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>> That would. Support a. Very strong always about a system school physics which I think makes the 1st person physics you've ever heard speak of this brown bag which I believe. Work is a kind of intersection of. All that you should be really fun to talk. About many things to do the career of.

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Their work is also fairly recently been featured you were told. Which is also so let's please welcome it's a bit of. Thank you. Who really excited to be here I'm looking forward to getting a chance to talk with you so I guess if anything I say gets confusing or you're curious about something else just interrupt me sort of culture and math and physics that is just shout out questions if you get confused or whatnot so.

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I mean it's more polite to ask a question than just sit there confused. So I'm going to be telling you a bit about a couple aspects of my research. So I'm going to be telling you. The most recent work that we've been doing about knitting in my research group and I'm also going to tell you about a couple of other projects that are related to using textiles in different ways to understand different ideas.

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And so that's sort of where a lot of my personal interest to and my research kind of collided with one another so. I guess before I get into this talk I should. Saying. In my lovely lab numbers for. All of their work on this so these are the 3 students I have that work on textiles I have another student who works on virtual reality which I won't get a chance to really touch on and that's particularly talk about I'm happy to chat with any of you afterwards if you're interested in not so most of the work that I'll talk about today was done by showing my condé the student and he's studying not theory in my lab so that's what I'll be talking about today.

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Mike Dimitri of Post UK and my group who's doing computations and simulations. Encouragement single as the pitch the student working on imaging and and doing hand thought experiments. So that's sort of a little overlay of what my group is and I'm going to be telling you a bit about knitting so I think knitting since I was probably about 12.

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I knit a lot with my mom it was sort of a thing that we could do what I was a teenager to keep from fighting. But my mom's. Is a textile artist and has spent a lot of her life doing different types of textiles and so I've been sort of brought up in this world for a very long time so this particular piece this was the piece on the.

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Cover. So this is a shawl that's called Do you mind helping me. So it's a nice sort of gray background. So so this is a shawl that's called the dry kind of happiness that's by Sharon wins our and this is really the piece that got me interested in the particular topic I'm studying now and as you can see this is a really really sort of complicated intricate design and one of the things that I found really striking about this particular piece is you know I had been knitting for a really long time by the time I decided to do this and I noticed that she used to type Bostitch that I had never seen before and I was like I pretty much seen every step that exists I've been doing this forever and there was a new one and it's the sort of in sort of poofy things coming out of the Dragon's head and also in his beard which are kind of down here and so normally needed stitches kind of make up and this sort of chain of viz that goes up through the.

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Pattern and this particular one made a chain of one sideways and that was something I'd never seen before and kind of got me interested in thinking about the idea of what kind of stitches are even possible. Topple Logically this allowed what manipulations can be done with needles to create a fabric.

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And I guess one thing that sort of nice about these particular lease patterns is they have this really nice sort of. Almost programatic language to lose a diagram that tells you. Depending on what little symbol gets filled in on this grid that tells you stitch our particular manipulation of yarn and stick over there and some little it's a bit interesting about knitting as opposed to things like weaving.

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So you may have heard that be. That the card lumens the 1st digital technology so the idea of the card lumens. It came up with a way of addressing each over under crossing individually so it basically takes everything as a pixel and a science to it a $10.00 and that tells you what color.

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The sort of weaving crossings will be that point in it is a bit interesting because. A. Card type of design. Each of these. Little bits here this isn't this is no longer a binary language obviously there are lots of different manipulations you can do but the manipulations don't exist.

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Only on a pixel they can act over many a whole string of sort of pixels and they can extend through many different rows so in that sense I'm going to say knitting is more a type of coating because things that you do down here dictate what is and is not allowed further up as you go.

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So this is this is kind of the starting point for what it is we've been thinking about so I'm a hand in it or in my lab we have a knitting machine sort of like an old school or a sort of a Brother machine where someone by hand has to kind of crank it back and forth.

