Ayliean has kindly hand-drawn a selection of stitch patterns as prizes of Patrons - find out how to win one here: www.patreon.com/posts/59579953
@vonantero94583 жыл бұрын
So when are we getting the shirt with the pattern stitched? ;)
@asheep77973 жыл бұрын
@@vonantero9458 probably in a couple days
@internetsydney3 жыл бұрын
For those curious, hitomezashi [一目刺し; ひとめざし] is a Japanese sewing technique. "Hitome" means "one stitch" and "zashi" is a nominalized form of the verb "sasu," meaning to sew or stitch. It's a kind of sashiko [刺し子; さしこ], which, as Ayliean MacDonald states at 10:19, is a traditional form of decoratively mending clothes, and is also used in quilting.
@niismo.3 жыл бұрын
How do you know this?
@MrEst973 жыл бұрын
Thank you, I hadn't learned the verb 刺す yet
@jamtea5733 жыл бұрын
@@MrEst97 It's the same kanji that you find in Sashimi (刺し身), so you'll often see it there. It can be used meaning slice/cut/stab/sew, there's quite a few meanings depending on the compound/context you find it in.
@internetsydney3 жыл бұрын
@@niismo. I speak Japanese and I live in Japan :D
@TheDirge693 жыл бұрын
Thanks mate!
@AKhoja3 жыл бұрын
There's something so beautiful about seeing larger patterns emerge when generated by randomness
@vigilantcosmicpenguin87213 жыл бұрын
@@Atamask Yeah, and there's also the psychological instinct where we're comforted by familiarity and excited by novelty, so it's just the right balance of the two.
@WestExplainsBest3 жыл бұрын
A blended class of geometry and art should be taught at the secondary level. It would be extremely intriguing and engaging for students!
@revimfadli46662 жыл бұрын
@@WestExplainsBest along with 'practical creativity', showing that technical minds and creativity aren't mutual exclusives
@motherisape2 жыл бұрын
no can't see any patern in randomness
@plackt3 жыл бұрын
Everyone talking about proofs for two-colourability while I’m here wondering how 0.5 wasn’t the intuitive/obvious answer to “most random pattern”.
@VinceOfAllTrades3 жыл бұрын
Same. That's why I came to the comments.
@alexanderwatson98453 жыл бұрын
I agree but I guess that goes to show how different people's intuitions are
@reidflemingworldstoughestm13943 жыл бұрын
Funny, I thought the .5 probability _was_ the obvious pick for most random.
@PhilBagels3 жыл бұрын
That's exactly what I was wondering. How could anyone think that a 0.9 probability would be any more random than a 0.1 probability? And likewise, isn't it obvious that a 1 probability isn't random at all (just like a 0 probability)?
@mr.cheese56973 жыл бұрын
If we shift the whole pattern by 1 unit, all on's will be transformed into of's, and other way around, but since it's the same pattern, chaoticity will stay the same→ Chaos([A,B])=Chaos([B,A])→ Chaos([of(.9),on(.1)])=Chaos([on(.1),of(.9)]) In other words there is no difference between those two patterns.
@trombone_pasha3 жыл бұрын
Ayliean is very cool! Would be happy to see more videos with her.
@tbpotn3 жыл бұрын
Every region always has only 1 region on its outside, that's why it's always two-colourable. As having two regions around it would require an intersection of 3 dashes, but only 2 dashes intersect at every point.
@juanignaciolopeztellechea94013 жыл бұрын
Good proof!
@MitkoNikov3 жыл бұрын
It would be cool to be able to approximate the number of components...
@martimrocha90673 жыл бұрын
That is not a proof. If you placed the lines however you wanted, you could create 3-colourable images, eventhough there are still 2 dashes intersecting at each point. That's because it has nothing to do with the number of dashes intersecting, since each kndicidual shape can touch others in different places
@juanignaciolopeztellechea94013 жыл бұрын
@@martimrocha9067 ohh, right.
@HarzemTube3 жыл бұрын
@@martimrocha9067 you can't create a non-2-colorable map if you don't have three dashes intersecting on a point. That's a basic requirement.
@tqnohe3 жыл бұрын
During the shut down I learned to knit. I can totally use this to design patterns. Live it.
