Googol and Googolplex - Numberphile

We're talking pretty big numbers here... And an interesting idea about what it'd be like traveling in a Googolplex-sized Universe!
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With Antonio (Tony) Padilla and Ria Symonds from the University of Nottingham.
About the brown paper: periodicvideos....
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[@RedSkyHorizon]

My job is repetitive and that's only 8 miles away.

[@FeyFox]

+Tom Mulligan made my day :D

[@andrewnimmo8010]

Tom Mulligan well played sir...well played.

[@jay1185]

Best of 2017 material

[@Articulate-Fabrication]

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

[@lumonox]

This goes perfectly with your profile picture

[@o4_]

"How many grains of sand can I fit in the universe?" I know no faster way to give someone existential crisis.

[@whimsy5623]

👀

[@danishdude_]

*copys this comment*

[@openlog1c]

Just as much as you thought in your brain

[@kaulterloli5955]

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

[@adamtideman4953]

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

[@ilustrado7291]

Who would've thought that 9-year-old Milton suggested the word "googol" and now his random word is now on every human beings head?

[@barryinglett7034]

Ilustrado Some People misspell it as GOOGLE 🤪

[@ryanstock7094]

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

[@maxnullifidian]

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

[@alexandercarder2281]

Not every

[@voicustefan9370]

indeed not every, not even just a half..

[@StonedSpagooter]

This is one of my favorite videos on youtube 10 years later I still come back to this and it blows my little mind

[@shinseiki2015]

same bro, this prove nietzsche being right all along

[@GroovingPict]

This always annoys me, the whole "if you travel far enough in such a big universe, you would eventually encounter exact copies of yourself". Because that implies that every configuration is equally likely to occur, which surely it isnt. For it to be certain, the universe would have to be infinite. And even then, certain configurations would occur more frequently than others. Just like, yes there are an infinite number of prime numbers, but they still dont occur as often as for example even numbers; encountering an even number is much more likely than encountering a prime number.

[@crcaccounts]

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.

[@aoinokitsune]

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

[@dmitrypetrov1753]

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.

[@SidV101]

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.

[@dmitrypetrov1753]

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.

[@robloxlover69outofcontext62]

Mom: *playing candy crush* Me: what level are you on? Mom:

[@Tengspeakfootball]

Googolplex

[@Gamerxxnoob]

@@Tengspeakfootball Googleplexianthenialarisian ( yes exist )

[@Tengspeakfootball]

My dad have Level 1649 in Toy Blast

[@AirshipToday]

@@Gamerxxnoob Gigolquintiplex

[@tria-taxisandclickyes4073]

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

[@leecain5460]

I'm not great at math but I totally understood exactly what he was talking about. Awesome

[@Frostrun445]

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

[@YouTodayKing]

how is a particle larger than a grain of sand?

[@ramongonzales1007]

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

[@burgerfood8076]

Considering the suffix -illion, the googol can also be called 10 duotrigintillion! (The prefix's number is 32; the prefix is duotriginti-) The -illion function is Y = 10^(3X + 3), where X = the prefix's number & Y = the actual number. Doing the algebra, 10^(3 * 32 + 3) = 10^(96 + 3) = 10^99 (or 1 duotrigintillion); multiply that by 10 & you get 10^100, which is commonly called the googol!

[@gustabarba]

If you decided to travel across the entire universe so that you could meet an exact copy of yourself, you would eventually meet them halfway through.

[@prabhdeepsingh5642]

Hmm. Very interesting inference.

[@0mathgaming]

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

[@gustabarba]

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

[@p4l4sh2]

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 💀

[@knxcholx]

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

[@Lucavon]

My friend's ego is over 9000 googolplex

[@lare290]

What is the unit of ego though?

[@CaesarTheGreatGaming-Julius-]

this reference was forced a bit too much

[@vehicleboi5598]

So it’s 9x10^10^103 egos.

[@geneschwartz]

what part of this comment was the funny part?

[@vehicleboi5598]

@Rayan I am not a math.

[@Joe005]

logic.dll is corrupted. Brain.exe has stopped working.

[@adkuya0306]

life.exe is corrupted and cannot funtion

[@terencesterling6839]

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

[@SiriusZcs]

+terence sterling maybe ask Google?

[@tillicollapse182]

i love you

[@eyeglutchedowtleenkzstoped4234]

+A muffin all you did was ruin it

[@ahmedouerfelli4709]

But this supposes that all quantum states are equally likely.