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So that makes me think things a lot easier but as I handed her to me it makes a lot more sense to deal with the sort of process of taking a loop that lives on one needle and and pulling so that when you insert. The 2nd needle through that 1st meeting all through the loop on the 1st and all when you wrap a piece of yarn around it and then you pull a loop through that loop and then you slide it to the side and also knitting from my point of view from a point of view is sort of a process of creating loops that are pulled through other loops and there is a couple of ways that typically this goes out so if I were to pull a loop from the back of the material to front of the material that's called an it.

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And if I pull it from the front of the material to the back of the material that's called a pearl stretch so these are basically the same thing this in fact is the same piece of fabric that I just picked up rotated 180 degrees and took a picture of the back of it so these 2 stitches are related by symmetry a rotation about this axis here.

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But it turns out that even just using these 2 stitches these 2 stitches are effectively the same as saying by combining them into different in different ways you can create a whole bunch of different fabrics that have a whole bunch of different sort of mechanical properties so the 1st.

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So the 1st one I showed. You there that's just a name or just pearls is. Called stock in that state if you are a hand and it's called Jersey if you are or a machine that are so so this is kind of the typical fabric This has everyone in this room is wearing something made out of Jersey now.

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So I mean most t. shirts are made out of this socks army and out of this the cottony part of underwear is made out of this. So I guarantee you everyone's wearing a so this is also sort of interesting because it doesn't lie flat it wants to curl up.

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So I'll let you pass this around you should pull at it and try to feel what thoughts like. So the other. The other stitches we have here or these patterns one is called garter So here I am all turning rows of pearls and knits So this one you'll notice 1st off has a much more rectangular aspect ratio.

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And it's very stretchy in this direction and also very stretchy in this direction so this is. A lot more and last a city than the other one. So the next fabric is called. Here this is also something. More than 50 percent of us are wearing something that has ripping in it my dress for example is actually a ribbon.

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It is a custom color of socks there is a woman in a white sweater over there who has a lovely ribbing on her sweater. So one of the things that's really useful about this is that the removing stretching in the left and right directions is really really really stretchy this way so looking at this it looks virtually identical to this chair but it turns out that there is actually a whole row of all of these pearls stitches are kind of in in like a little ruffle behind it so what it's doing that sort of taking up a lot of sort of sucking in a lot a lot of that area.

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Of all of the stitches and then it all out to be. Released when you pull on. Then the last one we have here is a checkerboard lot of us and that's what we call seed stitch where. This is something that is really nice it's sort of long lasting it wears very well.

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It's a really durable material it's a bit less stretchy than all of the other ones so this is something this is not as common in commercial but I do you have like my. Headband for when it's cold it's made out of this and I've a couple scarves made out of this so it's something that is good for being reversible it's good for of wonder ability and things like.

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So we're interested in what it is about this this sort of silly little bit of topology change like am I pulling a loop from the back to the front or from the front to the back that's generating all of the different mechanical. Of this yarn so this is the main question.

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Dimitry of a graduate student Christmas single are interested in asking. So we're also interested in thinking about. In terms of knots so if you look at this picture I have I've got a single knit stitch here but it turns out that everything is just a lot of support so all I need to know is this little bit of information here I need to know something about one stitch and then based on using different types of symmetry I can extend it to create the full fabric and so for this since it is.

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Periodic I know that the left edge here is glued to the right edge here when I move to bend next one and then the top edge here is glued to the bottom adage break here and so that's going to define the type of symmetry that I'm interested in for the stitches these ones over here require more stitches so this requires a column that has 2 stitches This requires a row that has 2 stitches and this is a 2 by 2 grid so those are the basic units of symmetry about we need.

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So if I wanted to take this little kneading unit and treat it like not I need to say that like I'm going to glue the left side of my yarn to the right side of my yarn on the top side of the bottom side of my yarn and then that operation of gluing will create something top illogically not and not just a side out of 3 arcs that I could pull apart.

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But there is a bit of a problem so it dipped the way I do you have. A kind of depends on the order so if I were to say glue the left in the right sort of behind each other there 1st and then the top and the bottoms of around behind I consider Paul the top and bottom.

