channel is when we dive real deep into philosophy.
Fantasy is not useful. Avoid Harry Potter and the Bible.
@@marcosolo6491 Some people are curious about the nature of reality. Go figure.
@@marcosolo6491
No and I've made this point previously, they're definitely running out of material, (lets face it results from the LHC for example, have so far not lived up it's hopes/expectations,) and the question; is a mathematics something that we invent or something that discover is an old one and unlikely to be resolved any time soon.
When scientists get lazy they get philosophical. Cause philosophy doesn't require proof
How machines enslaved humanity 👉 The Connections (2021) [short documentary] 🔥
The book Permutation City by Greg Egan is a really interesting exploration of this idea. I highly recommend it if you're into science fiction (which, given this channel's subject...).
I was about to write the same thing. And both it and this video drew my mind to Stephen Wolfram's Theory of Everything.
Seconded... Egan is next-level and 'Permutation City' is a really good book... kudos for suggesting it here
I'm wondering how many takes this episode took, there are some serious mouthfuls! Cracking job Matt and the PBS team
Amazing episode, and one of my favorite theories, along with Conformal Cyclic Cosmology! I think it's very related to the problem of sentience and defining what it "feels" like to exist as any given entity on a subjective level. For example, I have heard theories that sentience is simply what it "feels" like to process large amounts of information, whether or not that sentience results in a single entity that is self aware or not. So in that sense, it must "feel" like something to be a computer, to be the internet, to be a planet even, and the only difference between all that and us is just that our sentience results in the experience of a single consciousness.
Does it feel like anything to be unconscious? If so does something/someone else feel it? Or is it all a series or instantaneous moments or awareness with no memory to provide continuity… and if that’s the case is that what any universal ‘consciousness’ would be like?
@@PatternShift That's something I wonder: if we imagine that planets might have consciousness, then you might also imagine that the universe has a consciousness... but does that mean your arm does as well? Your hair? And if so, which part of reality holds "you"? I mean, I guess it's really not much different to the general hard problem, but it's even more fun to think about in the context of universal consciousness and sand-sized consciousness and the endless matryoshka dolls in between 😊 All simultaneously infinitely separate and one
Look into the attention schema theory of consciousness. I think that theory does the best job of at least describing what “feeling” is in a mechanical and unbiased way. And to me, it’s definitely the most logical working theory of describing consciousness and how it emerges
There are no answers to the “hard problem” to be found in physics, both Penrose and Crick are just wrong about that. Consciousness, as you would think of it (what it means to “be like” something) is not a physical object, it’s a process of the evolution of *abstract* objects. Well beyond the reach of physics just as psychology or sociology are.
@@dismalthoughts no.
Awesome episode as always.
This reminds me a thought I had about the mathematical expression zero which can not be found in nature because in reality we can't really work with all the things that do not exist and the universe is fundamentally based on existence and not absence of things. So the questions like why the universe exists might not be applicable since it maybe the the only possible state it can have.
If you want to explore this ideas you could read Gregg Egan's books. For example Permutation City, Diaspora (my favorite one) and Schild's Ladder.
In Computer Science, we have multiple models of computation. The two most popular models are Turing machines and Lambda calculus, both of which are equivalent and can compute anything that is computable. We can use one to prove things about the other. We can use Turing machines to prove things about Lambda calculus, and vice versa. For example, if we use the Turing machine model to prove some problem is undecidable, then that also proves it's undecidable for Lambda calculus. Otherwise, we use known undecidable problems (halting problem) to prove other problems are undecidable. Such a proof is called a Proof by Reduction. This works because the different models of computation are (presumably) consistent.
I think the relationship between physics and mathematics is the same Proof by Reduction. We take some physical law and *reduce* it to a mathematical equation, then use mathematics to manipulate these equations, and reduce that back into physical terms. Presumably, both mathematics and physics are consistent, so a proof by reduction usually yields a true statement about the physical world.
Something else I don't think was covered in this video, mathematics is essentially founded in the physical world. One of the earliest forms of mathematics is geometry, and geometric shapes are great ways of modeling physical objects. Thousands of years ago, mathematical proofs were largely in terms of geometry, not algebra or similar. So I think the strong relationship between physics and mathematics is no coincidence.
I think viewing it as using one consistent system (mathematics) to prove things about another consistent system (physics) via proofs by reduction explains much of the "unreasonable effectiveness of mathematics".
