How Many Ways Can You Fold a Map?

[@santoast24]

This video is VERY important because it adds more, and perhaps so far the most conclusive evidence to the lore that the voice is NOT the Bird but rather they are two distinct entities

[@theminecraft4202]

it's called physics FOR the Birds, not physics BY the Birds...

[@hopperdown811]

Schizo

[@idontwantahandlethough]

@@theminecraft4202 well what if one assumes that it's most plausible that birds are best taught by their fellow birds? HMM? WHAT THEN?

[@tickaten]

​@@hopperdown811wtf are you on about

[@CrispyGFX]

I'm not convinced

[@TheBillzilla]

I was a pilot for many years and as you'd expect we use a lot of maps flying around the world. When they get folded too many times the corners start to fail, and the map starts to come apart. I flew with one clever chap who figured out how to get around this - He simply scrunched the map up into a ball when we were done with it, so the fold lines didn't get used all the time. Weird, but it worked.

[@Waccoon]

I guess that's why scrolls were invented.

[@tinnguyen5055]

Scrolls for maps is genius

[@bartrammeloo5046]

Scrolls for maps have a practical limit: the width of the map. They're also heavy,. So from a conservation pov: good choice. But usability? Not so much.

[@Tahgtahv]

@@bartrammeloo5046 You could fold and roll your map. Plus, I'm pretty sure I've seen scrolls that were only the writing material? Maybe some of them had block rollers on the ends, but I'm sure not all were that way.

[@TomasGradin]

Heresy!

[@ixiai8294]

Paper folding maths is one of those XKCD 1831 things that feel easy until you try them. Thanks for making these videos, I would have never heard about all of this without you.

[@Gaming1Doge]

there really is an XKCD comic for everything huh?

[@DukasFiguliras]

I can't believe I got the reference. Maybe I really am a giga nerd after all

[@Nate-bd8fg]

I HATE that I'm a big enough nerd to not have to google that

[@AdrianHereToHelp]

I can't believe you didn't mention the best part about "boustrophedon", which is that it's commonly translated to "as the ox plows", directly describing the kind of covering problem that's being solved by robot vacuums!

[@ovencake523]

isnt that also the description for how greek texts were written or something? left to right and right to left so your eyes dont have to jump back over a large gap each time

[@AdrianHereToHelp]

@@ovencake523 It is! "Boustrophedon" is the form of writing where, when you get to the end of the line, you just start from that end one line down and head back (including writing the letterforms backwards). That's where I (and most people) learned the term from - it's an incredibly interesting, like, "writing direction" that a language can have

[@deltamico]

So both lefties or right handed peeps will smudge their letters

[@AdrianHereToHelp]

@@deltamico Sort of! In most ancient examples, where boustrophedon writing is mainly seen, this was done when carving writing into stone, so that's not as much of a problem (and for some examples, like writing across a massive wall, you can see why someone would want a system where you don't have to keep walking back and forth between lines). That said, there are some modern scripts that do actually use a boustrophedon writing direction, such as Avoiuli (though unfortunately I'm not super familiar with that example).

[@impendio]

It comes from ancient greek writing in one direction and then flipping so the guy carving the rock wouldn’t have to go all the way to the beginning to keep writing after finishing a line

[@scarletbard6511]

Thank you for the wonderfu1 video as a1ways, Physics Bird.

[@deleted_handle]

1o1

[@1224chrisng]

1mao

[@user-qw9yf6zs9t]

did you lose the L key

[@scarletbard6511]

@@user-qw9yf6zs9t It's a reference to the video.

[@jaydentt]

homestuck

[@Canadian_Teemo]

Seeing the number of possible ways to fold a map, then I can finally rest knowing, I wasn't bad at folding the instructions manual and mathematicians also don't know how to fold a map.

[@Zippsterman]

Boustrophedon was a super oldschool way of writing, our Latin teacher had an extra credit assignment once where you had to transcribe using it. There are no spaces, reading direction changes every line as well as letters flip horizontally, and words that are cutoff at the end of a line are just continued on the next in the other direction. It's wild.

