Where are the White Holes? - Sixty Symbols

Two viewer questions about huge numbers and white holes. Learn more about the Jane Street internships at jane-st.co/int...
More links and info below ↓ ↓ ↓
More from this Q and A session: • Ed and Tony Answer Som...
Featuring Tony Padilla and Ed Copeland.
More videos with Ed: • Ed Copeland - Sixty Sy...
More videos with Tony: • Tony Padilla - Sixty S...
Some big number videos on Brady's Numberphile channel: • Big Numbers on Numberp...
Tony Padilla on Amazon - amzn.to/3U6DRSM
(Check out “Fantastic Numbers and Where to Find Them”)
The Unreasonable Effectiveness of Mathematics in the Natural Sciences: www.maths.ed.a...
Patreon: / sixtysymbols
This project features scientists from The University of Nottingham
bit.ly/NottsPhy...
Video by Brady Haran and Pete McPartlan
www.bradyharanb...

[@timseguine2]

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.

[@kbrizy1]

That’s super interesting - thanks for sharing.

[@_ilsegugio_]

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

[@appa609]

Probably some recursive application like e^ix/π or fourier series?

[@JAzzWoods-ik4vv]

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

[@aqua-op]

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.

[@nickjohnson410]

I completely understand how and why Cantor went insane.

[@c.jishnu378]

Did he?

[@JonnyCM]

Real treat to see Ed Copeland again, another excellent video Brady.

[@aL3891_]

"treat" is a the perfect word to describe it :)

[@busybillyb33]

Ed Copeland can read me bedtime stories and I'd never go to sleep.

[@Pinkfongfan24]

Ed Copeland is my favorite ❤❤❤

[@mastershooter64]

Ed is awesome! (so are others but yk he's my favorite because he's a theorist)

[@firstplacelast2]

I love the idea of "holding my nose" to pass through the singularity at the center of a black hole.

[@andycarlson4701]

Gotta love Tony. It's so incredibly British that he didn't plug the crap out of his book :)

[@rosiefay7283]

It wasn't an advert. It's so incredibly American that you think this is a matter for ridicule.

[@candyland195]

0:20 Praise the Bucket Man

[@eryqeryq]

Emptying out the maths barrel to make room for more maths

[@ExcitedCoyote-qm3nx]

Praise be unto him.....

[@jacobeby7990]

Praise be!

[@MichaelOfRohan]

🙏🤲🍯🪣

[@samuelbush2765]

🪣🪣🪣🪣🪣

[@reservetruls]

Yes, I need more questions like these being answered by people like Tony and Ed. They might even deserve their own channel.

[@gencshehu]

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!

[@theograice8080]

Thanks for the reminder that the bell icon exists! I've just toggled it on myself 😁

[@atimholt]

I watch these videos whenever they're suggested. After reading your comment, I went to check if I had the bell on, and to my astonishment I wasn't even subscribed! So thanks for that.

[@rafaeldelimasantos1879]

I love hearing Dr Copeland talk about stuff, his voice is so calming

[@m00niee]

Whenever Sixty Symbols uploads a video is a great day!

[@yashbutno]

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.

[@Quiltfish]

Love the engagement bait of spelling it "Googleplex"😂 Totally fell for it

[@phillipsiebold8351]

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.

[@isatousarr7044]

White holes, the theoretical counterparts to black holes, remain one of the most fascinating yet enigmatic predictions in astrophysics. According to general relativity, while black holes draw in matter and light with their intense gravitational pull, white holes are theorized to expel matter and energy, functioning as the "reverse" of black holes. However, their existence has yet to be observed, leaving them firmly in the realm of theoretical physics. One possibility is that white holes might form in scenarios tied to the early universe, potentially acting as time-reversed black holes or even as gateways in spacetime, akin to one end of a wormhole. They could also emerge as the final state of certain black holes, as predicted in some quantum gravity theories. Yet, their apparent instability and inability to sustain matter in our current understanding of physics make them elusive. The search for white holes challenges our comprehension of space, time, and causality. If they do exist, discovering one could provide revolutionary insights into the nature of the cosmos, the interplay between quantum mechanics and relativity, and the ultimate fate of matter falling into black holes. For now, they remain an intriguing mystery, pushing us to expand the boundaries of both theory and observation.

