I had no idea where this was going, but that was really beautiful in the end. Well worth the long view!

@p.mil.1147

7 жыл бұрын

Peg Y do a video explaining how we express numbers like a bigg or a big boowa.

@PeguinDesign

7 жыл бұрын

I agree, I really want to see an animation of a huge sandpile toppling.

@fossilfighters101

7 жыл бұрын

Agreed!

@devling6606

7 жыл бұрын

I'm halfway and was like "this ain't going nowhere!". Taking your word for it and checking the end result :) EDIT: It was worth it in the end. Cool!

@marksmod

7 жыл бұрын

my thoughts exactly

I've done an REU (research experience for undergraduates) and worked with Luis on this topic. He certainly has a knack for explaining concepts like these (in this case, implicitly illustrating the axioms of a group using sandpiles as an example) in way that even a general audience can grasp. Thanks Numberphile for showcasing Professor Luis' work and talent!

@DrKaii

Жыл бұрын

🎉

Group theory is such an underappreciated area in mathematics. Thank you for this great video!

Those 23 dislikes must've been sand grains that fell off the edge

@Someone-cr8cj

7 жыл бұрын

L

@daniellebarker7205

5 жыл бұрын

best version of this meme I've ever seen.

@jasonstone1833

5 жыл бұрын

yep, opinions are like grains of sand--everybody is one.

@TruthNerds

5 жыл бұрын

Well, I changed my like to dislike after realizing that he calls 0 a natural number.

@sirhasslich536

5 жыл бұрын

@@TruthNerds I thought it is a difference in Russian and American versions of definitions, but, in hindsight, mathematics is not the place to have these kinds of inconsistency. Natural numbers ARE starting from 1 for every nation, then, correct?

The best handwriting on Numberphile so far.

Wait, what happend if the sandpile, is the parkar square?

@robinsparrow1618

7 жыл бұрын

I'm on it...!

@robinsparrow1618

7 жыл бұрын

I had to create a program to do it, but i got: 1 3 1 3 1 3 1 3 1

@idanzamir7540

7 жыл бұрын

Amazing! you're awesome!

@robinsparrow1618

7 жыл бұрын

Idan Zamir Aw, thanks!

@TheGamblermusic

7 жыл бұрын

you have proven Parker's identitiy !

Would be cool if there was a video of the topple taking place.

@iAmTheSquidThing

7 жыл бұрын

It'd be difficult to choose colours which would show the detail in that range of numbers though. Probably not impossible, but difficult.

@ihrbekommtmeinenrichtigennamen

7 жыл бұрын

+Andy Brice "{{0,0,0},{0,0,0},{0,0,0}} + {{0,0,0},{0,2^32,0},{0,0,0}} and topple until valid" results in the same value as "({{0,0,0},{0,0,0},{0,0,0}} + {{0,0,0},{0,1,0},{0,0,0}} and topple until valid) 2^32 times" So this sketch would work: while(true){ AddOne(); Draw(); while(!Valid){ Topple(); Draw(); } } No cell should ever have a higher value than 7. The highest valid value is 3 and then it could "get toppled into" 4 fom its neighbouring cells.

@quaternaryyy

7 жыл бұрын

Check out the second link in the description, press DEL and then shift-left-click somewhere in the center of the grid to add a "source" cell. That simulates having a huge pile in the middle of the grid (essentially of infinite size), and you can watch the animation in real time.

@Xnoob545

4 жыл бұрын

@@quaternaryyy how does that thing work? I try tapping and no sand appears I set it to drop sang

@draganjonceski2639

4 жыл бұрын

@@Xnoob545 go into brush, click set clicked cells to n grains type in your number and then just click anywhere

By far, this is one of the most inspiring videos on this channel. I can't really explain why...

The word "mindblowing" is used incredibly liberally these days but this really did blow my mind. I'm still feeling numb from trying and failing to grasp the implications of this. I'm excited for every Numberphile video that shows up in my subscriptions because they are interesting and entertaining but this stuff played in a whole different league.

@numberphile

7 жыл бұрын

+Penny Lane thanks. Lovely comment.