[@kaitlyn__L]

Oh, like the fairy language in Artemis Fowl

[@error.418]

As as survivor of 6 years of Latin, same. Also, for anyone else chiming in, the original term comes from Ancient Greek: βουστροφηδόν, boustrophēdón, a composite of βοῦς, bous, "ox"; στροφή, strophḗ, "turn"; and the adverbial suffix -δόν, -dón, "like, in the manner of" - that is, "like the ox turns [while plowing]". Yet another occasion of Romans "borrowing" from Greece.

[@ShankarSivarajan]

@@kaitlyn__L No, Gnommish spirals outward. (Well, at least _Classical_ Gnommish.)

[@kaitlyn__L]

@ clearly I haven’t read them recently enough, since I even forgot the species name :) I just remembered Artemis cutting them up into “normal” lines for his translation software.

[@DanK-d3b]

​@@error.418 bou-strophe-don ox-turn-like ox-turn-wise new words?

[@NomadicVoxel]

About that thing at the end about vacuum robot path-finding. My parents have had three robots I helped set up and fix. None really follow either of the path algorithms you suggest. - The first was an early Roomba, as far as I could tell it was completely random. Walk straight until it hits something, back up, spin around anywhere from 90 to 180 degrees either side, repeat. It didn't even have a smart way to find the charger, it would just turn off the vacuum but keep doing this until it could see the charger's beacon. Though it did have the spiral mode if you put it on a spot and hit a button, but it wouldn't get the whole room. - Second was a RoboMow. It was random too, but it would follow an "invisible fence" wire back to the dock at least. It also had a remote control like an RC car, buuuuut then they broke the remote control in the app and then never brought it back... - The newest is a Bissel wet/dry vacuum with a mop attachment. (I wonder how it knows what carpet is and where not to bring the mop?) It does attempt that zig-zag pattern, but it isn't perfect. It doesn't go parallel to the walls, it doesn't go all the way to the wall if it starts in the middle of the room, it doesn't really compensate for bumping into a chair and forgets what direction it was going in... But it's doing *something* right, when it mopped the kitchen I didn't see any dry areas except for where it couldn't reach.

[@johnfinkbiner3599]

The original Roombas used a random walk combined with a measurement of the average distance between collisions to estimate how long to run. There was no guarantee that the entire floor would be covered, but it was good enough most of the time.

[@deltamico]

A moving average would make sense in that case

[@thomasgreenhill2482]

The birds can SPEAK!? the plot thickens...🐦🐦

[@sethmusker6571]

The plot chickens

[@SaHaRaSquad]

The flock thickens

[@darkguardian011]

If I could give some constructive feedback? Lower/less harsh tones for the bird squeaking would be highly appreciated. It may be just me not jiving with the audio and not an issue with most other viewers though. Thank you for the wonderful video 💜

[@michaelf8221]

That pseudocode was clearly written with FORTRAN in mind IMO

[@pierrecurie]

It could be argued the other way around: fortran was designed to mimic pseudocode. As does basic and python later. If you ignore the {}, C/++ and java are not that different.

[@cinaeth83]

Hey all, stop what you're doing. There's birds doing physics

[@physicsforthebirds]

You guys are so awesome for watching these

[@cinaeth83]

@physicsforthebirds you're awesome for making them! I always look forward to your videos. Even if I think I have a general understanding of the topic, you somehow bring a fun fact into each one that no one else really talks about - which is usually the real world application of why a physics problem is important to solve. I kind of wonder if the map folding solution can also explain The Traveling Salesmen problem.

[@chixenlegjo]

Yeah, I know. We’re right here.

[@scarletbard6511]

@@physicsforthebirds "No _you're_ breathtaking!"

[@maxwelljennings4178]

who are they doing physics for? themselves? seems selfish...

[@not_David]

5:48 I don't know why, but something about this method of encoding the folds is genuinely beautiful to me.

