Where are the White Holes? - Sixty Symbols
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- เผยแพร่เมื่อ 4 ต.ค. 2024
- Two viewer questions about huge numbers and white holes. Learn more about the Jane Street internships at jane-st.co/int...
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Featuring Tony Padilla and Ed Copeland.
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Real treat to see Ed Copeland again, another excellent video Brady.
"treat" is a the perfect word to describe it :)
Ed Copeland can read me bedtime stories and I'd never go to sleep.
Ed Copeland is my favorite ❤❤❤
0:20 Praise the Bucket Man
Emptying out the maths barrel to make room for more maths
Praise be unto him.....
I completely understand how and why Cantor went insane.
Did he?
Gotta love Tony. It's so incredibly British that he didn't plug the crap out of his book :)
It wasn't an advert. It's so incredibly American that you think this is a matter for ridicule.
The longer these channels progress the more Brady resembles Jared Harris' Professor Moriarty
65 digits of pi are enough to calculate the circumference of the known universe to within a Planck length. So the natural question is: does the number pi even meaningfully exist physically in our universe? If even using the largest possible circle you can think of observing, pi is in practice basically indistinguishable from a rational number.
That’s super interesting - thanks for sharing.
in mathematics we don't care much If an object may or may not exist you know, strictly speaking, no mathematical object can really "exist" clearly there is no such thing as a straight object, or a 3 pounds object, or a circular object.
if you ask me, mathematical objects do exist, but they exist their own way
Probably some recursive application like e^ix/π or fourier series?
Argument one would say that no. A perfect circle only exists in the world of ideas and every circle in the universe is imperfect when checking for enough precision, therefore pi is nowhere in the physical universe.
Argument 2 would say yes. Although no physical circle with the "full" value of pi actually exists, pi is an inherent property of space that describes how a set of points distribute when uniformly around a centre. Similar to temperature: the number describing temperature isn't "real", but you could measure it with a bit of mercury. Would you get an "exact" value by measuring? Absolutely not. Yet, the true temperature is objectively there. The analogy breaks down if you got o the nitty gritty, but the point stands. Pi in our universe might be unmeasurable, yet it must exist since all observations, aproximations, and calculations converge to it
I'd say that you've already shown it meaningfully exists with your example. Pi represented in base 10 is just that, a representation - all digits of pi from the first to the infinite minus 1 are as much a piece of pi as any other without one it is no longer pi. Pi is its own complete entity, we merely mark it as we do other entities.
Love the engagement bait of spelling it "Googleplex"😂 Totally fell for it
Yes, I need more questions like these being answered by people like Tony and Ed. They might even deserve their own channel.
"I don't know my white holes very well" - Ed Copeland, 2024
Whenever Sixty Symbols uploads a video is a great day!
This one of a couple of channel's I have hit the bell icon on, and this video is a perfect example of why that is so. Cheers mate!
Thanks for the reminder that the bell icon exists! I've just toggled it on myself 😁
I love tony... he brings across the craziest maths ideas across in such a funny way.
Aw I was hoping Brady would repeat Prof Padilla saying "the universe resets itself" like in the original tree 3 vid 😂 cool vid!
Idk. The other day I thought about an insanely large number. I define it as such:
Take the planck space, and think of it as a point that can interact with other planck spaces. Now, think about how many planck spaces in the whole universe are in one snapshot. Then, each planck time forward, calculate ALL the possible interactions and variations that can happen from snapshot A to snapshot B after one planck length. After that, go in time t until the end of end of time, and add the planck spaces that will be created from the expansion of the universe.
The result is a mad mad mad big number. And yet, it pales in comparison to Graham's.
I think of the "planck frames" of the universe for how time might work at a fundamental level
@@basedbasepair8664 what do you mean?
@@ticketforlife2103 Assuming that a Planck time is the smallest unit of time possible, that would give the universe a “frame rate” of 10⁴³ frames per second. In between each frame, matter would be frozen in place until the next frame. That’s my understanding of it, at least.
@@basedbasepair8664 There is no reason to assume that Planck units are the smallest units physically possible; they are (sometimes) the points where our current theoretical understanding of physics 'breaks down', but otherwise they are not "limits".