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Looing out the science and I get the sort of Dumbo ears that I can. With just a loop so there's nothing sort of nothing interesting about the not here but if instead I take the left and right side and glue them around the foot and then the top and bottom and glue them to the bat I end up with this structure here and the way I go about trying to untangle this I find I can't that this really is a logically not is something that I cannot untangle.

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So we were stuck here for a little bit and then we realized that there was a bit of a problem so what. I have lost a slide here. Where this not actually lives so the top logically defines a tourist but there's an idea of crossing so there is an over and under which means it has to live in a bit of 3 dimensional space so this turns out it lives in a space that's called the thickening Taurus.

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Or basically it's the glaze on the surface of a donut so every. Leaves in that way is on the surface of a donut so I had a picture of really cool donuts apparently left out of this talk but there's supposed to be some cool donuts here so what.

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So what we do is now we construct this again only we have to keep track of the fact that this has thickened so I have a left side and I. And I talked about inside and these are now not just lines but they're full 2 dimensional surfaces and I need to make sure that they.

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Connect to them so there are 4 edges when this all gets glued up that turns into one well defined. So what I have done is I want to make sure that when I do this I end up wrapping. Greenside around this green curve and the red sides around this red curve so what these really are is me taking regular 3 dimensional space and sort of carving out a loop that goes through the hole of the donor in a loop that goes through the media part of the dot so that's going to guarantee that everything else is that I.

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Don't know a single space. And so by making sure that my surface is wrapped around the correct coloring of sort of carved out don't space mean make sure about not will. Well follow the rules. So the sense is that actually the whole thing I did in the beginning was just wrong.

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So basically. I showed that there's an ambiguity. That the world. Uses or it was wrong with us Ok so what I should have said is not that one is correct and the other is wrong but that we left out a crucial point and what the point that we left out crucially is but it really lives in this other space so when I've added 2 curves in that's created that space so what I left out from the other picture isn't the shape of those knots it's these 2 curves that live there.

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Why. Yes. You. Will so what matters most. Of them is. No So this is this is really. Top logical So what matters in in these particular ones is that the manifold that I was looking at not. Was not the correct manifold so in that sense I was looking at something that was living in our 3 like our regular 3 dimensional space where I really should have been looking in this the contorted space so that.

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The different so this is this is mathematically correct in this type of knots living any sort of periodic knotted structure can be defined by this process of creating. Creating sort of a knot with this auxiliary link associated with it or you can just look at the knots in that manifold by itself so this is a way of constructing not manifold.

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From are 3 of. Them that. Know so that there will never be a way you can do that because that would have meant that it wouldn't live Actually it wouldn't be pajamas for a tourist would there would be it would always have passed through it self to be.

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So so I'm going to walk through this construction once more so I'm going to route a green sides around the green this is actually a circle it's just right now passing through the basement in the ceiling of this building and it's meeting somewhere over near my apartment a few blocks down.

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So this is what happened so I have no clue those together and now you can sort of see that this thing is not actually an infinite line it really is a loop then I want to do the same thing with red faces some going to kind of pull them up like this and then continue to wrap them all the way around.

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And glue this up so this is now the a textile not that we have an s.o.c. link that now this lives in 3 dimensional space our regular 3 dimensional space. So I can kind of unscramble this and make a canonical picture of it so I have basically the original picture if here and then this whole gadget on the outside so the whole gadget on the outside is there to ensure that the apology is right but there is an interesting set of questions of what can I put in this box here and so that.

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What my student has been thinking about so he noticed. Every not every not that can be knitted or knit when viewed as not has a property that it is something that's called Rybin which means that if you take your an eye and new sort of dip it in water and sort of have a disc that sort of has this not as its boundary.

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A disk only passes through itself in me a set of edge pairs so I can have a bit that passes through itself like this or I can have 2 and on intersecting that's what I can't have is a set of alternating clocks so it turns out that every single Not that we've noticed can be constructed this way to kind of make sense because you're sort of pulling loops through loops so if I have a loop and it's got a little patch of a disk I pull a loop through it it's always going to have that correct type of singularity.