[@kaitlyn__L]

I loved “higher-dimensional paper” being said so casually

[@blyan4g]

I adore his sense of humor. I still giggle about "Think back to the time when you were a single fertilized cell-a zygote."

[@pncka]

For the valuable contributions you have made to the flock, I wish you plentiful good and many shiny things.

[@higztv1166]

the kind of videos I watch youtube for, I'm always amazed at how silly questions like this one may lead you into a rabbit hole

[@auroreinara7322]

This was fun. I wonder if you posting this video will have a direct result of someone discovering the 8x8 number.

[@enochliu8316]

Will probaly do so.

[@DantevanGemert]

All you need is a couple people going "it can't be that hard", making a relatively efficient implementation and running it on a high end computer

[@Windeycastle]

My hands are itching to give it a shot, and see if I can get it running on a good server from my uni XD Just checked, and students can use our high-performace-cluster for free. Interesting... I first need to finish a graded project though

[@cipeman3498]

this feels like an incredibly easy problem for a gpu to do unfortunately i have no clue how to write in a gpu based programming language, nor do i know how to write asynchronous/parallel code lol

[@haskucy]

Ill be honest with ya, I kinda want to tinker with it a little bit. I gonna dive in, will update you guys later!

[@anindyaguria6615]

Absolutely fascinating! Love your content man, awesome balance with the technical details.

[@buchel3364]

There are videos that are very informative and interesting and then there are videos like yours. You make it very interesting and also cozy and cute at the same time. I don't only feel intrigued watching your videos, I feel comforted and good.

[@forever_stay6793]

Hooray one of my favorite niche channels that teach math with real world examples posted a new video!

[@eduardorodrigocayansanchez8824]

I'm so genuinely happy that you made a new video. Thank you and I'm sure it will be amazing.

[@fadran11]

and yet my dad always puts the atlas back together with perfect precision

[@qwfp]

Yet another W for the Meat Thinkers

[@deltamico]

You can reconstruct a fold from a O(log(creasts)) memory

[@breznknedl]

Your Videos are always such a pleasure to watch with all the detail you put in them, like the map as a background. Thank You!

[@MaloneDunlavy]

HURRAY! Another Physics for the Birds vid!!! seriously, love your content... I watch a lot of science/physics/math channels... yours is by far my favorite! :) Thank you!

[@christopherfaytvlarknsassi9013]

The approach I would take, if a map were a checkerboard (8X8) to be folded only along all the 7 horizontal and 7 vertical borders ("creases") that fell between two rows or between two columns (not that I would have any idea what "fold it along the line at its edge" would mean anyway), would be to try cope with the fact that you can't just assign unique numbers 1 through 14 to unique creases and then believe that there are as many ways to fold a map as there are to put 14 objects in an order. The problem is that if you fold along a crease that is one square inwards from a square, you've only eliminated one crease from all future creases to fold. But if you choose a crease that is two folds in, then you end up stacking the crease to its left on top of the crease to its right. They've become one possible future crease-location. You started out with 14 possible choices, picked one (eliminating it, leaving 13) but also eliminated 1 more future choices because two choices have merged to become one choice. So you have only 12, not 13, possible moves left. But this elimination of 2 choices applies only if your first choice is 1 inside from the edge. Start by folding a crease TWO from the edge, and you stack TWO remaining choices on top of two others. This means that you had 14 choices before you started, executed ONE of them, but not have only ELEVEN choices remaining. It seems to me that maybe it'd be easier to start with a folded map that shows only one checkerboard square when it's lying on a table (another square touching the table). What are all the possible results that can be achieved by unfolding only the last fold made?

