It's unfair that Thue got his name on it first. Couldn't we call it the Thue-Morse-Morse-Thue... Sequence?

@emc2dtls1

8 жыл бұрын

+TheMasonX you sir are a fucking genius

@austynploshnick841

6 жыл бұрын

Truly a missed opportunity.

@mekkler

6 жыл бұрын

Math humor, the best kind.

@jackscrivens9520

5 жыл бұрын

But thue still goes first

@matthewstuckenbruck5834

5 жыл бұрын

@@jackscrivens9520 in that case it should be the thue-morse-morse-thue-morse-thue-thue-morse-morse-thue-thue-morse-thue-morse-morse-thue-morse-thue-thue-morse-thue-morse-morse-thue-thue-morse-morse-thue-morse-thue-thue-morse-morse-thue-thue-morse-thue-morse-morse-thue-thue-morse-morse-thue-morse-thue-thue-morse-thue-morse-morse-thue-morse-thue-thue-morse-morse-thue-thue-morse-thue-morse-morse-thue sequence.

if the prizes decrease value exponentially, fair would be ABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

@oliverxu7027

5 жыл бұрын

hahahahahaha nice

@slayerofthebad9265

5 жыл бұрын

Depends on your exponent's base, no?

@tcoren1

5 жыл бұрын

SlayerOfTheBad if it is half then this is true

@marcusscience23

4 жыл бұрын

2

@vblaas246

3 жыл бұрын

Publishing papers be like, first and second author? Fine I'll be second author but then infinitely many..

I'm sure that if you buy that many rounds in a pub, there are no winners, only hospitalised losers.

@rentacowisgoogle

8 жыл бұрын

+Penny Lane And one hell of a good night.

@transcendentape

8 жыл бұрын

+Penny Lane clearly, the pub wins.

@HaniiPuppy

8 жыл бұрын

+Penny Lane Unless it's over a longer course of time than one night.

@jumpman8282

8 жыл бұрын

+Penny Lane ...hospitalized, but perfectly equally drunk losers.

@G597TN

8 жыл бұрын

Let n be the number of drinks served (and drunk) the difficulty of following the sequence correctly increases exponentially with n. I really want to see someone trying to follow this sequence after some good drinks ;-)

So, it could be said that sharing is a Thue street.

@TheZotmeister

3 жыл бұрын

Underrated comment.

@g.tucker8682

3 жыл бұрын

Bam!

At 3:52 he originally said "odd" but overdubbed it with "even." I have to commend the fantastic audio editing and the almost magic-like misdirection with the terms showing up on screen though, it's very hard to spot if you're not looking for it!

3:53 That's a very unique pronunciation of the word "odd". With your thick Aussie accent, it almost just nearly sounds like you're saying "even"! But I wasn't fooled, I'm a consummate lip-reader. ;)

@RichConnerGMN

7 жыл бұрын

roasted

@kyay10

5 жыл бұрын

It's a Parker odd

@felixroux

4 жыл бұрын

@@RichConnerGMN How...?

@IkeFoxbrush

3 жыл бұрын

He didn't mix up odd and even, or did he? Edit: according to another commenter there was a mistake in the original video that has since been edited...

@galoomba5559

3 жыл бұрын

@@IkeFoxbrush he said odd on video but then voiced over and said even. you can't edit videos except for trimming out parts

To be fair shouldn't the sequence be called the Thue-Morse-Morse-Thue sequence?

@JNCressey

8 жыл бұрын

+Satchboy71, or the Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse sequence?

@uriman9502

8 жыл бұрын

+Satchboy71 To the top with you

@Nicbudd

8 жыл бұрын

+JNCressey Or it could be the Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-­Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-­Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-­Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-­Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-­Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue-Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-­Thue-Morse-Morse-Thue-Morse-Thue-Thue-Morse-Morse-Thue-Thue-Morse-Thue-Morse-Morse-Thue sequence

@draevonmay7704

8 жыл бұрын

I came down to the comments to say exactly this, and found it was already top comment

@PassiveMarmelade

8 жыл бұрын

+Nicbudd You really have nothing else to do >

"an infinitely long game of chess" ... until you hit the 50 move rule.

@icedragon769

7 жыл бұрын

+Art Schell yeah, that was the point. The Thue Morse pattern not only does not repeat thrice in a row, you can also never find a trio of identical subsequences of any size.