@KrupaHebbar15

7 жыл бұрын

+

@bernardweisblum2060

7 жыл бұрын

Numberphile

@otonanoC

5 жыл бұрын

>> failing to grasp the implications of this. This has something to do with complexity in biological ecosystems, and in immune systems, and in genetics.

@fasligand7034

4 жыл бұрын

@@otonanoC nice

anyone else notice that the magic sandpile for S had values in each square representing the number of grains of sand that are lost to the grid when the pile topples?

@Jared-ss3jx

3 жыл бұрын

what do you mean by that?

@debblez

3 жыл бұрын

That’s actually not a coincidence

@cheshire1

2 жыл бұрын

@@Jared-ss3jx He means the zero-pile has a 2 in the corners, where 2 grains fall off the edge, a 1 along the edges, where one grain falls off, and 0 in the center.

@DrKaii

Жыл бұрын

​@@Jared-ss3jx that has many definitions

I like how I fail all my Precalculus tests but still enjoy and understand all of Numberphile's videos.

@trickytreyperfected1482

4 жыл бұрын

How did normal/AP Calc work out for ya?

Dr. Garcia-Perente is probably my favorite interviewee/lecturer with only a single video with numberphile.

should we push this to the next dimension? A 3 dimensional grid?

@Nulley0

5 жыл бұрын

Yes and infinite dimensions

@whatisthis2809

4 жыл бұрын

6 topples, you might have 5 grids?

@ferencgazdag1406

4 жыл бұрын

Prepare your 4d eyes to see it

@NesrocksGamingVideos

4 жыл бұрын

@@ferencgazdag1406 The cells can have very small but different levels of opacity for each value.

@ferencgazdag1406

4 жыл бұрын

@@NesrocksGamingVideos It would still be inconvenient.

This dynamic reminds me of Conway's Game of Life work.

@St3venAU

7 жыл бұрын

I thought this also. It's amazing to see such complexity arise from such simple rules and starting conditions. I'd be interested to see what happens for different starting conditions, like if randomly dumped a few large piles around instead of just 1.

@alexanderf8451

7 жыл бұрын

It is, in fact, a form of cellular automata.

@maxkolbl1527

7 жыл бұрын

It's more than that: it's a set of cellular automata with an actual group structure to it, which is something I've never seen before

@peppybocan

7 жыл бұрын

to be honest, I was not sure if that's cellular automata because I don't know the formal definition of it, so I can't really say, what it is...

@drskelebone

7 жыл бұрын

I clicked out of my full screen playlist to suggest "isn't this similar to Conway's Life?" Glad I'm not the only one.

The end was really surprising and beautiful. Do watch it to the end

woah. started with such simple concept and ending was out of the park. great video

@cheeseburgermonkey7104

4 жыл бұрын

HOW U LOOK LIKE THE PERSON WHO MADE THIS VIDEO HOW???

@DrKaii

Жыл бұрын

​@@cheeseburgermonkey7104 🐒😊

Did this guy go through your whole "brown paper" budget for 2017?

This was by far one of the most satisfying and interesting videos I've watched in a while. I hadn't realized how long it was till I paused to get a more detailed look at the fractals. Thank you for producing such unique and wonderful content

I love this host, he makes this seemingly trivial aspect of math not only engaging but extremely easy to follow, you love to see it

Wow, ive been following this channel and others of yours for over 3 years by now and i honestly say this is my favourite video so far. I think the professor did a really good job at explaining this very abstract concept by giving so many examples. i found myself even skipping back to grasp the full concept so I was happy you made the video as long as needed. Good job and thanks to both of you!

I was tempted to stop watching a little past halfway through. It really took a turn towards 'woah' and all came together at the end.

@numberphile

7 жыл бұрын

it has its rewards!

@nowonmetube

4 жыл бұрын

Haha that's exactly when I went to the comments. But then when I saw your comment, I stopped reading and watched to the end!

I hope we get more Numberphile videos on sandpiles in the future! There are so many concepts to explore! -How do you calculate the identity for any given sandpile? -What if you changed the rules for collapsing in some way? (Maybe collapse the four by distributing one to each of the diagonal cells, rather than each of the adjacent ones?) -What if you considered all numbers up to and including 4 as "stable" (don't need to be collapsed)? What about up to and including 5? 6? -What kind of cool patterns are there when dealing with sandpiles that don't have symmetric patterns (randomly generated numbers for each cell)? -What happens when you subtract sandpiles from each other, rather than just add? What about multiply? (Too bad you would run into issues with division) And most obvious of all: -Why do identity sandpiles and sandpiles collapsed from one center cell result in such beautiful fractals?