[@d4rk0v3]

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

[@joshandrews8913]

@@Bluelightzero 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.

[@joshandrews8913]

@@Bluelightzero 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.

[@benhayter-dalgliesh5794]

@@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

[@joshandrews8913]

@@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.

[@renaissancemonke]

We might be living in a googolplex sized universe which makes our universe look like a galaxy

[@shrimpbisque]

This reminds me of something mentioned in Star Trek called Hodgkin's Law of Parallel Planetary Development. It's basically a version of convergent evolution that applies to entire planetary ecosystems in comparison with other planetary ecosystems, and to some extent to societal development as well. It also brings to mind the idea that duplicates of planets and people would arise in an infinite universe, basically for the reason given in this video: that there are only so many ways you can arrange particles before you have to start using the same configurations again.

[@difrractsliver1031]

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

[@victornaut]

6:07 is what made me understand the entire thing. Amazing!

[@superrandomuser]

Same here!

[@thatoneguy9582]

and then there's a googolplexian (10^10^10^100).

[@toomanycarz]

STOP MESSING WITH MY MIND

[@Lendalas]

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

[@thatoneguy9582]

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

[@psychotic17]

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

[@thatoneguy9582]

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

[@somedumbhoe7123]

Who else is here cause of Vsauce?

[@rushi7558]

+Austin Mendoza Me :P

[@fotiafotiafotia]

+Austin Mendoza Me!

[@BarakAlmog]

+Austin Mendoza I came for this comment

[@fuvincent3555]

+Austin Mendoza me

[@chswaroop9274]

+Austin Mendoza me

[@AJ-Channel]

After watching the video about Graham's number, I'm no longer impressed by any number you throw at me. They all seem small in comparison lol.

[@Magnacardia]

What if i threw a pair of deez toward you?

[@AJ-Channel]

Magnacardia lol, yeah that would defintely impress me.

[@livefromhollywood194]

+Magnacardia Deez what?

[@AJ-Channel]

livefromhollywood194 DEEZ NUTS!

[@AJ-Channel]

Magnacardia lol hehehe

[@blowmeliberal]

Somebody messed up. If 10^80 = number of particles in universe then 10^90 couldn't possibly be the number of sand grains to fill it. There is no way in hell that's accurate, like, at all, not even remotely close.

[@joshlucas4269]

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

[@s4nsk_]

2:26 "which is like a little *cube* with the *radius* of a Planck length" Seems legit

[@isaacchen3857]

Yeah there was a lot wrong with that sentence

[@DerRobert28]

😂😂😂

[@mrpedrobraga]

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.

[@Mautinuee]

@@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.

[@mrpedrobraga]

@@Mautinuee Yes it makes more sense indeed :3

[@skarmoryfly]

The reason that you will see the EXACT copy of YOU... Well, the Universe ran out of randomization for the next stuff to make Universe: Hmm... I can't think something cool to make... Let's just copy stuff I already made... THEY WOULDN'T NOTICE! *Evil Laugh*

[@Dubby999]

code cracked

[@PiroEfekta]

Unsuccessful try to make something like that funny

[@vladimirstroganoff4404]

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.

[@Noimcuban]

I hope someone sees this. If you say the universe isnt a googleplex across then it must have a distance, thus it must end, right? now if it does what is at its end, what does it look like? Are there other universes? and can , if possible , somone, human or not, travel to another universe. Please i really want to know

[@darKILLusionnn]

Does he mean the entire universe or the observable universe?

[@michaeldarley7980]

just watching these makes me feel like a genius!

[@johannesmokry3758]

so there IS life in the universe!

[@randomthoughtstheories6681]

Johannes Mokry if it was that big.

[@alephnull5662]

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

[@dbrook14]

i think that's a really cool idea, but i dont really like how he keeps saying "if you go far enough". the point is that there could be an exact replica of me on earth right now, its mathematically POSSIBLE however unlikely. he is pointing out that if the universe were that big, my double would pretty much be a mathematical certainty. it's a really cool idea, but its not like there is a specific distance you would have to travel to find your double. i guess technically traveling would increase the number of arrangements matching your approximate mass thus increasing the chances of you FINDING your double.... but traveling in one direction i don't think would guarantee you would find that particular arrangement in such a vast universe

[@ethanleyden4935]

The marker on the paper is just one of those sounds that make me shiver.

