The Humanly Infinite

Today we explore this paradox of the ‘humanly infinite’ - the idea that there are concepts and numbers in our universe that, while they can be defined and understood mathematically, are beyond our ability to tangibly comprehend or visualize.

[@magicien233]

Its cool to think that by removing a single card from a deck you are practically erasing an infinite amount of possibilities.

[@smileyp4535]

Interestingly enough, if you count the jokers you could add doubly infinitely more!

[@TheMasonX23]

Playing solitaire till dawn, with a deck of 51

[@ObjectsInMotion]

No, you just divide the total by 52. You are only erasing 98% of the possibilities by removing one card.

[@NummyGD]

@@ObjectsInMotionYeah, but 2% of 52! is still A LOT

[@magicien233]

@@ObjectsInMotion which for a number so large is effectively an infinite amount.

[@faastex]

I absolutely love the little 3d figures you're using, and their animations

[@irakyl]

me when I'm bald and my girlfriend looks identical to me except she has hair

[@Memeposter999]

0

[@ashercd6487]

me when i'm isaac and i'm binding

[@mihailmilev9909]

​@@ashercd6487I love this

[@mihailmilev9909]

12dx36d

[@3rdJan]

Well yes and no... 52! does fit into humanity. It's the amount of possible combinations a simple shuffled deck of cards has, in case you didn't know. :)

[@UnChannelDuVulpineX]

YEAH!! You tell him!

[@witchilich]

It does not because you can't recreate all the 52! combinations. You can theorize that there are 52! possible combinations, but you can't demonstrate all of them. Kinda like how we know it takes 4.3 light years to reach Proxima Centauri, but we can't reach it with our technology.

[@leonardotiezzi2904]

@@witchilich You don't need to demonstrate it physically, when you have a mathematical explanation

[@SUPERBLUE09]

@@witchilich We can theorize that 1+1=2 but we cant prove it.

[@qwertyuoip]

@@SUPERBLUE09 There is a proof of 1+1=2 in the book Principia Mathematica

[@edog5707]

facinating.... i started playing chess, and was shocked to find out there are more possible games of chess then atoms in the observable universe.

[@CheckmateSurvivor]

There is no such thing as the universe. We are the centre of creation. Space is fake, made in NASA basement. As a chess player, you should be able to use logic.

[@zhiqiangchen6235]

The amount of chess games easily dwarfs 52! there are already 18! possible moves in 1 move. You’ll surpass 52! by the 6th move

[@CheckmateSurvivor]

@@zhiqiangchen6235 Wrong! You only have 400 permutations after one single move per player. But calculating all game permutations you can get to 10^120.

[@jazzabighits4473]

@@zhiqiangchen6235 I'm not sure what you're saying is correct. Do you mean 1 "move" as in both players take their turn, or after 1 player takes their turn? At the start of a game of standard chess, there are 20 possible moves for white, then 20 possible moves for black (so 1/20 chance of guessing where white moves their first piece and 1/400 chance of guessing where white moves their piece and then black moves their piece). So at the most, it's 1/400 after 1 "move" (if you're counting both players taking a turn as 1 move). That being said, it becomes extremely more complex as the numbers add up (e.g. to guess the two previous moves and then whites next move would be 1/8000 assuming the same 20 possible moves. This formula can be expressed as 1/(20^n) where n is the number of moves taken. Turn 1 is 1/20, turn 2 is 1/(20^2) or 1/400, turn 3 is 1/(20^3) or 1/8000, etc.

[@microwave856]

@@jazzabighits4473"move" in chess usually means both players take their turn

[@wgoulding]

I'm not that kind of engineer, but I feel like I know enough about electromagnetism to be skeptical of the whole concept of 'how many electrons have been produced by humans' (given that transformers exist which turn that power into much lower voltages, and that the electrons aren't really being created & destroyed but instead given bulk average movement), though not enough to say that definitively with a scientific explanation to back it all up. However, I think you missed a trick by going with electricity. When you said 'human scale', my mind went immediately to the immense number of operations that go on in all of our bodies every moment of our existence, all powered by the hydrolysis of Adenosine Tri-Phosphate (ATP). Our bodies produce an average of 125 moles per liter of ATP a day. The human body has an average volume of 65.22 liters (this probably is an overestimate given historical food shortages, but humans were probably exercising a lot more back then). With avagadro's number, that's 4.9 *10^27 molecules of ATP per human-day. There have been an estimated 117 billion (1.17 * 10^11) humans who have ever lived. The average life expectancy at birth was pretty low, there are a lot of numbers out there but I've gone with 25 years. All multiplied by 365 days per year, that's a grand total of 5.24*10^42 molecules of ATP ever synthesized by human beings. Not enough to get close to 52!, but it's above your figure for total electrons produced, and your nominal target of 10^40.

