Check out the Jane Street star puzzle at www.janestreet.com/numberphile-2023/ Tony Padilla's Fantastic Numbers and Where to Find Them - amzn.to/44Zotd7

@paulkanja

8 ай бұрын

Loved the pun. Top notch stuff

@VenomousCamel

8 ай бұрын

That Jane Street puzzle is excellent! Kudos to them!

@ytmarten

8 ай бұрын

Nice pun 😄

@dibenp

8 ай бұрын

Cool! Jane street made a star battle puzzle.

@blueskytoday2230

8 ай бұрын

That was a fun puzzle. Maybe I don't really want to know, but how long did it take people to solve this?

If he collected 6.022 x 10-to-the 23 stars, mole would have a mole of stars.

@cstusa554

8 ай бұрын

Underrated comment!

@PMA_ReginaldBoscoG

8 ай бұрын

"You didn't have to cut me off" plays with an image of a 3d model of human brain

@jamescollier3

8 ай бұрын

You have to have had 1 year of college chemistry at 8am to appreciate this joke

@benjaminbeard3736

8 ай бұрын

Nicely crafted

@PhilBagels

8 ай бұрын

@@jamescollier3 Nah. I learned about Avogadro's number in high school chemistry.

Tony is the only guy I know who replaces his ladders after a single use. He is a mathematician though, we do famously write "problems" about such things.

@QuantumHistorian

8 ай бұрын

To be fair, he is going by the illustrations in the books.

@synchronos1

8 ай бұрын

_Actchually_, he’s a physicist

@Varksterable

8 ай бұрын

"A mathematician and a physicist were asked the following question: Suppose you walked by a burning house and saw a hydrant and a hose not connected to the hydrant. What would you do? P: I would attach the hose to the hydrant, turn on the water, and put out the fire. M: I would attach the hose to the hydrant, turn on the water, and put out the fire. Then they were asked this question: Suppose you walked by a house and saw a hose connected to a hydrant. What would you do? P: I would keep walking, as there is no problem to solve. M: I would disconnect the hose from the hydrant and set the house on fire, reducing the problem to a previously solved form. " Unfortunately, though, Tony is a physicist. So my solution would be to take Tony to one side, teach him mathematics, then fall back on the old "It has been shown that.." and let him disconnect the hose, etc.

@dhayes5143

8 ай бұрын

Do you want to try moving those ladders? A very practical assumption on his part, in my opinion.

@Varksterable

8 ай бұрын

@dhayes5143 ".. moving those ladders?" This, again, is where mathematicians have an advantage. "How do you cage all lions in Africa? Build an empty cage, then perform a latteral transformation w.r.t. the cage." It can all be done with transformations: no need to actually _move_ anything. Crikey; that would be a whole lot of work!

I believe he may have overestimated the number of stars roughly by a factor of two as the Mole will only see the half of the sky corresponding to the Earth's hemisphere where the Mole lives. If you adjust for this you'll see that Mole's plan is much more feasible.

@drenz1523

7 ай бұрын

what if he is an avid traveler?

@glasswingbutterfly

7 ай бұрын

LOL

@tofuhunter3797

7 ай бұрын

Yup. Totally feasible once you take that into account.

@drenz1523

7 ай бұрын

@@tofuhunter3797 is that sarcastic

I like how he's bothered by some aspects of physics, such as mass and speed, but totally ignores others, such as gravity and stellar motion. 😂

@numberphile

8 ай бұрын

Gotta pick your battles

@watcher314159

7 ай бұрын

@@numberphile Gotta pick your star battles.

@WillToWinvlog

7 ай бұрын

You could build the ladder toward a point you anticipate the star will be there! @@numberphile

@JamieJamez

5 ай бұрын

and oxygen

Imagine Tony reads stories to his children while they falling asleep. Every page he drops the book and starting some calculations 😂 Pretty weird childhood.

@SeanSMST

8 ай бұрын

One page of the book for each half hour of tangents 😂

@Cernoise

8 ай бұрын

It would get them to sleep, though!