[@lufycz.]

ASMR

Right?

[@highguardian13]

“So theres not another me in this universe?” “Probably not, you would need a universe with a length of a googolplex” Phineas: Ferb, I know what we’re gonna do today

[@zemoxian]

🤣🤣🤣🤣🤣

[@aaronbalchand5475]

Havent seen that show referenced in a while

[@_kijetesantakalu]

Wait so if the universe was in fact infinite, there would be an exact copy of the Sol system somewhere down the line, with the same exact people living on earth? Holy sht

[@theulf3780]

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

[@Infernalhypernova]

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

[@MrDs-ek7bc]

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

[@guy3nder529]

the universe *is* in fact infinite

[@Infernalhypernova]

+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.

[@johnfrost6750]

whatching stuff like this late at night hurts my brain

[@Sergeeeek]

Could you please explain why you would see repetitions? I mean, if you travel that far away why there wouldn't be just repetitions of vacuum or stuff like that? How many chances there is to see the exact same repetition of our solar system and galaxy and whatever?

[@massimomoro5895]

i could watch this all day, beautiful video, as always

[@CoDRagna]

this is wrong.. this is simple accounting the probability, but it doesn't account for the time and materials needed for this to occur.

[@gaefrogge5806]

To clear things up for a few people, he's speaking of the observable universe not the actual size of the entire universe.

[@joemarcus2586]

A particle is much smaller than a grain of sand. What he means is that there are less particles than you could fit grains of sand into the entire universe because much of the universe is empty space. There are no particles there but you could put sand there

[@fno6164]

These kind of videos make me think too hard and I love it.

[@TheSquintyninja]

Wow. Thinking about this video makes me feel so small.

[@mikestoneadfjgs]

Grahams number makes a googolplex look tiny. Very funny to see this video after the grahams number videos.

[@jakethornton7]

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

[@dheemanghoshal2330]

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

[@TestTest-bc9on]

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

[@mikestoneadfjgs]

lol g64

[@alikassem9501]

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

[@curtisscott9922]

It's frustrating and exciting to think that when we answer one question about the universe another question presents itself. You can ask why Infinity times

[@MegaScytheman]

Before I watched this video, I had forgotten that a googolplex is so large it can't be concievably be written by hand without simplifications such as exponents. I thought that was kind of cool.

[@jlrockafella]

this is only proof of why you are unique and special, and is another reason why you should never end your own HEALTHY life.

[@MarcoManiacYT]

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

[@itskmillz]

I think this is proof of the opposite

[@jlrockafella]

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.

[@MarcoManiacYT]

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.

[@itskmillz]

Jlrocka what scientific evidence do you for this soul theory?

[@BoardGameClub]

This conclusion seems wrong. Just because there are 10^10^70 different states available doesn't mean that every meter is some random combination of atoms. There are huge pieces of space where the state is almost identical for long stretches.

[@rabitjuno8777]

+

[@Liliou]

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)

[@BollocksUtwat]

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.

[@dschwartz783]

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.

[@kendallcarlson3572]

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?

[@MattsGamblingSlots]

"Im not sure what a Googol is but I think it's Craig David. No, it's A1." (cough) "No, I'm gonna go with 10^100." - Charles Ingram

[@Yhsanave_]

well the entire concept of this video is really based on the multiverse theory

[@xKopGx]

how the fuck could they know how big the universe is right now? how do we know it's not a googolplex meters across allready?

[@safir2241]

2:30 ten to the MMAAAAIINNUSS 35 meters

[@anonym3]

nice Mandelbrot menge.

[@Ball-oo4nw]

10⁻³⁵

[@findystonerush9339]

your channel looks like the manbrot deep zoom

[@findystonerush9339]

the plancks lenth is 10^-35 meters

[@TheEgglet]

assume there's a number that is 1, every planck time it doubles, how much time is required for it to become a googolplex?

[@Simpson17866]

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.

[@kevinc9059]

@@Simpson17866 bet

[@russellfautheree4650]

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

[@captainjacksparrow1518]

@@Simpson17866 I knew that.

[@beyondhaircraze4418]

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

[@kieransquared]

I remember when I was kindergarten, I was debating big numbers with a classmate. I brought up a googol, and the kid has no idea what I was talking about, and he asked the teacher, and she said it was just a website. In my mind, I still won that argument. Thinking back, I should have mentioned graham crackers.