[@josephcoon5809]

How about the number of photons striking the Earth whether they are seen/detected or not since the first human existed?

[@funky555]

numbers of molecules of ATP used by all life?

[@wgoulding]

@@funky555 That would be extremely difficult to calculate, but I'd guess it would add at least 12 to the exponent

[@smileyp4535]

It wouldn't make much difference but considering there are more humans than ever living longer than ever I'm sure the total average of human lifespan would be at least 40ish but I could be off

[@lmost]

@josephcoon5809 The total number of vibrations of all molecules, all atoms, all subatomic particles, and all fundamental particles since the Big Bang + 1 Planck Time until 0000 20250101.

[@thosewhowish2b693]

7:32 the prefix "peta" is upper case "P", it should be "PWh". Lower case "p" would be "pico", or 10^-12. SI units are all case-sensitive, so don't confuse milli (m, 10^-3) with mega (M, 10^6), or seconds (s) with siemens (S) like in 10:22. The names of the units are also not capitalized, even if they are named after someone. Also, meter (m) and kilo (k) are lower case, so kilometers per hour are written as km/h, all lower case.

[@h.a.9880]

k being written in lower case when it should be in upper case is kinda like the only thing about the metric system that doesn't make sense. Still a huge step up from Imperial, where _nothing_ makes sense lol.

[@leochinchillaa]

nerd

[@ZephyrysBaum]

@@leochinchillaawe’re all nerds here!

[@Ohokk0]

@@leochinchillaado you know what video this is lmao

[@h.a.9880]

@@leochinchillaa _Wow._ Rude.

[@audrey-chan6290]

1:03 that animation was hands-down the best explanation of the birthday paradox i've ever seen. the visuals just work way better than any verbal description

[@Gretchen_Trouble]

I learned a while back about how wild 52! was, but the way you broke it down in this video really showed how unfathomable it is that two decks have ever been shuffled the same. Thanks for this.

[@longtermpillow]

This will last certainly be buried, but I just wanted to tell you your videos on physics are by far some of the best I've ever watched to help with my comprehension of the subject. I *almost* grasp the concepts now whereas before most things never "stuck" and I ended up with the same questions. Like it's right at the tip of my fingers vs before I felt like I was in a separate room. I absolutely couldn't explain the concepts in any way that would help someone else understand but it almost makes sense in my head. So just wanted to say thank you for the knowledge! If you had a Patreon page or the likes I definitely would contribute. Keep up the great work!

[@josephwodarczyk977]

That's so wholesome.

[@KGTiberius]

Brilliant comparisons (and math). A pleasure to see educational videos like yours. 🤙

[@johnnybedir]

Man i love this channel's animations.

[@hibou-cool]

I love the new character design

[@Theblazingarmy]

Thank you for making these beautiful videos! I put your channel mix on and it helps me relax. Please don’t phase out the But Why custom intro 😢

[@AgusVallejoV]

Trying to get closer to the real world case, do you think the chances would be higher if we considered the shuffling event as non fully random? i.e. all decks of cards come ordered by default. A single initial shuffle would likely put two new decks in slightly closer configurations than if they were perfectly randomized. Hell, I'm sure expert casino dealers are so used to shuffling by muscle memory that if they shuffled two ordered decks, the results would be very similar between them, not sure if we could reach a human reachable probability of two shuffled decks to be the same. Similar to the difference between a fully randomized Rubix cube versus one that has been shuffled in 5 "random" moves.

[@JMD501]

This is why we have to wash the deck before it is shuffled.

[@stefan_popp]

Yes, fascinating thought! One could estimate the mean 'level' of randomization per typical shuffle of different shuffling methods (Numberphile has a video on it, I think) and estimate the distribution of #of shuffles per deck to come up with a more accurate distribution of probabilities for each card sequence. Might not be tractable, though. I wonder whether there are any patterns there or how many shuffles it takes to approach the 'practically completely random' state. In any case, I'd love a follow-up video!

