Googol and Googolplex - Numberphile 

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*copys this comment*

Just as much as you thought in your brain

if the universe is infinite, i could fit infinite grains of sand, right?

How is it possible that you can fit more grains of sand in the universe than particles?

+Tom Mulligan made my day :D

Tom Mulligan well played sir...well played.

Best of 2017 material

Now go 16 miles in the same direction and see if you can find yourself

This goes perfectly with your profile picture

Tree(3): Hold my beer

You can't even write the number of digits contained in Graham's number, or the number of digits contained in that number, and on and on more than a googol times.

NoriMori my mind has been blown

@@user-ix5zf2ro1m Rayo's number +1

@@nolanlitz1665 Tree(grahams number): Bow down to me

Googolplex

@@Tengspeakfootball Googleplexianthenialarisian ( yes exist )

My dad have Level 1649 in Toy Blast

@@Gamerxxnoob Gigolquintiplex

@@AirshipToday 10^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^100

Ilustrado Some People misspell it as GOOGLE 🤪

Barry Inglett The creators of google actually went in to type to see if googol was taken, and typed in google by accident

Probable only a very small percentage of people have ever heard the word "googol."

Not every

indeed not every, not even just a half..

same bro, this prove nietzsche being right all along

Execute i'm great walp here, ∞ - 1 = (BEN(100))

Hmm. Very interesting inference.

Or you wouldn't meet them at all, since they might be going the same direction and therefore remain the same distance away.

​@@0mathgaming Absolutely yes. It did occur to me later but I forgot to edit the comment.

You won't actually meet them let's suppose, 1. 1. 1 So you traveling from left to right, soo your other repetitive form will also travel from left to right, your three form going in same way, so no chance you gonna meet them, what's I'd thats life wtf 💀

Explain why I would meet an exact copy of myself......

Yep, I had the same problem. He assumed equal probabilities of configurations within a volume. Therefore I believe that even in a googolplex sized universe, I'd still be the only me. The analogy he presents is still useful for understanding the size of the googolplex number, however.

crcaccounts in addition, it seems to also assume a universe with a identical model to ours in terms of physics and energy.

I think you are correct and the reason is the second law of thermodynamics - the more enthropy states must occure more often then the less ethropy states. Hence, humans are rather less enthropy state so we are very rare state of atoms.

crcaccounts You guys are being silly. Pretending that the universe is a googolplex meters across is arbitrary. If we instead pretend that the universe is a googolplex^googolplex meters long, you'd end up with an incomprehensibly large number of copies of yourself, even taking into account the uneven probability of various configurations. It's just a thought experiment meant to make understanding this stuff easier.

SidV101 Two things: you say that universe is infinite by size while discussing the combinations of matter which is also energy. Shortly I am in a sort some state of energy ( and a wave if we add quantum theory). Continuing universe is infinite in a way that in 3 dimensions you would never reach the edge of the universe but it can contain inside finite amount of energy (all the rest is just vacuum). So to state that there is infinite amount of my copies you would need to prove that infinite by size universe contains infinite amount of energy/matter in it. Like 2d world can be infinite but finite in 3D ( like surface of balloon) and s contain finite amount of some other attribute. Second what was pointed out in vid they state that there is finite amount of combinations of matter and then they limit the size of universe by some very large number. Then simply divide assumed size of universe by number of combinations to result the expected amount of our replicas in the universe. We pointed out that for this result to be correct they also assumed that probability density function of matter combinations is uniform what may be wrong by- more natural in the world is the Gauss distribution and second thermodynamic law states that simply contradicts to uniform distribution of energy\matter. So in my opinion their calculation is wrong as they made a hidden assumption that that I thing is wrong. If you can proove that more naitral for matter distribution in the universe is the uniform distibution than I must be wrong otherwise please buy a book of level 1 statistics and learn something useful.

It's not. There are just not that many particles in the mostly empty universe (on the risk of getting whooshed here)

OriFl googolplex

@@rhyse630 googolplex +1

@@juliano345 rayo's number

Googolplexian 10^10^10^100 10^Googolplex

{10,10[1/2]2}

Uh... that's a big number...? What do you want to hear?

Any number that is defined by a finite number of digits is by definition smaller than infinite. And a googolplex to the googolplex'th power is big, but still finite. Even if you won't ever have enough ink in the universe, or particles in the universe, to write it down.

that's so small compared to Graham's number.