@petertaylor4980

7 жыл бұрын

+icedragon769, of course you can. There is a finite number of positions, so there cannot be an infinite sequence of them such that no three elements of the sequence are equal. I think the point is rather that by avoiding repeating positions for long enough you can either run out the clock or give your opponent a chance to make a mistake.

@Idran

6 жыл бұрын

Yeah, it does today. The paper was from 1929, when chess organizations were still in the process of debating the form the rule should take, and part of the purpose of Euwe's paper was to demonstrate that it shouldn't just be based on performing the same set of moves three times in a row by proving that there existed an infinite game that obeyed that rule. The 50 move rule wasn't solidified in chess until like 2001 either; from like the 1900s until 2001 there were all sorts of exceptions depending on endgame, after the early-20th century discovery that there were winnable endgames that required more than 50 moves to win. In fact, part of the reason the discussion was such a big deal was that they were trying to come up with an alternative to having a fixed move count rule, because people were discovering endgames that could be won, but only with longer and longer move counts. So they were trying to find a rule that would force all chess games to be finite without just cutting it off at a certain arbitrary number of moves.

@aknopf8173

5 жыл бұрын

Also: The draw-by-repition rule does not care about moves but only about positions. And you can reach the same position 3 times even when you have no repition in the moves.

When I was younger, I seemed to have had OCD tendencies. If I tapped my left foot, I had to tap my right foot so it would be equal. But then I would realize that my left foot went first so I had to let my right foot go first to even it out. As you can see, it would have turned into this sequence. I had no idea what I was doing was an actual mathematical sequence.

@Tayrtahn

8 жыл бұрын

+Yogi I did the same thing. Drove me crazy sometimes, what with it being an infinite sequence.

@Lightningfootjones

8 жыл бұрын

Same, i did that with blinking

@andrewxc1335

8 жыл бұрын

Same with me walking over cracks / seams in concrete walkways.

@cloudycloudi631

8 жыл бұрын

same thing kept happening to me. It took a lot to make myself ignore the urge. Really distracting

@Joecool20147

8 жыл бұрын

+Feathercrown's Channel I did the same thing, I tapped two of my fingers to it, of course I didn't know about all the other cool stuff about the sequence

When I was a child, I had this sequence stuck in my head every day for 10 years. I used to drum it on things or write it down and see how far I could go into the sequence before I got bored. No one ever taught it to me. Honestly I feel really fortunate that I eventually got it out of my head or I could have wound up with some life difficulties.

@robinder_

3 жыл бұрын

SAME LMAO like if i accidentally touched something or did a movement on one side i needed to do this sequence to equalize it out or it would bother me, i still do it now but way less than when i was a kid, as i would also do it while walking for example

@user-yx1bk6ic4w

Жыл бұрын

I am very surprised that I am not the only one who learned this sequence myself when I was young.

@conure512

Жыл бұрын

I DID THIS TOO. It was because I had OCD, whenever I touched something with one hand I had to touch it with my other hand, but then I realized that my right hand had gone first which was uneven so I had to do it again with my left hand first... so on and so forth.

thumbed up at the abba joke

@omfgmouse

8 жыл бұрын

+veggiet2009 Went to thumb up after seeing this comment, noticed I'd already thumbed it up and hadn't even remembered

@LUKE17992

8 жыл бұрын

Same!

@gredangeo

8 жыл бұрын

+veggiet2009 I was waitin' for it. I just knew he couldn't resist. Quite happy now. I was thinking I was going to be quite upset if he managed to get through that whole video and not bring that up.

@boomerboxer3574

5 жыл бұрын

someone explain?

@programaths

3 жыл бұрын

@@boomerboxer3574 Money money money

This sequence has been a large part of my childhood. I had very mild OCD, and if I were to step on a crack, the other foot would have to step on two cracks and then back to the other foot. I would then have to start again with the second foot starting. This would go on for like ten minutes after I realized this would take an eternity to reach equality, because the first foot always stepped on a crack first.

@indigo-lily

8 жыл бұрын

+Snakeyes244 I have a very similar story, only I did it with tapping my feet! Although I don't think I have OCD, I do have autism (also mild) which can cause the same types of repetitive behaviours.

@pvanukoff

8 жыл бұрын

+Yulex I did it with all sorts of things: Chewing food -- I would chew left, right, right, left, then right, left, left, right ... clicking my teeth, twiddling my toes, singing notes (low, high, high, low, high, low, low, high...), etc. I'm glad I grew out of it. But sometimes not glad.