[@wanderingsystem9674]

In a more realistic sense, I do believe in most cases we can consider a deck shuffle to be “practically random” for a couple reasons. Yes, decks come in a premade order but most people I know are weary of badly shuffling a newly bought deck and will tend to “overshuffle” those. Even so, after being used only once most decks are stored in an unorganized manner so the vast majority of decks won’t be shuffled from a predictable position. As for the dealer case, not only I don’t think muscle memory is precise enough to create such a problem (improper shuffling techniques are more likely imo), my experiences with being in relatively competitive board and card game scenarios are of people going to great lengths to be as random as possible, and I am pretty confident a dealer that always seems to create similar orders in those scenarious would be easy to catch and fire. That being said, also in a more realistic sense, I have seen before two identical “”””shuffles”””” caused by some awful methods that create the illusion of a shuffle when they actually aren’t shuffling decks, so human error can definitely alter the actual probability, I just feel not in a manner that we can properly measure the impact.

[@theendofthestart8179]

Yeah the common “bridge” shuffle requires 8 shuffles before being considered shuffled, while the best method, mixing the cards around face down on a table, still requires doing it twice for it to be shuffled.

[@Galatheam]

Love these tiny little guys grappling with massive numbers.

[@user-rm2qj2jh4l]

So interesting!! Statistics never ceases to amaze, and neither do you!

[@CountryMozart]

It still always fascinates me that numbers like 52! or Graham's number are still 0 when compared to the harmonic series if you give it enough time.

[@chrisgaming9567]

?

[@andrewmenke8581]

@@chrisgaming9567 The harmonic sequence is 1, 1/2, 1/3, 1/4, 1/5 ... and the word series here means to add all the numbers in the sequence. Lots of series with infinite terms are convergent, meaning they get arbitrarily close a specific number with enough terms. But the harmonic series is divergent towards infinity, which you could say means that it adds to infinity. The commenter says it's fascinating because the harmonic series is sooo close to convergent, but instead it tends towards infinity. There are lots of good KZbin videos on this if you're interested. Most of them are probably about calculus 2, but some probably won't require calculus.

[@tobysuren]

how is that any different to other divergent series like the sum of natural numbers?

[@Tubeytime]

But... that's like saying a finite number is like 0 next to infinity... you're just replacing "finite number" and "infinity" with fancy words.

[@CountryMozart]

The harmonic series just diverges so slow. The first 10^43 terms (which is an unfathomable number) only sums to about 100.

[@rohancleare]

The nature of shuffles isn't random though. In an overhand shuffle, the top cards usually end up near the bottom, and the bottom cards the top. In a riffle shuffle, it takes three whole shuffles to change the order of a chunk of cards. Cards are interlaced into the chunk on the first shuffle, meaning the order of the deck changes, but not the order of the chunk. Also, perfect bridge deals happen every so often, requiring two perfect shuffles from a new deck, which happen purely by accident. Faro shuffles from new deck order are guaranteed to go though several combinations that have been gone through before.

[@ecMathGeek]

He specifically mentions a properly shuffled deck. The first shuffle of an ordered deck is obviously not going to be unique. Nor are the first 2 or 3 shuffles. You're effectively using the counter argument "if people shuffle too badly (or too well), the shuffle won't be unique." Of course, but that's really not the point either. If the deck is shuffled enough times and with enough variation, any patterns that might have existed in the first few shuffles should be chaotically distributed and unpredictable.

[@rohancleare]

Yes, but most people don’t shuffle the cards 15 times when they play. The casino procedure in most places is a riffle shuffle, a riffle shuffle, a strip cut, a riffle shuffle and a one handed cut. The chances of getting the same order after that from a new deck are almost infinitely higher. Still small, but a lot higher.@@ecMathGeek Some just give the deck a quick overhand shuffle, some do a riffle or two.

[@jamesredgrave1331]

⁠​⁠@@ecMathGeek I think he’s saying that there’s less variation in the way people shuffle decks despite the amount of re-shuffles, I think the assumption that a deck of cards is shuffled complete random each time is overlooked more because everyone has the same techniques for shuffling cards even if the cards are “being shuffled enough times and with enough variation” whilst the disclaimer acknowledges this I think it’s unfair to rule out any exceptions that are considered “bad shuffles” as in the real world scenario everyone will have muscle memory routine on how they might shuffle cards and a lot of people will have the same techniques. So I think the world that has been set up in these videos is very cool and mind blowing but this isn’t the world that we live in

[@ecMathGeek]

@@jamesredgrave1331 Something I think needs to be mentioned is that the majority of times people shuffle a deck, they are not shuffling an organized deck. Unless it's a new pack, or someone went through the effort of ordering the cards before shuffling, the cards will already be relatively shuffled before you even start re-shuffling them. As to your point: unless the person is intentionally being lazy, or they are so good at shuffling that they produce a perfectly repeatable pattern of shuffles (1-to-1 for example), it only take about 5 or 6 shuffles to properly randomize a deck. When people shuffle, the natural inconsistency and imperfection of their shuffling technique produces a sufficient amount of chaos that -- again -- it doesn't take that many shuffles to produce a properly shuffled deck.