Mathematics is a language that is the most suitable language for describing the physical world, but it is still just a tool. And just as with spoken language, mathematics can get it very close to correct but it can also get it very wrong or it can get a really good prediction for a very specific situation and have ridiculous artifacts along with it. As was mentioned above, this is just a step closer to religion based on philosophical gobbledygook.
Wow, this is exactly the conclusion I had come to years ago about what the universe is... weird to see it verbalised exactly point for point in a Spacetime video! Great to know it has a name and something I can share to help explain it to people, I've struggled with that part!
Yup, I've been a mathematical monist since the 70's, and it was such a great surprise (and relief) to learn about Tegmark. I'm not alone!
I would love a video going through the math of Gödel’s theorem. I haven’t come across a good deep dive yet
There's a good one from Veritasium.
Yup, as said above, Veritasium has a good one here - ruclips.net/video/HeQX2HjkcNo/видео.html
Yes second Veritasium, it's brilliant I was searching for something like this for years before.. there was never a proper science communication simplification of this. There was only the real thing, Goedels paper that is very hard to read, and there was the book Goedel/Escher/Bach.. but it's a whole book that doesn't get to the point and plays a lot around with recursion.. and there is lots of lots of lots misunderstanding what the theorem says and what people believe it says (including Matt it seams).
Do you speak German? This is the best one I can recommend: ruclips.net/video/z1e4Ko7u7wM/видео.html
@George Lionon a short book which is accessible but focused is Godel's Proof by Nagel & Newman
On the ending note, about typical universes - if mathematical structures can get infinitely complex while still supporting life, and at every step up in complexity there's more & more options to choose from that support life, then we should expect to find ourselves in an arbitrarily complex universe. Ie from our perspective, the further we keep digging down to smaller scales to find fundamental laws, the more layers we'll find, & it could well go on arbitrarily (infinitely?) long
P.S. thanks for covering my request on this topic 😁 had been super curious about more well-established thinking on this type of multiverse
Hey that’s pretty good. Bump so Matt sees this
Only if you can take yourself as a random sample. And the Doomsday Argument suggests that you can't do that.
i was just feeling existential about this too
It seems this theory is fundamentally untestable. Any universe we find ourselves in would be part of this theories multiverse. Unless we somehow discover that the universe does not follow rules at somepoint, it would be impossible to tell if this was true or not.
At least with current physics, we have a difficulty with measurements below the scale of the planck length, given that they would produce a black hole (I cannot remember the exact reason why or if this is 100% the case, remember hearing it from Sean Carroll).
I remember thinking about this in my teens though. I think it's plausible, though unlikely testable. How are we to get past the fact that our observations are already collapsing and changing the physical systems we try to measure such that we could even make a deeper measurement?
I don't know. Interesting question though.
16:39 This makes me think finding explanations for things we do not currently fully, or at all, understand can be approached from multiple directions. Fascinating.
It would be awesome if two groups of scientists worked at a problem from two opposite ways of thinking and came to the same conclusions.
This was a particularly heavy episode, I’m going to have to rewatch it several times before it fully sinks in. Seems my calculator is having trouble with the equations 😂
Recommended watch is the "Math's Fundamental Flaw" from veritasium
Here is the full clip ruclips.net/video/I7S74SxIjn4/видео.html
I'm going to have to rewatch a few (dozen) times as well...
General gist from a first casual watch is that this theory would turn gamers into very cruel deities of a sort, as the environment in which they "play" is entirely mathematically derived and self-consistent as well. I had to stop the video there, and ponder my vast sins..
@@innocentbystander3317 gamers? what about your thoughts.
@@Boardwoards
Luckily, I'm blonde! That's why we're supposed to mind our own thoughts... 😘
I mean, at this point i don't even know what to think the universe really is. It's always good to learn new things everyday
Wow, what an episode! Joined your patreon ❤ thanks for the awesome content!
Think you fell into the trap of the Third Man Argument which Plato himself refuted: The Form of 'Circle' isn't itself a circle but the principle of circularity, among which circles are expressions of. Nor would the form of Cat itself be a cat but rather the essence of 'catness'.
This becomes obvious when we consider the 'Form of Difference', it's not itself some particular difference but 'difference' and 'differentiation' itself. If it were itself different it would be different to all things including itself. Though, of course, Plato does say this about 'the One' in Parmenides, that it is different from itself...
Recently I had the opportunity to ask Michio Kaku a question and even more recently I had the opportunity to ask ChatGPT a question, obviously, and I asked them both what the implications of being restricted to the rules a formal set would mean if we lived in a universe constructed by mathematics. I got no satisfactory answers. I should have known that Matt and PBS Space Time would eventually save the day with their invaluable content, and I didn't have to wait for long! Thank you so much for this video
They wouldn't have a clue as to the implications of NP Completeness and hence would be way out of their depth. It's a shame but that's life.