@Snakeyes244

8 жыл бұрын

I didn't entirely grow out of it xD I did it in all sorts of ways too! Im glad im not the only one lol!

@jacksonpercy8044

8 жыл бұрын

I didn't even know it was a proper mathematical sequence until seeing this video. For me I would actually say out loud "up down down up down up up down...." while raising and lowering the pitch of my voice. I think I did it because a full cycle is symmetrical, nothing to do with the actual value of the "ups" and "downs". I don't remember doing this sequence for many other things, but yeah, it's weird that a lot of people here seem to have discovered this pattern as a child.

@rickhatch4793

8 жыл бұрын

+Snakeyes244 I did that a lot too with stepping on cracks. I was usually satisfied if the total number of times I stepped on a crack were equal for both feet, but not if the process was repeated a lot, such as eating food. I still do it, except i usually just avoid the cracks entirely as it is easier then trying to step on a crack in the same way with my other foot.

It's pretty fun that the optimal sequence for sharing among two people was created by a pair of people.

Great video! I had never heard of the Thue-Morse sequence before. I like how you showed the sequence arises in many different areas. Fascinating.

This should be used to distribute players in ranked matchmaking in games.

@jmarkellos

7 жыл бұрын

Prophet and every gym class in the world.

3:53 nice overdub of 'even' for your 'odd' mistake Matt

I became accidentally obsessed with the Thue-Morse sequence as a teenager, and wrote pages and pages of it (using 1 and 0) into notebooks. I learned years later that this is actually quite common, many people get obsessed with Thue-Morse long before they ever know what it is or what it does.

5:20 also the Feynman point at the 762nd decimal place :)

@SoI-

4 жыл бұрын

999999

I'd love to see this worked out with a randomly generated list of "values" to see how well it works with normal and skewed distributions.

The Thue-Morse sequence is a good way to put players onto two teams. First, put the best player on team A and the next-best player on team B. If a third player then joins who is the worst so far, but them on team B. If a fourth player who is the worst so far, join them into the game by adding them to team A. (Shuffling may be needed if players don't join the game in decreasing order of skill.) The next players go to B, A A, B, B, A, A, B, A, B, B, A, and there you have 16 players.

@zilvarro5766

3 жыл бұрын

Even if we did it like that I would still have been picked last back in school :D

@ElZedLoL

3 жыл бұрын

Btw this is how drafting works in many video games. Picking 10 champions in dota or LoL for example

3:51 - Dat dubbing is so good. SOOO GOOOOD! :D

Oh my god, I have this problem where I'm always doing thinking and acting on these types of patterns, but I thought it was too weird to be common among other people.

@pupnoomann7866

8 жыл бұрын

I just clicked on "answer" with my right index finger on the touchpad, then two times with my middle finger, then with my index finger again, middle finger, index finger, index finger, middle finger. I do those things since elementary school. You're not alone.

Lmao I discovered this sequence like when I was 8 or something. And that is the power of overthinking

I also 'discovered' with this sequence when I was 7 y.o. or so and became slightly obsessed with it. *very Very obsessed. Til today I sometimes knock on tables with my left and right hand alternating in the Morse sequence.

@big0bad0brad

3 жыл бұрын

Don't feel bad, even some computers are irrationally obsessed with it - x86 processors calculate a parity flag after ALU operations that represents what he described in the video as whether there is an even number of 1's in the resulting number or not. It is extraordinarily rarely used, but it's there. Imagine thinking about whether it's an A or B number every time you do a math operation on some numbers.

Lol at 3:50 he clearly says "Odd" with his mouth but then dubbed over it with "Even". Kudos to him for making it so smooth in the audio!

3:52 Haha, that had me in stitches for a bit, so unexpected. Every [odd] EVEN!! position....

Dear Matt Parker. This video has inspired my first ever research paper. I generalized the idea of sequence of turns for sharing resources to any number of entitys more than just 2. Thank you so much for all your content, truly!

I personally think that Matt is going to make his own sequence with amazing properties which maybe makes his own face out of that sequence.

Thank you for this video. I discovered this sequence about four years ago and noticed it had some neat properties and kept popping up in unexpected places, but I never knew it had a name or any sort of a history.

What.. I literally came up with this sequence on my own one day when I was bored in my bedroom. I never realised it was already a sequence

"The winner takes it all" - who saw that Abba reference coming? :)

I already discovered some of the mathematical properties of this sequence as a small child. Great to see a video about it >10 years later!