[@thomaskaldahl196]

I ran the numbers for a much more extreme situation: If, since before dawn of time itself (14billion 366-day years ago), 10 billion humans each began shuffling a deck of cards every SECOND, there would STILL be a 1 in 8 TRILLION chance that any two decks would match

[@seyedmatintavakoliafshari8272]

How much I enjoyed this video. Thank you for putting the time and effort to really give the insight we all needed!

[@aSpyIntheHaus]

Thank you for revisiting. I love the original video so much it gladens my heart tremendously that there is now 2!

[@mikumin727]

2!

[@r.henryjr.1533]

That's a lot of videos

[@nidhishshivashankar4885]

This might be one of THE BEST KZbin channels I have ever seen. Amazing

[@JonMurray]

Ridiculously brilliant work as always. Can’t wait to bust out the total electrons used by humanity vs unique card deck shuffles discussion next time everyone’s real high.

[@teraz76]

The characters are very cute. You should name them as It would be fun to see them in other videos.

[@tekjess_]

Every time I see a new video from this channel I have to watch it.

[@Biglight127]

I love the way you explain things. It is very concise and clear to understand. Thank you!

[@chicken29843]

Rubik's cubes have fun stuff like this too. If you were to draw every possible combination of a Rubik's cube on an individual sheet of paper for each possibility you could stack them to the Moon and back. 40 times. A 7 layered Rubik's cube has more possible combinations than there are particles in the observable universe, by a margin of an entire order of magnitude

[@tuams]

This was infinitely well explained and illustrated!

[@hugolandheer7008]

This is one of my most favourite math videos.... Maybe my most favourite! Thanks!

[@thisguy00]

Happy Birthday Paradox!!! 🎉🎉🎉

[@NexusGamingRadical]

Okay, if i wasn't sold before, I am now.

[@JasonSmith-jv7wl]

I love the evolution of your 3D art gorgeous these videos :)

[@GadgetBoy]

Just a little cheeky input from an engineer. You were only one order of magnitude off, not three. This is why engineers prefer engineering notation, as the exponents only increase in orders of magnitude. For instance: the difference between 1kW (1e3) and 1MW(1e6) is one order of magnitude. Also, all electrons are identical anyway (yay quantum mechanics). ;-P Glad I found your channel, you're an excellent science communicator. The comparison to electrons was an angle I wasn't expecting, really drove the concept of 52! home for this old electronics engineer.

[@willsmith618]

I’ve took statistics in college and never really understood the birthday problem even though I knew it was a fact. That simple diagram was so helpful, why have I never seen that before! Haha

[@ViliamF.]

7:32 Lowercase p signifies the prefix "pico-", note "peta-".

[@sebastiandierks7919]

And "note" signifies a written memo, the act of remarking or realising, or a bill of money, NOT the negation of what comes after it. (sorry for that xD)

[@Trash7Trash7Trash7]

0:19 rip to the 10% of people who commented 53!

[@meowmeowsaymeowmeow]

This is really well animated and cute, and well presented too!

[@cadaeib65]

Just discovered your channel and it's 1bsolutely amazing

[@sizzle9682]

I absolutely love how real this video is, true masterpiece perfect analogy's. props to you man.

[@rachelmay23]

For reference, if you were to set a timer for 52! seconds, let's just say you right now waited a billion years, took a step, and repeated the process until you went all around the world, picked up a drop of water, continue that process and when the entire pacific ocean is empty, put a piece of paper down. When the stack of papers reach the sun, there will still be a third of the timer left.

[@AlexW-]

close. you missed the last part. If you reach the sun 1000 times ... then you will be a third of the timer down

[@alonyouval3452]

Such a good video, this amazing graphics is great! keep creating!

[@NickCombs]

It's a bit odd to measure something in the number of "electrons used." When we flip on a switch, the electrons actually flow very slowly because the current that does the work is the EM field of the electrons and not the particles themselves.