[@ticketforlife2103]

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.

[@basedbasepair8664]

I think of the "planck frames" of the universe for how time might work at a fundamental level

[@ticketforlife2103]

@@basedbasepair8664 what do you mean?

[@basedbasepair8664]

@@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.

[@dlevi67]

@@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".

[@basedbasepair8664]

@@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).

[@zhadoomzx]

I love tony... he brings across the craziest maths ideas across in such a funny way.

[@diraziz396]

Cool. waiting for next. Thanks Y'all.

[@n0tthemessiah]

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.

[@GeoffryGifari]

The longer these channels progress the more Brady resembles Jared Harris' Professor Moriarty

[@shaunnichols4664]

The Red Dwarf explanation of White Holes has worked for me all this time. I believe

[@greatquux]

So what is it? 😂

[@Kingstallington]

@@greatquux I've never seen one before, no one has, but I'm guessing it's a white hole.

[@jmcusack]

@@Kingstallington A white hole?

[@robertkalinic335]

Feels like i missed the rest of your comment.

[@quinn7894]

Talking about analytic continuation of solutions to equations that lead to white holes (the opposite of black holes) reminds me of when I found equations to work out the number of faces, edges, and vertices of platonic solids with faces that have *p* sides that meet around *q* vertices, and I decided to plug in negative integers into the equations and I found 4 infinite families and 61 special cases including the original platonic solids, euclidean tilings, etc. They satisfy all the equations, but who knows if they can exist in any meaningful way? (e.g., many of them have negative numbers of faces, edges, and vertices)

[@bobtk2352]

One of my math profs was fond of saying: It's vacuously true. I.e. It holds in theory, but there exist no examples.

[@aqua-op]

Im a simple man, i see ed copeland, i click, i watch, i listen.

[@pluto9000]

Do you read and write in the comments during the video or wait until the end?

[@OBGynKenobi]

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.

[@garywalker8493]

If the universe was 1-dimensional and constrained to always be the same fixed length span between particles with no gaps.

[@SpaveFrostKing]

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.

[@ianstopher9111]

Example of a second solution that's thrown away: Bessel functions of the second kind you are taught to throw away as unphysical. There may be some niche cases when you keep both the first and second kind, but I don't know of any for physical phenomena.

[@stasglazkov8734]

Our past actually fits the description of a white hole in terms of many aspects like things getting expelled from it and that you'd need to move faster than light to enter a white hole, which conincidentally would cause you to travel to the past. At the same time the very distant future of every particle will eventually end up inside one giant black hole.

[@laurendoe168]

The moment you make Tree(3) relevant to our universe.. we move on to Tree(4).

[@abcabc-uv6ce]

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?

[@LolUGotBusted]

pi to 65 places will draw a circle around the observable universe, accurate to a Planck length. I think we've calculated it to 105 trillion digits. This is a level of precision useful to literally no one. Except for the guy breaking the record.

[@juliavixen176]

​@@LolUGotBustedIt is useful for purposes other than measuring physical material objects located in space. For example, if you discover an algorithm that allows you to calculate the trillionth digit of pi, without needing to actually calculate the previous trillion digits first. That method could be used to solve many other difficult problems. If you need ten years of CPU time on the world's fastest supercomputer to calculate the answer to some problem. And then you discover a way to calculate the same answer in only ten seconds. That is of significant practical importance.

[@LolUGotBusted]

@@juliavixen176 that thing you describe doesn't exist. If I could clap hands and wish myself to Andromeda that would be useful too.

[@sixtysymbols]

Learn more about the Jane Street internships at jane-st.co/internships-ss More videos with Ed: kzbin.info/aero/PLcUY9vudNKBNtF1y-sneLuyCTE-Mda561 More videos with Tony: kzbin.info/aero/PLcUY9vudNKBPJmX64Jay51cdZTKMz4ACs

[@fleetstreet11]

They're the photo negatives of black holes. Like that key command on a Mac that inverts the colors.

[@JaredHerdlevar]

Lookin good, Brady!