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And I guess he asked the question of the converse is like well can all. Be needed and then he came up with this not here so it's sort of. A half hitch that's been needed through itself and he calls it. Turns out but yes you can it and this is what it looks like it makes these little kind of hoofs and it and this is kind of incredible this is my student who had never picked up needles and thread before working for me never thought I'm going to be a Ph d. student in physics leg he would be thinking about these structures that this student who just by understanding the mathematical structure of it was able to create a new stitch that no one had ever thought of before possibly no one had ever thought of it because it's not the most.

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Practical of stitches but it's really incredible that this stitch can exist. So that's that's really something that is quite profound that we've been thinking about recently there's also all sorts of different types of things you can do within it so in that way you see you notice that there are lots of different types of stitches.

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And. They involve taking these rows existed and gluing and having sort of 2 rows tied together or inserting a new row in. The textile and these can be used for a couple of different things so in this rabbit over here this is something that is used to create.

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Out of plane defamation such as giving it an intrinsic. In the race over here what this is doing is it's taking these normally straight lines and asked of adding curves to sort of adding sources and sinks for for curvature in a plane. So we're hoping to be able to take some of these mathematical ideas we've built up about knots and then apply to to these types of structures of my future.

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So I'm going to sort of switch gears a little bit and talk about. Different symmetries and sort of interesting things that come out of thinking about symmetries and then sort of extend some of these ideas to think a little bit about the geometry and topology of how our clothes work.

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So this is the definition so symmetries are transformations. That leave an object looking the same so for example in this shawl rate here if I were to I think there are 2 and. So there's 12 pedals so if I rotate this. 360 degrees divided by 12 so I guess 30 degrees at.

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The same Scholl back. So we can look at that 1st of a different type of. System so these are flags so what type of symmetry do I have here. So I was left right in Albania dolls. For for Ga So each of these 4 or I guess well I guess this is this is I'm going to call this who.

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Gets the diagonals 2 so we've got. Going to. Although I think I have not counted the diagonals because these are 2 rectangular. So these are all what's the name of this class of cemeteries. Because anyway. I'm hearing a lot of different. Reflections Yes these are reflections right well.

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So some of them are both rotations and reflections so so this is what I'm going to do is I'm going to put a bunch of mirrors in. And then I'm going to say Ok well for each of these things I only need to know a little bit of information to reconstruct the whole image all I need to know is one little bit of a unit here so this when you say is also a rotation so it turns out that I can get in a smaller area by using reflections than I can using rotations so I'm going to defacto call that.

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A reflection So these are the minimal bits of information needed to reconstruct the entire structure so. So I'm going to call these mirrors Here's another set of flags so I guess these ones ignoring that this is now rectangular and the dashes and you straight. What type of symmetry do we have here.

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So these ones are rotations so again I can use a smaller bit of information so these 2 are 180 degree rotations so you can imagine what all I need to do is take a small chunk of this so take this chunk here imagine sort of wrapping it up into a cone and then sort of stamping it out around and I can do the same for things like Hong Kong or the Isle of Man these are kind of fun symmetries that we don't see very often.

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So here again you can kind of roll this up into a koan and roll it around and that gives you that whole symmetry Center right here so. This is another 5 this is Martinique but I don't have any of those symmetries Does anyone have any idea what symmetry what might I call this symmetry where I take a snake and I and I have another snake here and another snake here so it's a translational some a tree excellent and so it turns out that I can use very similar ideas.

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So I had this idea where I either took a mirror and then kind of flip things over and stamp them down I had an idea where I sort of took these cones and rolled them out so I can come up with a whole bunch of different surfaces that I can use total roll out any plainer symmetry on so this is a translation from a tree so all of these are videos from not my software but the software called attractor.

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Spelled this way it's available for free online and I recommend everyone check it out so this is looking at how to create a translational cemetery so here is be. Our initial motif this is the minimal motif and then is going to sort of roll this up and glue the red edges together and now glue the glue edges together and so this is a Taurus so this is the same structure that we had in the knitted stitch and now by rolling this out.