@angelmendez-rivera351

Жыл бұрын

That final question has no answer, because beauty is necessarily subjective.

I was waiting for Brady's usual question... "Is this just a game that someone made up, or did it have some real practical reason for exploration?" "Can we learn something about other things because of research in this area?"

@numberphile

7 жыл бұрын

+Dave Brosius I don't think I ask that as often as you may think. I quite enjoy these things just for being awesome.

@TheGamblermusic

7 жыл бұрын

My instinct guess is that it is too beautiful to NOT have usefull applications for anything else

@SlackwareNVM

7 жыл бұрын

I actually was hoping for the question. The ending was really beautiful, but sometimes it seems that mathematicians are doing things just for the sake of doing things. It's interesting to see the reasoning behind this thing existing, even if it is "we just wanted to see what would happen".

@gerstensaft2936

7 жыл бұрын

Change "grain of sand" to atom, or proton and go back to the start of the universe and evolve the pile. :D

@tpat90

7 жыл бұрын

The most hilarious point about this is, that it mostly leads to some adoption down the road. Just take a look at Surreal Numbers, Quaternion or Fractals. Everybody agreed they are useless, until somebody found them useful and they started to pop off. Surreal Numbers found their way into to Algebra, where they belong. Quaternion are the basis for any fast approach to 3D Rotations. Fractals are everywhere, from your mobile device, to decryption, to randomizing and even in modern medicine. There is most likely always an adoption at some point in the future.

Thank you very much for the sound correction right around the 20-minute mark, I saw it hiccup and then heard the switch to the different microphone and that was far preferable to an audio de-sync or loss of audio. Audio guys don't get a lot of recognition for the work they do and I want to say thank you to whoever caught and fixed that. I really liked Luis' presentation, both the subject matter (which I am a huge nerd for), as well as the manner in which he presented it. It was very clear and easy to follow and I hope he shows up in future Numberphile videos.

Perfect! Best numberphile video ever! Was a little Boring at first, but thank fucking God I watched it whole!

@numberphile

7 жыл бұрын

thanks for sticking with it!

@yugandhardesai8493

7 жыл бұрын

Numberphile ,this sandpile algebra is insanely beautiful in its fractal form but are other arithmetical operations applicable in it and what would happen if we keep on increasing the no. of maximum sand grains in each cell of the infinite sandpile grid.

@8bit_pineapple

7 жыл бұрын

Yugandhar, if you're curious about these kinds of questions you should learn to program and have a play ;P that's half the fun of it.

@bestnocture

7 жыл бұрын

8bitpineapple can you please teach me how?

@Endoterrestrials

7 жыл бұрын

+

Join Brady's occasional email list (or Numberphile's Patreon, of course) for a chance to get occasional freebies, such as signed Numberphile postcards... eepurl.com/YdjL9

@johnsmith-ke3nb

7 жыл бұрын

Numberphile Why should i donate you?

@nickyboy909

7 жыл бұрын

there is no obligation to donate john just do it if you want

@veggiet2009

7 жыл бұрын

One reason is if you appreciate the creator of the videos. Another would be for the benefits, you can read about the benefits to support on his patreon page.

@johnsmith-ke3nb

7 жыл бұрын

veggiet2009 Nobody did ask you

@SachielxLAEx

7 жыл бұрын

john smith for a chance to get occasional freebies, such as signed Numberphile postcards!!!! don't you listen?

I'm amazed with the richness of Mathematics, and the hidden beauty lurking in the dark, waiting to be unveiled. Keep it up Brady! Love your videos!

That left me speechless. What a great finale.

The long videos are always the best

IT did not feel like a 24 min long video, but way shorter. Great video

@jursamaj

4 жыл бұрын

On the contrary, it felt way too long. A lot of the tedious small number addition should have been cut.

Wow, i was kind of skeptical about how abstract this was going in but it blew me away as it progressed. Talk about beauty in numbers. Im glad im subscribed to Numberphile.