Thank you so much for this! I have been obsessed with this sequence since I was in elementary school. I would walk home from school and try to be fair to my feet by going right left left right left right right left left right right left right left left right. I tried to explain to friends and family that it was the fairest way for 2 different teams to be distributed in terms of scoring, like team a gets 1st and 4th, team b gets 2nd and 3rd, so both teams are as fair as possible, and that it only gets fairer with larger teams especially when the amount is 4^n, n an integer. As a stress relief I always try to carry the sequence in my head as far as I can going up down down up, down up up down, down up up down, up down down up, down up up down, up down down up, etc... I had no idea this was a famous sequence, it's been a pattern that's been my friend since I was a child that I've never been able to explain to anyone properly or show them why it's so interesting. You have no idea how happy I was to see this even from the thumbnail, I instantly recognized ABBABAAB as the pattern I've spent so much of my life playing with.

Holy shit, that sequence I've been thinking about for years actually has a purpose, like I expected. I felt excitement being overtaken by sadness that I wouldn't be able to be the first to make that discovery anymore.

Actually used this the other night when the kids were fighting over some badges. It worked really well.

I thought of this pattern when I was like 7 but I didn't know that's an actual thing!!! Man, that video just made my day, made my week, made my life worth a little more.

This is so interesting to find a video of something I've been thinking about my whole life. I was always wondering what the fairest order to tap my toes in class was and came up with the same sequence. Easy to write it out on paper, but hard to keep track in your head.

1.- There is a fold in the black background. 2.- Once again, awesome video, thank you. 3.- By the time I'm writing there are 491 likes and no dislikes. It is awesome how it happens in every single one of your videos. They are amazing. Thank you again.

What I find most interesting, and extremely useful about this is the binary integer parity values generating the sequence. It’s obvious in retrospect, and makes it trivially easy to generate his sequence for any given length.

What a fantastic way of describing this concept! Thank you for making interesting videos

What I like about the binary way of coming up with this sequence is that it doesn't depend upon knowing previous instances. With the classic wait of splitting things of A-B-A-B, if you were to go to the pup the answer of who gets the drinks this time is simple... you answer the question of "Who got the drinks last time?" but without the binary way of coming up with the fair sharing sequence you don't have an easy answer to that question. You would need to keep a log book of all the previous times the two of you have considered the question of who got the drinks last time. With the binary way though you just need to keep track of how many times you've gone to the pub. So much easier.

Back in junior high I developed this sequence as a drumming warm-up that would never repeat (RLLRLRRLLRRLRLLR...). Years later while playing with math, the sequence came up while I was experimenting with continued "vertical" fractions, like ((1/2)/(3/4))/((5/6)/(7/8)...). The simplified form would follow Thue-Morse for which numbers wound up in the numerator and which in the denominator. Even better, these fractions would converge to nice numbers. The preceding example equals root(2)/2. Suffice to say, this was totally amazing to me and Thue-Morse has been my favorite sequence ever since!

Another fractal - If A's are zigs and B's are zags, you get the Dragon curve

@YambamYambam2

4 жыл бұрын

Yes I noticed this too! :)

Great. Thanks Matt. Now my wife is in the kitchen making dinner, shouting "I go you go you go I go you go I go I go you go!"

What about when you have ABC and more? Because I rarely go to the pub when we're only two people :p Nice video btw ^^

@MrCreeperX

8 жыл бұрын

+LazyMasterGamer Heyo! Always nice to see people from other parts of the community watching maths vids :D

@jayjoshi9834

8 жыл бұрын

+LazyMasterGamer +standupmaths I am not sure but according vidio i want to say, assume a=ABC;b=BCA;c=CAB then this sequence should be abcbcacab....=[{ABC}{BCA}{CAB}][{BCA}{CAB}{ABC}][{CAB}{ABC}{BCA}]..... NOTE:Brackets are only for better presentation it is not really exists(ghost Brackets}

@LazyMasterGamer

8 жыл бұрын

Mr_Creeper Maths is love, maths is life! :p

@LazyMasterGamer

8 жыл бұрын

Jay Joshi thanks ;)

@KarolKarasiewicz

8 жыл бұрын

+Jay Joshi I'm not sure - I'm bad in math at all. But I believe there are 3!=6 combinations of three participants. I think, but I can't proof it, that I have to have k^k goods (e.g. numbers from 0 to k^k-1) to divide them into a k equal groups minimasing the sum of squared differences.... I've bootsprapped this formula for 3 thru 5 participants - it worked. But I don't have any proof for n participants.... It could be someone have found it?