@osmia3 жыл бұрын
I'm a knitter and crocheter and that was my first thought also :-)
@rfldss893 жыл бұрын
Im so eager for my next pair of jeans to rip so i can create a random mending stitch pattern.
@5thearth3 жыл бұрын
Saw a thing recently, someone calculated you could knit a Doom installer in about 3300 square feet (~300 square meters)
@osmia3 жыл бұрын
@@5thearth what is a doom installer?
@bordershader3 жыл бұрын
@@rfldss89 overlay the rip with new fabric (cut to shape if you prefer, use same or contrasting fabric as you prefer) then use the stitching to go through both layers. Use proper silk thread for strength. In Sashiko mending, you use a really long needle so you can do a long line of running stitch on one go, it really does help (look up videos on here). The repair really is pretty tough and looks fab. Enjoy!
@smallishkae3 жыл бұрын
Textiles and fibre crafts have a surprising amount of mathematics baked into them and I love seeing maths nerds come across interesting ways it’s been applied.
@SuLokify3 жыл бұрын
One of the first "computers" was an automatic loom.
@WestExplainsBest3 жыл бұрын
A blended class of geometry and art should be taught at the secondary level. It would be extremely intriguing and engaging for students!
@Triantalex11 ай бұрын
false.
@HPD11713 жыл бұрын
the proof for two colorable is very simple. in order for the map to require three colors at least one vertex would need three lines connected. since lines only are drawn from two directions at each coordinate and every line segment is always preceded and followed by a space then at most and exactly two line segments can ever touch at any vertex. this means that no region will never touch more then one on its border.
@ShankarSivarajan3 жыл бұрын
Huh, that _is_ trivial. Thanks.
@floyo3 жыл бұрын
I don't think it's that simple because your first statement is not trivial. It doesn't generalize to higher numbers for example. A map that requires four colors does not necessarily have a vertex with four lines. In the video there are many examples using the hexagonal/triangular patterns.
@AngryArmadillo3 жыл бұрын
I don’t think this is correct. The relevant transformation is to create a vertex for each connected region of space, and an edge between two vertices if those regions are adjacent. Also, your first statement is incorrect. There are plenty of 2-regular graphs that are not 2-colorable. Take any odd cycle for example.
@lonestarr14903 жыл бұрын
@@floyo They never claimed it would generalize to higher numbers or other patterns. And while it's true that a map which needs to be colored in four colors doesn't need to have a vertex where four lines meet, it is in fact the case for three-color-maps. If I'm not completely mistaken, that should be equivalent to the Venn diagram problem (you cannot draw a complete Venn diagram with four circles).
@lonestarr14903 жыл бұрын
@@AngryArmadillo Can you do an odd cycle in Hitomezashi stitch patterns?
@captplanet86883 жыл бұрын
"I didn't come here to spell" - might be the most mathematician thing I've ever heard
@Luca_54253 жыл бұрын
She is back!!! She is soooo coooll, bring her back pleeeassee!!
@0brokeJaw Жыл бұрын
You just got to take the "L" on this one
@Luca_5425 Жыл бұрын
@@0brokeJaw wut? Outta nowhere, why that bud?
@0brokeJaw Жыл бұрын
@@Luca_5425 Your profile pic is an "L."
@Luca_5425 Жыл бұрын
@@0brokeJaw fair enough
@Triantalex11 ай бұрын
??
@SometimesDrawings3 жыл бұрын
This is an opened door to a branch of knowledge I knew nothing about, and is mild-blowing. Thank you!
@mtranchi3 жыл бұрын
9:20 Ah nice little editing trickery. I was like, "that ain't the mirror of the first one." Then through the magic of editing (at 9:42), the last one turned from P(on)=0 to P(on)=1
@ThisIsStapes73 жыл бұрын
Was about to comment the very same.
@Bronzescorpion3 жыл бұрын
Spotted it as well.
@scottmansfield21972 жыл бұрын
Was here to say the same.
@WolfRose113 жыл бұрын
When you catch that she wrote the same thing as the beginning at 9:40 but drew what she intended. They must have noticed because they switched paper a few seconds later to the one with P(on) = 1.