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They were able to create the entire. Planar structure that comes from this translational summitry So just to give you a little overview Here's another couple of different symmetries that one can haul of so this is when using mirrors again so this is going to take a little wedge and every time you see a mirror what it's going to do is it's going to take and rotating it over the mirror and itself down so.

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Starts here and it's going to stamp itself out and then. Is just this little teeny triangle is enough to recreate the entirety. Of what's going on in one place. So for rotations is the next one so so is this her beautiful star pattern so this one starts out with these different symmetry centers so there's 3 folds here 6 fold here and 180 degrees about here so it's going to fold it up and inflate it out until like most and now it's going to all roll around on those some most the edges and this will construct the entirety of this pattern.

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So it's similar to it's similar in a lot of aspects to being a mirror but in the rotational one the front in the back of the sun Most do not have the same pattern on so that's enough to create this rotational pattern and you can do all sorts of things by combining it so this is this is a wide symmetry so this is a combination of like a twisted loop and a mirror so the white lines of the mirrors and the twisted loop I want to glue the dark blue to the dark blue and the light blue light blue.

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And so this is going to create a mobius strip with. A bunch of different. With a bunch of different mirrors on it and then it sort of going to again we're all itself an imprint its texture so. Again I highly recommend this software attractor it's a really great way of understanding to be symmetry means.

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So this is this is one of the qualifying so you can do. But since I've been talking about symmetries and mobius strip so I figured I would throw in a little blurb about the scarf I'm wearing so this is not just kind of a cool q.r. code scarf this is actually a bit of a mathematical construction so this is a picture of it where you can see clearly that it is a mobius strip this is joint work with Henry Segment a.

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Small company called knit yak where she makes one off generative textile and small batch of textile scarves and wraps and things like that. So typically she does. This type of scarf that is these are called. On the next flight I'll define that. But they're sort of street scarves and then one day on Twitter someone posted a ha I wonder what happens if this is on a mobius strip so we set out to figure it out and just to give you a little insight into the construction this is a type of knitting that's called Double knitting So what's happening is you're sort of knitting one color on the front and another color on the back and then you can sort of pass each of those fabrics through one another so if this is the front and this is the back you have everywhere that you see white on the front you see blue on the back and then the seeing So this is sort of a middle cross section of that same picture so this is the back in the same place that this is the front of.

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So we wanted to see about creating a mobius strip and so all of her structures are made by cellular automata elementary cellular automata And so these are these little code so you have 3 pixels and these are all of the combinations of 3 pixels you can have and then they dictate what the central pixel below is going to be and then there are sort of different codes so these are I guess there are 256 of these these are supported by an area these are ones and zeros and that gives you the sort of number for each of the codes so it turns out that there were only 2 that had the rate symmetry for us and the rate symmetry for it is that if we want mobius strip to existed then the last row of one scarf must be the inverse of the 1st row of the next scar and so that's what it takes to have this Mobius symmetry.

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And it turns out that these patterns we define this thing that's called sort of a scarf inverse square each row is sort of inverse of itself for the 2nd half of it so I've got half of a row that's like one string and then the 2nd half is the inverse of the reverse of string.

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And so that's what we used to do this search. And so these were the 2 roles that work consistent with that didn't generate just like straight something really boring and these are rules 105150 so this is what we end up with we were looking for we were looking for cycles were approximately 100 stitches why and 1000 stitches long so something with roughly scar size we got plenty of them that were like 8 by 16 but that's not going to fit around may not very.

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So we're looking for sort of longer ones and these are the 2 we found so I'm wearing. Rule 151 which you can see going along here so this is sort of reading down one side of it turns out that we used a very. Boring greedy algorithm for this there's if you use sort of smart things more related to the symmetry you can come up with other patterns but these were the 2 that we found over and over and over again using a very simple minded algorithm.