[@sephdebusser]

These kinds of pseudocode are oftentimes just the _worst_ for readability. Once spent several weeks trying to understand a piece of pseudocode in a paper like this and it turned out to be just a heuristic search, basically a variation on A*, but it was so riddled with symbols defined five pages earlier that it was near incomprehensible

[@Metruzanca]

I love the pauses before the unit measurement. Reminds me of my favorite icarly quote.. "3, 4... maybe 5"

[@Y81715]

Hi Physics for the Birds Ornithologist and mariner here. Wrapping my head around the numbers, I got one question for you (had two until I started folding paper and numbering them myself this morning) 1 Cancelled question 2 At certain size there will be material constraints (yeh I get it, it's math), you can at least simulate paper thickness and yes is it a fold if the paper curls around in a tube? Ie. turning ratio for vacuum robots too. A fold is super efficient as technique, but if you travel on the edge of a fold, it is incredibly inefficient to not short cut edges. Ie. the moment we aren't in paper no more, how to estimate when to soften the waypoints? (Think rute calculation for commercial ships) just a thought

[@mikki429]

I recall seeing a news report about the young woman who developed an equation to find the maximum number of folds you can put in a piece of paper. She had to answer exactly the issues you raise in your second question.

[@peterirvin7121]

My roomba does not appear to follow a map folding pattern all of the time. When it reaches a new zone, it starts moving in a curve with a relatively large radius of curvature. The roomba will bump into an object and then turn with an angle that looks suspiciously like some fraction of the golden ratio ~137 deg. I have not measured this but I suspect the turn angle is irrational to prevent the roomba from getting caught in a repeating path across the floor and to guarantee that it will (eventually) cover every bit of area.

[@Marcel-yu2fw]

Wait, what does the "if" in the second line at 9:39 do? it tests if == /2 *2 !? How can that possibly make any sense?

[@physicsforthebirds]

It's not obvious, but this is an absurd way of checking if the number is even. It assumes that the programming language it was written in divides integers into other integers (so 5/2 = 2 and 5/2*2 = 4, not 5), which is NOT an assumption you should make while writing pseudocode!

[@timseguine2]

@@physicsforthebirds It is weird today for sure, but I wouldn't necessarily call it absurd. It is more or less exactly the rigorous definition of divisibility.

[@Marcel-yu2fw]

I guess it makes sense if the language used had limited operations, e.g. only +,-,*,/ and no %/"modulo" operator. But even in that case, just write a mod() function for it please.

[@Alceste_]

I, too, like to present "the following pseudocode:" followed by exact assembly implementation.

[@leave-a-comment-at-the-door]

@@Alceste_ at that time, that's how you wrote pseudocode. code was the literal numbers that you punched into your cards, your pseudocode was the equations your code is designed to solve.

[@K_Boar]

I'm not a fluent Java developer, but C++ (which I do know) tends to be very similar syntax-wise. Reading the code against the pseudocode reveals some shorthands: - The if statement in the second line will always be true, unless working with integers. That's why I think that the "delta condition", which involves a bitwise and operation, wraps the underlying logic that is equivalent to that seemingly useless if statement. That 'bitwise and' basically checks if the number is even or odd in binary, and acts accordingly, and the second line in the pseudocode seems to do the same check (even integers will be 'cleanly' divisible by two, but not odd ones, thus multiplying by 2 again and comparing with the original number). As I said, I don't know what each variable represents so I could be wrong. - From line 4 onwards, the developer used terniary operator syntax, which is very common in many programming languages and permits summarizing "if (condition) { doIf(); } else { doElse(); }" as "(condition) ? doIf() : doElse();", but in some cases (like in this one imo) can make it difficult for a programmer to read. - I'm not aware of what the p array is, but it seems that checking that "C[i][m]==p[i-1]" or that "m + bigP[i-1] > l" is the same as checking that both that last condition (m + bigP[i-1] > 1) is true and that "C[i][m]==p[i]" is bigger that "m+bigP[i-1]". Maybe there's some mathematical properties that make it that way, note that p[i-1] may not be the same value as p[i].

[@K_Boar]

TL,DR: The Java code should do the same as the pseudocode when working with integers, and the only line that's different is the last if on the pseudocode, which corresponds to the last line on the Java version (which is the one involving the "1 vs l" conundrum

[@colin3504]

I wasn't expecting the video to turn out how it did and it was super interesting!