@DaleHawkins3 жыл бұрын
Thanks!
@alecj34543 жыл бұрын
Ayliean is such a good explainer. I love her appearances. This was a fun one.
@user-el4np5xt8c3 жыл бұрын
Love the accent!
@AB-Prince3 жыл бұрын
each vertex has only two edges (in the square arrangmeny) meaning there is no point where three edges meet, thus no point where three regions meet, therefore every arangement must be two-colorable
@tudibelle2 жыл бұрын
Thank you for this, I love patterns and embroidery, it is so nice to see these two brought together, and I love that I can use them as a physical representation of words. Going to have a play with this 🥰
@liamogrady58683 жыл бұрын
This brings the idea of naming your clothing to a whole new level
@_wetmath_3 жыл бұрын
this is some vihart stuff right here, amazing
@Shad0wLucky3 жыл бұрын
9:43 Sneaky edit (fix) on the mistake of writing P(on)=0 and P(off)=1 ;)
@padenzimmermann18922 жыл бұрын
I made one of the golden ratio and my siblings names. Loved it thanks :)
@HontubeYT8 ай бұрын
I used to make these patterns using my friends' name and found some patterns. Now I practically have degree level knowledge in these patterns. Also I can take any pattern of my choice and convert it to hitomezashi code (literally any pattern)
@everydaykronicler99743 жыл бұрын
I'm so happy that you started your fourth ISO with the exact same writing as the first and then after you had begun adding the third axis we get a jump cut to a different ISO with the correct writing 9:41 and 9:45
@gizatsby3 жыл бұрын
Aaa! I've been following her on TikTok for a while. Great to see her on this channel
@KaiKunstmann3 жыл бұрын
4:03 On an infinite plane, every node in this construction always has exactly two edges (one vertical, one horizontal). Both edges part the local region around a node into two areas. Every string of edges must either be a closed loop, parting the plane into "inside" and "outside", or it must be an infinite string, parting the plane at infinity into "this" and "that". There may be multiple closed loops, multiple infinite strings, and even nested loops, all of which still have exactly two different colored sides of their string of edges. The necessity for three colors can only arises from nodes with an odd number of edges.
@whofan12123 ай бұрын
im a mathematics student going into third year, im actually just looking into repairing some jeans with sashiko stitching, so this is a fun rabbit hole
@TwoCherriesIns3 жыл бұрын
I love the combination of art and math; this video is amazing.
@sethgilbertson24743 жыл бұрын
Oh man, I LOVE this! I love playing with math in ways like this!
@TheAstronomyDude3 жыл бұрын
I love it! I hide my passwords in plain view as artwork and this would look great. None of my guests have ever asked me if there is any significance to my geometric statutes or my chaotic wallpaper.
@xyz398083 жыл бұрын
does your office also have secret doors that activate when you pull a certain book?
@NogueiraVini3 жыл бұрын
Its beautiful! Reminds me of the amazing embroidery of Peruvian elders Shipibo Conibo. Incredibly detailed, handcrafted patterns inspired by shamanic visions of Ayahuasca
@michaeldeierhoi40963 жыл бұрын
Very cool. This ended up being complex yet with an underlying simplicity.
@iamavataraang3 жыл бұрын
Yet another way I can enjoy using spreadsheets
@BinaryDash3 жыл бұрын
This is by far one of my favourite channels
@lindsey30382 жыл бұрын
This would be a really cool way to design a crochet pattern. Kinda like a temperature blanket but more pretty. Now to start another WIP lol
@wobaguk3 жыл бұрын
Im wondering what happens to the average of the shape size (if a square or triangle is 1) when the probability changes, is it constant for sufficiently large grids because as you make a big shape you break others? Or is there a peak around max randomness. I guess number of shapes per starting area is basically the same question just the inverse, because fewer shapes mean bigger area.
@hurktang3 жыл бұрын
Yes it seems like, given a big enough distribution, the mean size of the less common color will tend toward the more common color when the randomness is maximized. I was observing the same thing.