[@irrelevant_noob]

Also i found it odd that the emphasis was on electrons "used"... Why not try to work out how many electrons there ARE within all the atoms on Earth? 🤔

[@protonix07gaming8]

​@@irrelevant_noob But is that by any way related to humans or a human life? Obviously there are various ways you can count things more than 52!, but the argument here is that it has to have something to do with human lives, so we can say that this number (52!) is not essentially infinite as far as our lives are concerned.

[@protonix07gaming8]

​@@irrelevant_noobAnd to answer your question, the number of atoms in the planet Earth is about 1.33 × 10⁵⁰, and even if we imagine that each of those atoms is the one with most electrons possible, or discovered (which is clearly not the case, as you might know), then each atom will have 118 electrons. Now all the elctrons there *are* in the planet Earth is 118×1.33×10⁵⁰, which is more like 1.57 × 10⁵² electrons. So even that number is nowhere close to 52!, which is on the order of 10⁶⁷

[@irrelevant_noob]

@@protonix07gaming8 thanks for the values. 👌 But the thing is, he said at 6:05 that we could use anything within "humanity's world". The number of electrons on/within/around Earth should fit that description. And it's getting closer, clearly better than the 9.8e37 he got. About "half-way" there in fact. ^^

[@MRHSDD11]

this is so good dude, thank you

[@jamesmnguyen]

At least until we become a Type 4+ Civilization.

[@ModernGamerX]

Its actually insane. There are more possible combinations of a deck of cards than there are every possible combination of a digital 5 minute song. Not only are the more possible combination in a deck of cards, but there are so many more possible combinations, that the difference is so insanely large it isn't even really quantifiable. There are more freaking possible combinations of a deck of cards, than there is possible music. That's just absolutely nuts.

[@zxqwerxz]

Another wrinkle to this question is that because all decks come ordered in the same order (or similar) the starting position of all decks is the same. So after the first bridge shuffle, lots of decks will have the same sequence.

[@Lucas12v]

That's why the video specified properly shuffled. Real decks are probably shuffled poorly often. Although it only matters if starting from some common order.

[@williamstotzkowski148]

This is the math that I was hoping to see because i feel like this number is easily achievable with a small sample size of people shuffling once on a brand new deck. Which happens by the hundreds of thousands across the world daily because of casinos. Same order deck of cards split within +/-5% of half of the deck due to human eyeballing. Then shuffled as evenly as possible by skilled dealers who shuffle cards for a living. That to me sounds like the first crack shuffle of a fresh deck must have happened mathematically already in human history.

[@riskorikkinen3498]

Casinos don't just crack the deck and straight riffle shuffle it from there. There's a step before where you spread the deck on a table and scramble it. That makes it so much more random that odds of same order is back to practical 0.

[@Paul_Bedford]

​@@Lucas12vBut at the same time, certain orders of cards are more likely after a few shuffles given a set starting deck. For example, a complete reversal requires more shuffles than a thorough mixing, so the mixing is more likely.

[@spikarooni6391]

This animation is so pleasing to the heart and brain

[@wailingalen]

Great video! There is another visualization out there about the intangible immensity of 52! I think Vsauce did it. It's crazy

[@joelarson6884]

Great video with sick animations. 52! Might just be my favorite number

[@RaccoonEatingCacti]

Honestly speechless. None of my intuitions were correct watching this video. The exponential notation hides the hugeness of the big numbers. Thanks for the video

[@RetroGameSpacko]

I would rather argue that there is no such thing as "properly shuffled" in a real life situation. First: card games have rules, these rules lead to decks having very similar orders after a game. That limits the starting orders before a shuffle. Second: Human shuffling is quite imperfect from a math point of view. Our movements are rarely really random. So, probably still super low odds, but a little bit higher than 1 of 52!

[@OhhCrapGuy]

I think it's more valuable to think about the number of events as compared to the actual integer 52! itself, rather than the specific method used to shuffle cards.