[@YOUTY209]

In my experience, robot vacuums really limit the amount of efficiency in their route in favor of just covering areas many times over just to be safe.

I absolutely did not expect a video about map foldings to transform into the topic of my dissertation, coverage path planning :D Going to look up the paper right now :) Thanks!

[@jaspermcjasper3672]

6:35 - I'm really glad to find out that the On-Line Encyclopedia Of Integer Sequences keeps track of sequences of integers, but, further, I'd like to know if we have to buy it as a paper book or can we just find it on-line?

[@blackamaterasuflame]

12:42 never have I been more excited to watch my roomba clean.

[@mateoguerreroschmidt5278]

I really like your videos and these cool problems you always bring up. And i was wondering, how do you find these niche problems? Are problems that you already heard of or do you find them searching?

[@physicsforthebirds]

Many of my videos are things that I notice myself and then they turn out to be real problems, and many are things that I find while reading. This one was something I read about, I think I first got interested when I saw it on Wikipedia's list of "unsolved math problems". In any case, each of my videos involves lots of searching through citations and books and trying to solve things myself to get interesting examples. I always put the most relevant references in the description, so feel free to explore it yourself!

[@mateoguerreroschmidt5278]

@physicsforthebirds wow, thanks for answering! I didn't know about that page of Wikipedia but I will definitely look at it! I'm a Data Science student and it's gonna be fun trying to advance in some of these problems.

[@impendio]

As a hobby origamist, paper folding feels like this impossibly deep rabbithole with infinite knowledge waiting at the end. You can do so many things and it lets you visualize a bunch more, and in general it gives you an intuition of space that you wont find on digital media.

[@ZagRS121]

Love this channel, the topics you cover are so niche, but exactly the kind of interesting topics I wonder about!

[@HululusLabs]

I have a Roborock and my friend has a Roomba, both are pretty new, and the Roomba has the vaccum dock, so it should be a higher end model. The Roomba seems to always have a random pattern (although my friend says it has the house mapped), but the Roborock always circles the outline of each room and then fills it in with the Boustrophedon pattern (thanks for making me look this up). It even rotates the pattern and repeats if you have it do multiple passes. Obstacle avoidance is done with both lidar and the bumper, and it just moves around the object until it can resume the path.

[@Leander_]

Hi! Just wanted to say this was an incredibly charming video, very well presented. It struck a great balance between being too technical and being too general/wishy woshy with details.

[@basketcase77]

I actually noticed exactly what you were describing about my robot vacuum a while back. Really interesting to see the why and how of the decisions it made planning a route.

[@jiffylou98]

In 6th grade I asked my math teacher if you could math out origami patterns and he said "yeah, probably." I had never seen an honest reaction from a mathematician before then

[@ewmcrab]

I legit grt excited for this 🎉❤

[@pauljones9150]

I never thought this much about folds before. Thank you mr. Bird

[@HorseEmoji]

Yes, Mr. the Birds, I also enjoy Folding Ideas.

[@afonsomartins969]

Nice vid as always!

[@andrewchen6226]

Loved the bird looking unimpressed

[@gamingmeetsmath]

IM GOING TO MAKE THE FUNCTION, NO MATTER WHAT IT TAKES

[@petribalanceisnice]

Im so happy you are back

[@kamo7293]

4:43 birds like "how dare you ruin my tangent"

[@PhyMath2]

i absolutely love content like this

[@matthewse2882]

Super neat video! Last year I also got interested in enumerating over (and visualizing) all closed meanders - which have a one-to-one correspondence with open meanders (the 1D stamp folding case but the stamps aren't labelled). Highly recommend checking out the paper "A Fast Algorithm To Generate Open Meandric Systems and Meanders" which I used for my Python implementation. It has some nice diagrams and the pseudo-code is a bit easier to comprehend (though still pretty complicated).

[@ares395]

It is absolutely hilarious to me that the paper might be wrong in this specific place for so long

[@Whatalunatik]

The outro music is wonderful! did you write it?