@biggiemac423 жыл бұрын
Yeah this is the question I'm most left with by this video. During a numerical methods in physics course I took, we had something similar with porous materials. A phase transition when the probability a cell is empty gets high enough, when you go from it being nearly impossible to find a clear path from one edge to its opposite, to it being nearly certain. I imagine something might apply here that is similar
@SaveSoilSaveSoil3 жыл бұрын
Yup! It's hard not to think of the Ising Model.
@danielemazzali98103 жыл бұрын
4:05 It's Always 2 colors because to have the Need of three colors there should be an intersection point with at least three edges. This never happens. For every point there are always exactly two edges. So you'll never need a third color.
@presbarkeep3 жыл бұрын
what if its plotted in 3 dimensions, X, Y, Z?
@danielemazzali98103 жыл бұрын
@@presbarkeep Idk, i've only ever studied plain graphs xD I don't even know if this pattern would still be duable. But if it is i'm pretty sure you'll always would have to use only two colors, because to need a third you would have to have an intersection point with four edges, and in the pattern every node would have 3 and only 3 of them.
@myvh7733 жыл бұрын
There are graphs which vertices all have degree at most 2 that are not 2-colorable. For instance, an odd cycle.
@danielemazzali98103 жыл бұрын
@@myvh773 Oh yeah. But here we are coloring regions, not nodes. I used a bad terminology i guess...
@darreljones86453 жыл бұрын
I just LOVE Ayilean's Scottish accent!
@ultrakatiz3 жыл бұрын
I used to doodle those on my notebooks, although with a different method. I would draw a rectangle with two relatively prime numbers as side lengths, and then draw a line making a 45° angle with the sides starting from a corner, going on / off whenever i hit one of the sheet's small lines. It is important that the two numbers are relatively prime, or else you will finish in a corner without passing through all of the diagonals. I never bothered trying to find if each pair of relatively prime numbers give a unique pattern or not, but it could be interesting to prove or disprove.
@nemecsek692 жыл бұрын
Have you got an example somewhere to see? I don't understand the algorithm and very curious about it...
@harpalvaghela27983 жыл бұрын
lovely nail paint there!!
@JCCyC2 жыл бұрын
"I do love it when chaotic things happen" MUST have been a line spoken by the Joker in some Batman story.
@macronencer3 жыл бұрын
This is one of my favourite videos of yours, thank you! I've been interested in steganography (hiding messages in plain sight) for a while now, and I have a design on a mug that encodes my own name, which I made myself in software and ordered from Vistaprint. Hitomezashi stitching is a lovely new steganographic technique to add to my collection :)
@Cellottia3 жыл бұрын
How intriguing! I shall look up steganography...
@00000ghcbs3 жыл бұрын
Wait but how do you invert the process...?
@macronencer3 жыл бұрын
@@00000ghcbs Well, it's easy enough if you can see the whole pattern - you can read the code from the edges directly.
@00000ghcbs3 жыл бұрын
@@macronencer I mean it is a way hide binary messages, but I guess you also need to read it using ascii or something
@macronencer3 жыл бұрын
@@00000ghcbs Yes, my usual approach is to simply use 7-bit ASCII, though of course the encoding is a matter of personal choice. The idea is to make the message easy to decode, despite being hidden from view at first. It's fun! I have a mug with a design on it that involves a weaving line, turning left for 0 and right for 1. It spells my name on one side, and on the other side is a similar design that simply says "NERD!" :) I call it "Turncode", and I spent a long time getting the software just right so that it optimises the path and makes a nice compact pattern. It was a great project.
@HandyClock3 жыл бұрын
Simple proof that it's two-colourable: For every dot (where a stitch ends), it will always have exactly 2 stitches touching it. (Because they alternate over-under-over). Therefore, only 2 "areas" touch at each vertex. Since you never have more than 2 areas touching, you can always alternate from one colour to the other. ...I don't know how parseable that is.
@GaryDunion3 жыл бұрын
The iso one looks like it would be three-colourable, is that right? And could you keep generalising that as # of axes = # of colours required?
@HandyClock3 жыл бұрын
@@GaryDunion I believe that's right, yes.