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And so this is now going along the backside of the same scarf So this cycle is in fact not one scarf length but if you include the reverse it will go around twice. So this is sort of a different type of symmetry but here's one that. Maybe we're not as used to so we're looking at this down here let's look at sort of a zoom in this is great this is a basket we if we can say Ok I see there is a mirror through here and a mirror 3 here and a 180 degree rotation through here that's all fitting in with our system that we worked out before but there's something kind of weird going on up here I've got a place where I had a straight coming in and then it doesn't go out so there's those point rate here where my symmetry doesn't exist anymore.

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And so I'm going to be spending the rest of the time talking about this type of structure and what this has to do with making clothes. So we're going to talk a little bit about symmetries but now 7 trees that involve curvature. So how many people here have sewn a shirt.

[00:38:59]
Awesome so turns out you might think it looks something like this. To gather I mean I guess you can use not glue but iron on. Stuff you know when your. Hands on your jeans go you could probably use but say you start out with something like this it turns out that this is the actual pattern for a men's dress shirt so it's really really complicated there are dozens of pieces that go in but something really interesting about this is you'll notice that there's almost no straight lines on this entire design you'll notice that probably the places that have street Lions have the word for old so like fold here is where the straight line goes pretty much everything else has some strange curve structure.

[00:39:54]
And still it turns out that all of these curved seams are there because it's necessary to have the van in order to go from this flat one structural piece of fabric to fitting around the curvature of a human body is. One. So. Not exactly I mean so these are developable with.

[00:40:28]
I have her with. The disease. So this seems fit so yeah so these are piecewise developable. But there are there are some see one singularity. So so in this particular example I'm going to break this down into 2 possible types of structures for adding in curvature so not quite so this is talking about like a point why it's singularities but everywhere else it's to follow people.

[00:41:10]
So in this structure so this is called a dart so for a dart Basically you take a piece of fabric you fold it in half and so a diagonal seam into it so when you pop it back out you have a cone. And so this is a place where you have what's called positive curvature so I'm sort of taking away a little bit of the area of the structure and I end up with positive curvature and so this is used at places like where I have positive curvature on my body.

[00:41:40]
Places I can do the opposite of that this is called a go day where I take a triangular wedge and insert it into another flat piece of fabric and I and with another point with singularity but this gives us negative curvature so negative curvature is characterized by a saddle structure so it's curving one way in and one way out.

[00:42:05]
And so this is used for things like mermaid skirts and things like that where you want to have like a lot of kind of value metric flute to. So we can look at what this means in terms of symmetry. So I've got this fabric that has a honeycomb so interest I've taken one 6th of what I'm going to do is I'm going to sew it together along this scene here so I end up with this structure here so what you'll notice is at one point I have now a perfect con but everywhere else I have what appears to be the correct symmetry so I still have the correct mirrors passing through everything locally.

[00:42:54]
And it looks like it's normal apart from this one place where I have a single sort of pentagonal structure and I can do the same thing I can take that cut out and glue it into this so I've now sort of added in I guess 60 degrees of angle and to this point and I end up now with a perfect cup to go on in the center but everything else everywhere away from the well looks like it's sort of the normal plane or a tree.

[00:43:23]
So friends of mine under issue we and Robyn so injured decided they were going to use this to me to dress so this is called The 567 dress and so this is me using regular Pentagons hexagons and haptic on and then me angles between our deficit or access of the angle between them is what makes the curvature in structure so the Pentagon's are places where you have positive curvature so those are the bust and the guns are places where you have negative curvature sort of around the waist.

[00:44:03]
So I was interested in the side. Sort of locally developable structures and so I was interested in playing with the idea of having a sort of planar curvature as a way to give 3 d. structure to objects so here this is just sort of an egg carton surface mead with some cosigns And so from the top down this looks like it is a perfect.

[00:44:31]
Cover mainly. Symmetry but from the side you can see that it really has a 3 dimensional structure to it so I was interested in making an algorithm out of this type of structure so I created a jacket so this is a model of my body. And these are what.