@MrMctastics

8 ай бұрын

Grows up to cure cancer. Childs play, really

@tomkerruish2982

8 ай бұрын

There's an xkcd comic about that.

@jebus456

8 ай бұрын

takes two weeks to get through a single book

This is why I come to this channel. Arbitrarily breaking down a children's book with math and poking holes in the plot just for a good laugh at the numbers. Well done, gents!

When Tony said “there’s not enough surface carbon” I half expected him to say we’d need to turn animals into carbon for these ladders

@mvaalh

8 ай бұрын

I think most of the surface carbon is contained in animals and plants.

@SeanCMonahan

8 ай бұрын

Stamp collector Tony?

@daddymuggle

8 ай бұрын

The biomass of the planet would be included in the surface carbon.

@charlottelanvin7095

8 ай бұрын

I think most underground carbon used to be biomass. Like oil, gas, coal, etc

@pierrecurie

7 ай бұрын

@@charlottelanvin7095 It's probably referring to carbonate minerals even further down. Most of it would still be in the mantle crust, as the core is mostly iron/nickel.

If Tony publishes "The Annotated Mole's Star" I'll definitely buy it!

6:13 Wood is typically only about 50% carbon by mass. There's a lot of oxygen in there, especially in the cellulose/hemicellulose but also to some extent in lignin etc.

@wadehines9971

8 ай бұрын

close to C6H12O6 C12 H1 O16 simplifies to 12 parts in 30

@deyesed

8 ай бұрын

That's still not quite enough. He said it was short by a factor of 5, so it'll still be 3/5 of the required wood.

@thomasfevre9515

2 ай бұрын

I was windering about this. The hydrogen should be roughly 1/6 of the mass also. That's assuming around 2 hydrogen atom for each bigger atom.

@Sakkura1

2 ай бұрын

@@thomasfevre9515 For glucose itself you have C6H12O6 of which hydrogen makes up 12/180 or 1/15 of the mass. Shifts a little when you polymerize it into cellulose, and of course different again for other things like lignin, but it gives you a decent idea of the fraction hydrogen accounts for.

@thomasfevre9515

2 ай бұрын

@@Sakkura1 carbon is 13 mass and oxygen 16?

Tony reading bedtime stories and calculating the practicality of the story should be a thing on this channel! It is funny and educational like the calculator unboxing with Matt Parker. Great job on the video!

@numberphile

8 ай бұрын

I’m thinking about it. Have a big range of baby books here.

@QuantumHistorian

8 ай бұрын

It has a strong XKCD what-if vibe

@ecospider5

7 ай бұрын

@numberphile Yes please

@murphygreen8484

7 ай бұрын

Aww. I miss the calculator unboxing

@sammichaels3757

6 ай бұрын

A new segment! This is a fantastic idea! We all would love this to be a regular occurrence! Wow!

The mole says "I wish I could own all the stars in the world." Well, he already does; there are no stars in the world, they're all at least millions of miles away.

@walterfristoe4643

8 ай бұрын

Well, more like trillions of miles, I think... 🤓

@laurendoe168

8 ай бұрын

@@walterfristoe4643 Well, there's one star 93 million miles away.

@alfadog67

8 ай бұрын

Maybe he meant Taylor

@walterfristoe4643

8 ай бұрын

@laurendoe168 Yeah, he did say "at least." 🤠

@laurendoe168

8 ай бұрын

@@walterfristoe4643 If by "he", you mean Walter, then there is one star that's MUCH closer than 1 trillion miles, and therefore not at least a trillion miles.

Tony's analysis has a moral that the book totally missed out on. You can't just fix something because you're sorry. In the book, mole realizes he messed up and gets to just put everything back to normal. As Tony points out, though, there would be no fixing how badly he screwed up. He would only be able to wait for 10^10^122 years.

Haven't watched Numberphile in a while (been so busy with college math that I forgot my roots), so didn't know Brady had a newborn. Congratulations 🎉

Sounds like the ladders all radiate out from the Earth - I think Mole should, instead, solve the travelling salesmole problem to find the shortest loop that visits all the stars and ends up back at his burrow.