[@kaushaltimilsina7727]

Black holes seem to have this relation: Everything falls in hawking radiation is emitted. I was thinking about a reversal of this, if something just collapses from a thermal bath of radiation and then begins emitting things. A description of primordial black holes being formed from collapse of vacuum fluctuations in the early universe, sounds quite similar. I think primordial black holes have been investigated as candidates for dark matter, and Carlo Rovelli has proposed a model for white holes as dark matter based on loop quantum gravity. That sounds quite related to me.

[@MrMichiel1983]

If things have an infinitesimal chance of occurring in comparison to all other possibilities, then there can be no recurrence on the scale created between eternity and infinity. Another way of saying that is that "particles" in a system under scrutiny will at some point randomly "tunnel" outside of the "boundaries" declared by that system. Therefore the system's configurations might repeat for infinity given the description of what is known about the system itself, but given other hidden variables could never do so ad infinitum.

[@EmanuelsWorkbench]

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.

[@tobuslieven]

If anything in the universe is smooth even at a single point, it must have derivatives of all orders at that point. That is an infinity. If there is an infinity anywhere in the universe then large finite numbers like TREE(3) exist in the universe.

[@tonywestbrook9876]

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.

[@juliavixen176]

What do you mean by "follow through"? In the 1960's is was hypothesized that quasars might be white holes (they're not). One of the big issues is that white holes are a vacuum solution to Einstein's field equations. Basically empty spacetime with no energy in it, forever. Just a 4D manifold that has always existed for no reason and always will exist forever... it's a shape.

[@treborsenaj9169]

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

[@mr.bennett108]

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 ;-)

[@hesgrant]

Awesome video, can't wait for more! Tony and Ed are fantastic

[@kbrizy1]

Volume of the universe in plank lengths? What’s that number brehv? Also, MORE SIXTY SYMBOLS? More of these guys! Pls :-)))

[@xway2]

You'd think but it doesn't even get close. A Planck length is about 10^-35 m and the observable universe is about 10^27 m across. So that's about 10^62 Planck lengths. If we think of "cubic Planck lengths" that's just (10^62)^3 or 10^186. So nowhere near a googolplex even.

[@Cossieuk]

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%

[@invariant47]

brady at the end looks like professor moriarty from the sherlock Holmes game of shadows moive

[@GeoffryGifari]

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

[@GeoffryGifari]

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

[@RobinDSaunders]

@@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.

[@jazzabighits4473]

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.

[@jazzabighits4473]

@@RobinDSaunders It's factorial growth

[@RobinDSaunders]

@@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.

[@PersonalChannel-ht4rb]

You go into dark hole - you come out from white hole, but there is twist.

[@OmateYayami]

It also involves a bit of a stretch =]

[@Peter-o9n6p]

It's not only absurdly large numbers that are "too big" for the universe, but virtually every "real number" with their infinite decimal expansions. Swiss physicist Nicolas Gisin has been exploring the question of how a presumably finite universe could entail a physics featuring numbers that can't be computed or even named.

[@jansenart0]

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?

[@METALSCAVENGER78]

Tree (3) does not have any applicaion in physical sense unelss the universe is infinite and then every number

[@Djarnor]

You look great in the outro Brady btw!

[@ianstopher9111]

Assume the universe is unbounded in some direction. Now assume there are 3 particles arbitrarily close to one another in a line of sight, but not parallel, so as to form a triangle to a distant observer of these three particles. The solid angle subtended by those 3 particles can be made vanishingly small. This number of these solid angles that form 4π steradians can grow without limit. Of course, if spacetime is quantised and you impose c as a limiting factor on any lin-of-sight argument, then you will get a large number that would fit in 4π steradians, but nowhere as big as a Googleplex. But if you are allowed a thought experiment about line of sight to ridiculously large distances then it will be a big number (though really not much bigger than the distance to the distant particles) but the point is not to have to physically traverse the distance, just consider from your position as an observer surrounded by a sphere that can be tessellated by these arbitrarily-small solid angles.

[@Fleshcut]

"I don't know my white holes very well" - Ed Copeland, 2024

[@heavyecho1]

So what is it?

[@Steve-nuru888]

Who is here from numberphile

[@GeoffryGifari]

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.

[@lornacy]

Excellent point. We can think about thinking about them 😃

[@HyenaEmpyema]

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.

[@100percentSNAFU]

What's mind-blowing to think about is how large a googolplex is. Take a googol, and subtract 100 and that's still a ridiculously large number, a 1 then 97 zeroes, then 900 at the end. A googolplex is that number of orders of magnitude bigger than a googol.