[@eveleynce]

let's also consider the prevalence and speed of virtual games, which means that we currently shuffle exponentially more virtual decks of cards a day than they did physical decks in centuries prior

[@OhhCrapGuy]

@@eveleynce interestingly, that's actually related to how several electronic gambling games managed to operate legally in certain jurisdictions. (All of this is [citation needed], I'm lazy at the moment) Many jurisdictions carve out exceptions to gambling laws for Bingo, for some odd reason. So companies realized they could implement their RNG for video poker or whatever by simulating bingo games between two players, and if player 1 won the game, that was a zero, if player 2 won, that was a one. Now by piping /dev/random through this function, and using the output as the input for any gambling game's RNG, that game was literally just a frontend for the physical player to play electronic bingo. (Heard about this like 20 years ago, unsure how accurate the original telling or my memory is)

[@JavierSalcedoC]

good card players account for card rules and shuffle +10 times before each round. No way to keep a trend

[@OhhCrapGuy]

@@JavierSalcedoC the league I dealt for had a standard of a full wash every 3 hands, with a full 7 shuffles on every hand. In terms of entropy, that's about the same number of bits.

[@jugbrewer]

my favourite illustration of 52! comes from Scott Czepiel: to pass 52! seconds, pick a spot on the equator, and take a step. let one billion years pass, then take another step. keep taking a step every billion years, and once you've made it all the way around the earth, take a drop of water out of the pacific ocean. repeat this process until the pacific ocean is empty, at which point, place a piece of paper on the ground and fill the ocean back in. repeat all of the above steps over and over, until the stack of paper reaches the sun. at that point, you'll be about 0.003% of the way to 52! seconds.

[@TheBluePhoenix008]

You're criminally underrated!

[@JohanSebastianCorn]

I don't like many videos but your videos are awesome enough. Thumbs Up.

[@camelliascholl6564]

didn't see your original video but I actually said "that's a nice large number" when you said 52! was your favorite. nice vid.

[@Plokmin]

Like the video! Not sure if this is the best name for it - perhaps "52! may as well be ∞ | But Why?":

[@wgoulding]

Great job with the 3D models! Super adorable!

[@lumotroph]

Holy crap. Amazing! Note: I’d love to see you get there with a story… Something along the lines of: You’re a god, shuffling a deck of cards at normal speed and then dealing them out to check for a match. While you’re doing this… An infinite Joshua apple tree grows an apple every season of a thousand years. Every hundredth apple is a twin, with a special seed. A rare peacock bird appears and grows larger every time it eats a seed, and once it has eaten a hundred seeds it has to sharpen its beak on the top of Mount Fuji 🗻. When the bird has ground down Mount Fuji into dust, what’s the chance of having found a match in your cards?

[@vadym-beep1241]

My mind can not comprehend how a simple deck of cards can have so much combinations...

[@rajtiller5347]

Amazing animations! Keep it up

[@o0Donuts0o]

“52! will forever be out of reach for humanity” Holds deck of cards in hand.

[@noomade]

weak

[@pnghumor]

my boy Isaac grew up and started an educational youtube channel

[@rafaelcalderabebber1198]

So a deck of cards is the most powerful thing ever created

[@whatisrokosbasilisk80]

Add another card for something even more powerful.

[@rafaelcalderabebber1198]

@@whatisrokosbasilisk80 I don't think we are ready for such power

[@agranero6]

You took The Sand Reckoner by Archimedes to a new level.

[@lotofAlexa1221]

Yoo my birthday is today and here goes this video

[@n-steam]

Your assume every deck of cards is perfectly random. In practice, cards have a starting order, and limited shuffling. Chances of getting a pair of matching decks should be greatly increased when starting from a "new pack" organisation, and only making < n shuffling moves.

[@Antifag1977]

That's why he uses the term Properly shuffled to mean fully randomized.

[@oxonomy2372]

@@Antifag1977but no deck can every be fully randomised

[@BoBoN4Uto]

"Will be forever out of reach for humanity" is an underestimation of future possibilities

[@_shadow_1]

You should make a video about deep time. Assuming infinite time does some weird things to probability and entropy because all randomness effectively becomes pseudorandom or even ordered at infinity.

[@ohnonomorenames]

I remember once running the numbers ad working out that if you stacked unique arrangements of playing cards one on top of the other they woud span further than the observable universe. I from memory they could also form a disk with the radius of the observable universe. I can't remember if they could also do the ball but i have a feeling that was about the point where the orders of magnitude got close. 52! is universal in its magnitude.

[@harshchittora3468]

The voltage you have used is distribution voltage at consumer end. High tension lines will have voltages way above this, so fewer electronics

[@forbiddenera]

8:04 electricity is generated and distributed at much higher volts, like high voltage transmission lines are like 10kv or more

[@timothyosborn637]

Could there be any consideration taken into account for cards always being printed and packaged in the same order and the, then shuffled. There will be a distribution of card orders that occure from different types of shuffles. We then use those distributions to narrow down the likelihood of repeated decks.