Having seen the interview John Michael Godier did with Michio Kaku on his Event Horizon channel a while back I lost any semblance of respect for him as he showed he is no longer capable of thinking off script probably not having had to actually think since he left academia behind for science popularism
I studied the Halting Problem in my theory of algorithms class, very interesting to see it applied to physics!! Thank you for the video!
Surely the very fact that we as humans can identify and recognise the halting problem(and not get stuck in an infinite loop) goes a long way to proving that the universe is not purely made of math/logic?
Is that too reductionist a view, or on point?
We recognize existence of halting problem. We have no stronger ability than computers to know when the halting problem actually occurs
I don't believe that everything in the Universe IS math, but can be broken down into a mathematical foundation to be explained. It's truly amazing. Wish I had this kind of drive for knowledge 15 years ago in School
I'm curious as to what alternative candidates you'd suggest for the substrate of reality beyond logic
Math is a human construct and I don't believe anything humans create can be what our reality is made up of, that seems pretty arrogant
If everything in our Universe can be broken down into and explained by mathematical concepts (and as far as I know, we haven't yet discovered anything that wouldn't be describable using consistent language of rules), then the Universe is isomorphic to a mathematical structure which has the same properties and relationships as the ones we discover in the thing we find ourselves in. What I mean is, there is no difference between our Universe and an abstract mathematical structure which describes our Universe. If two things have exactly the same properties, they are actually the same thing. We tend to intuitively think that there is some special property that the Universe possesses called "physical existence" which makes it "real" as opposed to abstract. In reality, "physical existence" might not even be a meaningful concept, how would you define it? If there is no additional property to our Universe, then it actually is the mathematical structure that its laws define. This to me is truly amazing. There is no reason to even ask why there is something rather than nothing. Mathematical structures just are. That's the only possible option for reality to be free from contradiction.
@@szymskiPL i wouldn't say the universe is math then, but rather like a giant calculator that simulates itself.
Besides, there are many theoretical mathematical constructs that don't represent the laws of the universe, otherwise we wouldn't need practical experiments since everything could be derived from math.
You can also do mathematical equations at any time while the things that happen in the universe are bound by the laws of physics.
@@SteveAcomb it might just be that the deeper we go the more incomprehensible the universe becomes to the degree that not even math can describe it. Math is something that humans came up with, doesn't mean the universe can be fully described with it.
Like for example if the uncertainty in quantum mechanics is truly nom deterministic then math can only make probability predictions but not actually describe what actually will happen. Then there's also no other logic to why it ended up in a certain way in a certain case. Then all physics math is just like statistics with emerging patterns on a bigger scale. It's still super useful but just a simplified model
8:41 I like the touch of the calculator being a spacetime brand TI Infinity
Sabine Hossenfelder might have a few interesting words to say about this. But hey - on another topic all together, here is an idea I would like to see you pursue in some future episode: Nested black holes. I've seen a lot of vids lately on the "is a the universe a black hole". True or not, it got me thinking about nested black holes. For example it seems like not too big a leap to envision supermassive black holes swallowing stellar mass black holes that would continue to have some existence after crossing the event horizon. But then I started think about what really happens when any black holes merge. Why should we assume the singularities somehow merge. And on that topic .... how close does matter have to be to such a singularity before the density of matter is so high that it would cause black holes to exist. So maybe there are like infinite little black holes surrounding the singularity? Don't know. Needs math I guess.
I like this idea
"Why should we assume the singularities somehow merge." Because that's how gravity works. It pulls matter towards _one_ point.
No lol. Wrong. The earth is actually flat so don't fall off the edge. And there's no such thing as Australia. It's a lie perpetrated by the government.
@@gabor6259 Ys-ish. But infinity is funny, and not usually intuitive. When you have two points of infinite density approaching each other (and I'm not even sure the concept of "approaching" makes sense - these are not "points in space" - these are "space") things might be weird. We have infinite natural numbers. And infinite even numbers. And infinite odd numbers. And they all exist happily together, all equally infinite, none greater than the other. Not intuitive, but mathematically sound. Could there be wormholes hidden in nested blackholes? Even numbers bet "yes". Odd numbers bet "no". Who wins?
@@donald-parker Seems you don't understand infinities in mathematics.