I'm a long time viewer of numberphile and I freaked out when I saw this video with Dr. Garcia! He was my calculus 2 teacher in college and that was the class that I discovered my love for math and made me change my major to math along with graduate studies in math.. and now i see him doing the same inspirational stuff on this channel. Crazy stuff man

@thewarlord6529

5 жыл бұрын

Jon Woek Shoah that’s pretty epic

I would love to see that sand topple from the beginning for the 2^30. Many iterations per second of course

@debblez

3 жыл бұрын

I doubt that the person who made that actually calculated it iteration by iteration, so it would likely take much more computation to do that

Every video keeps amaze me... The end here is beautiful, ppl thinking video is "too long", stay until the end, it worths the effort.

@numberphile

7 жыл бұрын

+Flandre Scarlet ;)

Bravo. This is easily in the top 5 videos this channel has ever produced.

Dr. Garcia-Puente is by far one of the best Math lecturers at Sam Houston State University. I had him for Discrete Math and Applied Algebra, and I can vouch for his unparalleled quality.

Probably the best and most interesting video on this channel.

@utl94

7 жыл бұрын

It is high up one the list, for sure.

Those fractals are amazing

It went from "okay" to "interesting" to "fun!" to "cool" to "woooooow". Really well explained, really well put together, and what a payoff!

I can always watch old numberphile videos and still be amazed

Could we get zero for 1920x1080 sandpile group, please.

@wesofx8148

7 жыл бұрын

And recursively fill the center rectangle with zero sandpiles of the rectangle's size.

@FLooper

7 жыл бұрын

You can download the program from the description and basically do everything they showed you in the video!

@DrGerbils

7 жыл бұрын

In the identity for the 1920 x 1080 group, the middle 392 columns are all 2's. You're on your own for the rest of it.

Super fascinating and well explained!

@numberphile

7 жыл бұрын

+crashtextdummie thank you

One of THE best videos on Numberphile! Thanks!

That was a really great episode - thank you very much. It was very well explained as well!

It's nice to see some algebra on numberphile.

The concept of zeros in sets like this are interesting. I wonder if they contain other properties of our normal set of numbers such as "even/odd" or "prime."

@Aodhan2717

7 жыл бұрын

AlabasterJazz I wonder how you would define factorization in this system.

@zairaner1489

7 жыл бұрын

Primes can be more generally studied in "Rings", which are sets like in the video but where you also can multiply (which you obviously need to even make sense of "prime" and factorization) and the "normal" rules for multiplication apply (like associativity/distributivity) and probably also the existence of "1", meaning something like a zero just for multiplication. If these thing would work for the sandpiles, then you could define "a divides b" via "there exists a sandpile c thus b=c*a", and start talking about primes and factorization. The most obvious way to define multiplication is via just multiplying correpsonding entries and then toppling, but wether that has an identity I'm not sure (considering the all 1 grid is not in S)

@DrGerbils

7 жыл бұрын

For the 2x2 or 3x3 sandpile groups, defining A x B with cellwise multiplication will not make them rings. In a ring, if I is the additive identity, then A x I = I x A = I for all A. Let A = 0, 2, 2 2, 2, 1 2, 1, 2 A + I = A, so A is in S, but A x I = 0, 3, 0 3, 0, 3 0, 3, 0 For the 2x2 group, the sandpile 0, 3 3, 3 deals the death blow.

This is similar to what I am studying right now, and I love it. This might be my favorite numberphile yet!

That ending is amazing. Definitely worth spending my 24 minutes watching this.

Identity sandpile, like identity matrix?

@schmuelinsky

7 жыл бұрын

Penguin Design Yep, it's the neutral element concerning addition in the set of sandpiles coming from All-3s. Just like the identity matrix is the neutral element concerning multiplication in the set of matrices.

@TiKayStyle

7 жыл бұрын

Now you talk about multiplication, and that was also my thought. They introduce the +0. But what about the *1? The neutral Element in Mulitiplication

@-yake-

7 жыл бұрын

Thiemo Krebsbach isn't +0 and *1 the same though? They are both identities.