[00:44:53]
What the pattern pieces actually look like so I did this I used a craft cutter to cut out the strips with these exact geometries and then rivet it together and I end up with something that fits me pretty much perfect Lee So this is the idea of using curved strips to create a curved structure and again this is basically playing around with changing local angles sort of the idea behind it.

[00:45:24]
So all. We've got. We've got these 2 things now we've got this like beautiful friendship where one. And I've got some human and Austin's. So what these guys have in common. They give a negative curvature I've got a plant in the audience so yes in fact both the answer how so these have negative curvature of these.

[00:45:58]
Everywhere but it turns out that these 2 structures not only do they have. Negative curvature but the mechanism mechanical mechanism by which they have negative curvature is exactly the same so for the dress what you do is you have some tool or you've got tool which is a structure she sort of match a bit of and you've got boning which is the stiff bit of it and you take a long piece of the boning and a small piece of tool and you stretch the tool out as far as it all go and you sew it on to be on to the boning and then you let it relax and what you end up with is the boning can't shrink any and the tool wants to shrink so what you end up with is this sort of weekly we're awfully structure here what's going on in the human interest.

[00:46:55]
So a little a little bit of biology but. I don't know maybe this is not so lunch appropriate but. There is a transition when when you're an embryo which many biologists will say is the most important. Most important part of your life the most important thing that happens in anyone's life is gastrulation and this is the process by which you go from a ball of cells into a tortoise of cells so this torso cells is eventually going to form your intestinal tract and as apologist I mean I agree that this is the most important part of anyone's life of gaining genus.

[00:47:43]
So what is so what's going on in the human intelligence is parallel to be this guy that has formed is something that's called a neural tube and this is eventually going to form your spine in your spinal cord and your thoughts will nervous system and there is a little membrane that connects them which I learned like you.

[00:48:05]
Yesterday is called The Messenger Harry which I've been giving this talk for well this little blurb of this talk for a long time and I never knew about word for it but I learned it's called them as in Terry. A membrane that connects the. Sort of neural to the.

[00:48:23]
Connective tissue part to your intestines later the out will help filter blood and bring nutrients from your food into the rest of your body and what happens is in development is your gut who grows a lot faster than a mess and very can grow and. You end up with this structure this scenario again you've got a long stiffer tube that is attached to some sort of flexible membrane and you and up with it buckling and ruffling like this so so this is so this is why human intestines don't just look like someone shoved.

[00:49:06]
A rope inside knowing this is this is why everyone kind of has intestine fits in the same place as everyone else this was a mechanical process. So I'm going to take just one last a minute to talk a bit about negative curvature so negative curvature is something. I particularly love and this is.

[00:49:32]
This is a work of art but probably many of you are familiar with this is one of the lithographs This is called Circle of 4 and so. On this question he wanted to figure out how do I visualize infinity so we're used to thinking about this regular flat space where infinity is so far away it's something you can't see it's where you know points converge far away you know it's really hard concepts to visualize and so in talking with the mathematician ****.

[00:50:05]
He was introduced to this object that's called the hyperbolic plane so this is a structure that has everywhere negative curvature and this is this particular version of in it. Has infinity as the boundary of the unit disk and so this is captured in this graph and so what's going on is you've got central $66.00 figurines you've got 3 angels interlocking with 3 demons and their wing tips there are 3 or 4 of these units that go to gather but what you're supposed to imagine is but this angle here is identical to this little angel here they're supposed to be the same size in the same shape in the same everything and that's kind of a hard thing to do.

[00:51:01]
So this is this is that central unit I've sort of inscribed a circle around it. These are the neighboring units I'm supposed to assume but these circles I can sort of deformed that circle of stretch it out so that everything inside it is the same size and shape it's in the circle and they can continue our from there so if I sort of take the motifs that way I'm supposed to assume that I can come up with a structure like this so I'm going to say that this is a hexagon and I but sic I've got 4 hexagons meeting every vertex.

[00:51:37]
And so that will look like this and so what I want to do is create some structures so this is this is a blanket that is a chunk of hyperbolic space and so this is actually what happens when these are all the same size and so this is also the basis of some of the virtual reality work we've done we've sort of tried to come up with ways of visualizing what it would be like to actually live inside a hyperbolic space and not just sort of look at.