[@MacroAggressor]

Fascinating.

[@aukir]

The thing that gets me is that the vast majority of printed cards "started" in 1 of 4 positions usually. 2-A ordered by suit. That's gotta cut 52! by at least 1/4. :)

[@TheOobo]

That's why everything is qualified by 'properly shuffled,' meaning effectively randomized. But you're absolutely on to something in that assuming any given shuffle is actually random could be a poor assumption. I'd assume that most shuffles actually aren't properly randomizing the deck. So if you shuffle a fresh deck of cards without rigorously ensuring it's properly randomized, someone has probably ended up with the same sequence! The odds are just way, way higher than the theoretical 1/52!. Though I don't actually know how rigorous you need to be to properly randomize a deck. It could be easier than I'm assuming.

[@Kaazikin]

Great video

[@PRIMEVAL543]

My favorite point about this if you ask what the chance of getting the same deck twice in a row. 52! Is 8*10^76 as you said, but the coolest thing I found was an estimation of the Milky Way having 4 * 10^76 atoms.

[@cw6043]

the smiles are just so amazing

[@ProjectGladiatorWeather]

can you please do a video following up on the core collapse supernova about why black holes form?

[@TheDJOblivion]

The word "properly" in properly shuffled is doing all the work here, the likelihood most people are shuffling them to the degree to make this work is highly unlikely. So, in that sense, yes people have shuffled the exact same hands a humanly infinite amount of times. Just think of how many times you've gotten almost the exact same hand, or someone else at the table plays something you just did, it's more apparent in uno, and that has twice as many cards.

[@haniyasu8236]

There've been multiple documented instances of people dealing a perfect deal of Bridge (Stand Up Maths has a video on it), so it's not even "probably"', it's actually happened.

[@smexijebus]

@@haniyasu8236 But that's only matching suits, not a matching order of cards, is it not? It's just that each player was dealt spades, clubs, diamonds, or hearts respectively, not that every single card was in the same exact order as the other shuffle and deal, no? And was the whole point of his video that he believed they did a trick shuffle, i.e. it was not a properly shuffled deck of cards?

[@teamofsteve]

What a silly point. We are talking about the whole pack of 52 cards not a hand of cards.

[@TheDJOblivion]

@@teamofsteve it's not silly, you just don't understand, I wasn't talking about a hand. I'm saying that the amount of times the same pattern goes around during 1 game is indicative of "improper" shuffling, to reach "proper" shuffling as defined by this theory would require significantly more time to achieve than the vast majority of people use in casual gameplay. It probably only even comes close at casinos, or other professional card game settings.

[@teamofsteve]

@@TheDJOblivion stop talking such silly rubbish, please

[@CountJeffula]

Most card games also involve creating order from a chaotic deck. Is this order fully erased upon shuffling as it is normally done? I’d be curious to see how different games affect the resulting decks and which shuffling methods work best for different games. Lots of times, sequences of cards are generated. I feel like this even happens with dominos where the same or similar strings appear when dominos are drawn even after shuffling. Maybe it’s just chance too.

[@Jack__________]

Given the enormity of 52!, I would guess that any pattern would show up many times… but the rest of the deck would not necessarily be the same. However, I’m sure a machine could be designed to shuffle exactly the same each time… and if you have two decks with exactly the same order to begin with, you should get the same result after the shuffle. But, I would not consider these measures of designing a machine and controlling the initial order to fit with in the definition of “properly shuffled.”

[@tongpoo8985]

I'm sure a lot of people have said this, but I think "properly shuffled" is a big stipulation. Cards are mass produced, and are typically ordered in exactly the same way when you buy a pack. And most people use one of 2 or 3 shuffling techniques and don't sit there shuffling for hours. What I'm getting at is that the result of a "properly" shuffled deck by most human definitions is not a perfectly random distibution of cards. Like you dont have a python program that uses the random library, with a seed determined by datetime or measurements in atmospheric fluctuations or something, and then arrange the cards in the order determined by that script. People might open a deck of cards, bridge shuffle it 4 or 5 times, and most people would find it perfectly acceptable. So the odds of two properly shuffled decks at some point in human history being the exact same get a lot better when you consider the practical concerns and a different, more human/realistic definition of "properly shuffled". Could be an interesting video to mess around with those calculations. You could explore "how random" different techniques are. And you could try to guess how many packs of cards were sold, and make some assumptions on other factors for simplicity and go from there, and see how the odds change

[@mastershooter64]

Wait are you enabling subsurface scattering on those humanoid characters?