[@100percentSNAFU]

Also it's pretty amazing what orders of magnitude do with numbers. A million seconds is a couple weeks and a billion seconds is 33 years. Imagine even if you did have enough material to write the actual numeral of googolplex the time it would take. Surely time beyond the heat death of the universe!

[@juliavixen176]

This is known as Kolmogorov Complexity. In Algorithmic Information Theory, the actual amount of _information_ contained within famous transcendental numbers, like pi, is finite. A (finite length) symbolic description of the algorithm to calculate and output the number is all that is necessary. You execute/evaluate the short finite computer program for as long as you want, possibly forever, to output the number (like pi). The total amount of information is only the program and inputs, not the arbitrarily long output. It's data compression, basically.

[@cheeseburger118]

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

[@hypercomms2001]

Where are all the white holes the same place as where all the antimatter has gone!

[@natedawww]

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.

[@user-wv5bn4dv3d]

True. The matter accretion of a Schwarzschild black hole is 0, a vacuum solution. The expulsion of matter from that same black hole analyzed in the opposite direction (its associated white hole) is also 0. This causes the necessary symmetry to exist to construct the Schwarzschild white hole as an inverse solution of the Schwarzschild black hole. But this same cannot be done in the case of Kerr, because when applying time inversion to the Kerr black hole we do not obtain a Kerr white hole, the Kerr black hole does not allow the symmetry necessary to construct its associated white hole.

[@user-wv5bn4dv3d]

So that you understand it, it improves if you film the life of a Kerr black hole and we observe that it swallows 3 apples in 100 years, when we see the complete film in reverse we may see a different number of apples ejected. Where were the missing apples? They are not even contained in space-time, what we understand by loss of information.

[@MacDKB]

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.

[@dlevi67]

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.

[@MacDKB]

@@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.

[@dlevi67]

@@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.

[@MacDKB]

@@dlevi67 Yeah, no thanks. I'm'a take a hard pass on that.

[@dlevi67]

@@MacDKB Fair enough - no shame in not attempting the impossible. FWIW, I think you are confusing physical observation with physical law.

[@Fourestgump]

Infinity makes sense when it comes to love.

[@SuneJorgensen]

The newly released 49x49x49 rubik cube has around 10^9131 combinations.

[@quantumzoflyne]

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?

[@tokajileo5928]

if you have a bar magnet just behind the horizon of a black hole, how do its magnetic field lines look like?

[@juliavixen176]

It "looks" exactly as it does at the event horizon... just like electric charge does... static and unchanging. It doesn't "go away", the magnetic potential energy is still in the magnetic field that fills all of the spacetime outside of the black hole

[@alanwilson175]

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.

[@natedawww]

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).

[@MagruderSpoots]

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.

[@100percentSNAFU]

Although we aren't even certain the actual size of the entire universe, it potentially could be infinite. We can only measure the observable universe. But in terms of the observable universe your statement is accurate.

[@rtg_onefourtwoeightfiveseven]

I think Ed slightly misinterpreted the "fast-growing hierarchies" in the question, but the gist was covered anyway.

[@devintinney9394]

You have to go through a singularity … you have to go through an area where maths breaks & we do not understand what is happening … uh, okay, duh. Not saying white holes exist, but singularities, when they occur, seem like great places to explore & research whatever the question.

[@Monothefox]

Everyone knows that you need a medium and a cute, floating robot to pass through a black hole.

[@mirador698]

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.

[@scotchandrew]

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?

[@breadfan262]

The volume of the universe in cubic Planck lengths

[@100percentSNAFU]

Still less than a googolplex. Possibly even less than a googol as there are around 10^80 atoms in the universe and even a googol is 20 orders of magnitude larger. A googolplex is nearly a googol orders of magnitude larger than a googol. It's 10^googol.

[@benbooth2783]

The largest number needed to describe a physical property of the universe? Surely it's the number of ways to arrange the universe? Classically this would be something like: 2^(the volume of the observational universe in Planck units). Or if you like the holographic principle: 2^(the surface area of the sphere that bounds the observable universe in Planck units). Quantum mechanically you have to think about the number of states the observational universe can be in, I have no idea how to calculate that. I can't think of anything bigger.

