The Meaning of Cake

The Meaning of Cake

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 say “hey,
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.”

100 thoughts on “The Meaning of Cake

  1. Wait.
    This video was uploaded on February 28.
    February 28 is 14 days before March 14 (Pi Day).
    14 days = 1 fortnight.
    Fortnight is pronounced like Fortnite.
    PewDiePie did a Fortnite live stream.
    PewDiePie ends with Pie.
    Pie is pronounced like Pi.
    Vihart plays Fortnite on Pi Day confirmed?

  2. Vihart, I love you, and I've been loving your videos for as long as I can remember, but please please please put out a separate normal version of your videos or something because most of us dont have VR gear and I at least, wont speak for anyone else, find the VR thing really annoying and so distracting I cant really enjoy the video

  3. I thought in the end you were going to say "if we all do our part, then pewdiepie will stay number 1 subscribed youtube channel" 😀 Your philosophical answer came out better. 🙂 Nice video

  4. I love that geometry is evident even in the format of video you use! For example, look at the decidedly odd pencil at 2:53

  5. Your videos feed my hyperactive brain. I love your them so much, even if I only get 85% of what you're talking about.

  6. I couldn't pay attention because I cant stop thinking about how accessible VR is. Also I couldnt tell it was VR till you metioned it.

  7. the idea that we are big complicated things made of small things that follow simple rules, is really cool when u think about it, thank u doggo

  8. Hi I am going to stop and get my stuff for you and I have a game for a game and I have a game for a game and I have a game for a game and I have a game for a game and I have a game for a game and I have a game for a game and I have a game for a game and I can go to see you and I have a game for a game and I have a game for a game and I have to stop for game of a stop and I get a chance and you have a game I can play it if it’s super hero 🦸‍♂️ I like you I don’t want it and it’s so cute omg 😲 I am out and going on the road and I’m super glad I got a game and I have a game for a game and I have a game

  9. We are still part of a tube but the tube is so broken now compared to what it used to be. I used to like the tube a lot more when it was like pie, but now it seems to be more like mass-produced tea.

  10. Okay I thought the camera angle was faulty. But at the end of the video, it all made sense. I am seeing this video from the perspective of an epithelial cell. And I think it's genius.

  11. Fantastic I think you could be a great teacher with this interesting mash up of the slightly esoteric nature of mathematics with the entirely practical nature of cooking.
    I mean who doesn't love learning about something that you can eat afterward

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