@siddharth_desai

7 жыл бұрын

0 is the additive identity, and 1 is the multiplicative identity. It depends on the operation. For exponentiation, the identity is 1. For matrix multiplication, the identity is the identity matrix. For matrix addition, it is the zero matrix.

@dermaniac5205

7 жыл бұрын

Well, they didn't even define a multiplication operation between sandpiles.

Wow, this is amazingly beatiful

That may be my favorite Numberphile video of all time, just for the big WOW factor at the end!

love the sandpile distribution graphic!! Great video, as always.

I need more

@N3bu14Gr4y

7 жыл бұрын

When I read this comment, it was at the bottom of the truncated comments. Right under it was the "Show More" button. I got a giggle out of that. :3

Wow this video showed how beautiful numbers can really be! ^^

That was awesome... I absolutely adore numberphile keep it up, proud of you.

Really liked this, it's probably the best video I've seen here in a while.

So the maximum amount of sand for a cell is n-1 where n is the number of neighbors one cell has?

@livedandletdie

7 жыл бұрын

The triangular grid one had 6 stable states, which I find weird seeing as triangles only have 3 neighbors. And if they count the triangles touching at each vertex then it would have 12 neighbors. And if they counted the opposite facing triangles it would be the correct number of 6 neighbors but it would make the square have 8 neighbors. It is weird.

@Keithfert490

7 жыл бұрын

PerunaVallankumous yepp. that's the maximum untoppled pile

@mangomalarkey

7 жыл бұрын

I am guessing that it is each intersection, or node in the triangular grid were you put the sand, which makes it more of a hexagonal grid but it is the only explanation I can think of.

@EebstertheGreat

7 жыл бұрын

I believe it has to do with the minimum length of cycles (6 for the triangular grid, 4 for the square grid, 3 for a hexagonal grid), but that doesn't seem to match the definition used on Wikipedia, which has it depend only on degree (3 for a triangular grid, 4 for a square grid, 6 for a hexagonal grid).

@JohnSmith-zq9mo

7 жыл бұрын

Yes, that is correct according to wikipedia. en.wikipedia.org/wiki/Abelian_sandpile_model

So there is an identity, an inverse for every element, commutativity and closure. Is the operation associative though? The set S being an Abelian Group would be so cool

@zairaner1489

7 жыл бұрын

Thats the question

@zairaner1489

7 жыл бұрын

Googling a little bit, I believe found an answer saying indeed, it is

@sebster100

7 жыл бұрын

TG MrNacknime at first I thought the sandpiles would be a subgroup of (GL_3(Z/4Z),+) and then he threw in that odd decomposition and I was really wondering whether it would have any group structure, and it's really cool that it does!

@Risu0chan

7 жыл бұрын

Yes it is associative. To prove that, consider these grids as equivalence classes 'modulo', where modulo here means that you can substract 4 in any cell while adding 1 in the adjacent cells (or the opposite, add 4 in a cell and substracting 1 in adjacent cells), any time you need. In that new set, the addition is the usual one for matrices, cell-wise, and it is nicely commutative and associative. In addition (pardon the pun), that gives you a simple algorithm to find the inverse of a grid g. The identity [2,1,2,1,0,1,2,1,2] is equivalent to [4,5,4,5,4,5,4,5,4] in which every number is greater than 3. Therefore you just find the complement of g by a regular substraction (and if needed, you 'modulo' it).

@Risu0chan

7 жыл бұрын

In case I wasn't clear, here is an example. You find to find the opposite (or inverse) of g: g = [[1,1,1],[2,2,2],[3,3,3]] identity is i = [[2,1,2],[1,0,1],[2,1,2]] ~= [[4,5,4],[5,4,5],[4,5,4]] i - g = [[4,5,4],[5,4,5],[4,5,4]] - [[1,1,1],[2,2,2],[3,3,3]] = [[3,4,3],[3,2,3],[1,2,1]] (regular matrix substraction) ~= [[1,3,1],[1,1,1],[2,3,2]] (equivalence by toppling the sand where needed)

Dr. Garcia!! I loved your Discrete Mathematics class and Linear Algebra class. I can't believe you're featured on Numberphile, that's awesome!

love it!! math is really beautiful and with your videos you make us appreciate it, thank you!!!