@walterkipferl67293 жыл бұрын
I could parse it! Nonetheless, my try to make it more understandable: The only way for this to not be two-colorable, is to have a vertex, one of the points, where three faces or areas meet. With just up to two faces meeting at every corner (and obviously up to two faces meeting at every edge or line) you can always find a two-coloring. Now, every stitch follows the on-off-on-off pattern. So, at every vertex, there is either a line coming from the top or going out the bottom. Similarly, every vertex has either a line to the left or to the right. So, at every vertex, there are exactly two edges (except maybe the start and end, but those don‘t matter here.). Thus, the patterns are two-colorable. QED And this does generalize to the iso version. Three-colorable because at most (or rather exactly) three edges at every vertex.
@jeremylakeman3 жыл бұрын
Following a line around the plane, it must either stretch to infinity or form a closed loop. Because if it formed a spiral, there would need to be a vertex with either 1 or 3 line segments at the end, which is impossible.
@jordanweir71873 жыл бұрын
thanks bro im pleasantly surprised its that elegant, nice work
@mouwersor3 жыл бұрын
That flex of casually writing out tens of digits of pi
@ShankarSivarajan3 жыл бұрын
With "May I have a large container of coffee? Thank you …" you too can do ten digits.
@TranquilSeaOfMath3 жыл бұрын
@@ShankarSivarajan ☕😀
@Triantalex11 ай бұрын
false.
@mataichi142 жыл бұрын
In the colored pattern there is an 8 acting like an odd number in Pi. I drew it out to use as a cutting board pattern and it came out different twice. I thought I was doing something wrong the first time but got the same thing the second time. It’s surprising how much the pattern changes from one line being switched.
@jasonremy16273 жыл бұрын
This is such a beautiful process to watch.
@paulbennett70212 жыл бұрын
I think I'm in love!
@Syntax7533 жыл бұрын
What a fantastic video! Thanks for putting this together... will be using this technique in my "game development" hobbying :) I say game development but mean "terrain generators" and leave others to build games on top of that :D
@828burke3 жыл бұрын
This would be great for designing a quilt pattern. I made one of a Hilbert curve (as the line between colors) using 3 types of 2 by 2 blocks and I could do something similar here using only 2 if I'm thinking it through right.
@828burke3 жыл бұрын
@Doc Brown I thought of ONLY doing the line and having it be two pieces soldered along that and was like... maybe if you have magic
@alexchan32873 жыл бұрын
9:44 something magical happened
@rahulmooley32983 жыл бұрын
i'm going to draw a polar version of this. it'll be a bunch of concentric circles with an increment of one or half a centimeter in radius. every circle will be divided by radiating lines seperated by 10 degrees. same on/off logic. will post it on reddit and paste the link here. thank you for the idea
@EverlastingPinecone2 Жыл бұрын
It was very interesting to see the mathematician’s perspective on these patterns. In preparing these patterns for stitching you typically draw a grid like graph paper and as you stitch row by row you decide for the next row to be in or out of phase relative to the previous row instead of relative to the grid itself
@_rlb3 жыл бұрын
Ayliean has instantly become one of my favorite Numberphile persons. Nice shirt by the way, are those the Pleiades?
@Nickt010103 жыл бұрын
A Sierpiński Triangle, sir.
@_rlb3 жыл бұрын
@@Nickt01010 ah yes I know, thank you, but the stars look like the Pleiades cluster ;)
@herosnts3 жыл бұрын
Beautiful
@danibee5352 жыл бұрын
loved this one, makes me want to write a program to draw these! thanks, ayliean and crew!
@bioZone1013 жыл бұрын
These patterns are so soothing to look at, and I imagine to draw as well!
@abuk953 жыл бұрын
This is amazing! I have to create a program that visualizes different inputs. It reminds me of Wang tiles. Also, I didn't know that in English language the 'y' is no a vowel.. might learn also something else than math from this channel, nice.
@venuscarey3 жыл бұрын
>in English language the 'y' is no a vowel But it is! ...sometimes. Y is a consonant when it makes a "yuh" sound, like in "you"; Y is a vowel when it makes any vowel sound (usually "ee" or when it's present in a diphthong), like "baby." That's why when listing the vowels, you might hear someone say "A, E, I, O, U, and sometimes Y."