One thing not addressed here: nearing the speed of light changes an object's observable mass. Could Tony please calculate the Moler mass?

The mole only needs the ladder that goes to the furthest observable star from Earth (V762 Cas in Cassiopeia, 16,308 light-years away) and use it multiple times.

@randomname285

8 ай бұрын

The book said there were ladders going to all the stars tho

@VY_Canis_Majoris

8 ай бұрын

V762 Cas is much closer than that according to the latest estimates by Gaia DR3

@roneyandrade6287

8 ай бұрын

Also you can't use multiple times the ladders have made earth's rotation much smaller.

@ThreeEarRabbit

8 ай бұрын

@@randomname285 Fair point.

@renerpho

8 ай бұрын

Which makes me wonder: If the furthest observable star is 16,308 light-years from Earth, and there are 5,000 stars in total, the combined distance must be smaller than 82 million light-years. What does Tony need the extra 204 million light-years worth of ladders for?

15:25 the "prety reckless behavior from mole" made me laugh so hard

@mikew6644

8 ай бұрын

Same!

I’ve got three moles (at least!) in my garden. I’d be very delighted if they could just do a one-way trip to the nearest star!

@bevweb

8 ай бұрын

3 moles? of flowers?? you must have a pretty huge garden

@aguyontheinternet8436

8 ай бұрын

@@bevweb I wonder how much room they would need 🤔

OK, so after the Poincaré recurrence time, we go back to the initial point. At that moment, again a mole sees a shooting star, and wishes he could own all the stars. Basically, we have a never-ending story.

@KirkWaiblinger

8 ай бұрын

After the poincare recurrence, basically every story is neverending

12:22 But we’ve missed out on the acceleration forces on Mole. Repeatedly accelerating to just shy of the speed of light, decelerating to a stop, repeat… for 2 years and 4 months. He’s made of some stern stuff. He might be a fair match for Chuck Norris.

@coweatsman

7 ай бұрын

Is there enough energy on earth for all that acceleration?

“That’s Mole’s best tactic.” I love everything about this

I think it's more plausible that mole confused some street lights for stars.

If we're going to take this seriously, Mole has the capacity to will ladders to the stars out of nothing. Accounting for the physics and concepts involved here, Mole is nothing shy of an ancient eldritch horror.

@luipaardprint

7 ай бұрын

I think it's more likely that the shooting star was some sort of self replicating constructor from an advanced civilisation.

"May you build a ladder to the stars, And climb on every rung. And may you stay... Forever Young." - Bob Dylan.

@pepehimovic3135

8 ай бұрын

Rung?

@rhesarozendaal

8 ай бұрын

@@pepehimovic3135 that's the steps of the ladder. they're called rungs.

@godfreypigott

8 ай бұрын

@@pepehimovic3135 You've never heard of "rung"?

This is the best example I've ever seen of something that physicists do recreationally all the time: take something allegorical or imaginary and say: "what if this were real?" It's actually very good practice, because it's basically making a whole sequence of Fermi estimates, and that is a core skill of a working scientist or engineer.

@nielsdegroot9138

8 ай бұрын

You might enjoy the "What If?" books by Randall Munroe, the guy behind XKCD.

Terence Tao gave an interesting talk called "The Cosmic Distance Ladder", a video of which is on KZread. It's not about actual ladders, but rather the way in which people determined distances from the Earth to other objects in space. It's pretty surprising how accurate some of the calculations were, even hundreds or thousands of years ago.

This is one of the best Numberphile videos to date! Nice work Brady and Tony! Lot's of giggles in there.

Absolutely loved the video and the puzzle on Jane's Street.

You all missed a very important detail: at 12:50, he reads from the book that says "THAT NIGHT", so even though at near speed of light, it takes mole just over two years. How fast does he have to be traveling to get it done in one evening per the book's narration?

@PhilBoswell

8 ай бұрын

Clearly moles also have a Santa Claus…

Ok, I never knew that there are twenty times as many galaxies as there are stars in an average galaxy. That’s surprising to me.