@@dlevi67 Well, having smaller units possible would make things more interesting, then you could use Time Wiki’s whacky units like a Googolgongosecond (10^-100,000 seconds).
If you went back in time a few hundred years and asked the leading scientists "what's the largest possible number that can mean something in our universe?" you'd get an answer laughably smaller than what you'd get today. Who knows what the answer will be in a few hundred years, or a few thousand.
0:19 that was me
You are lucky man to be featured in Sixty Symbols episode
@@jacekbochra867 Sixty symbols
Awesome video, can't wait for more! Tony and Ed are fantastic
I have two ideas to give meaning to the concept of big numbers in our universe:
1) Working with the concept of big numbers might lead to or inspire discoveries that influence the real world.
2) Mathematicians are part of the natural world, and some enjoy working with big numbers, which gives the concept its own kind of meaning.
If the question was about some kind of interaction between nature and large numbers in decimal form, I would say there might be something if the universe is infinite in some way?
brady at the end looks like professor moriarty from the sherlock Holmes game of shadows moive
The Red Dwarf explanation of White Holes has worked for me all this time. I believe
So what is it? 😂
@@greatquux I've never seen one before, no one has, but I'm guessing it's a white hole.
I love the idea of "holding my nose" to pass through the singularity at the center of a black hole.
Im a simple man, i see ed copeland, i click, i watch, i listen.
Cool. waiting for next. Thanks Y'all.
let‘s assume the entire universe has a diameter 250 bigger than the observable universe. that‘s 1.32*10^192 planck volumes. 10^200 should be the biggest number anybody in the observable universe might need
Most interesting is their reluctance to follow through with white hole speculation. It must be something like the difficulty of people like Einstien or Dirac to express confidence in the full implications of the equations or what can be found in nature. Even stranger than we can imagine.
The volume of the universe in cubic Planck lengths
The thing I find curious about super large numbers is that somehow we can find them and name them without having to "process" how large they really are (like going through each digit one by one).
Somehow even at those scales *information* regarding the numbers can still be compressed to the level manageable by us... we can manipulate those numbers without our wet brains exploding.
Excellent point. We can think about thinking about them 😃
They are only "large" due to our perception. We only use base 10 because we have that many fingers. I feel this is relevant because in software packages that deal with large integers they use bases that are CPU registers in size, e.g. base-4-billion.
If we're in a universe where entropy tends towards a maximum, and if black holes are considered maximally entropic objects, then it's makes perfect sense for a black hole to exist. Indeed, it would seem that it's necessary for black holes to exist.
However, it seems to me that this leads to another necessary conclusion about white holes. White holes would be *minimally* entropic objects by definition, and must therefore be the literal least likely objects to ever exist in the universe.
Surely the number of field interactions between particles in a galaxy is greater than a googleplex
I think a citation is needed on this one, and stop calling us Shirley!
I posit that the fact "there are numbers so large that there are not enough particles in the Universe to write them" determines for us that that number (how many particles exist in the Universe) would be the largest number in nature with any relevancy.
If parallel universes of consequences exist, then tree 3 must as well.
Along those same lines, 52! which is the number of card combinations in a typical deck of cards is greater than the seconds in the universe, YET it exists.
Googleplex is part of the tangible numbers. The topmost figure I have for tangible numbers is less than 7×10^244. After that is completely combinatoric.
New measurements show that black holes scale with the expansion of the universe over time - this could be the realization of the solution for white holes. Interesting time for cosmology
Lookin good, Brady!
Volume of the universe in plank lengths? What’s that number brehv?
Also, MORE SIXTY SYMBOLS? More of these guys! Pls :-)))
When thinking of what can the largest number that can exist to describe our universe, the largest "number" I can think of is the total number of particle (quantum?) interactions in the universe since the big bang.