[@physicsforthebirds]

Yep, the music I use is mine, made for these videos. We'll see if I ever release it alone.

[@Kwauhn.]

Lucida Console is by far the best monospaced font. I used to be a Courier stan, until I realized that readability was trash compared to LC. LC just works better as a vector font, and it uses sarifs in the best way possible. As a plus, it looks better on modern IDEs, and is less grating on they eyes somehow. LC FTW.

[@MatthijsvanDuin]

7:45 uhhhhh, no? Are there actually programmers who would voluntarily use such a font? I'd consider the ability to clearly distinguish between 1, l, I, and | (and also 0 and O) to be a pretty basic and essential feature of any decent font used for programming

[@WindyHeavy]

babe wake up new Physics for the Birds upload

[@CurlBro15]

Hi, this was another great video! I am curious, so the problem seems to be set up in such a way that one would expect todays computers to be able to compute the number of folding for more n than was previously known in the 60’s. However, through the process of trying to get a modern computer to solve the problem, your code wasn’t able to run properly. If you were able to get your code to run properly do you think this would output more values of map foldings for a given n?

[@physicsforthebirds]

My code, which was based off of Sean Irvine's code in the description, did work. Sean used this code to calculate up to a 7x7 a few years ago (and the original paper in the 60s calculated up to 5x5 if I remember correctly). He might say somewhere what hardware he ran it on, but I wouldn't be surprised if it was his personal setup. If people dedicated more advanced hardware to this problem for some reason, I'm sure they could do better, but there are many, many sequences of integers that need to be calculated!

[@enochliu8316]

@@physicsforthebirds Sean Irving version is based on a C implementation by Fred Lunnon, the original paper author, which is corrected from the paper.

[@sodiboo]

13:00 this reminds me of the punchline at the end of the intro to Dylan Beattie's "Art of Code".

[@user-.--.-]

fascinating vid. i always assumed there would be an equation about combinatorics, but i learned something new :)

[@iquemedia]

1oved this one now l wanna see someone compute 8x8 on a DS

[@acidnik00]

Since we're talking about folding maps, there's a specific way of folding a map that prevents it from tearing at the creases, it's called Miura fold, you should check it out. It's even used to fold solar panels of spacecrafts!

[@topherthe11th23]

10:55 - I wondered for a long time what a "booster-feed-on" pattern was. It turns out it's "boustrophedon". The boustrophedont was some kind of big powerful dinosaur, that, as you can guess from the "dont" ending its name, has a distinct kind of tooth. Cavemen had to use this dinosaur for plowing because the ox wasn't domesticated (or maybe not even evolved) yet. (A lot of Indo-European words for "ox" come from a root "bos" that is named after the boustrophedont). The boustrophedonts always wanted to get the plowing done as fast as possible, and so turned around at the end of a row and pulled the plow over the next row walking the opposite direction as they had just walked to plow the previous row. There were some scribes in the ancient Mediterranean and Sumerian worlds who, rather than carving or writing every line always left to right, or always right to left, wrote every-other line left-to-right and the other lines right-to-left, like an ox or dinosaur plowing a field, turning around and going the other way rather than always going back to the same end of a line or row. There's no example of an ancient Assyrian typewriter where the end-of-line lever makes the carriage go all the way back to the beginning for the next line, instead of just reversing the gearing and typing the next line in the opposite direction. This way of writing back-and-forth is known as "boustrophedon".

[@FllamingBarfiYT]

I think the roomba problem the way you described it, can be compared with maze generation or snake bots. Code bullet made a video about snake, where it follows a hilbert-like path (iirc) and then chooses shortcuts to get to the apples faster. The maze algorithm I saw (in another video) started with a space filling path, and then changed some paths into walls and vice versa semi-randomly.