[@davidgillies620]

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.

[@Brice23]

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.

[@davidgillies620]

@@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.

[@Brice23]

@@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.

[@OmateYayami]

Probably not practically. You could maybe manipulate stuff at the verge of thermodynamics i.e. akin to superconducting stuff but you always put input and read output and I don't think it's possible to do it without using energy, even if you could do computation without any dissipation in energy, like you can run electricity through superconductor or you have superfluids without friction and loses. And there problems with quantum tunneling and stuff. Information manipulation and storage is actually pretty complex stuff. I'd say it's becoming more challenging that actual computation itself.

[@brian8507]

0:19 that was me

[@jacekbochra867]

You are lucky man to be featured in Sixty Symbols episode

[@rhoddryice5412]

@@jacekbochra867 Sixty symbols

[@Triantalex]

ok?

[@bryn.1tbs]

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

[@Yora21]

How many Planck lengths is the diameter of the observable universe? What's the volume of the observable universe in Planck lengths cubed?

[@aqua-op]

5.45x10^61 planck lengths, you can figure out the volume from there

[@mihaiga]

Surely the number of field interactions between particles in a galaxy is greater than a googleplex

[@backwashjoe7864]

I think a citation is needed on this one, and stop calling us Shirley!

[@100percentSNAFU]

Googolplex is so unimaginably large that even such interactions, I suspect, wouldn't even number anywhere near it. There are less than a googol (10^100) particles in the observable universe, a googolplex is 10^googol, so a googol minus a hundred orders of magnitude greater than even a googol.

[@markkaidy8741]

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.

[@OmateYayami]

Does it though? It's a theoretical number of all possible combinations, nothing will ever physically realize it. Like, you won't make a set of every possible deck combination and actually count it. It impossible and not physical.

[@markkaidy8741]

@@OmateYayami My point is ir is physical and exists and yet its "impossible"..... There exist in the real world infinities known yet uncountable.

[@OmateYayami]

​​​@@markkaidy8741 To be clear I was talking about combinations of deck cards. Those combinations do not exist, you cannot enumerate them, you can only say how much there is. So I am asking a question is the number of combinations real if you cannot physically count it? For example, you say there is 52! combinations, I say it's 52!+1, you cannot show directly that you're right. We won't be able to setup a physical experiment that will falsify one of our claims. We have to trust math and deduction and will never verify it. In other words all of the combinations of deck sequences will never exist in the universe. It's physically impossible.

[@markkaidy8741]

@@OmateYayami This is where we disagree. Just because you cannot count something does not lead to conclusion it is not real. If you have a deck of 10 cards it has 10! which you can count...and if you have 11 cards there are 11! combinations...as you get to 52 you wont be able to count them but it is PROVEN that there are 52! combinations... also (going now to the infinitely small) with irrational numbers . you can graph on a number line root 2 and root 3 and Pie but their decimal definition is infinite.(you can calculate them infinitely)..yet.. they exisy.

[@OmateYayami]

​​@@markkaidy8741you bravely assume the math works. Maybe it breaks off reality after 42 cards. You will never show me and will never check it. It will be only your belief. You yourself openly admit you could do it for 10 or 11 but not for 52 and I should just trust your math proof. It is an abstract extrapolation. I hope you see the difference. This number is too big to describe anything existing. All deck permutations will never exist. Conversely you will never measure pi or sqrt2. Only approximations.

[@MnJiman]

Theory: All mass affects all other mass. All particles affects all other particles. Their spins... their movements should have an affect on everything! But the effects are so small.... so nonexistent... that it's disregard. So I do think that big numbers play a role in practical mathematics? In real life physics? Sure, once we stop simplifying every single physics equation!

[@mikesiurua5677]

I ike that you used 19937 in your graphics.

[@Jesse_359]

Never mind the set of all sets that don't include themselves and other such linguistic paradoxes - it seems fairly debatable whether the physical universe has any truck with concepts as simple as *negative* numbers at all - or even the number 0. Thus far 'nothing' doesn't actually seem to be a concept that functions particularly well within our physical universe. Everything in physics is ultimately about the relationships between things that exist, and unsurprisingly has very little to say about things that don't exist.