The implications of a white hole are a bit more subtle in the context of the black hole. The idea behind the equation's white-hole-ness is the implication that there is a looping effect in the fabric distortions, an implication that implies some unbeknownst curvature to create "bubbles," and "pocket universes," and, to tie it into the idea that the White Hole is itself a loop of a Black Hole in a larger, higher-dimensional bubble-space. That's why, aside from the minor distributions of inconsistency implied by inflation, the lack of noticeable local curvature makes it nigh-impossible for there to be higher-dimensional shape to spacetime. I think that's why it's interesting to see this bit juxtaposed against the bit about Poincare recurrence. Maybe, by definition, timespace MUST curve back onto itself in an Ouroboros-like bang/crunch, and there is some heretofore unknown elasticity like Time-Gravity in the Time part of TimeSpace that needs to wait for the Heat Death before it can start crunching back and building up its OWN momentum, and numbers large enough for Poincare recurrence need to be achieved before curvature can be detected... Who knows. Speculation is a sport, not a science ;-)
No matter how far you move along the positive number line there are always more numbers larger than where you are than smaller numbers. So as a percentage of distance traveled along the number line is basically 0%
You can write down the size of the universe, in centimeters, on a sheet of paper, but there is no intuitive way to explain the size of TREE(3). Even many universes filled with sheets of paper would not be enough to write it down.
For me, the largest number that could be useful is the factorial of the number of particles in the universe. Because that how many combinations of thise particles can be rearranged as.
If the universe was 1-dimensional and constrained to always be the same fixed length span between particles with no gaps.
I think Ed slightly misinterpreted the "fast-growing hierarchies" in the question, but the gist was covered anyway.
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The newly released 49x49x49 rubik cube has around 10^9131 combinations.
A kilodecibel sounds realistic but is extrauniversally large
8:40 That 2001 reference 😂
Please never underestimate busy beaver. BB(20) is so much bigger than Rayo’s certainly. (Nope I’m wrong see comments)
Are you sure? I'd've expected a googol symbols in first-order set theory to have much, much greater expressive power, so to speak, than a 20-state Turing machine.
@@rtg_onefourtwoeightfiveseven we don’t have the ability to say much about BB(20), but I’d bet my life on it. What we do know for certain, is that BB will grow faster than any conceivable finite function or statement. As well to note , a Turing machine with much fewer states can produce literal infinity- the cheat is putting your finger on the greatest finite output possible, which is undecidable. This stuff is so much more fun than talking about war. Thanks stranger.
@@dhoyt902 I mean, BB grows faster than any COMPUTABLE function, but so does Rayo's function. It certainly doesn't grow faster than any conceivable STATEMENT (you can get into Berry's paradox here but it's trivial to come up with a statement which defines a sequence that grows faster than BB(N), just by using naïve extensions to BB(N)).
Remember that Turing machines can be defined using set theory. If you consider defining the following in FOST:
-The natural numbers;
-A Turing machine;
-A Busy Beaver TM;
-The Busy Beaver function;
-The number 20.
However many symbols it takes to do that, that's the value of N such that Rayo(N) > BB(20). I'm not a set theorist but I'd hazard a strong guess that N is far less than a googol, which would make Rayo's number far more than BB(20).
@@rtg_onefourtwoeightfiveseven the BB maximizes over all possible Turing machines though. FOST wouldn’t have the ability to say that in set theory, would it?
@@dhoyt902 Why not? It's just the maximum value of the codomain of BB: TM(N) -> Z, where TM(N) is the set of N-state Turing machines which reach the halt state. "Maximum value of the codomain" (or, at least, the supremum) is simple to describe in set theory once you've defined functions to Z.
Everyone knows that you need a medium and a cute, floating robot to pass through a black hole.
You look great in the outro Brady btw!
If every black hole connects/leads to a white hole somewhere, how would a black hole be able to grow bigger?
No white holes I’m afraid.
The moment you make Tree(3) relevant to our universe.. we move on to Tree(4).
I have a question: if you took all the quanta of energy in all the observable universe, and arranged it randomly in all the planck lengths, how many possible states are there?
I think this is not taking into account that we're only talking about the observable universe but i guess that's inherent in the question
Godel (EDIT: ah, he DOES get mentioned in this video. You pretty much HAVE to reference Godel in a video like this lol)... Obviously, yes, there are numbers that exist in theory that don't exist in the natural world. Because the universe is bound by constraints. Spacetime is infinite (as far as we know), which might be why numbers can exist in theory that don't exist in empirical reality. But matter is FINITE. That, ultimately, is the constraint that determines all other constraints. If there were infinite matter, or even matter in amounts orders of magnitude than currently exist, the nature of the universe would be different. The fundamental forces would be different, for example.