[@eddievasquez8045]

Can someone just tell me how many zeroes are in frickin googolplex?

[@chriswatson3464]

Googol

[@Theguyman]

There's a googol zeros in a googolplex.

[@fengwang7661]

Hey numberphile, you could write a googolplex in the observeble universe. If you wrote on every plank length (the smallest distance), you could get to about 10^10^183 to 10^10^184.

[@TheSpotify95]

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.

[@ryanfranz6715]

Finding repetitions would assume that each volume of space you encounter is a random arrangement of atoms, when nearly all of the volumes would be a vacuum. But perhaps a googolplex is big enough that on the rare occasion you are able to find seemingly random atomic arrangements (like the surface of a planet with life) you might find repetitions still.

[@dinesh665]

Just wondering .. how can you say that the universe is 10^26m?

[@FebruaryHas30Days]

Level 0 numbers are the fractions. Level 1 numbers are numbers that you can count. Level 2 numbers are numbers that you can exponentially stack. Level 3 numbers are numbers that you can measure with arrows and brackets. Level 4 numbers are numbers that you can denote with linear arrays. Level 5 numbers are numbers that you can denote with dimensional arrays.

[@warlord1981nl]

I dislike how "universe" and "observable universe" are used interchangably which they really aren't

[@nahalitet11111111111]

I think I can think of an even bigger number. It's 10^100^100^100^100^100. I call it bullshimeter. Where is my nobel prize now?

[@stephano353]

what about the gogolplexian

[@AtomicFusionProductions]

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

[@cdwpmaster3460]

It’s funny because they’re like : “That guy invented the googol and the googolplex” and I’m like : “Well, I invented the coocol (10^1000) and the coocolplex (10^10^1000). I’m a genius.”

[@system4225]

Has to be used i Functionality

[@Asaday]

It's impossible to run into an exact copy of yourself, because they are unknowingly moving further away from you at the same rate you're moving closer to them. From your perspective you'd simply be back where you started, even though your surroundings are (unnoticeably) different

[@alexdavidson7498]

You could run into an exact copy of yourself that’s been turned around, although those odds are probably still pretty bad.

[@MultiFusko]

And if I saw my repetition and kill him I'd get faster, stronger etc. just like in Jet Li's movie The One... He killed all of his replications and came to the last one he couldn't kill him but what would happen if he killed him, would he be the god? or would he suck whole space to doom with him?

[@YouCuberHD]

0:09 now you see, THATS social distancing.

[@ronm3245]

"It wasn't a big number at all, compared to infinity." This is true for ALL numbers, isn't it?

[@VINOTOR]

Well base knowledge wise he meant as Googole and googoleplex have an ending no matter how big it is but infinity it just keep going numbers Increase more and more so infinity is big so big it practically never ends numberwise. It all just based on how we categorised the numbers in a bunch

[@elzearcontelly2651]

KZbin's automatic subtitles : "and this is a google+" :(

[@mwgondim]

This got me thinking about intuitionistic mathematics and their problems with infinity... If we established a number that could represent all possible states of the universe, would this settle down a conflict between classic and intuitionistic math? By the way, could you guys make a video on intuitionism vs. formalism vs. logicism? I believe it to be a really interesting topic. Thank you for this channel!

[@ghr1990]

In response to Jakka Makka: "how is a particle larger than a grain of sand?" It is not, he was counting the total number of particles in the universe, not the number of particle you could fit. There is space between particles.

[@Missingo32]

The problem I see with taking the possible number of quantum states of a give volume being less than a googolplex to indicate potential duplication of an individual is that it assumes the configuration to be entirely random, and doesn't account for the probability of the necessary chemical reactions to produce that state. Still, it's a fun analogy :P

[@nicholasnolan4143]

this is truly mind boggling and so interesting

[@InSpadez]

If you fill the universe with particles, you get 10 to 80th power. If you fill it with grains of sand, you get 10 to the 90th power. How is a grain of sand smaller than a particle?

[@MrHillsidestrangler]

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

[@andrewfausey8773]

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.

[@InSpadez]

I think that just went over your head.

[@MrPassigo]

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.

[@InSpadez]

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...

[@a2j678]

10 in the one-hundredth power? How about 10 in the googolplexth power? Numbers are infinite!