Is there a generalisation for this for more than two people?

By the way, Matt, your theme song is brilliant!

I watched this when it released and I'm watching it again now. Good editing save at 3:52. Love you.

8:33 - "Fractal-i-ness." Thanks for teaching us all the correct technical mathematical terms for these things, Matt. XD

Thank you Matt, thank you for your work.

I figured this one out a long time ago via an OCD pattern: If I tapped something with one hand I'd have to use both hands to tap out four iterations of the sequence so that each hand did a fair amount of work (e.g. RLLR LRRL RLLR LRRL) before I could continue doing whatever it was I was doing. Occasionally the pattern appeared elsewhere like accidentally clicking a computer mouse or tapping my feet or closing one eye. I do it much less now though, it's not so much a compulsion as an easily ignored impulse :)

@kellangaming1108

5 жыл бұрын

SbAsAlSe HONRe I thought I was the only one who did this.

@OrigamiTwist

4 жыл бұрын

I do it too.

why am I not surprised a Norwegian was part of something fair.

All jokes aside, this has been a thought experiment of mine for a long time. I had no idea it had a name

This gives me inspiration to compose a piece of music that doesnt repeat.

Awesome video! I love how you are making them!

I used to tap this on the desk during school. So cool to know this other stuff about it!

That is one cool sequence! I solved the puzzle, though by adding the first and the last number so, that they add to the same amount with the second and the second to last one and so forth. The thing popped to mind, as I remembered the trick to sum a finite set of numbers such as {1,2,3,4,5,6,7,8,9,10}, in which one could add 1+10=11=2+9=3+8 and so on. I split the pairs into two groups,and the groups were equal, as they were supposed to, and, as it happened, their squares and qubes also added up to equals (when n

@ArtturiSalmela

8 жыл бұрын

+Artturi Salmela Oh, also, I spotted that the next group always had the previous group in it, and it could be used to build the new group (just like with a dragon curve!). And the second part of each group were also equal with the other groups second part (not sure about their powers, though).

Yooooooo a video about the sequence that I've had in my head for years and started counting up whenever I was bored

Mind blown...I was alwayd bad at math but watching these videos makes me wanna try harder to get bettet at math...amazing!

From 8:15 to 8:21, if you make the angle all 90 degrees instead of some being 45, doe this produce the dragon fractal? (The one where you fold paper in half a lot of times and then unfold)

Tfw the lighting intensity and colour keeps changing.

is there a solution for n number of people?

@xXsolar99Xx

8 жыл бұрын

+Linus Ilskens As explained in the video, with two people you have this: 1. Multiply the length of the list by 2. 2. Take the first half and leave it as it is (offset by 0). 3. Take the second half and switch everything (offset by 1; A->B and B->A). Extrapolating from this, you should get something like this with three people: 1. Multiply the length of the list by 3. 2. Take the first third and leave it alone (offset by 0). 3. Take the middle third and offset it by 1 (A->B, B->C, and C->A). 4. Take the final third and offset it by 2 (A->C, B->A, and C->B). The generalized form (with n people) should then be: 1. Multiply the length of the list by n. 2. Take the first n-th and leave it alone (offset by 0). 3. Take the second n-th and offset by 1. ... n. Take the second to last n-th and offset by (n-2). (n+1). Take the last n-th and offset by (n-1). Additionally, as +TheJman0205 said there's another easy way. With two people, like the video said you can just replace A->AB and B->BA every step. With three people, it would be A->ABC, B->BCA, and C->CAB. With four it would be A->ABCD, B->BCDA, C->CDAB, and D->DABC. The general solution, with n people, would be A->ABC...n, B->BC...nA, C->C...nAB, ..., n->nABC...(n-1). I hope that makes sense.

@brettbreet

8 жыл бұрын

+xXsolar99Xx In Settlers of Catan the sequence for four people (2 items each) is ABCDDCBA which seems fairest... With your solution: ABCDBCDA seems like B gets an advantage an D gets hurt!

@xXsolar99Xx

8 жыл бұрын

Brett Breet Yeah, this has a bias at the start, but it evens out within a few cycles and then remains fair. Or at least, more fair that most methods.

@NathanK97

8 жыл бұрын

+TheJman0205 using your abc idea ... i wonder if there is a fractal with left and right turns...