Why? There is nothing we know of that forbids infinite matter to exist as well, if the universe is infinite. There is no reason why the fundamental forces would have a different expression.
In any case, the fact that the universe is finite or not does not have any impact on the existence of mathematical concepts (including numbers of a certain magnitude) that do not have a physical reality. For example, look at the Banach-Tarski paradox.
@@dlevi67 Sorry, but that’s incorrect. We know CATEGORICALLY that the universe contains a finite amount of matter. If you aren’t aware of that, you are watching the wrong channel. The same goes for the fact that the fundamental forces in our universe if its size were the same, but it only contained, like, 2 atoms. Or even billion atoms. That’s an in-depth I’m willing to get in my response. If all this isn’t obvious to you, I’m not about to waste my time explaining why.
@@MacDKB We know categorically?
Then provide some categorical evidence of your ridiculous claims, namely:
1. That the universe consists of infinite spacetime.
2. That if the universe contained different amounts of matter, physical laws would be different.
Nobody is arguing that the visible universe - which is finite - contains infinite matter.
@@dlevi67 Yeah, no thanks. I'm'a take a hard pass on that.
@@MacDKB Fair enough - no shame in not attempting the impossible.
FWIW, I think you are confusing physical observation with physical law.
I always feel like physics has stolen Tony from our beloved math 😢
Whether a large number can be contained within the universe may be the wrong question. Can it be represented? Absolutely. Can it be counted? Maybe not.
The center of a black hole is said to be infinitely dense but carry finite mass, for example.
I ike that you used 19937 in your graphics.
I kind of think the very nature of a number being definable gives it a place in our universe. That is to say, you can imagine a number as big as you want by raising a bunch of nines to the power of a bunch of nines forever, and thats a really big number but we don't care about it like Tree3 because it doesn't define anything.
Tree3 might be describing a manmade game, but as soon as you draw three colored dots on a paper, Tree3 exists as the definition of that game's length. So it's not in "nature" in the sense of trees and nebulae, but it's still a thing that exists and the number pertains to it, which is why we consider Tree3 to have any meaning at all, whild the string of nines is uninteresting.
Need a video on how Poincarre recurrence works.
Imagine a ring of individual protons that lie on a perfectly flat plane to form a circle. Now imagine that they are not repelled by electromagnetic interaction and that the strong force is negated in this thought experiment. How many protons would it take to form a complete ring around the current observable universe when every proton in this ring is only one Plank length from its neighbours either side?
Seems like the number of microstates of a thermodynamic system through the lens of statistical mechanics can be arbitrarily large (while still finite) depending on system size.
Super large numbers in turn can be connected to entropy
In a way a possible recipe is to find a physical system with sufficiently large subparts, then count the possible configurations of the subparts in that system
The system could be the observable universe itself
@@GeoffryGifari The number of microstates of a system is exponential in its "size". So going from the size of say, the observable universe to its number of microstates takes you from around a googol to a googolplex, but it won't let you keep going far beyond that.
If the maximum different possible ways to arrange a system is calculated by permutations, then you could just say that if there are 10^80 atoms in the universe, than there are (10^80)! ways to arrange them.
@@RobinDSaunders It's factorial growth
@@jazzabighits4473 Well, atoms are generally treated as indistinguishable in which case rearranging them makes no difference. And regardless of whether they're distinguishable or not, they contain far more information than just "which order they're in", like their positions and velocities.
But I was thinking about the overall information content of the observable universe, rather than specifically of its atoms. There is far more information in the event horizons of black holes than in all ordinary matter, and far more still in (any of) the cosmological horizon(s). The information content of a horizon is proportional to its area in Planck units, and the number of possible microstates is then exponential in this.
I've heard there are something like 10^80 "particles" from the "Standard Model" in the universe. MAYBE you might want to calculate how many ways these particles COULD be combined if the laws of quantum physics allowed it...
Tree (3) does not have any applicaion in physical sense unelss the universe is infinite and then every number
The first question should be whether even the small counting numbers exist in the universe. I say "no" because numbers are just an idea we made up, and the rules of math and logic exist entirely outside of the physical realm, no matter how beautifully they map onto physical observation. And that's no coincidence because it's humans who chose both the rules of mathematics and physical systems to study. The common thread is us!
