BRADY HARAN: You got another

number for us? TONY PADILLA: I have, yeah. Yeah. It’s the– well, I’ll just write

it down, shall I? That’s probably the

best thing to do. So it is 10 to the 10 to the

10 to the 10 to the 10– and then this is the strange

bit– to the 1.1. OK? This has been claimed to be the

largest finite time that has ever been calculated

by a physicist in a published paper. This is the paper. It’s a bit of a weird paper. It’s not had a huge impact

or anything. It’s about black hole

information loss and conscious beings. We won’t go down that route. He actually calculates something

called the Poincare recurrence time for a certain

type of universe within a certain cosmological model. And this is the number

that he gets out. So this is the one

on I’m on about. Let me just check I got the

number of 10’s right. Yeah. I did. Here it is, equation 16. So he’s put Planck times,

millennia, or whatever, because basically, it don’t

really make any difference whether you use seconds, Planck

times, millennia, years when the number is this big. But there’s other interesting

numbers in here, which is this one here. You got three 10’s

to the 2.08. That’s the Poincare recurrence

time for our universe. BRADY HARAN: What’s all

this about, dude? TONY PADILLA: OK. So Poincare recurrence time. This is something that’s arisen from statistical mechanics. Very simply, if we had a pack of

cards, and we’ve only got a finite number of cards

in that pack. And let’s say we keep

dealing each other hands of five cards. Eventually, if we do it for long

enough, you’re going to get a royal flush, Brady. That’s guaranteed to happen. And if you wait long enough

again you’ll get another one. And so on, and so on, And that’s

true because there’s a finite number of cards. Now what Poincare realized is

that if you take a gas, the particles, you can put

the gas in a box. Now you can put all the

particles in one corner of the box, and then they’ll disperse

and then they’ll move around. But Poincare recurrence tells us

is that after a very, very, very, very long time, those

particles will eventually return to the corner

of the box. You always get a repetition. And it’s basically because the

thing that controls the evolution of that system only

has a finite region of what we call [INAUDIBLE] space, of

solution space, that’s accessible to it. And so eventually, you always

come back to it arbitrarily close to where you started. The time scales are truly

enormous before you start expecting it to happen. So you can apply this quantum

mechanically as well. So what you’re doing in quantum

mechanics, what you’re really talking about is the

evolution of microstates within the quantums, so these

sort of quantum building blocks of your system. And they will eventually

return– they will evolve, but eventually

return to their initial states. And what Don Page in this paper

has tried to do is he’s actually applied that to various

types of universe, models of various types

of universe. It’s a bit of a cheat, because

a universe is what we call a macroscopic object. It’s a large object. It’s not really a quantum micro

state, in some sense. What it is, is it an ensemble,

an average, of all the microstates. So what he’s tried to do is

he’s tried to say, OK, I’m going to treat the universe

as this average of all these states. But then I’m going to count up

all the possible averages and treat them as a sort of

microstate in itself. So it’s a bit of a cheat, but

he gets an extra exponential out from that. BRADY HARAN: Are we talking

about, Jupiter’s over there, the Andromeda Galaxy’s over

there, I’m in this room filming you. TONY PADILLA: Yeah. Yeah. All that. OK? Now there’s a very large number

of possibilities that you can have, but it’s finite. And so as the system evolves,

it’s only got to– and it can only evolve, the

system can only evolve through a finite number of

possibilities. And eventually, it evolves

back to where it started. So actually, it’s– I’ve often heard it said that

the universe, for example, will evolve, will expand. Eventually, everything will be

spread out very far because of the expansion of the universe. That all objects will have

collapsed to form black holes. That then those black holes will

evaporate from Hawking radiation, and all you will

have is this very sort of bleak landscape of just

radiation that’s come out these evaporated black holes,

that’s uniformly distributed, and it’ll be very boring. OK? But that isn’t the end state

of the universe. The end state of the universe is

that after these truly epic time scales, you will eventually

have a Poincare recurrence, and you’ll wind up

back where you started from. And it’s quite easy to see

how it might happen. Imagine you have this sort

of bleak universe, right? Just have a little

fluctuation. That little fluctuation sort of

gathers together, builds up other things. Eventually, it sort of forms

a sort of galaxy, even. From that galaxy, you

get planets, stars. And you keep going,

you keep going. Eventually, you’ll get back to

the situation where it looks like it is today. Now, what I think is fair– I think it’s a fair point– is that there’s no way of ever