[@DepFromDiscord]

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

[@janschmeink9296]

how about ten to a googolplex to a googolplex

[@marn200]

Let's make it 10^∞

[@puremath3491]

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

[@michaellaws25]

@@DepFromDiscord then 10 to the googolplexian is the googolplexianth

[@LKfan1234]

The notion of "this is how many possible quantum states the stuff that you are made out of could be in, therefore it's a 1/(that number) chance of it being you" isn't quite sitting right with me. It sort of implies that certain quantum states aren't preferred. And I don't know if this is true.

[@kueid]

+Otrakun If assumed that some states are preferred then the number will be smaller. Either way his logic is fine.

[@Makkovar]

This seems to imply that every possible arrangement of particles only occurs once in the Universe, not taking into account the relative probability of different states. :| Obviously, most f it is void or simple gases (Dark M&E aside), while more complex structures like living beings are less frequent. It could conceivably be a googolplex of nothingness.

[@Federico84]

how can he estimate the number of particles in the universe? the universe is infinite

[@jand6671]

That's what I was thinking

[@jand6671]

I think he meant observable universe.

[@matta5463]

How do you know it's infinite? You don't ^_^ nodoby does

[@Federico84]

Matt A scientists say that it's infinite

[@matta5463]

Scientists may predict it's infinite, but it doesn't imply it's actually infinite. There is no autority in science, and you can never prove a theory, only disprove it. Anyway, it may well be infinite, or finite but without edges, like a 4D sphere.. Point is: we don't have evidence (yet) of the actual geometry of the universe, hence every statement about it is just a guess.

[@shanemack06]

Its not about the space that YOU just occupy. Its about the probability of all the other spaces around you which allow for the organization of your place in space. And since those can be spaces are bigger, the probability for existence would decrease and then so would yours.

[@TitusT]

The thing about running into copies of yourself is BS, because it assumes that every formation of particles is equally likely, which is patently false. Furthermore the arrangement of particles *outside* of the cubic meter your doppleganger occupies quickly determines whether said doppleganger will be able to survive, which it almost certainly won't.

[@leoriopaladiknight7588]

Man if I ever found an exact copy of myself i would be friends with them so quick and then a minute it later i would get bored of myself and leave.

[@milaanpatel4997]

That is the reason why you are big enough to occupy just enough volume, that you won't find a copy of yourself in observable Universe.

[@DavidJamesHenry]

Or! The universe could be filled with identical burritos.

[@lazz1811]

+RobotGoggles now that's how you get profits from nothing! you get repetitions!

[@rewrose2838]

Heaven then? I prefer tacos though. . . . burritos are cool I guess, but maybe . . . . _some tacos too?_

[@saeedmaher9066]

...RobotGoggles

[@maybewellok]

RobotGoggles burritos world

I think it would be entirely possible to come across a universe that's filled with burritos.

[@Dingin4]

We are not a random collection of quantum states. We didn't poof into existence randomly, and neither would our doppelganger. It would be a configuration reached after following a remarkably similar evolutionary history over many millions if not billions of years. I suspect that the necessity of sharing not only an identical configuration, but of sharing a remarkably similar history would push the distance to your doppelganger out considerably. And what does it mean to be a perfect doppelganger? Do the electrical impulses in my nerves have to be identical as well? Dose this mean if I'm looking at you my doppelganger has to be looking at your doppelganger? If so we're talking about far more than 10^10^70 quantum states that have to have an identical configuration.

[@leventemolnar3540]

10^^^^^{5,10^100,x}^^^^^g^^^^^2^({a,b,c}^n = (2,3,4,5,6.....)

[@Malachi_Padilla]

Perhaps the concept of seeing an exact replica in a different universe that’s the size of a googolplex, is how we could perceive another “dimension”

[@MultiChrisjb]

but if in a googleplex universe my doppelganger would have also started traveling to find me. So I wouldn't run into them since we all would have took off in the same direction.

[@tryplot]

even if I were to be in a universe where everything was repeated once, I could still make an army of myself. with memories being stored physically, and with how little it takes to change things, I could have the front lines all be virgins, but some of them had pizza for lunch last week while others had fish and chips, and a third group that skipped lunch. I could have the me's that don't need glasses flying the jets, while the me's that actually went through with working out while watching youtube could be the on the ground. the generals could be the me's that have a lot of experience coordinating large groups of people, while the nurses would be the me's that tried a little better in school. they are talking about EXACT copies, but if you have tolerance of tiny changes (got a scar from slipping with a knife, different haircut, shaved vs unshaved) you can get a huge number of copies

[@himanshbishnoi1445]

W

[@TheLegoJungle]

Watching this young, I never got it. Now, giving it another watch, I’m amazed.