And so small compared to TREE(3). Which is small compared to SCG(13). But the biggest of all is yo momma (j/k)

googolplexian

It supposes all possible quantum states regardless of likelihood. That 10^100^70 is all *possible* quantum states, including the most unlikely.

@@MrBluelightzero Right. It's probability, not a fact really. However, you can definitely say that there would be exact copies of /something/ in a universe that is large enough. Using you example of a line of coins, with truly random probability you can't guarantee that you will ever see 2 Heads. Though unlikely, it's possible to never even get one Head. However, since there are only 2 states, you can guarantee getting either 2 Heads or 2 Tails within 3 tosses. In the same way, in a universe large enough, some of the states must repeat as soon as the sample size is more than the number of possible states. However, it might not be a person that repeats. The universe could just have repeated spaces that are just a Meter^3 sized vacuum.

@@MrBluelightzero It's not an incorrect calculation, though, mainly because they didn't really calculate anything like that. It's an estimate. In fact, it is a very strong estimate. For the numbers they use, 10^10^70 is the number of possible states and 10^10^100 is the sample size. I'm going to call these PS and SS for "Possible States" and "Sample Size." They didn't really emphasize this, but SS is unimaginably larger than PS. How much larger? Let's look at orders of magnitude (OoM). The OoM for PS is 10^70 and OoM for SS is 10^100. The difference in the OoM's is simply 10^100 - 10^70. Is it 10^30? No.... not even close. Let's look at the OoM of those OoM's. OoM(OoM(10^10^100)) = OoM(10^100) = 100 OoM(OoM(10^10^70)) = OoM(10^70) = 70 10^100 is 30 orders larger than 10^70, which means 10^70 is negligible in comparison. This means that 10^100 - 10^70 = ~10^100. No joke. The actual value would be between 10^100 and 10^99, but it's wayyyyy closer to 10^100. By extension, since 10^70 is essentially 0 in comparison to 10^100, 10^10^70 is roughly 1 in comparison to 10^10^100. Just by this, you can tell it is extremely unlikely to not have duplicates in a universe that large.

@@joshandrews8913 yes but the point of him bringing that up was simply to enthasize how big a googleplex is. And due to us not knowing our quantum states exactly, we still have a rough estimate, and a google plex is so big that even if our estimate was too low, the chances of seeing duplicates is still high

@@benhayter-dalgliesh5794 We're talking about exact copies, too. We wouldn't be able to tell if two things are exactly the same as long as they are close enough. If we include states that are similar enough that we couldn't tell the difference, the probability would be even greater. I don't think you're disagreeing with me, though. Emphasizing the size of a googolplex is the point.

Same here!

Thanks..😊😊

it's almost 4 am, phone battery is at 1%, I'm hungry, need to take a leak, and I think I might need some sleep especially since I'll need to get up at 9.

LJ Bartley way better than getting drunk in a bar, isn't it? ñ.ñ

lol, same boat over here

same...

Hello ech. I am echmega. You just can’t see it yet.

Yeah there was a lot wrong with that sentence

😂😂😂

Cubes do have radius. It doesn't mean the same as a sphere tho. The radius of a cube is a line from the center of the cube to a surface perpendicularly. Also known as 1/2 the side of the cube.

@@mrpedrobraga I think they're pointing out that it has to be the diameter of the cube, not the radius, as Planck's Length is the smallest possible measurement. My guess is it was just a little verbal slip-up, happens all the time.

@@Mautinuee Yes it makes more sense indeed :3

🤣🤣🤣🤣🤣

Havent seen that show referenced in a while

You could technically find a copy of the place where you spawned.

Stop it, get some help.

64-bit memory can't handle numbers the size of googol or googolplex, it only goes as far as 18,446,744,073,709,551,615

specifically that number, not joking

The better question is: Can you find your replica being tortured with "Mine Diamonds" during a second Spanish iquisition on a christian Minecraft server?

What is the unit of ego though?

this reference was forced a bit too much

So it’s 9x10^10^103 egos.

what part of this comment was the funny part?

@Rayan I am not a math.

STOP MESSING WITH MY MIND

Can I name the next one? Googolplexianoid (10^10^10^10^100)

@Lendalas I feel like that's bigger than (Graham's number)^100 edit: i am wrong

+Noah G I feel like not even close :-)

+David Fischer I mean come on, it's a googolplexian+1 (lol) digits long.