being aware of these repetitions over these

large times. And the reason is, you could

never build a device. You could never be an observer

that could measure this. And that’s because over these

huge time scales, such a device or such an observer would

definitely thermalize, would definitely become part

of this recurrence itself. And so there’s never anybody

or anything that could measure it. It’s this sort of idea, this

sort of notion within physics, is that if you can’t

measure it, it’s irrelevant in some sense. So. BRADY HARAN: But according to

this, in this number of– in this time, in this number of

years, you and I are going to make this video again? You and I are going to make

this video again? TONY PADILLA: Oh,

I know this is– less than that. This is for a special type

of universe that’s particularly large. The number for us is at least

less than this other number that he’s written down here,

which is 10 to the 10 to the 10 to the 10 to the 2.08. I’ll just say years. So this one is the one that

applies to us in our physical universe, what we call

our causal patch. This one applies to seeing

what is the Poincare recurrence time for a truly vast

domain of universe that you can get out of certain

models of cosmology. So they’re all based, of course,

on the same idea. We can work through where

these numbers come from. So the Poincare recurrence time

of any system is roughly proportional to the number

of states in that system. Because we’re applying this to

the universe, this is really the number of macrostates, the

number of these averages of microstates that you

could talk about. So let’s call this Nmacro. This, then, where we’d expect it

to be about the exponential of the number of microstates. Now why is that? Well, this doesn’t really

have to be an e. It could be a 2 or whatever. Basically, any microstate is

either in or out of the averaging with some weighting. And so this is the number

that you get out. The number of microstates when

you relate to the entropy is e to the entropy. Let’s look at some volume

of the universe, of some radius r. Then the entropy– we’ve done this before. This is the same arguments

you have before– the entropy that you could

possibly have in this region of space, basically it’s

proportional to– I’ll just be a bit sloppy

with factors– r squared over the Planck

length squared. So the next step is e

to the e to the– So now let’s apply it. So let’s apply it to

the really big number that he does. The question is, what’s r? Well, the radius of the universe

is about 10 to the 26 meters, our visible universe,

so far as we can see. What we call our causal patch. The Planck length is about 10

to the minus 34 meters. So r over n l Planck squared is

about 10 to the 120, which is a number you often see

in physics, actually. This is sort of the number

that’s associated with cosmological constant

problems. But anyway. Well, 120 is about

10 to the 2.08. That’s where that

is coming from. I don’t know why he’s so precise

about this 2.08, because what he’s going

to do next is– the number we have is e

to the e to the 10 to the 10 to the 2.08. But what he does here is

he just approximates these e’s as 10’s. Which is fine, really, in the

broader scheme of things. e, 10. For the sake of cosmology,

they’re more or less the same thing. All the e’s become 10’s, and

you’re got 10 to the 10 to the 10 to the 2.08. Which hopefully is what he’s

got there, and it is. So that’s where that

number comes from. So this is basically the

Poincare recurrence time for our visible universe,

for our patch. BRADY HARAN: Why is the

other number bigger? TONY PADILLA: Well, because

the other number– there, he’s looking at– he’s trying to get a

big number is what I guess he’s doing. He’s trying to get

a bigger number. What he’s looking out there

is a model of inflation. Now, inflation is a model of the

very early universe, where the universe grew really quickly

out of a very small patch of the universe. The amount by which it blows

up depends on various parameters in the model. But basically, the thing that

you get is you get to the size of the universe. So r, for that case,

is of order e to the 4 pi over M squared. So this is actually

r over l Planck. He’s done everything

in Planck units. But M here is the mass of some

of this influx, what we call the inflaton field. It’s just some field

in the model that causes the expansion. 1 over M squared is

10 to the 12. I think this might

be 13, actually. 10 to the 12. So this is about 10

to the 13 overall, because 13 is about 10. Bear with me. So this is e to the 10

to the 13, roughly. The 13, well, is about

10 to the 1.1. That’s where the

1.1 comes from. He’s very precise about this

1.1, and yet he’s very sloppy with some of the

other factors. You get e to the e to another

e to the 10 to the 10 to the 1.1. And then we do the same thing. We turn all the e’s into 10’s. BRADY HARAN: Help me understand,

because obviously, you have bit numbers there. How long a time is this? TONY PADILLA: OK. So this is truly vast. Like I said, there’s no device,

there’s no observer, anything that could survive

this kind of length of time scale. In fact, you would probably say

that the universe is more likely to tunnel out of the

current state before this could happen, in some sense. This is such a long time scale

that one might say that actually the probability of

tunneling to a new phase of the universe, completely

different, is actually going to dominate over this. That that would occur first. So maybe this is kind of

an irrelevant point. Yeah. It’s truly vast. It’s bigger than a

googol, clearly. Way bigger. Is it bigger than

a googolplex? I think so. So you know, let’s

just check that. Yeah, clearly it is. It’s enormous. It won’t be as big as Graham’s

number, but you know, Graham’s number’s the daddy, right? So. Well, I didn’t actually

know about this paper. But yeah, I was just– I just thought, oh,

big numbers. Let’s see what’s interesting

about big numbers. And then I stumbled

across this paper. What he claims– in

fact, he says it– he claims, “So far as I know,

these are the longest finite times that have been explicitly

calculated by any physicist.” So whether somebody

has calculated a longer one– and I’m sure some of the viewers

will try to calculate a longer one and then

claim that they’ve– but this is in a published

paper. So you’ve got to get the

paper published. But the challenge is on, I

guess, to find a longer one. There probably has been, too,

but he was the one that pointed it out.