I had never think about the relation between Godel theorem and the "mathematical world" 'I feel a sort of disillusion for thinking that with maths were possible fully understand reality. Nice video, I enjoy it and will make me think a lot of things:). Best wishes for the project, greetings from Colombia.
Is "desilution" like desalination?
no, I forgot the correct word:c
GOOD ON YOU 🙏👏👍
Fair enough, it surprises me so much with these types of theories that reputable scientific figures often just forget about Godel and math being incomplete.
@@teok5665 It's because the PBS guy doesn't understand Godel Incompleteness.
Godel incompleteness doesn't say there are statements that are neither true nor false. It's that they are not provable true or false. But instead PBS guy extends that to say that if the universe is math then there are physical laws that are neither true not false. No, no, no: Godel says that for a given set of axioms used to explore the mathematical landscape, there are true mathematical statements that are not provable within that set of axioms. Hence if the universe is math there will always be physical laws that are not provable. But not provable is not saying the law is nether true nor false. It's about our limits of understanding rather than whether the universe is math.
Imagine going to the hairdresser and giving them a vector field to make your hair into
I've been an adherent of this hypothesis for years. It just seems like a natural conclusion that if there is a mathematical structure that can give rise to consciousness, the universe it describes would physically exist from the perspective of that consciousness, even as that universe remains just a hypothetical to us. Existence is relative in this view.
These ideas put forward by Tegmark are not only good, but are the *only* ideas that I know of that are capable of reaching down to and sensibly address the most fundamental question of all - Why is there something rather than nothing?
Exactly the question that led me to the MUH and why I believe it.
Yup!
Indeed, mathematics (or, more fundamentally, logic) is the only thing I wouldn't question the necessity of existence of. Truth doesn't need a universe to be true.
"Something rather than nothing" is a non-question. The only answer is Mu, the answer that un-asks the question. How could there "be" nothing? Nothing doesn't and can't exist, or it wouldn't be nothing. So how long would nothing exist before something existed? It can't, because time isn't nothing. The universe necessarily has always been here, because there was never a time when there was no time.
Yeah it's the closest thing we have to an answer to that question but we still have no explanation of why mathematics has to exist, i mean we can't imagine a world without math, it seems impossible and it probably is, we can't prove it tho, at least for now.
A theory of everything (in philosophy) requiers 3 properties : the principle of sufficient reason (every fact t has an explanation t'), comprehensiveness (each facts t are explained by the theory T) and finality (the theory T has no deeper explanation so T explains itself).
Tegmark's guess (in his book) is that mathematics, computer science and logic are different ways to look at the same thing, we already know that there is a correspondance between computer programs and mathematical proofs (curry-howard isomorphism) and even a relation between intuitionnistic logic, cartesian close categories and lambda calculus, basically between math, logic and computation (cf : computationnal trilogy), so his guess ain't that crazy.
I've always thought of this. I'm so glad I have a word for it now and also a video to show people whenever it might happen to come up in conversation. Also to now know the phrase "Anthropic Principle" which is another thing I'm always trying to explain to people. I always thought the universe as a whole can be completely explained by a single equation. If you start anything from exactly the same place with exactly the same numbers and exactly the same variables it will always result in the same answer. Now that I've seen this video and some real science behind it, it only makes me think this further. If an equations existence implies it exists physically and can be viewed from outside of itself then that, to me at least, explains everything. Our universe exists everywhere everytime all at once in the same way you can view an equation that will describe a ball dropping and as long as all the variables are the same it will drop the same every time no matter what. You don't need to see the ball physically drop to know that's what it means and it's inevitable outcome. We're simply living inside of the equation so we cannot see it from the outside as a whole, we are the ball dropping at this point incapable of discerning the equation that inevitably lead to the drop. If the equation of the universe is exactly the same in another universe then it will inevitably lead it to create you exactly as you are now, doing exactly what you are right now because at the most fundamental level everything is an equation moving forward through the variable of time. If you rewind time it will always lead to the same place, if you go forward it will always lead to the same place. The atoms that were created in the very beginning will always travel through space in the same way, form the same stars that will then explode in the same way until it inevitably will form the neurons in your brain that are reading this right now. From the outside of the equation it just exists, all the time, everything all at once because just by simply reading the equation and the numbers you can know that it will always end up creating everything as it is, was, and will be. From the beginning to the end.