Pandemic players when they see 4 grains spreading to other cells *war flashbacks

I love his shirt :)

This is one of the best videos on the channel.

At 5:06, the appearance of the zeroes are synchronized with him saying "zero", loving the little attention to detail

Okay, one question though: Do these numbers have rules like a-b-c = (a-b) - c = a - (b+c) or do they not behave that way?

@rovingfortune395

5 жыл бұрын

The question of subtraction is a weird one when it comes to sandpiles - mostly because saying that a pile has a negative number of grains would create a kind of "sandsink" - then arises the questions of how a sink would topple, if at all, and how it might return to zero. Better to restrict the operations to ones that don't necessitate negative elements, like addition and the extreme weirdness of sandpile multiplication

@sahilnaik3079

5 жыл бұрын

@@rovingfortune395 so why can't we have sand sink...we can define that whenever there is a sink it will gain 4 grains from its neighbours.....just an idea....also If we do consider this I think there might be some boxes which will keep on oscillating and would never reach a solution in finite steps.

How *do* you calculate the Identity?

@wesofx8148

7 жыл бұрын

A brute-force method I can think of is just creating a set of all possible sand-pile grids then adding them to a sand-pile grid full of 3's to get the special set of sand-piles. Then you pick a sand-pile from the special set and start adding other sand-piles from the set until you find the one that doesn't change anything.

@lucashoffses9019

7 жыл бұрын

Surely there has to be a way other than brute force.

@aashishkariya8328

7 жыл бұрын

Lordious

@katzen3314

7 жыл бұрын

You don't need to add two different sand piles to each other from the set, can't you pick single sand piles to add to themselves and brute force until you find the right one then?

@DrGerbils

7 жыл бұрын

He said there was an algorithm that generated the identity for m x n grids and hinted that the run time grew exponentially.

Numberphile is my favorite channel to watch *really* early

Didn't think I was gonna like it at first, but now I am amazed :)

It would be cool to do this on like a toroidal grid by which I mean the edges are connected. Then it would be cool to see if sand could topple indefinitely on one of those. You'd probably need to modify the rules a bit.

@reuben2011

7 жыл бұрын

In generalizations of the sandpile model, the sandpile is modeled with a group (a network of nodes connected by edges where grains are placed on the nodes and travel along the edges to neighboring nodes). In these generalizations, there is usually a "sink" node where the grains of sand go to disappear in order to prevent infinite toppling. In the case of the grid model, the "sink" is the edge of the "table" where the sand falls off.

@reuben2011

7 жыл бұрын

One method is by brute force. Take any sandpile s in S (for example, the maximal sandpile) and add it to every other sandpile in S. Once you find the sandpile t such that s + t = s, then you know that t is the identity sandpile.

C++ has just called me. It wants to do something cool tonight.

That's pretty amazing. I've never seen these kinds of group structures with weird zeros before.

Super cool. The end definitely justifies the build up. The phrase, it blew my mind, gets some experiential understanding here...

Why did he only allow 0, 1, 2 and 3 in the square grid, but allowed 0, 1, 2, 3, 4 and 5 in the triangular grid?

@MrMakae90

7 жыл бұрын

Thanks, but I got that. Yet, why not allow more? Why not topple when 7 sand grains are in a cell of the square grid?

@christrengove7551

6 жыл бұрын

theFizzyNator can you expand upon "to make toppling make sense" please?

@yaeldillies

6 жыл бұрын

I think it's quite arbitrary but there's still a constraint: you need to topple with at least the number neighbors grains. If not, you wouldn't have enough grains to give to every neighbor. But, as orochimarujes pointed out, it would be possible to select randomly which neighbors get a grain. I think that could give interesting results, still. I'll explore myself toppling at an higher threshold

@Euquila

6 жыл бұрын

Not necessarily. I think random toppling would still have structure because the randomness would average out. It would be interesting to see this.

I wonder what would happen on a toroidal grid?

@aion2177

3 жыл бұрын

yes. or what will happen for objects with more then 1 hole. Like a double-donut. It might have application in topology.

Beautiful how math does the unexpected and yet demonstrates an intricate pattern.

Totally blown away at the end!

If you're reading this, have a Great day! 😄😄😄

Is there one for a hexagonal grid?