## 100 Comments

Oh boy LITERALLY can't wait to comment this again when it's uploaded again e^e^10^10^2.08 years later!

woooooah-oh-oh (for the longest) for the longest time

It's the time we have to wait before avengers 4 title.

Wouldn't 10^10^10^10^10^1.1 just be the same as 10^11000?

Deja vu

I've just been in this place before

Boltzmann Brain anyone

If a research paper from non US or non Euro country has a word 'whatever' in it, it's guaranteed to not get published😂

Poincaré recurrence will occur for a finite solution space but applying it to our universe which is expanding (increasing in space) does not justify how universe will stop expanding and start contacting.

sometimes i have dreams about events months before they are going to happen, when i already clearly forget that about the event, then they occur and i'm like – wait…

If this recurrence is true, it implies there's no free will

"science"

10:27 i got confused as there was three e’s but the other e is part of the entropy

You seem to imply though, that the universe will stop accelerating in its expansion and collapse. No. More likely, It will reach heat death, and then over an epic time scale every particle will tunnel ask to the same exact point in spacetime and a new universe will be created.

HIs idea of a recollection of particles to form a galaxy (4:45) doesn't take into account that the baryons may have decayed long long before the recurrence time. That universe would only have a gas of photons and maybe neutrinos

5:48 lmao!!!

B I L L Y J O E L I N T E N S I F I E SI've worked out a larger number. It's 10^10^10 repeating till it starts sounding like The Overture to William Tell.

But doesn't the constantly increasing entropy mean that this recurrence is not possible, because we keep adding to the finite amount of entropy?

physics be like pi = e = g = 10

If the universe is infinite wouldn't things be repeating right now?

I love this guy he is brilliant at explaining bonkers concepts to mere mortals like myself..

But is universe finite? doesn't universe expention apply anyway?

I came back here after watching A Ghost story and a Futurama episode.

１０（３）＝１０＾１０＾１０

１０（４）＝１０＾１０＾１０＾１０

…………..

１０（３）＜ Universe ＜ １０（４）

The Universe ≒10(π) ｍ

I have thought that way before. I think that it is close to your way of thinking.

I agree with your way .

But what if the box – or the universe – is expanding exponentially? Does the Poincare recurrence time still apply?

Surely in a recurrent universe it's more likely for there to be small fluctuations that resemble some past state of the universe as opposed to an enormous fluctuation. We're far more likely to live (if we do live in a recurrent universe) in a small fluctuation, an isolated pocket of low entropy in a universe of high entropy. Yet when we look out into the night sky, we see order as far as we can see. Why is this? Surely the chances of there being a fluctuation the size of at least the observable universe is minimal compared to the chances we would be living in a small fluctuation.

I hope the universe doesn't reset.

Impossible. Particles will have to move faster than light to interact with each other.

Like if you’re here after the universe resets itself

Us plebs: e~3

Don Page, an intellectual: e~10

This guy looks like the kid from Toy Story who tortured the toys

You really need to normalize the audio volume

5:47–5:52

5:47–5:52

I strongly recommend reading "The Last Question" from Isaac Asimov. It's a short story that talks about all this crazy entropy stuff. …In the 50's. When you finish reading it, you end up with that strange sensation 🙂

engineers get ridiculed for e=pi=3

e=10 is next level i love it!

10^10^10^10=

10^10^10'000'000'000=

10^1…(ten billion zero's)=

1…(ten billion zero's of zero's)

watches videoEntropy: AM I A JOKE TO YOU?

How that particles can return to the corner with 100% probability? Even when there is finite states, that doesnt mean, that it return to the start… it can cycles between some another states :-o?

So is this poincare conjecture also imply that, if we dissolved a cube of sugar in a cup of coffee, and stirred that cup for liquid for 10^n years, where n=10^10^10^10^on and on, we'd eventually get back our cube of sugar?

Sounds like a subject tetration would apply very well to

Billy Joel would be proud

"How long can we do this math?"

Fooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooor the longest time

Does not happen if the universe keeps expending.

His chompers are gargantuan!

Is the Universe very big or very small?