[@soupisfornoobs4081]

Honestly I'd do the same

[@R0bert811]

what about all the photons produced by all the suns in the universe over 14 billion years?

[@isk8atparks]

well thats got nothing to do with humanly infinite and also the universe is potentially infinite, so the point is moot.

[@c3cris2]

Yay! New video!

[@harry2b2t]

I LOVE your videos!

[@joels7605]

I thought this was going to be a video about the Hayflick limit. 50 is about how many times your body's cells can divide, which is interesting. So if each cell could divide without restriction, there would be 2^50 cells worth of you in a big blob. Which would probably fill the Grand Canyon. Which is interesting.

[@alterablebark54]

I got excited having not seen much new videos but why did I get a notification for a 6 day old video?

[@iulianandries2647]

Best animations on KZbin

[@pulverizedpeanuts]

8:49 Ah yes, coloumbs

[@johnfitzgerald2339]

5:49 "Is this it?" 😂

[@xboxpro360]

surprisingly excellent video

[@habadababa31415]

And what about the number of people that joked about 53! in your previous video? that seems pretty close to 52!

[@marverickbin]

Grasp that: Suppose I have 52! coins. I want to throw all of them until all of them are heads. How many throws I have to make until that happens (in average)? 2^52!, far beyond this human infinite. Now I just change a little: Suppose every turn I will only throw the coins that got tails. In first turn throw, about half of them got heads, and I only have to throw the other half in the next turn. Repeat. After around log2(52!)+1 turns I git all of them heads. This number is surprisingly low, around 226. This means that after only hundreads of throws to turn human infinite number of coins to all heads. It also can show the power of an selection mechanism (imagine each turn as a generation, where every throw is a random chance to survive and landing heads is like surviving)

[@beaumatthews6411]

But why isn't 51! for 53! the humanly infinity? Edit: I literally just realized an hour later your channel is called "But Why?"! Complete coincidence- I had no idea- no recollection of noticing. I think this is the first video I watched. Although this question remains, I really appreciated your video- subscribed!

[@ptorq]

A few years back I heard about Graham's number and started trying to understand how large it was. I started with g(1), the first term in the expansion. As I was trying to grasp the magnitude of that number, I slowly came to the realization that it was significantly larger than my former conception of infinity. To put it in terms that are physically meaningful, if you divided the observable universe into cubes with the edge being one Planck length, not only would there not be enough room to write g(1) if you could write one digit per cube, there wouldn't be enough room to write the exponent of g(1) expressed in scientific notation. You need to invent a new system of notation to express it.

[@Alexandar358]

And you're still on g(1)

[@isaacdrum8009]

The concept of 52! is what got me obsessed with Googol and then Googolplex and now I lie awake at night thinking about numbers like (Googolplex!) ^ Googolplex! all factorized. It's weird, obviously infinity is larger than any number, but does not have the same effect of thinking about "real" numbers. And then I think of things like heat death of the universe being something like 10 ^ (10 ^ 115) years which is unfathomably longer than Googolplex but, at some point, the hour glass will run out.

[@MaximumPasta]

Damn bro, the end of that video made my eyes water. Numbers be big

[@PVMChannel]

Just wait until this guy hears about 54!

[@artsmith1347]

03:30 I think you wanted "(52!)!" in the numerator. I understand that "52!!" means the "double factorial" -- which I learned many years after my last formal class in math. n!! = n * (n-2) * (n-4) * ... ending at '2' or '1' -- more info at wiki whereas, n! = n * (n-1) * (n-2) * ... *1 -- always ending at '1' wolframalpha says 52!! = 2.70644 × 10^34 It is a confusing notation. I agree with you that 52!! *_should_* mean (52!)! -- or "8.06581752 x 10^67 factorial" But no one asked me before the weird notation became entrenched in some circles.

[@irrelevant_noob]

TBF i'm not aware of any legitimate reason to use "factorial of the factorial of n"... while the "double factorial" comes up in combinatorics and apparently for "trigonometric integrals" too.. ^^

[@jonathanl8538]

I like the concept "humanly infinite". When you say something is so big it's as good as infinite, someone will always hit you with "ackchyually it's nowhere near infinity bla bla". And even though that's right, for all PRACTICAL PURPOSES, it could as well be infinite. That is "humanly infinite" :)