You can't even cycle through all states of a 256-bit binary counter without exhausting all available entropy in the observable universe, and compared to Graham's Number or TREE(3), 2^256 is basically zero.
Cycle through all states of a 256 bit binary counter? How does that go? It seems strange to think that 256 bits could be so exhausting for a digital computer, I am not doubting you at all, just curious about how that goes and thought I'd see how you explain it unless you are uninclined and I will just look it up.
@@Brice23 It's Landauer's Principle. Any irreversible change in information in a system dissipates _at least_ a certain amount of energy, which is given by the temperature of the wider system in which it immersed (our current systems are billions of times less efficient than this; it is a theoretical lower bound). An irreversible change in energy implies an increase in entropy. There's not enough entropy in the observable universe to allow cycling through all 2^256 (approx. 10^77) states of the counter.
@@davidgillies620 A wonderful and interesting explanation. I had not thought of computation in such a context before. It makes me wonder if there is a way to do computation that is reversible. I guess it is implied that this would defy entropy and so I gather that it would therefore be shocking to discover a reversible process of computation. Forgive me if I simply don't really know what the heck I am saying when I use the word reversible. Anyhow, I sure appreciate your reply and I thank you for the explanation.
As for the reality of math, there is the concept of the "Platonic ideal", or the perfect "Form", that existed somewhere in the universe, both for physical objects (the perfect "Form" of a "chair"), or for ideals ("Justice", "Love", etc.). But one could easily extend that to every physically possible formation of matter and energy or to any concept, including mathematics, and I find it hard to believe that that's the case as that would just mean that we're in the equivalent of a computer, with a long table of all possible things, waiting to be discovered by conscious beings, which I find difficult to accept. The universe behaves logically and consistently, and so math, which is rigorously logical, helps to describe it, but I don't think that the math itself is manifested somewhere in the universe itself (apart from our expression of it).
Wouldn't "photosynthesis is sweet" be more fitting/punny since photosynthesis creates sugar? See what i did there? Fitting? Because it's a shirt 😂
3:48 it's still real to me, damnit!
I saw in a weird video that Doom's Pi value was off by a fraction and this caused some weird effects in the game.
My question is, how many dimensions (possibly even fractions of dimensions) do we need to add to our real world, before our Pi reaches a non-infinite amount of decimals?
The white hole is just ONE STEP BEYOND
No number you can comprehend is anything but equivalent to 0 compared to infinity.
I'm still trying to figure out zero.
I was wondering how would Susskind's "generalised" version of the second law of thermodynamics, namely the second law of quantum complexity relate to all this?
Did I seriously think of Bad Apple when I saw the thumbnail
Warning you have just caused a universal buffer overload - please wait while the universe reboots - This may take some eons
So what is it?
Wasn't that the idea behind "transcendental numbers" -- they transcend the material world?
If you find a counting system that doesn't fit inside the grand number. 🎉 noble prize. Could be quantum geometry.
There are an estimated 10^80 particles in the observable Universe, and there are about 8.8*10^112 cubic Planck lengths in the the same region. Thus, is 8.8*10^112 the biggest "physical" number?
The larger the number the higher the probability that it becomes a philosophical construct rather than a mathematical one.
There are real uses for super large numbers like tree 3 in the real universe but its not for something as simple as an amount of X - they are used for counting things like tree counts- where you use them for counting recersive sets of sets of sets etc. So you might be discusing how many permutations /sets of real things there are- the object themelves exist in small regular numbers but the crazy number come into play when talking about recursions of real things.
Notable jane street alum:
sam bankman fried
Ive always had this intuition that any true complete theory of everything would have to be capable of yielding a theory that explains how humans do math. and in my mind, that would mean that it would have to be a system that encodes a sufficient amount of arithmetic to be subject to incompleteness. But that contradicts the fact that it’s a complete theory of everything!
if you have a bar magnet just behind the horizon of a black hole, how do its magnetic field lines look like?
I suspect that if white holes "exist", that they're just time reversed black holes. In other words, we couldn't ever encounter one unless we somehow travelled in the reverse direction of time, which we are fairly certain isn't possible (at least, not for anything with mass, like humans!). It just doesn't make sense that one could exists based on how we understand mass and gravity; as far as we know, true "negative" masses aren't possible, nor any sort of "anti" gravity.