@icedragon769

7 жыл бұрын

Catan is a bit different though, because you are not simply selecting the position that you think is best, you are also strategizing and planning forward, the decisions that you make and the decisions that others make affect your future decisions. The Catan sequence is fair because, while A gets to pick the best position on the board, D gets to pick two positions that synergize extremely well, so there's a tradeoff of value, rather than a simple sequence.

I've always tapped this pattern since I was a kid. Somehow it intrigued me. I guess I know why now

I've always wondered how Matt ends up with such well constructed videos. Is it because he has an extensive knowledge of mathematics or is it because he spends alot of time researching each concept?

I used to do this all the time when I was younger! I would write down the sequence and just go through pages and pages continuing this pattern

I lost it at the ABBA joke! I was waiting for it, and wasn't disappointed. xD

This is actually relevant for picking teams in sports! On my favorite five-a-side football, captains end up choosing from a pool of 8 players. Sadly, I did some simulations (well 20,000 of them) for and found out that the difference between ABBAABBA and Thue-Morse is negligible for 8 picks (0,3% difference). But ABABABAB came out 40% biased towards the first team. Now, I'll go to the guys I play with and convince them to pick teams Thue-Morse style. Should be easy enough...

@YambamYambam2

4 жыл бұрын

Did they get it, and did it work (out) positively for your football games afterwards? :)

i like how he said odd but dubbed over the audio with the word even

I think this is the same sequence that drummers refer to as a 'paradiddle'. It's the sequence that allows the very fast drum beats that one hears in a drum roll, for example.

omg i watched this video a few weeks ago and just now i realised if you take the first 2^(n+1) terms of the sequence you get a fair distribution for any polynomial return function. This sequence is fair to any return function you can write as a taylor series. Every time you do A->AB, B->BA you are evenly distributing one of the terms of the taylor series

thumbs up for the most efficient mix rotation

More Matt and Maths please. :D

Laissez-faire sequence: A starts with all the objects in the pile. A lets B select two items in exchange for services. B doesn't get another chance to choose because C will exchange services for only one item.

This is a pattern I've used in music any number of times without ever knowing it had a name.

thanks for showing yet another beauty of math! ending up with snow flake absolutely amazing! love math!

I remember when I was young I used to make my friends take turns on the slide (among other things) with this sequence; never thought I actually came across something at all useful.

I figured out that this sequence existed, and that it probably never repeated (but couldn't prove it) maybe 10ish years ago, and I had no idea it had a name, or what it could be used for, but I got to it in a completely different way: Start with A, then B (I used 0 and 1, but whatever), then repeat the first half of the existing sequence, followed by the first half (B and then A), then repeat that same step over and over again. Every time the length is a power of 2, repeat the second half of the sequence so far, followed by the first, and the new length will then be the next power of 2. [AB|BA]➡[BA|AB] [ABBA|BAAB]➡[BAAB|ABBA] [ABBABAAB|BAABABBA]➡[BAABABBA|ABBABAAB] I just noticed that reversing the whole sequence so far also works for every second step, i.e., whenever the length is an even power of 2, the sequence so far will be a palindrome.

So, if I understand the implications of what you said (which come from the WHEN THUE-MORSE MEETS KOCH paper [Ma, Holdener 2005]) then it is possible to follow a simple path which is infinitely long and closed. Is this the only such pattern of discrete steps, described by a simple formula which has these properties?

"Say you're buying rounds in the pub" ...as hundreds of letters scroll by 😅

ABCD-DCBA-repeat for choices for "A, B, C, and D" scoreboard for all variations A: 4-5-9-10 B: 3-5-8-10 C: 2-5-7-10 D: 1-5-6-10 just end on an even variation and you will have a fair distribution between 4 people

4:30 - that reminds me of another way of putting it, `popcount(n) mod 2`. popcount or hamming weight is very interesting in the context of succinct data structures, which i suspect fellow math nerds would find interesting

If you write the sequence out in 8 columns and some finite number of rows (like at 1:42), is it just me or does the sequence read the same row by row as it does column by column.

