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.

[thomaskaldahl]

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

[magicien]

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

[faastex]

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

[rdJan]

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. :)

[pnghumor]

my boy Isaac grew up and started an educational youtube channel

[audrey-chan]

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

[noscaasifilmstudios]

What so poetic is that while it's out of reach by humanity, it's also right there in a simple deck of cards...bringing this full circle.

[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.

[thosewhowishb]

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.

[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.

[edog]

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

[NUCLEARxREDACTED]

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.

[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.

[oDonutso]

“52! will forever be out of reach for humanity”

Holds deck of cards in hand.

[KGTiberius]

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

[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!

[johnnybedir]

Man i love this channel's animations.

[Slash]

52! Is one of my favourite things to tell people, they can't quite believe no 2 decks of shuffled cards have ever been the same or ever will be the same, it's amazing really

[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.

[aSpyIntheHaus]

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