One of the best videos that you've made!

1:00 "I've never seen a shooting star". Hmm, anyone else wonder how they came up with the myth about the mathematician/scientist that never leaves his desk? (Of course I greatly prefer Tony to stay at his desk and create content for us, but that is another story, as they say).

I love how they teach maths in creative ways. I have learnt a lot of maths because of this channel :)

Tony is the best!

Children’s author: “Here’s a cute story about sharing.” Cosmologist: “And I took that personally.”

2:24 Yup, Rigel is there twice, but 17301 is the "real" Rigel, aka Beta Orionis, while 51926 is Rigil Kentaurus, aka Alpha Centauri A.

This research needs to be peer reviewed and published by the Royal Society.

Perfect! That's exactly what I was planning on doing today!

@volodyadykun6490

8 ай бұрын

What, rushing to comment without watching?

Seems to me like there is a mistake in the maths! 😮 786 million light years for 6000 stars is roughly 100,000 light years average distance per star. That's bigger than the Milky way!

@dutchscrapper2317

8 ай бұрын

Yeah must be wrong

theres only one mole, so you only need one ladder- one for the furthest away star. after the mole reaches that star, move the ladder and it will reach any of the other stars.

Now THIS is the scholarly content I subscribed for.

Sounds like XKCD What-if kind of discussion. Keep them coming!

Clearly those ladders are going to be whirling about as the Earth rotates. What kind of flinging out force is Mole going to be encountering at stellar distances?

@AnthonyFlack

7 ай бұрын

The ends can't travel faster than light so I guess the ladders will twist up into spirals.

It baffles me that you can reach adulthood and have never seen a shooting star. I look at the stars way too often to catch a glimpse of one every now and then.

@Nehmo

8 ай бұрын

Many people live in polluted cities where the sky is obscured.

@itisALWAYSR.A.

8 ай бұрын

I grew up and lived in cities all my life. Really seeing stars at all isn't a common thing any more. I don't think I saw a shooting star until my mid-twenties, the Perseids, on a beach up north, far enough from the light pollution. Actually I once travelled to a Navajo reservation when travelling the USA when I was 21, that was the night I saw more stars than ever in my life.... perhaps there were shooters then, but I don't remember it well enough now. Enjoy the sky you have!

@Bronzescorpion

8 ай бұрын

@@itisALWAYSR.A. Well, not really leaving the city once in a while is also something that baffles me. I also live in the city, but that doesn't stop me from seeing the night sky every now and then. i am not even actively going out of my way to look at it, I just happens to be at places with low light pollution at times.

@brettbreet

8 ай бұрын

I think he was being literal. A shooting star is not, of course, actually a star 😀

@Bronzescorpion

8 ай бұрын

@@brettbreet could be, but it seemed to me that he was just talking about the phenomenon, not the technicality.

Your value of 786 million light years has to be off for 5,000 stars. If you figure the mean distance to a star given 5,000 stars and that total, you come up with 157,200 light years. That's well beyond the edge of the galaxy for the *average* star. There are a number of distant stars that we can see because they are extremely bright, but even those are on the order of 10,000 light years away or less. The most distant single star you can see is in Cassiopeia, and it's only ~16,000 light years away. There could be an error of a factor of 1000 in this response, or perhaps it was calculated for far, far more stars than the 5000 mentioned earlier.

This sounds very much like an episode of Randall Munroe's "What If" and I'm all here for it.

'I wonder if there will be a link in the video description" damn Brady is such a salesman hahahahha a loved the little banter at the end

Beautiful! Thank you.

Those are the important calculations we need on this channel. Keep it up, Tony!

LOVE this wholesome content! Brilliant! Plus it shows a lot of what’s done for usefully estimating scale to find answers to impossible questions

@mikew6644

8 ай бұрын

“Pretty reckless behavior by mole I’d say” 😂😂

I think Tony made an error calculating the distance: If the total distance to 5000 stars is 786 million light years then the average distance is 157000 light years - which would put these stars way outside of our galaxy.