@CraftQueenJr

5 жыл бұрын

James Moran probably.

@rovingfortune395

5 жыл бұрын

There is a game called Hexplode that works on a hexagonal grid - the only difference comes from the fact that it is played on a finite grid - when the cell only has 2 neighbours, its maximum is 2, when it had 4 its maximum is 4 and so on. Makes for more interesting strategy, but loses something if the unity of the real sandpile group.

Most interesting numberphile video in a while! I have so many question! Truly fascinating subject I had no idea about.

Many thanks for not spoiling the ending in the thumbnail! The gradual buildup of “holy crap” was most enjoyable :-D

Parker Sandpile. 1 3 1 3 1 3 1 3 1

Does the order of sand-pile toppling effect the end result? What if you have two 4's next to eachother. Surely the result changes based on which 4 topples first. EDIT: After some critical thinking, no the result does not change because a 5 leaves a 1 after it topples. Two 4's next to eachother always produce two 1's and the same surrounding numbers regardless of the order they are toppled.

I would have loved to attend MSRI-UP this past summer. Great video, thank you for sharing.

Great video! I've seen the abstract definition of a sandpile group before, but never really thought about what the zero in this group means... Very helpful to do calculations on small examples, and to see the color-coded picture towards the end!

Se llama Luis David Garcia-Puente porque es una puente que dirige a sabiduría y conocimiento

Awesome finale! But I think you should have made video a bit shorter, a lot of people will give up on watching.

I saw a book about this at JMM last year and wondered what was creating the beautiful images on the cover. It’s great to finally find out!

Hooooooly shit, this was the best numberphile video in a while. Super entertiaining. More of this man!

Sandpile! Notice me!

So is this an example of a group?

@forbesmccann5063

5 жыл бұрын

Only if this operation is associative. In which case, since each of them is finite and also abeliam has some decomposition into a product of Z_ps which would be pretty frickin cool. So i hope that it is.

Those images look awesome!

Sandpiles? More like Sandphiles. Fine, I'll go 😢

Sandiles?

@otakuribo

7 жыл бұрын

Salandits

@iAmTheSquidThing

7 жыл бұрын

Sundials?

@vojtechjanku2534

7 жыл бұрын

senpais

@ShinySwalot

7 жыл бұрын

Palossand

@michaelhird432

6 жыл бұрын

Shiny Swalot you're subbed to carl too, right?

This absolutely blew my mind. It seemed pretty boring during all the computing, and it seems frivolous to ask that kind of question (which is a way to describe a lot of math, haha), but it really drew me in to want to experiment with it once they showed those fractals. That was beautiful and I want to try something like that myself

Best Numberphile video, by far. So interesting.

Wait weren't Natural Numbers from 1,2,3... and Whole Numbers from 0,1,2,3...?

@justinward3679

7 жыл бұрын

That would be too easy gotta mix things up.

@alexanderf8451

7 жыл бұрын

No. The "whole numbers" are the integers and include the negatives. There is some inconsistency about what constitutes the natural numbers, though. Dr Garcia-Puente is using what I think is the best convention. The "counting numbers" are the positive whole numbers (since you can't count zero things) and the natural numbers are zero along with the counting numbers.

@911gpd

7 жыл бұрын

natural numbers include 0

@benjaminprzybocki7391

7 жыл бұрын

Sauradeep Chakraborty There's different conventions. It seems that excluding 0 from the natural numbers is more common in school curriculums, but including 0 is more common in professional mathematical writing. If you want to be unambiguous, you can say non-negative integers (i.e. 0, 1, 2...) and positive integers (i.e. 1, 2, 3...).

@Sauratheinferno

7 жыл бұрын

Benjamin Przybocki Yeah. That's what I do. Its just that through 5th grade we've been asked this question in numerous tests: do natural numbers include 0 and always the correct answer was no. So I thought after watching this that maybe my life is a lie.

Sounds like senpai amirite?

@bestnocture

7 жыл бұрын

MDFlight I commented the same before it was cool

@typo691

7 жыл бұрын

Can explain the joke here?

@rgzdev

6 жыл бұрын

Bragtime Notice me sandpile!

great great video. this show how sometimes math is about simple concepts that linked together create those beautiful and elegant theories.