@gumbykevbo3 жыл бұрын
Indeed. If Y were not sometimes a vowel, then my, by, try, wry, etc. would violate the principal that all english words are required to have at least one vowel.
@talideon3 жыл бұрын
There's a difference between orthographic vowels (what you see written) and phonological vowels (the sounds you make). Orthographically, 'y' and 'w' are semivowels, meaning that they represent both phonological vowels and consonants, depending on how they're used. Interestingly, there are some more consonants n that can behave as vowels in the right context, as they have a vowel-like quality to them. These are the liquid consonants, 'l' and 'r'. To give you an example, in many rhotic dialects of English (those that don't drop their 'r's), the 'r' in 'nurse' behaves as a vowel: if you sound it out, there's no 'u' there, and the 'u' is just there as an orthographic 'carrier' for the 'r'.
@TuberTugger3 жыл бұрын
You read my mind. I'm also going to start programming the visuals for this. I'd love to see this pattern scrolling sideways with constantly generated numbers.
@crumble20003 жыл бұрын
In the word 'yummy' the letter y is used first as a consonant, then as a vowel at the end
@ramdevgohil47573 жыл бұрын
So beautiful! I'll surely try this and teach to my siblings and parents. Thank you for bringing this Math-Art here!
@programmingpi314 Жыл бұрын
May the force be with yo!
@JohnGolden3 жыл бұрын
Isometric variation and controlling the randomness is AWESOME.
@emmaperry48673 жыл бұрын
More of these videos with Ayliean!
@palibebeh3 жыл бұрын
'who wouldn't want that stitched on the front of their shirt' Numberphile t-shirts with Hitomezashi Stitch Patterns on the front confirmed.
@vigilantcosmicpenguin87213 жыл бұрын
They have to do it now.
@kozymoon6644 ай бұрын
.5 looks like the perspective created by the pattern just turned inside out for 1/2. Very cool way to generate visual patters. Thanks
@beesareLameWasps3 жыл бұрын
I'm not much of a math person after high school, but I love these videos. They're so interesting and well explained. ty!
@mathphysicsnerd3 жыл бұрын
I see plenty of people have tackled why the square stitchings are always 2-colorable, so I'll generalize the logic a bit to point out why the triangular stitchings are only 4(+)-colorable. Noting that each stitch has a gap both before and after it, on the (infinite) triangular plane we can see that each point must have 3 stitches connected to it, else the pattern would break along one of the axes. The stitches divide the plane into regions. These regions necessarily touch at least 3 points. Each point in isolation is 3-colorable, but since the regions necessarily share points the stitching overall needs at least 4 colors.
@livedandletdie3 жыл бұрын
At least it's a finite color map. Unlike 3D and higher space.
@falpsdsqglthnsac3 жыл бұрын
and the four color theorem means that it will never need more than 4 colors
@belg4mit3 жыл бұрын
Y is a semi-vowel. In "may" it is a vowel, as it it modifying the sound of the A. In "you" it is a consonant; A, E, I, O, U, sometimes Y and W.
@maxlindemann14293 жыл бұрын
As nice as it is to see the patterns created live on paper, this video really would have benefitted from computer illustrations to easily generate large patterns with different probabilities
@hedger0w3 жыл бұрын
9:30 Matt be like: "Hang on a minute!".
@artertemisartzetakis30773 жыл бұрын
I love this!
@coliander41803 жыл бұрын
Surreal stumbling across a fellow Invernessian on this channel!
@atikahrostam57782 жыл бұрын
I'm a pixel artist and I'm going to try using this in my drawing.
@Krekkertje3 жыл бұрын
Are we just gonna ignore her incredible skill for making very precise drawings on plain white paper? Also, are we just gonna ignore the lack of brown paper?
@vcprado3 жыл бұрын
It isn't plain white, the paper has little dots
@HarzemTube3 жыл бұрын
It's a guide paper with dots.