[@shayneweyker]

Need a video on how Poincarre recurrence works.

[@stuckerfam]

There need to be numbers that are too big for the physical & temporal universe. We need them so that math can adequately and somewhat accurately describe it. If math couldn't handle it, then we would not have (at least not in my understanding) any other way to describe what we observe. Basically, the abstractions of math must be "bigger" than the universe or else we have no other means to comprehend it.

[@timovneerden]

Can the whole universe be the white hole, spewing out the energy (dark energy?) in it self from the black holes it contains? The fact that the black holes are then inside the white hole, can it give the universe a shape of a Klein bottle (where the inside is the outside of itself) ?

[@yerkeruiter]

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?

[@chaoticmoh7091]

What is the difference between White hole and a Star?

[@andrewwfrey]

If the universe is a computer, and each particle or wave is a flop re-computed each planck time, then how many flops have been required to calculate the universe up until this instant? That might be a really really really big number

[@OmateYayami]

But still finite =] I was thinking about similar concept to compe with estimate when natural numbers stop being natural, and Planck volume of universe came to my mind. I think there would be some practical limit where you can hit the number of possible microstates of the universe and going beyond that would not yield anything practical and doing some exponentation or factorial would give a number that could not be practically counted to for all the history of the universe, thus would be a very unnatural natural number =] I also think what you describe is related to limits of computation. Stuff like Bremermann's limit can be starting point for some reading.

[@AtlasReburdened]

Mathematics is just a language used to describe the behaviors we see from physical reality. There's no reason to believe that physical reality is beholden to the quirks of this language, any more than there's reason to belive that subjective experience, which is generally aptly described by spoken language, is beholden to it. The mere fact that I can type "sgaieiorbdvhakakebrvdghsjsjskwhehrvn" doesn't obligate reality to create some meaning for it, and the same is inevitably true for a number with a silly amount of zeros in it.

[@binbots]

Math is just counting an infinite amount of zeros.

[@quantumcat7673]

I was wondering about why a relativistic object in direct collision course with a black hole and so possess an enormous amount of energy, more than it's rest mass, why all that energy is not transferred to the black hole when it cross the event horizon buy only it's rest mass is?

[@michaeldunkerton3805]

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.

[@OmateYayami]

I think the problem is that you can't really say something is physical just because you can define it. You can define abstract things. Like pi, it's infinite - you will never find exact pi in nature, you can always make it a rational in a physical system. Another example can be a simple square, of you draw it and draw a diagonal, this diagonal will not have an infinite precision, as it will consist of discrete atoms. In theory it will be sqrt2 of atoms on the side but in practice it won't.

[@RonJohn63]

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?

[@OmateYayami]

Nah, that's low. If you look through comments you will see that most of people suggest to use Planck volumes of universe. So you can estimate all possible states of universe as far as current physics are applicable. It will be way higher but still finite.

[@sk8shred]

What's the "three three" number they are talking about?

[@kaylor87]

What about calculating all possibly outcomes from every single quantum interaction that have ever existed since the dawn of our universe. Surely that number is absolutely massive.

[@elevown]

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.

[@OmateYayami]

I think the point is that natural numbers started off as a thing precisely to describe amount of items, so you get into areas where they depart from their original definition. Of course combinatorics can basically go as high as one wants to, but at some point you will go beyond physical things. A rough attempt for current state of physics would be every possible state of universe, so you take circumference of casually influeancble universe - it's bigger than observable one cause of spacetime expansion - divide it into Planck volumes and enumerate states, then maybe take estimated lifespan of universe until heath death divide it into Planck times, and you will get all possible universes even if it were a random mess. Something like that.

[@Rando_Shyte]

8:40 That 2001 reference 😂

[@philipcoltharp918]

Are quarks and-or electrons white holes?

[@kennygrant6583]

What is it?

[@laurendoe168]

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...

[@100percentSNAFU]

Would that number then be (10^80)! assuming every particle, in theory, could react with every other?

[@tim57243]

As a black hole evaporates because of Hawking radiation, it gets brighter and brighter until the end. Is that the white hole you are looking for? I know the intended white hole is potentially as large as the black hole observed today that aren't dominated by Hawking radiation. I'm just wondering if there is something else resembling Hawking radiation that makes a large white hole as short lived as a small black hole.