[@thestudentofficial5483]

Tom Scott showed the origami they used for spacecraft solar panels that only take 1 axis to fold/unfold. It's quite genius for a quick map

[@CartoType]

When I was a Sinclair Spectrum programmer in the 80s I always had variables called i and o, equal to the constants 1 and 0 respectively. That was because numbers, even single-digit ones, took up 5 bytes of memory each, while single-letter variables took up one byte each. Yes, my programs were hard to read, but at least I didn’t use SGN PI for 1 and NOT PI for zero.

[@felipemldias]

The bird sounds like a whole flock combined. Like a meta-consciousness running on several birds at the same time to speed up the computation necessary to contribute to this video.

[@nujabraska]

I get so excited when I see a new bird upload

[@mateusvmv]

@9:33 C[i, m] = p[i] > m + P[i - 1] > 1 what even is the operator precedence in this how did p[i] become p[i-1]

[@19Bruno96]

Physics bird os still around, I can rest easy

[@Koroistro]

I'm sure there's a graph somewhere. Also it weirdly reminds me of vector multiplication, idk why. Now I started to think about how this would scale in N dimensions, damn

[@ShinSpiegel]

Thank you very much for the video. It’s a surprisingly interesting topic :D

[@bashkillszombies]

This is why you take the gigachad approach. Scrunch it into a ball and throw it into the back seat.

[@sahasananth987]

Hello, the code @9:35 makes sense to me and seem to be equivalent. I am confused about only one if condition (the hardest one perhaps lmao). This is how I understand the code: "delta = c[i, l] - c[i, m] d[i, l, m] = 0 if m != 0 then if delta is even then if c[i, m] is 1 then d[i, l, m] = m else d[i, l, m] = m - P[i-1] else if c[i, m] == p[i] > m + P[i-1] > l then #this is the if condition I only partially understand lmao. d[i, l, m] = m else d[i, l, m] = m + P[i-1]" My best guess for the if condition is there must've been a typo lol. What do you think? Cause if they f-ed up 1 and l then they can do a mistake like this too? Edit: I am a robotics masters (hopefully a PhD student soon) and cleaning robots are dumb af. Most of these papers are just for cases when you want to try out a new algo for funsies. That being said some companies do have fancy algorithms. PS, I think you have irked my curiosity and I think you have gained a subscriber. Hoping to see more cool videos from you!

[@leave-a-comment-at-the-door]

I think you mean piqued, not irked. very different meaning

[@LiamHighducheck]

This video got me thinking about folding things

[@koniginator]

Single character copy errors can plague us in biology papers too! I was iterating on an idea regarding reverse transcriptase enzymes (like the one used by HIV) that had been studied in depth in the 90s and kept getting confounding results until I found that the published sequence of an inhibitory aptamer (synthetic nucleic acid sequence) was missing a single base. It was depicted differently (correctly, i believe) in a drawing but transcribed in a table incorrectly.

[@azuln.3765]

You are my favorite part of the internet

[@AnastasiaSpangler]

My roomba goes in an up and down path like the first idea in the gardening illustration. Also, when you look at the internal map that the roomba produces after each clean, it is tiled.

[@timotay22]

Randomness seems to help in the actual real world for problems like robot vacuums that need to visit all points. Many use an algorithm like “go straight until you hit a wall, turn a random amount in place, then go again.” Deterministic path planning can break; if you get stuck a little bit, then you lose the whole process. Randomness gives robustness of having a chance that all points would eventually get visited even if your measurement or process gets disrupted.

[@SgtSupaman]

That works well enough in the real-world application, but the problem of trying to visit each spot once and only once would be virtually impossible with random direction selection. Moving about randomly is inefficient as it will cross the same areas multiple times and could take a very long time to hit every area (the more areas it's already touched, the less and less likely it becomes for it to get to untouched areas).

[@savagesarethebest7251]

10:52 Boustrophedon: As the ox plows.

[@zealotoffire3833]

13:06 i would never call a variable a single letter so dw no "l"''s for me

[@basketcase77]

Single letter variables are pretty common, x, y, s, t, i... And there's nothing wrong with using them, as long as they're distinct. That's the issue. Plus it's easier and less hassle than worrying about specifying it's not a string or something.