That was clearly the best guy to explain this

I've calculated the 10^10^10^10^10^1.1

It's over 1 followed by 315,027,680 zeroes

And this is why human scientists become fully arrogant dumbasses…

nowadays anyone can get anything published…

This guy's mumbling is all but unintelligible.

What if sleeping actually travels you back in time by 10^10^10^10^10^2.08 years and you dream about what you see during the travel????

Grahams number in years.

How many iterations of this particular comment did I make in that time span?

doesn't that violate the second law of thermodynamics because after maximum entropy is reached in the universe it won't go back?

As often happens, Roger Penrose supplies hopeful wisdom– with his CCC . Epoch follows epoch, over and over, time and again; time slows down, distance becomes stupifyingly enormous, but conformal rescaling saves us, the universe is recreated, carry on.

I can believe in this. But knowing you, we will argue about this forever.

No I don't think it is a longest time its a 357686312646216567629137^99999999^π

how could any timespan ever be greater than the reaccurance time of the universe?

So if mayo play in an infinite number of all Ireland finals we will eventually win one😉

Why didn't some college kid at the community college write this?

But our universe expands faster than the time where anything will happen. This reason only works with a non-expanding universe, and then it is like with the Boltzmann Brain, which is soo cool! Everything, independent how unlikely it is, will eventually happen. If there are finitely many states (if, then there are very, very many) it has to repeat after going through every possible sequence of events.

Wooooooooooooooooooooooooooooooooooooooooooooooooow

Seems like an incredibly small number for what his is calculating honestly.

10, to the 10, to the 10, to the 10, to the 10 to the 1.1

all e's become 10s xD

If you want to save time those numbers can be written as

E2.08#4

E1.1#5

10^120 is the number of chess games possible I read

The point behind 10 vs e is the curve in a square as you extend squares with a path that traces a Fibonacci spiral.

10^10^10^10^10^1.1 years

to the one point one.

Web Will be having this discussione again

e = 10

4:56 time will still exsist after gravity is no longer a thing?

For some reason I've watched this a second time. Mind boggling.

This is plain false. Here is the argument: I drop the ball into a pit. Question: how long it will take for the ball to return to where is was dropped from? Answer: as long as gravity exists, it never will. Generalization: system changes from higher energy state to low energy state and never returns until laws by which the system lives stop affecting the system. Gas molecules will NEVER all condense into a corner, if laws of thermodynamics never change.

Of course it is smaller then Graham's number

it is even smaller then g1 or 3^^^3

the longest time without power 1.1 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ( plank time )

So first law of engineering is e = π = 3. And the first law of cosmology is e = 10?…

I'm surprised no one has come up with a symbol to save time in writing the same power.

Matematicamente l'eterno ritorno di Nietzsche

Lol! e=10

I understand the finite argument that eventually everything will happen in a finite amount of time even exact repititions.

I would like to know that using the argument that finite change can happen at any time, isnt there an equal chance that it won't. IE picture that moment at the right before the universal Royal flush there is an equal chance you dont get a royal flush.

Thank you

Poincaré recurrence —> 5:43 …you and I are going to make this video again. You and I are going to make this video again…

Mathematicians:

"I'm not interested in approximations"

Physicists:

"e=10"

It's funny how he says some of the viewers will try to get larger time. 😀 yes they usually do, all the time, posting things like that and also using the classic Fermat's signature line. 🙂

5:47 I just freaked out when I saw that

Thats assuming the universe was finite/constant sized tho which we or the majority of astronomers these days assume it is not.

Engineers: e = pi = 3

Physicists: e = 10

1:42 why is it guaranteed? This seems like it’s possible to never get a royal flush, even if there is a minuscule chance, there still is a chance, right? That statement seems rather illogical.

I love how Numberphile video titles at first glance seem to be clickbaity, but are 100% of the time, totally legit and not clickbaity at all.

Hey subtitlers. He's obviously saying phase space

I am… oh I don't know, 10^10^10 whatevers old

There are currently pi comments, (3,141) which I'm now ruining by my claim that there were pi comments when I wrote this comment. Well, sort of, because there are now 3,142 comments.

Regarding the current subtitle gap after 2:15 ("[INAUDIBLE] space"), is it "phase space"?

Me, an intellectual: 10^10^10^10^10^1.2

So basically I have been lying in bed watching this video for about an infinite number of times already, and will do it a lot more…

Cool

OMG IT'S DON PAGE.

Dude's

infamousat his uni.Is 10^10^10^10^2.08 the same as 10^1000^2.08?

Some would say they experienced that time length during a 10g psilocybin mushrooms in dark silence.

10^10^10^10^10^1.2 years. There, calculated a longer time.

This is also the time span Rapid Wien will win its next title in Austrian soccer league. Last occurence 2008.

When you realize e^e^e≈3814280 and 10^10^10 is a 1 followed by 10000000000 zeroes.