I’ve never seen a RUclips comment I agree with more! The more I learn about math or science the more I stop believing in free will. Everything in your life was meant to happen and so is everything that will happen. People think they make decisions, but every decision your brain makes could be predicted if you knew all the variables present in the brain at the time the decision is being made. Which just means we think we have free will but all of this is decided anyways. We’re all just part of an equation! I always try to explain this to people and I think no one cares lmao 😔
@@ayoactually5284 your not alone my friend. I’ve been similar thinker. Unfortunately even mentioning the idea of determinism or no free will is like taboo to average closed minded man.
@@ayoactually5284 we live but just a few humble frames in an pre-recorded infinitely long movie.
I believe that, the universe is deterministic, or at least that free will is nothing more than a mental tool to keep us actionable. I also find this thought quite fascinating, but at the same time I don’t really care. After coming to that conclusion nothing really changes. It has no practical implication. I think that is, why many people don’t care in the first place. It’s just completely irrelevant for our lives apart from being fun to think about.
The current state of physics doesn't provide much support for a deterministic universe, because no one knows how quantum mechanics decides where a particle is going to be. It's considered random, which really means we just don't know. I suspect that we will never know whether the universe is truly deterministic, because it would be impossible to test.
Levels 1,2 and 3 are the multiverses in our level 4 mathematical structure, however according to tegmark in other mathematical structures may contain none of those, but completely new and different types of multiverses we can't imagine. This was all in tegmarks book it blew my mind.
What is name of the book
@@i_am_dumb1070 our mathematical universe by max tegmark
Awesome book. It’s fascinating to think about how much we could possibly discover about the Universe and beyond.
Tegmarkian baggage is just a generalization of how we conceptualize emergence; in computer science terms, the layers of abstraction a system has. The dichotomy between observation and absolute reality also reminds me of constructor theory and the participatory universe concept.
Ive always said maths is a fundamental element of the universe
PS: im glad no one even notices his Australian accent, they’re so used to it. This folks is the real Aussie accent...its stunning in its normalness.
I was confused when he said cats are made of cells. I thought he said cats are made of souls. Of course, cats don't have souls.
@@LughSummerson No, he meant cats are made of OTHER beings souls.
So sad that he uses the American nonsense "math" and pronounces "says" phonetically.
Pet peeve but it's distracting and drives me around the twist.
@@PeterKnagge the only nonsense about "math"is that anyone says "maths"
It's not plural, and it's an abbreviation of mathematics, also not a plural. So why would you cut out the middle and leave the s at the end!?
@@Welverin maths is short for mathematics, i.e. there's more than one sum...
Would love to see you talk about the Nov 30 2022 Nature paper by Jafferis et al "Traversable wormhole dynamics on a quantum processor". Some of the pop sci articles are touting it as "confirming the holographic principle". Curious if it's all hype. Sounds like extremely fascinating research being done on the Google Sycamore processor but I don't fully understand it myself.
Same, particularly interested in the idea that ER = EPR might be the basis for a unified theory of everything. That would be exciting!
I read this Max Tegmark´s book! It is really thought-provoking, I recommend it a lot
How machines enslaved humanity 👉 The Connections (2021) [short documentary] 🔥
... I love how the breakdown at 3:40 is very much like XKCD comic #435, "Purity", with the exception of Neuroscience
Yes, I'm glad someone pointed this out. Although the claim that human psychology is derived from pure rationality is... challenging.
I love your work and this is particularly well done.
This video made me think that maybe I should give Tegmark’s book another chance. I got it several years ago and while I have started reading it twice I haven’t gotten past the first few chapters. Also, my aunt was in the same high school class as Tegmark for about a year.
Having read it myself I recommend skipping certain chapters that are uninteresting to you, he jumps around from topic to topic quite a bit
This was one of y’all’s best episodes. Truly.
Science and spirituality coming together is the only way to move beyond a theory of everything.
This one blew my mind. Well done!
"If there's nothing else to an electron but a set of numbers describing its position, momentum, and charge, can we say that the electron is simply that set of numbers?"
It seems to me that if you have to describe the numbers as having particular meanings, then you've already answered your own question.
Well charge, momentum, and position are all mathematical quantities. Math in this case isn’t just numbers, geometry is part of mathematics, the math in this case is things like vectors, wave functions, spaces and fields. What do you think energy is? Is it some “spirit of motion” or some undefined thing like that? No, it’s a mathematical quantity that causes changes in the structures of other mathematical structures like space, fields, and strings. The concept of “matter” is also similarly undefined as that example, a lot of people think “well matter is made of mass and charge” and other properties, but when you go down to it things like spin, mass, charge, and any other property in physics, they’re all mathematical quantities.