[00:52:05]
One even if it is a blanket and I guess with that I want to say thank you. Can spend an absolute pleasure to be here this Q Our code is the pattern for this. And you can see it in knitting Unfortunately this is not scannable I tried really hard but it didn't work.

[00:52:32]
And you can find me on Twitter. This is the actual link for the. Shop that has a lot of the. Well you guys can. Surround as well. So any questions. Yes. I do. On. My. Own call. I think I think there is a lot of the like the Japanese aesthetic is really off and on about almost mathematically elegant simplicity so I think there's probably a big overlap and how about aesthetic plays into math seems to fit really well into that kind of idea.

[00:53:50]
When you are discussing. This with. The. Ones or you. So needing is. Yes it is assumed to be made out of a single thread although me taking the assumption that it's periodic will break that will assume that there are individual threads so what I normally would say is I can give you an infinite thread where you can never access the Ns I can handle that and give you an ending needles and you can make any object you like so that's kind of top of logically what is allowed and.

[00:54:45]
What is allowed in our knitting is we're looking strictly. To periodic structures so every time I have a new row that's going to introduce a new thread to it so this and has to be glued to this and so I have broken here. And then sorry I forgot the other half of your question.

[00:55:12]
The question you dispose of the. Same book. Because. Existing. Or do you. Buy. More complex ones like that. So that that's really. All we have a framework that does it was sort of too technical for this particular talk but I take the what's called the. 3 manifold complement him my link and then what I can do is do any less surgery so I along.

[00:56:01]
Parts of that link and I cut along parts of another link and I can glue them together along a pair of a new I am not so way of building up a living patterns together that doesn't cover the things that take like 2 stitches so there's say a basket weave structure would take like 2 stitches here and then I cross them over it like this and I get to stitch something like about is not going to try it out but we have worked into another structure that takes like a whole bunch of different sort of.

[00:56:34]
Loops of yarn and gives us structure that creates I call them watches. So we have a paper on the archive if you're interested in more of the it's not the technical it's enough to expose a Tory version of it will get a technical one out but that has all of the details of.

[00:56:55]
Its. So old this is it. So. But it's not. It's. There are worries. It was. A fantastic question. So there are some really cool things that happen if you have over twisted yarn in you knit it together if you were to create a stitch up with like basically.

[00:57:39]
An intrinsic shear in the structure. So that's something that is sort of built into the code working on getting a particular yarn yarn interactions so we've got some reports of term that keeps the topology but. Working out the sort of spring interaction that would cause twist we haven't implemented yet but that's a great question and.

[00:58:12]
I guess I saw your 1st one and now. I just. Don't get it but. That's a great question so as someone who is a candidate or I'm much more familiar with how about works things like twisting. Is something you can't do easily in knitting machine like you have to have a specialized to knitting machine that allows you to do a twist to where there are all sorts of kind of fun whole garment machines so they can really do well with things like.

[00:58:58]
Top top logical changes but they can't do things like twisting but that's sort of an interesting. And interesting thing that doesn't appear very often in but is one allowed in hand that that's not allowed in machine. Or your. So I would want to look. For. Every. Word. In the Life.

[00:59:55]
Of the really. I was. One. Of them. So there's a lot of things that are kind of interesting if you play with the ball they are in itself and then geometry you can get things respond in different ways to different stimuli so it's kind of what we're interested in the long term saying like I want this geometry with these properties.

[01:00:42]
Come up with like a set of stitches and parameters but. So we're trying to find well. Maybe this is maybe not answering your question but you know if you can come up with some smart function of your text I also say like it changes color. My glucose drops or something like that if I'm if I'm diabetic.

[01:01:06]
You know a way of sort of constructing Well maybe that's not quite the right example but something like say I'm an athlete and you know I stretch **** a certain amount during certain muscle areas and then something happens you know so I can use that record in my progress of like I don't now or something like.

[01:01:34]
Thank.