[@TheXDS]

ok, what if we take the particles that make te entire universe, and count how many different combination of location can each one have, and then we check what is the possibility of finding an entire copy of our whole universe?

[@jstyles266]

so that means there is at least one other me out there... we are all doomed

[@evoman1776]

GOOGOLPLEX: "I am the BIGGEST"! INFINITY: "HA HA HA! Shut up, Tiny"

[@princesszeldaofhyrule7694]

please deposit that amout of money into my bank as soon as possible. thank you.

[@the.invincible.9542]

The bank would explode.

[@runshorts5254]

Koowluh you could say 0s your whole life but u would still die instantly when u got da money

[@bailey125]

10^26 x 10^10^70 is the possible quantum states of the observable universe?

[@shubhamkandpal4775]

the limitations to 5:00 is that 1)we don't know that every m^3 will contain different no. of particles it may be possible that for certain lightyears the amountof particles may remain constant for every meter cubed . considering above to be false 2)As there are over 200 elements, So the doppelganger you may find might be made of a radioactive dark element or a glow in the dark madame tussade's replica of yours.

[@vickyx09]

What about a googolplex to the power of a googolplex?

[@drearyplane8259]

Even better - googolplex factorial.

[@emilbruhn4748]

+DrearyPlane8 (googolplex to The power of googolplex)! :)

[@jupitereuropa-e3w]

A googolplex to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex, to the power of a googolplex. Big enough?

[@vickyx09]

Pee no

[@dtrinitypersonal]

+Pee (That number, to the power of itself, times Graham's number) to the power of itself

[@BennettCHS]

can someone please explain to me how you can fit more grains of sand (10^80) than particles (10^70) in the universe?

[@Patrycz4k]

Universe is mostly just expanding space with no particles in it

[@BennettCHS]

alright I guess that makes sense but couldn't you still fit particles into the empty space of the universe just as if you wanted to fit grains of sand into it? Maybe I'm over thinking this

[@narrexxsarius631]

Bennett Fife Of course you could fit particles in it but you need to take them from another place --> it would not make any difference

[@858469278558610248]

he means grains of sand packed tightly across the whole universe, in terms of the amount of particles, most of the universe is empty space

[@rolan638]

Narrex sarrius you would have to take the sand from somewhere to :)

[@markhansen4258]

This is fascinating, yet somehow troubling. I guess because it's so hard to imagine on a linear concept of numbers. Others probably imagine numbers in some way that I don't.

[@lxxwie9407]

A googolplexianthian. (10^10^10^10^100)

[@r.a.6459]

ZScentral Googolyottaplex 10^10^10^10^10^...^10^100 (with septillion plexes or septillion+1 10's)

[@BluJellu]

Googol Googolplex Googolplexian Googolplexianite Googolplexianiteron Googolplexianiteronhedron Googolplexianiteronhedron I forgot

[@dragmasanimation]

Googol 10^100 Googolplex 10^10^100 Googolplexian 10^10^10^100 Googolplexianth 10^10^10^10^100 These are what I use.

[@uweperschke6799]

Revisiting in perspective of the Tree vs. Graham's Number. Wondering which sequence grows faster: Tree or G^(G(n-1)) where G(1) is a Googol.

[@aiza9052]

There are a lot of assumptions made in this video that I would like to see explained. This video lightly brings up the universe being finite, and uses a number to represent its size, or 'quantum states' that make up an entire individual being theoretically repeatable. Where are our videos on these? I feel like my understanding of these numbers is vastly worse than my understanding of a googol or googolplex -- and that they'd be fun and interesting to hear explained.

[@apothecurio]

Aizak they mean the observable universe

[@joshuasusanto6626]

5:20 you're assuming that each array of quantum state filling a space(let's say a meter cube) is equal to any other array of quantum state. There's more likely you'll see a more repetition of empty vacuum then a single repeat of an organism, let alone a human. Basically not all arrangements of quantum state filling a volume is made equal, some repeat more than others in a very skewed distribution

[@intrance96]

Hes talking about the chance of it happening and its on average. Its hard to even imagine since the universe is extremely tiny, almost nothing compared to one the size of a googolplex meters in diameter.