@Qermaq3 жыл бұрын
@@vcprado are the dots at least brown? ;)
@colinberg33423 жыл бұрын
The brown paper is under the white paper
@fusion673 жыл бұрын
it’s just reeeeeeaaaaaallllyyy light brown
@Igahwanoiar3 жыл бұрын
I belief the 50% maximum randomness can be explained by the entropy ( H(X)=-sum(p(x)*log(p(x))) ). Maybe if we'd take a closer look at the joined entropy between the axis, we could predict something about the pattern that emerges
@TuberTugger3 жыл бұрын
I don't believe it needs any proving. It is pretty intuitive. If you flip a coin that's weighted to one side, it doesn't matter which side.
@ezg52213 жыл бұрын
@@TuberTugger Math is all about formalizing intuitions. Information theory is scarcely a century old in part because of that dismissive attitude. If you ever feel like you really understand a loosely reasoned argument, go and collect your Fields Medal.
@TuberTugger3 жыл бұрын
@@ezg5221 Math is about elegance. Not heavy handedness. Don't try and justify over engineering. That's childish and arrogant.
@ezg52213 жыл бұрын
@@TuberTugger Right, so this is just about the Constructivist vs Intuitionist argument that plagued mathematicians of the 20th century. "Don't be a conspiratorial looney" vs "Don't get lost in the weeds". I'm a programmer, so I must be a conspiratorial looney in situations where deterministic logic is too restrictive, but I must also provide a witness for my ideas so the compiler knows what I'm on about. My only advice to you is to learn to tread water, so you'll never be afraid of drowning. The computer can choke on the symbols for all I care; I just need a language that's precise enough that I don't have to explain myself further. Mathematics is an ancient field, precisely because it is a concentration of natural, logical thought. We use a terse notation, because written English has a habit of saying more than we meant and simultaneously, being too vague to communicate anything specific without expounding further constraints. That's why Socrates held disdain for the written word; you can't ask it to clarify what it meant.
@peterbrockway59903 жыл бұрын
Suppose we came (however unreasonably) to the belief that max randomness occurred at 40%. We might test that not by drawing, but with actual "under/over" stitches with 40% starting with under stitches. Now turn the fabric over (and possibly look at the result in a mirror).
@fedesartorio3 жыл бұрын
Great video! I’m no programmer but I’d love to see larger patterns generated like this, anyone has an idea on how to make this for example in Processing or any other free software?
@Lykrast3 жыл бұрын
That glitter nail polish is legit soooooo cool!!
@piotrarturklos3 жыл бұрын
Those are beautiful, they have a kind of a harmony to them even though the inputs may be random.
@davidgillies6203 жыл бұрын
Of course I now have to go and code this up in Mathematica.
@erictaylor54623 жыл бұрын
For Y, which is sometimes a vowel the way to know when it's a vowel is my how sound. If it sounds like a vowel it is a vowel. So in the word "yes" Y is not a vowel, in the word "my" it is.
@maneeshyadav49362 жыл бұрын
Another way of thinking or another type of perception , to draw a lot of related such figures . And study about
@HontubeYT8 ай бұрын
I did just that! Best 2 years of my life.
@CamAlert23 жыл бұрын
If you substitute for the fibonacci word bit pattern on both axes you get a fractal like pattern
@annabarabanna76683 жыл бұрын
Wonderful. Thank you.
@flotador73 жыл бұрын
I believe I said this in a previous Ayliean appearance on this channel: Mathematicians: Oh, cool fractal pattern on her clothes. Gamers: Oh, she has a triforce on her clothes! It's dangerous to go alone, take this!
@JRH21093 жыл бұрын
Be great to see good old Matty Henderson get this animated on his computer.
@eindeutiglevin3 жыл бұрын
At 10:00 you missed the last line at the bottom right corner :) Great video though, I love your channel ❤️
@Projacked13 жыл бұрын
Very cool, we learn everyday :)
@AngryArmadillo3 жыл бұрын
A proof of 2-colorability: Construct a graph by taking each connected region as a vertex, and connect two vertices if their regions are adjacent. The claim is that this graph is actually a tree (meaning that it contains no cycles). To see why, choose any vertex v and notice that v’s region partitions the plane into an interior and an exterior. Let u be in the exterior and w in the interior. Clearly there cannot be a path between u and w that doesn’t pass through v. Thus the graph has no 3-cycles. By inducting on the length of the cycle, it is easy to show that the graph cannot contain any cycles whatsoever. Finally, to show that a tree is 2-colorable, first choose an arbitrary vertex to be the root and color it red. Take all vertices which are an odd distance from the root and color them blue. Take all vertices that are an even distance from the root and color them red. That should do it! This was really more of a sketch of a proof but I think this is the meat of it :)
@ilovethesmellofdbranesinth79453 жыл бұрын
Alternatively you can do this: we can complete every curve into a cycle by extending it along the boundary if we have to. It won't matter how we do this. Then since we're in the plane every curve is the boundary of a region. Each point not on a curve shall be colored by the number of regions mod 2 that it's contained in.