@cube4923

3 жыл бұрын

Yea

omg thought I was alone in this the sequence would play in my head but for me, I eventually forgot it for a year or 2 then it came back and i haven't been able to get it out my head since. there's a new thing for me though I can't seem to go past a certain amount i remember as a kid pulling this sequence into the thousands but as i got older i wouldn't be able to do it for as long as I used to be able to. Now its permanently affected me to the point where if i walk up stairs and start with my right foot i have to start the next stairs with my left foot and I would also have to end off with the same foot as I started with. also another thing, for me when i was 3/4 yrs old i would also do it with sound most of the time. so i would go da-dee-dee-da-dee-da-da-dee but the pattern is still a little off with me because for me it started as being fair but grew into seeing how far i can go and they would be divided so i would have (I used 1 and 2 because it's an easy visual aid) 12 1221 1221-2112 12212112-21121221 1221211221121221-2112122112212112 my brain would automatically keep doing this and id just be sitting thinking of this sequence until there were thousands of numbers and I would end up losing track of them i was also at an age where i didn't know how to count past 100 so for a child to be able to keep track of thousands in their mind is a little weird for me But it could also end up like this for me 1221-2112-21121221-2112122112212112-21121221122121122112122112212112 anyways that's my story/issue/weird mental OCD game

funny story, when u was younger (still young lol) I would create patterns in my head using this sequence, I would do something like tap once with my pointer finger, twice with the middle, then once with the pointer. since I had started with the pointer for the first set of four, I then started with my middle, then did two sets of those four, then one with the original four sequence, and then continue

I showed this video to another American friend of mine, all he had to say afterwards were, "What's a pub?"

I googled it and found out about the Prouhet-Tarry-Escott problem, though I can't find any more information relating to this specific case.

This is really interesting. As a kid, I constantly repeated the pattern "abbabaabbaababbabaababbaabbabaab" in my head. It just sorta stuck because it had a nice rhythm to it. I've been passively thinking about it lately, but didn't expect to learn that it was part of a well known mathematical sequence! I wish I could recall when I picked it up, because I'm rather curious as to how my young brain came upon it.

Yes I was right! I'm quite proud of that because when I first looked at the puzzle I thought there would be no way I could solve it, then I started trying to find patterns in which numbers go in which group and solved it in 20-30 minutes (I also had some problems with entering the numbers into my calculator incorrectly which means I spent even less time getting to where I thought I had the answer). Anyways thanks for the puzzle!

3:53 I like how his voice says the opposite of what his mouth says xD

"Do you just keep doing ABBA over and over again?" - Matt Parker November 2015

How come you have dropped almost 200 subs today Matt?

My jaw is dropping at 300.000 km/s. How can such a simple sequence have such interesting and diverse properties?

This is basically the same code as in the Huffnam optimalization, which you get from binary tree nodes ;) Interresting ;) I always create this sequence by that, this method (switching) is more simple ;) ;) I love it ;) ;)

Holy shit! I figured this sequence out when I was a kid. I was bored in class and tried to make a finger tapping sequence that was consistently equal.

At 4:14, where you're talking about counting the number of "1" bits in the binary number, that's a "parity bit", that makes the number of 1 bits up to either an even or odd total. There is a clever algorithm that can count the number of 1-bits (which is then easy to check for even/odd): en.wikipedia.org/wiki/Hamming_weight ... Some processors even have a built-in assembly-language instruction to do this count.

Is there a version of this for further people/bodies to divide between - e.g., ABC, ABCD, ABCDE etc., and are these each independent solutions, or is there a single solution where K can be the number of bodies to divide between, for example?

@im.empimp

6 жыл бұрын

from another post, see - "The Prouhet-Tarry-Escott Problem and Generalized Thue-Morse Sequences", by Ethan D. Bolker, Carl Offner, Robert Richman, Catalin Zara - arxiv.org/abs/1304.6756

I have followed ABBA sequence when picking cricket teams and that makes both people make cricket teams of equal strength. It's also known as "snake draft" as order reverses after every round

I have OCD, and every time I do something to an object and something to another (like tapping on a table with two fingers) I always think it's unfair how one object gets treated differently (it sounds useless, bit that's OCD). For this reason I came up with the sequence in my head, and every time I do something like tapping on a table I use this sequence.

Note about that chess anecdote: At least in the modern rules, that doesn’t apply. The threefold repetition rule applies nonlocally. There’s also a mandatory version called the fivefold repetition rule, and in at least one case, a game that someone resigned was later ruled a draw because the arbiter had missed a nonlocal fivefold repetition.

Is there a generalization for n parties? For example a string quartet (4 members) wants to decide in a fair manner which piece they want to study next. In which sequence should they be able to choose?