[@PZJOKER6]

Idk why but just seeing him Antonio smile makes my day

[@victor6543211]

Can anyone explain me if this probability of arranging particles does REALLY mean that you would expect to find other exact copies of yourself? I mean, it maybe true that there are 10ˆ10ˆ70 ways of arranging particles in 1 mˆ3, but when traveling through universe you dont expect to find other forms of life, you are just likely to find other "common universe things" such as stars and meteorites, the particles arent dispersed in a random way. For a human to exist he depends on much other bigger factors: a planet with water, close to the sun, with an atmosphere, etc. etc. etc..., so you are not likely to find other humans even in a googolplex-long universe

[@vigneshsella]

By exact copies I think he means physical copies, however the events that occurred/choices/ or 'things' that happened may be different, after all the chance that every single person ever, and every single thing on earth did the same exact thing like did in our earth is very low. The question arises, is there free will? Or in the circumstance where the same atom arrangement as us, will act the same way we always did?

[@victor6543211]

no, you have not understood me, i mean physical copies, but even those wouldnt happen in this universe, the propability of happening a human does not depend only upon arranging the atoms in his volum, it depend at least of aarranging a planet with water, etc... for example, if the universe was a see, even a big see, what would be the probablity of you fiding a flame? even in a googolplex long see it wouldnt have any fire

[@elkeamber1173]

Does that mean that their would be planets with dinasaurs still alive?

[@justaperson9155]

***** not probably, the answer is straight out yes. The concept is hard to get your head around :P

[@jamez6398]

If the universe is a googolplex metres across, yes...

[@Ni7ram]

LeRenaissanceMAN yeah but i have a question. when he says that, he is assuming that every possibility of quantum states only exists once, and thats obviously not the most probable scenario. so even in that size of universe, the chances of that are tremendously lowered. am i right?

[@Ni7ram]

Ni7ram since english isn't my native language, im going to be more clear here: lets take for example a dice. it has six numbers, but it doesnt mean that if i throw it seven times (and even if i get every number once), im going to get a, lets say, 5 again. i could get 1,2,3,4,4,4,4,4,4,4,2,3,4,2,4,2,3,2,4,2,1,4,1,2,4,1,3,4,1,3,4,3 and never get a 5, consuming every meter of the googolplex universe

[@justaperson9155]

Ni7ram no you're wrong there Ni7ram. The point of a googolplex universe is that it is so big that every possible version of everything is there. Meaning that it is a CERTAINTY that you will roll a 5 in this universe as well as rolling only a 5 somewhere in this universe and everything possible combination of 5's. Just try to get your head around what was said in the video. A googolplex universe is so mind blowingly large, that entire universes of our size will start to repeat themselves down to the finest detail. That means an EXACT copy. If in one universe the wind blows your hair in a specific direction on one day and if in another universe EVERY thing is the same as this previous universe besides the way your hair blew in the wind on that one day, then there will be a whole other universe somewhere made specifically to correct that direction in hair movement. And that's the same for the second hair movement and the third and so on, FOREVER. But its not just about repetition, every possible combination of EVERYTHING will happen before these repetitions occur. Meaning that everything that can happen differently will happen. Every possible combination of the way atoms move in the universe for example, whether it be a group of atoms or a single atom. Every different form of life that can exist on Earth or any other planet will live in one of these universes. Meaning that on one of these Earth's dragons will exist. If in one universe there is only a single star, then there will be a new universe for each subsequent number of stars, eg 2,3,4,5,6,7...etc leading up to the number we have in our universe and far surpassing well beyond it. EVERY POSSIBLE DIFFERENCE YOU CAN IMAGINE THERE WILL BE A UNIVERSE FOR IT, as well as a galaxy for it, and two universes for it etc. It truly hurts your brain to think about.

[@elliotexists8681]

You might not find and exact copy of yourself, but an exact copy of everybody in the universe apart from you multiple times.

[@phencyclidine5456]

Why would you be exempt from meeting yourself?

[@lolgaming-bq3vs]

The amazing things is that our brain calculate those stuff that our universe dint create different

[@scotttimothy64]

This was brought to you by the makers of google, er googol.