I think the place for big numbers is in the realm of information theory. A "reasonable" program like Microsoft Excel is 66.4MB on my machine. If this is represented as a single number, which it is, then it would be about 10^160,000,000. To say this in prose, it would be a decimal number with 160 million digits. This is certainly a big number. Microsoft Excel is not even a particularly big program as such. If we look at databases, they can be much, much larger - gigabytes instead of megabytes. The only reason ordinary mathematics divides such large numbers into smaller chunks like 8-bit bytes, is that the small chunks are more easily comprehended by our intellect, and they can be more easily processed by computers that we can build.
Cartoon Ed is best Ed.
The universe only contains a finite number of planck volumes, that presumably, with our current understanding of the universe, can only be in one of a finite number of states. Wouldn't the number of states to the power of the number of planck volumes be a reasonable upper limit on the number of possible mathematically "useful" or "possible" or "physical" numbers there are? It would be a very large number but still not even close to tree(3), so I feel that that kind of implies that there must be numbers that are too big to be useful
It seems like we are roughly in the middle of the scale
you look more and more like jared harris everytime i see you brady
There certainly is a place for any number in the universe, no matter how big or small: our heads.
Except we know that’s not true, our brains are finite so there are absolutely numbers that cannot be held in our heads
@@jb76489 Hmm, had to think about this for a minute. I think I disagree. Yes, our brains are finite (I mean anything in a materialistic world kinda is) but since information is stored as relations between neurons, which is an analog process, practically anything that can be expressed as a relation „should“ fit. The readout would be discrete and finite again of course.
@@jb76489I'm not sure that's correct, as obviously mathematicians deal with quantities of infinity all the time. If there is a number that can't be represented somehow, how would we even know? Infinities can be expressed in a finite space. In my view, this isn't actually a problem of whether a number can "fit" in our heads or not, but rather a consequence of literalizing a metaphor ("head" or "mind").
@@bsadewitz I think when someone is referring to the matter of fact that very big or infiite things cannot be "held" in our heads this is actually referring to our imagination. We cannot imagine a number this big but we can nonetheless think it.
@@TheELectricStylezWhat I'm saying is that "inside our heads" is not a place, so the metaphor is misleading. The word "imagine" means "form a mental representation of". How could we think of anything that we cannot imagine, or vice versa?
One of the jobs of mathematics is to make sure you have all the numbers you might ever need, and to make sure arithmetic works in those numbers. So Tree(3) isn't needed today, but maybe one day ... .
Does the ability to arbitrarily construct any finite number using a much more finite amount of information, not make it "real in our universe" in the same way that the endless digits of pi exist even though we cannot write it down digit by digit? We can compact pi into finite constructions, and it must "exist" in some complete way because otherwise circles would not be possible.
Does the concept of infinity itself have a place in nature?
Beyond the singularitu of a black hole is the region of the white hole.
But what does that actually mean?
As I understand it, that is a time rather than a place: when hawking radiation dominates the interactions at the event horizon.
This is a way of thinking about the connection between black holes and quantum entanglement.
Yes. It's weird.
I'd argue numbers become less relevant gradually as they increase in size. And arbitrary big numbers are SO big, they vastly pass any cutoff point.
The cutoff becomes, is the only use for this number to denote it's own absurd bigness? If so, it's beyond useful.
The numbers being useless is somewhat relative to the numbers around it. Since there is a gulf of unnotable numbers between them and some other number, that's partly why they are useless.
You could define a cutoff number or point, but by doing so, you'd give relevance to that number and the cutoff point would shift comparatively.
It becomes a measure of human requirement, not physical relevance. And as such, like a proton in a quantum state, by observing, you change. Schrodinger's Large Number Usefulness Cutoff or SLNUC if you will.
So if someone ever asks you for that number, you can say, "Yes, it's SLNUC". Which is as good an answer as any.
What's the "three three" number they are talking about?
Does the universe cool down or heat up when someone invents the new largest number?
If the universe did not exist would math still exist? Or, is the existence of the universe required in order for math to exist?
A white hole is the brown hole of a black hole
wheres the clip at 7:43 sourced from? wild imagery