Pá

XD

● ● ₩

Theyre officially called googolplexian and googolplexianth.

ASMR

Right?

Theres even a googleduoplex which is a 10 elevated to a googleplex

@@MiguelSucksAtUrbanism that's also called googolplexian Then 10^(googolplexian) is called googolplexianth, After that I don't know, you can go on and on.

Well there's Graham's number, and then TREE(3). Then there's TREE(G64). That video was quite interesting

@@arrash4388 Yeah, i can still somewhat comprehend a googol but those numbers no chance, its something else entirely :D

What if i threw a pair of deez toward you?

Magnacardia lol, yeah that would defintely impress me.

+Magnacardia Deez what?

livefromhollywood194 DEEZ NUTS!

Magnacardia lol hehehe

the fact that there could be clones of me is proof that I am unique?

I think this is proof of the opposite

MarcoManiac do you think they all do the same things as you? No they do not, just because they look like you does not mean it is you. Your closest friends and family would tell the difference between them and that is what makes you unique, it is your soul not your flesh that makes you... you.

jlrockafella I'm was kidding, even though if you look far enough, there would at some point be another universe that is exactly as ours, not just in shape, but also in history.

Jlrocka what scientific evidence do you for this soul theory?

So we're looking for 2^x = 10^googol, and by taking the log2 of both, we get x = googol * log2 (10), or approximately 3.32 googol (that's 3.32 * 10^100) 3.32 * 10^100 planck times * 5.85 * 10^-50 years per planck time = 19.4 * 10^50 years (more properly rewritten as 1.94 * 10^51) That's 194 trillion trillion trillion trillion years, or 14,160 trillion trillion times the current age of the universe.

@@Simpson17866 bet

Nice mathematics. You have your ducks in a row on that one.

@@Simpson17866 I knew that.

@@Simpson17866 So even almost less than Time itself is 194 Trillion years

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 zeros

Googolplex Is Larger Than You said Googolplex Is 328128X More Massive Than Obsevarble Universe.

25!

HA! Spongebob reference

Ptfffffff hahahahaha

+Rohan Mishra It's not that big relatively speaking. Most people would over-estimate, I know I would. I would probably guess somewhere in the septillions.

+Rohan Mishra LOOL!

But that's long-scale billion. What most of the world knows as trillion. I understand your point though :P

ok :P

Its because most of the universe is actually empty space so if u fill the universe with grains of sand (that obviously contain particles) then it would be larger and have more mass and a higher density

Has to be used i Functionality

life.exe is corrupted and cannot funtion

SYSTEM ERROR. WOULD YOU LIKE TO RESTART YOUR COMPUTER GOOGLOL TIMES?

+terence sterling maybe ask Google?

i love you

+A muffin all you did was ruin it

actually the number of planck volumes you could fit into the universe is about 10^185, which is less than Googolplex by a long shot.

Johannes Mokry if it was that big.

Well as far as I know there's life on earth so yeah there IS life in the universe.

Elementary, lol

Still probably smaller than tree(3)

Googolplex is literally NOTHING compared to Graham's number (the size of that truly is beyond any kind of real comprehension)

Or, how about TREE(googleplex^Graham's Number)

Imagine 3(Tree) to the power of 3(Tree) 3(Tree) amount of Arrows between, to the power of 3(Tree) 3(Tree)Times. Etc etc

code cracked

Unsuccessful try to make something like that funny

Skarmory Fly Like many, many companies on earth does. They are out of ideas and copy alot from others but make their twist on it.. So you might find a copy of yourself but with 3 eyes.

WAIT. would that mean that the universes length is infinite, because an exact copy of you could also travel halfway across the universe to find another exact copy. Meaning that as long as there are as many copies that could be found, the universe would be that length? In my head, this makes sense, but may not prove scientifically accurate. What do you think?