[@zealotoffire3833]

@ i know, just my personal opinion

[@Kwauhn.]

This feels exactly like the problem of finding an equation for prime numbers. Each additional step, whether it be the construction of the number line or a valid fold pattern, seems to add a new "fundamental" property to the system that can only be checked algorithmically with some O(n) that is greater than linear.

[@murffist]

"Boustrophedon" is an ancient Greek word and means zigzag. Actually, it means "like the ox plows" and describes, especially in epigraphy, a way of writing where the first line is read from left to right and the second from right to left. What is it good for? If a text is written on a long wall, you only have to take half as many steps to be able to read everything. Fun fact of the day!

[@durarara911]

The variable being lowercase "l" is the plot twist I did not see coming. :'D

[@lordrusk6118]

5:06 wrong. That fold is described by another method, which gives the same end state, but does not include the fold described (folding inside a pre existing fold) - this simplifies calculation heavily.

[@theorixlux]

A bird complaining about monospace l's and 1's in a map folding video talks about snake for 1/10th of the video. XD great video!

[@happily_blue]

great. now I'm gonna spend all night figuring out how to fold a map into a spiral

[@aaronsantos4675]

These are always great!

[@Asterism_Desmos]

HES BACK!

[@TheLurker]

At 9:02 -- this line only makes sense if the comparison is `m + bigP[i-1] > l` rather than `m + bigP[i-1] > 1`. To see why, note that `bigP` stores cumulative products and `bigP[0]` was defined as 1. `m`'s first value in the loop is 1, which means that the sum is bounded at 2. You would always wind up setting `d[i][l][m] = m` if you compared the sum of these variables to 1. Now, as for me, my reimplementation of this code in Python did not work initially because I didn't realize that in Java, the division of two integers is truncated (so that you only get the integer quotient). Anyone else trying this will need to replace the `/` in the Java code with `//`.

[@I.____.....__...__]

11:00 Boustrophedon doesn't mean zig-zag, it means "as the ox plows" as in plowing a field. Zig-zag has sharp points as the ends, boustrophedon has 90° turns.

[@ObsidianHoax]

that bird that goes ' C[l,a,w] C[a][w] '

[@digama0]

Regarding your "l" problem: this is exactly why I never ever use this letter in math papers as a variable and instead use the tex \ell symbol, which looks something like "ℓ", basically the cursive form. IMO it fits better with the other math letters anyway. I think we should try to use this style of ell more in monospace fonts too for distinguishability reasons.

[@blockshift758]

4:43 there is a pretty good way to fold into 3 without 2 extra folds. By rolling it.

[@sternmg]

Bang-on right! At first I thought "Isn't that just like guessing to jiggle a 'Z' fold just right?" But I realized you mean to roll up two turns _so that the ends line up_ before squishing. That is not only pretty good but-for infinitely thin paper-perfectly exact.

[@Acceleratedpayloads]

The insight that 2d paths are just folded string blew my mind.

[@tenix6698]

3:31 I feel like it can be folded without crossing itself in real lif even in the presented case atleast

[@d3vitron779]

Nuh uh, you’re gonna make an infinitely tight pinch point and disintegrate it into steam if you pull it through itself

[@rebelsy4134]

I don't know if I misunderstood this, but at 3:00 you say there's only one way to fold the paper in that leaf order, but there's an obvious second way to fold them in the example on the screen, too bad I can't post picture to show it, but you fold it to the other way after leaf 4 and then leaf 2 over leaf 3

[@leave-a-comment-at-the-door]

if I'm understanding your folds correctly, that would be labeled as 4123 -- you've flipped the stack over.

[@robinsparrow1618]

i can fold a map into a hilbert curve? i thought the point of folding was to take up less space, not fill it!

[@SaHaRaSquad]

Another example could be a 3d printer doing a layer's solid infill pattern. The nozzle needs to move back and forth filling the area, but it has to fit within the 2d shape of the layer and you want to minimize the amount of time the nozzle travels without pushing out filament.