Tony Padilla. Legend !!

If the total distance is 286 million light-years, and you have 5,000 stars, then these stars are on average about 60,000 light-years away. That's a problem, considering there are very few stars that are visible to the naked eye beyond a distance of 1,000 light-years. Something is wrong with the distance calculation.

@renerpho

8 ай бұрын

Not to mention that the 286 suddenly turns into a 786 half way through the video.

How could the total distance to reach the 5000 visible stars be 786 million light years? That would be an an average distance of 157,200 light years each, which is well outside the milky way. I'm guessing he meant to say 786 thousand light years.

12:45 bonus question: objects moving near speed of light are "heavier" - they have more momentum than their mass and speed would suggest in Newtonian physics. So, how much energy is needed to make a turn when reaching a star and starting the return home? (I wanted to ask for force but realized it's either infinite or you need to specify non-zero time it takes to make the turn)

@Misteribel

6 ай бұрын

And how much every is needed to get the star up to speed, and then get it to stop again in time? 😅

The mole's star puzzle over at Jane Street was really tricky! Fair note, there is at least one solution that isn't the "correct" one, but it's only slightly different.

@tomhoward4906

8 ай бұрын

Are you sure? I worked through the puzzle and believe I came to a unique solution.

@kwinvdv

8 ай бұрын

I also came to one unique solution. Maybe you didn't apply all the rules correctly (or maybe Jane Street realized their mistake and corrected the puzzle; is the current puzzle displayed on their website still that same as the one you initially did?).

@lollo863

8 ай бұрын

It was fun, had to whip out the paper

@trigonzobob

8 ай бұрын

It seemed fully constrained to me. I have an app called Star Battle on my phone that is essentially the same puzzle but I think they are all 9x9.

@TheVictorpenha

8 ай бұрын

That puzzle was pretty tricky. But I found one unique solution though.

This quickly turned into mole-made horrors beyond comprehension

These are the types of nerdy thought puzzles I love :)

This is by far my favorite numberphile video.

This musty be the funniest Numberphile video yet, and I watched a lot of them! One more thing: Tony forgot to calculate Mole's relativistic mass as he was travelling at that insane speed to snatch all the stars. He must have weighed millions of tons!

Side note: Mole is super strong since he seems to be able to accelerate a whole star to .9999999999 c withing seconds.

Sounds like an attractive book for smaller kids. Mole with a ladder to the stars? At 4-5 years old I would be totally into that stuff!

I think this should be a new series of annotating children’s books

I laughed when he began his analysis from the first or perhaps the second page of the story questioning moles visual acuity.

Nothing can convince me this isn't a parent venting frustration at having to read this book to their kid several times a day.

I have a solution to the ladder problem, just use one extension ladder that can reach the furthest star away. Then just move it from star to star. There will be a problem moving it of course, but no worse than the rotation of the Earth, around the solar system, as it moves about the galaxy. All the stars you can observe are within the Milky Way (with the exception of a galaxy, maybe two), so at least mole doesn't need to worry about the super cluster, etc.

I love comedic understatements like "I think this [10^10^122 years] is exceeding a mole lifetime, by the way"

8:22 simple solution to the resource deficit. Build ladders to some planets, near some stars. Go to those planets and use _their_ carbon to build ladders to the star and other stars. There must be a numberohile episode on scalability

9:45 - 9:53 imagine being the little child hearing this midway through the story before Tony closes the book and storms out …

Ah a math video that is fun and easy to understand

I ❤ this channel so much. Been watching since it started. ❤❤❤🎉🎉🎉😂😂😂😊😊😊😮

20:16 While it is guaranteed to get back to an arrangement of cards that you saw before, due to the finite amount of arrangements, it's not necessarily guaranteed that you actually get back to the original arrangement of cards. For shuffling a deck of cards, the likelihood of getting back to that original arrangement does approach 1 when the number of shuffles approaches infinity, but for the universe, it could be that certain states can only be reached from another specific state and if there is no process by which there is a state that leads to the big bang starting state, it might be impossible to get back to any specific point after the big bang until a state is reached which could also be reached from a future point. So in essence , it could be that the first Poincaré recurrence could only happen 10^50 years after the big bang, which doesn't help mole who is at 10^80 years after the big bang and tries to get back to about 1.3*10^10 years after the big bang.