@AngryArmadillo3 жыл бұрын
@@ilovethesmellofdbranesinth7945 what about on an infinite plane?
@yaseen1573 жыл бұрын
1:11 "Uhh, I'll have a consonant please (Rachel)" - Ayelian Didn't know we were playing Countdown :DD
@rcapracp38673 жыл бұрын
"I do love when things get chaotic." I'd buy that T-shirt.
@Nuovoswiss3 жыл бұрын
I would love to see a follow-up on this, extending these patterns to different dimensions or grid angles.
@RalphDratman3 жыл бұрын
Ayliean MacDonald is fun to listen to.
@honkynel2 жыл бұрын
not entirely sure what i witnessed but really appreciated the skill with which the patterns were drawn. no tipex was used in this video.
@procrastinator412 жыл бұрын
Reminds me of Native American textiles from Southwest US, especially Zuni, I think. Also make you wonder, what might be coded into those?
@nialltracey25993 жыл бұрын
From a practical standpoint, I'd say that as a stitching pattern we should take the base case as alternating lines starting on, off, on, off. I just scribbled it out, and curiously enough, I got a mirrored version of the base pattern MacDonald gives with the isopaper version, althought the square version is, as you'd expect very different -- MacDonald's base case gives single-stitch squares, the on-off-on-off base case gives proceeding staircases.
@Astromath3 жыл бұрын
I think this is the first time I saw it live when a Numberphile video released. Usually I'm a few hours late
@Yulenka-3 жыл бұрын
I was caught off guard when Ayliean switched to white regular-sized paper instead of the Numberphile Brown. I thought it was prohibited.
@romanski58113 жыл бұрын
I wish this video were an hour long with Ayliean drawing random patterns
@travismiller55482 жыл бұрын
This kind of reminds me of a drawing I once did... also based on a bit of Japanese culture: the origami crane. I had to do a drawing to help me visualize the careful and specific tearing of paper I would have to do to divide a square into multiple little squares (still joined at diagonally opposite corners) to create a chain of cranes, still joined at their wing tips, from a single square of paper.
@Olfan3 жыл бұрын
I love hard stuff that takes days to compute on a rackful of accelerators and years to figure out to first formulate at all and then to program somewhat efficiently. And then I apparently love fun stuff like this which reproducibly manages to touch me in a surprisingly soft spot. Nice one, Ayliean, thank you for sharing this, even/especially if/since it cost me the better part of an evening. ;)
@tehdudeh1013 жыл бұрын
She's great, hope to see more of her videos in the future
@MisterMobius3 жыл бұрын
# I enjoyed this video so much that I had to write some python code # to print random Hitomezashi stitch patterns import numpy as np import random def stitch(rows=24, columns=16): pattern = np.empty((rows, 4*columns), dtype='object') horizontal = '' vertical = '' for i in range(columns): horizontal += '_ ' for k in range(rows//2): vertical += '| ' if rows % 2: vertical += '|' horizontal = np.array(list(horizontal)) vertical = np.array(list(vertical)) for l in range(rows): pattern[l] = np.roll(horizontal, random.choice([0, 2])) for m in range(2 * columns): pattern[:, 2 * m + 1] = np.roll(vertical, random.choice([0, 1])) for v in pattern: print(''.join(v)) stitch()
@WestExplainsBest3 жыл бұрын
A blended class of geometry and art should be taught at the secondary level. It would be extremely intriguing and engaging for students!
@jeffreyleonard7210 Жыл бұрын
Yes yes yes yes! To help non-math kids grow confidence and trust in numbers, and to help numbers kids respect art