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• Ok so I know I keep saying my next video is going to be a papercraft scutoid tutorial

• but I can't help myself because I have an idea I really want to try.

• So you know how last time we made monkeybread and talked about how the random balls of dough

• expand into shapey shapes, also there was lots of melted butter and I love how melted

• butter looks in VR so I wanted to do more of that or if you're on desktop just click

• and drag the screen to see where I am pouring brown sugar butter stuff over this pan full

• of pre-prepared refrigerated biscuit dough.

• To start with, we're making simple cinnamon skin cake. Which is definitely not what we're

• calling it, maybe Epithelium Cake? but I'm thinking of each biscuit as a a cell that

• we bake into a sheet of cells, like an epitheli-yum.

• Anyway the shapes are pretty predictable: when you have four biscuit blobs where the

• centers are in a kind of diamond shape like this, then the close opposites are gonna touch

• and squish together, while the far opposites are gonna not touch. In this example, the

• far opposites end up being pentagonal prisms and the close pair are hexagonal prisms because

• of the extra squish face.

• So flat sheets of cells are one thing but what if it were curved, or if it wrapped around

• into a tube? So let's get back to the bundt pan, and imagine it's a section of a simple

• epithelial tube. Cells in the body have to make tubes sometimes, right? So each cell

• needs to touch both the inside ring and outside ring of the bundt cake for it to be the kind

• of epic epithelium that's totally tubular.

• One thing you might notice is that these cells are gonna have to be bigger on the outside

• end than the inside end. So what kind of shapes should we expect?

• While that's baking, let's take another look at our diagrams. Let's say this diamond

• arrangement of cell centers is on the outer surface. And if the cells go straight through

• to the center, the inner surface should be the same arrangement except squashed into

• the smaller radius of the inner tube, which we can roughly measure out to make this squashed

• diamond arrangement.

• And that's when something strange happens. If you don't think about it too hard, you

• might think that whatever the cells look like on the outside, it will look the same but

• squashed smaller on the inside. Which might be the case sometimes, but there's another

• kind of thing that can happen.

• For this particular diamond where the long way points around the tube on the outside,

• well, once it gets squashed now it's the other kind of diamond where the long way points

• along the tube on the inside, and look what happens: the two close cells on the outside

• with hexagon ends will end up not touching on the inside of the tube and have pentagon

• ends. Meanwhile the two cells that don't touch on the outside and have pentagon ends

• will be closer on the inside of the tube and squish together to have hexagon ends.

• So what kind of shape has a hexagon on one end and a pentagon on the other?

• Why, doesn't that sound a lot like our friend the Scutoid?

• And in fact, this cylinder argument is from the original Scutoid paper, it's legit math,

• but here's the important thing: on the outside, there's a pair of cells that don't touch,

• and that means they can't communicate directly. But on the inside, it turns out that they

• do touch and can communicate though that special scutoidy triangle face. The topology of scutoidal

• cell arrangements creates network possibilities you won't find in a prismy cell arrangement.

• What I don't know is whether the theory is bake-able but let's dissect our epic

• epithelium cake to see if our scutoid construction is gastronomically sound.

• We might not get perfect pretty scutoids but what we're looking for is that extra triangle

• face that lets four dough bits all share faces with each other while still being efficient

• cell shapes. See, here's the kind of thing we're looking for: look at this set of doughbits

• where on the outside of the ring the two on the side don't touch because the bottom

• one puffs through to smoosh into the one that was above it, while on the inside the two

• on the side squish together to touch while the top and bottom ones don't. In fact I

• am quite pleased to find a few examples of this kind of arrangement.

• They may not be as perfect as a paper model but to me, this little scutoidy triangle of

• dough-smush represents a tiny piece of the puzzle of life. Cells can't step back and

• see whether they're part of something that looks like a tube, they don't have eyes

• or brains to help map out whether they're in the right place to help form something

• as complicated as a human being, or a dog full of needs and desires. Yet somehow these

• cells do find the right place and do form incredibly complicated structures from only

• local information. How does that work? I don't know but maybe scutoids are part of it, maybe

• a cell can look at its neighbors and sayhey, we're in scutoid formation, we must be part

• of a tube, I can't see the whole tube but I know I'm supposed to be part of one so

• at least I know I'm doing my part and if we all just do our parts then maybe, just

• maybe, together we'll create something incredible even if we can't see it or understand it.

• And I know there's things I can't change, there's billions of other cells responding

• to forces beyond my control, but as long as I do my part and help my neighbors do theirs,

• life will go on.”

Ok so I know I keep saying my next video is going to be a papercraft scutoid tutorial

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B1 tube arrangement touch diamond cake squish

# The Meaning of Cake

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林宜悉 posted on 2020/03/30
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