@danielyuan9862

8 ай бұрын

To respond to your comment, repeatedly shuffling a deck of cards will guarantee that you'll reach the original arrangement in a finite number of shuffles, but if you give yourself a finite limit to the number of shuffles, you can get close to, but never reach, 100%.

The owl should have told Mole that his wish was already being fulfilled. Starlight is energy that belonged to the stars, but is coming to us. Part of all those stars are coming to us.

Great story, as always!

I wasn't sure what to expect when I clicked on this, but this was exactly what I expected

Btw, 2.33 years for traversing all the stars is only (approximately) correct when the incorrect total distance to the stars (786M ly) is used, the correct (or at least way more correct) 786K light years will yield around 19.5 hours using the same method, i.e. instant acceleration/deceleration to/from 0.999999999999999999c at will.

Yay Tony’s back!!

12:04 “Mole is traveling super fast so time ticks differently for him.” No, time ticks exactly the same for him as it ever did. For him, the relativistic effect that matters is the length contraction of the distances between earth and the various stars.

Moles are having a great week!

Delightful. I'd love to know whose idea this video was.

5000 stars and 786 million light years sum of the distance does not sound right. It would mean that on average a visible star is 157,000 light years away, which would mean that most visible stars are outside if the galaxy. I think the sum of the distance is off by a few orders of magnitude? Cute story and calculation, though. 😁

@ScienceMeetsFiction

8 ай бұрын

Came hear to say this. 786 thousand light-years might be about right, but there is no possible way it's that far into the millions.

I'm imagining an absolutely exhausted child begging to go to sleep while dad is brewing yet another cup of coffee saying that the numbers just don't add up, crumpled papers on the bedroom floor and a worn pencil behind the ear.

I need more of this for sure! Do three little pigs! What would it take to blow down the houses and whatnot. Or jack and the bean stock. Let's math out children's books

You haven't seen a shooting star? I've seen at least four separate ones. I have also seen extreme Northern Lights that extend right down to ground level, causing an extremely eerie, dense coloured fog all around me. You need to see more space weather!

"So Mole couldn't have-" "Dad... can you just read the damn story?

Just a very cool video, tnx!

This played out like a Randall Munroe "What If?" article - very fun!

Eagerly awaiting the publication of Kip Thorne’s “The Science of Mole’s Star”

I love this channel

Stay tuned for next week's episode of Realistic Animal Stories where Tony analyses how the amount of sugar and toxic substances in food would have definitely killed the Very Hungry Caterpillar

The star battle puzzle is reasonably approachable for someone with experience doing that type of puzzle. Very tricky for someone new to that type.

@luipaardprint

7 ай бұрын

I thought it was pretty doable tbh, and pretty rewarding figuring out the system.

@Misteribel

6 ай бұрын

Isn't that basically true for any puzzle? If you've done that kind before, the logic will appear simpler.

Tony's next paper: amending mole's star

Question: Can a rogue planet be far enough away from any star or galaxy that it remains even after all the stars have turned into black holes? It would be so cool, like the last material than in the universe.

I've just recently purchased Antonio Padilla's book, Fantastic Numbers And Where To Find Them. I think I will enjoy it greatly! 🤓

It's confusing that "Rigel" appears twice in the list of brightest stars. I think that the first one should actually be Rigil Kentaurus.

_"And that, My little sweetheart, is why moles are blind."_

"I have a data of them"... Of course you do! 🥰♥

The most mathematical way to collect all start is to redefine the notion of collection and assume, that all stars are already collected (are part of mole property).

According to ChatGPT, Carbon makes up roughly 50% of the mass in balsa wood (depending on the density of a specific sample and how dry it is). Oxygen makes up about 44%, Hydrogen 6%, and Nitrogen about 1%.