The RUclips channel ScienceClic has a video on quantum field theory that describes the conserved quantities and things I’m talking about if you want to look into that more, though there are other channels too, that one just describes it really well.
Basically it goes down to that if you’re saying “well the universe is made of matter” and that the mathematical descriptions are just tools used to describe some mysterious substance, then that mysterious substance is just some undefined thing that somehow is not the sum of the mathematical properties like energy, charge, spin, etc. which we know are mathematical in nature. You’d basically be saying the world is made of the essence of god or magic or any other undefined thing.
Now, what is a mathematical structure is a tougher one to explain, from the stuff I’ve thought about myself, a mathematical structure is just an element, some thing, that’s described by logic, the idea came from how there is an equation that describes lines, basically the line is the information contained in that description, or if you want to call it, logical arrangement. That’s probably not the best explanation I could write but it’d be a lot of work to write more than that and keep it from being a pain to read.
(Also sorry for writing this super long damn comment in your replies, I just wanted to talk about this and I found it very hard to make this a comment by itself, so apologies)
Here is the full clip : ruclips.net/video/DIyI8__1RUEQ/видео.html
@@Rudol_Zeppili lol
That something else are the relations of those numbers with everything else.
why? if you mean words like "position, momentum, and charge" then those are just convenient labels used to talk about these concepts. if you mean the actual concepts to which these labels refer, they're described by laws of physics which would themselves also be a part of the computable mathematical structures Tegmark describes. the "meanings" of space, momentum, and charge are all mathematical in nature so certainly no question has been answered
I'd highly recommend Permutation City by Greg Egan! To those who enjoy these ideas and entertaining what these mathematical universes might look like.
He takes this idea in a sci-fi future, and explores what would happen if one man decides to *really* test out this hypothesis by simulating himself inside one
If you liked Permutation City be sure to check out Diaspora too!
I love PBS videos in general. Sadly, there were multiple wrong math statements in this video. About Godel's theorems and the Halting problem.
I've always liked Tegmark's Mathematical Universe Hypothesis. It seems plausible and it solves the paradox of how something can come from nothing.
I completely agree with you. If its possible to derive mathematical constants like e from just the concept of numbers, which themselves can be derived from just boolean logic it seems very plausible that the physical universe we know is also a direct consequence of logic itself, just like another constant and exists simply because it can.
What paradox? Something definitely comes out of nothing. Think of sound: what do you really hear? Especially with low pitched sounds, there's some sort of graininess to it, because sound is a wave and every wave is intermittent with a through of silence. There can only be sound when before there was silence. Otherwise, how could you tell sounds apart at all? Non-existence IMPLIES existence, and the other way around as well.
I don't like tegmark's hypothesis for two simple reasons, it lacks predictive power (which is the whole reason we do science) and is ill-defined. What do you mean that something is made of math? How does consciousness come into play?
@@FunkyDexter I don't think you grasp what is meant by "nothing". Before there was sound, there was air for the new sound to take place in. There's space for the air that's teaming with particles and time. There's physical laws governing the spacetime. Hardly "nothing".
@@Quarkburger Then what is it that you mean by "nothing"? In that sense not even empty space is nothing, spacetime has elastic properties that respond to the energy in it. I don't think you can even really grasp what nothing truly is, because as soon as you try thinking about it you immediately end up assigning it some properties, like"black emptiness" or similar. The only possible way you can define true nothingness is by defining what it isn't, and work like a sculptor by removing stone piece by piece, except you'll always end up with some stone in your definition.
The crux of the problem is that there is no way to define a lack of something without referencing that something. You need existence to define non existence, so in that sense sound DOES come from nothing, because the only way to tell it apart from other air motions are specific attributes that air lacked before. It's not about cause and effect, which is simply a linear sequence of events that always happen in succession. A natural cause is also very rarely linear: the universe is a closed system only as a whole, but if we trace back the "cause" of every event we always end up encompassing the whole visible universe, as interactions tend to spread over time.
You'll find that tracing the causes of a phenomenon back in time is not that useful to understand the full nature of the phenomenon; for that you need a description of what the phenomenon is doing that it wasn't doing before. Only after you cleared that up you can safely investigate a bit further back.
@@FunkyDexter True Nothingness is extremely hard to grasp. Anything other than Nothingness needs to have an explanation, and this is where cause and effect and the paradox comes in. You can't trace causes and effects back to true Nothingness. So either you start with something, which has no explanation, or you trace causes and effects back to Nothingness. I don't see how either one is possible.