That’s was already a number before you were born. It’s called a googleplexian.

how about ten to a googolplex to a googolplex

Let's make it 10^∞

@@marn200 infinity is not a number so that expression makes no sense

@@DepFromDiscord then 10 to the googolplexian is the googolplexianth

Friedrich Nietzsche thought something similar. Because time is endless but the things that are possible to happen are not everything is forced to happen again and again and again. Meaning you're not only having doublegangers but will live again and again and again. en.wikipedia.org/wiki/Eternal_return#Friedrich_Nietzsche

+CuffRox Not infinite, but just an extremely large amount of distance.

well if the universe is infinite, that doesn't necessarily mean that there is infinite matter in it.

the universe *is* in fact infinite

+Guy Ender No, it *may* be infinite. We can't see outside the observable universe because the light on the outside hasn't had time to reach us and the universe is still expanding.

+Austin Mendoza Me :P

+Austin Mendoza Me!

+Austin Mendoza I came for this comment

+Austin Mendoza me

+Austin Mendoza me

+

That's what I was thinking too :) but I believe he presented it that way so that we can imagine how impressive the number is, but most of the universe is empty space ^^ (sorry if english mistakes)

I think the assumption is that you'd have an observable universe with particles in it to match the scaled up size. Otherwise you'd reach the end of our universe, the extent of the expansion of space from the original singularity and simply have emptiness.

Which makes it even more likely. We know that the universe isn't some random number generator, and typically things happen for reasons, albeit chaotic reasons. This means that, because the universe is rule-bound, it would be far more likely than the chance mentioned in this video that you'd find a copy of yourself somewhere in a universe that large.

Think of it as a dice with 10^10^70 sides. If you rolled it 10^10^100 times, you would expect to see at least one roll of the same number. Of course, it's not even possible for you to not get the same number twice. You would get 10^10^30 (I think) duplicates. FOllow me?

Why would you be exempt from meeting yourself?

+Charmonium Pentaquark Right? I'm reading all these comments that are like "wow a hundred zeros." Heh. Eheheheh. Plebs.

+Charmonium Pentaquark Graham's number is basically infinity so that doesnt count >.>

+Dheeman Ghoshal no it is not . g64 is finite.

lol g64

How about rayo's number? It's way bigger

If the universe was infinite as you say there would be an infinite amount of stars in the sky which would mean night would be just as bright as day but it is not therefor the universe is not infinite.

Victor Moreno that assumes all the light actually reaches us.

Considering we can't even confirm if the universe is infinite, or if it closes in on itself like a sphere. Wasn't too long ago when people thought the Earth was flat.

Its because those figures are made from the OBSERVABLE universe. That is the universe that we can actually calculate.

and the universe could be finite, but without an observable edge to it. like, if you fly out of the universe, you would just come back at the other end

Googol

There's a googol zeros in a googolplex.

Yes.

10^26^3 is 10^17,576 which isn't too shavy of a full universe...

+‫יותם ענבר‬‎ זה לא בשלישית, זה מטר מעוקב,יחידת נפח כאילו

אה סבבה

+Parau1990 the observable universe is something like 92 billion light years across because space has been expanding for 13.8 billion years too

Theoretically, anyway.

W

+Melissa Geckensmerf Brain.....malfunction. Initiating emergency shut-down.

+Öykü Özer its bigger than googol and googolplex its even so big that we only now the last 10 numbers ...2464195387

We actually now more than that, I read somewhere that we know the last 500 numbers

lol

Bob McMullan not as big as infinity,

Huh? Is it like 10^10^10^100?

yea i was thinking the same thing. He probably meant it the other way around

In the universe there is a lot of empty space with no particles what so ever. If you were to fill the universe with sand, it would be assumed that there would be no empty space not occupied by sand.

I think that just went over your head.

MrHillsidestrangler InSpadez You are wrong, watch the video again. 10 to 80th power is the number of particles in the universe. Since most of the universe is empty it makes sense, that if you fill it with grains of sand, the number of grains of sand is larger.

Peter Enis no... if grains of sand are larger than particles... then it would take fewer grains of sand to fill the universe. Hence, 10 to the 90th power is a larger number meaning, that the "object" is smaller, therefore taking up less space meaning you need more grains of sand. Which doesn't make sense because we know from observation with the naked eye that a particle cannot even be seen with the naked eye, which would logically mean that a particle is MUCH smaller than a grain of sand, meaning that 10 to the 90th power was incorrect in his statement referring to grains of sand. Just like MrHillsidestrangler said it best... please refer to his comment. Also, I don't think the presenter of this video was speaking in terms of space, already filled up or used by another "object". Even if he was... my argument still holds true to the fact that even if we are only talking about the AVAILABLE space thats left...