Jim StormdancerA cube has six faces. There should be 64 named food shapes on this grid. In 32 of them, the filling should fall to the floor immediately.
Don't play like you're doing science if you're not really willing to think it through.
The interior is the undocumented 7th face. A block of chocolate has all 7 faces solid.
The exterior is the undocumented 8th face. Culinary science has yet to discover how to make that face solid.
Andrew Plotkin@mogwai_poet If you use a projective tortilla, the inside and the outside are the same and your taco is nonorientable.
brettwitty@zarfeblong
@mogwai_poet
Those are pretty popular since there is always a line from it to its origin (where you bought it)
@mogwai_poet
Those are pretty popular since there is always a line from it to its origin (where you bought it)
@zarfeblong If there's anywhere in the world with a food truck offering mobius tacos it'd be here in the bay area. I'll report back.
Noah K
Krystian Majewski
AT@mogwai_poet I don’t think that’s quite right: the filling cells should be of dimension one higher than the starch cells: this is already true in the toast case (nobody would apply just a layer of butter of volume zero to toast), and certainly in the case of popular 𝑆³-sandwiches (food complexes with a two-component starch subcomplex whose universe is the one-point compactification α𝐑³≅𝑆³ of 𝐑³) such as the beef sandwich with none at infinity
Joe@mogwai_poet It's only 64 if you count rotations of foods as different foods, right?
A sandwich, rotated 90°, is still a sandwich?
Wanja@hungryjoe @mogwai_poet Well, they mentioned food falling to the floor, so rotation is not always irrelevant. Only rotation about the vertical (Z or Y) axis is.
Using Burnside's Lemma, we get that there are (64+8+16+8)/4 = 24 shapes of food that are distinct under that rule.
Not a Spring OnionPartially. If you take gravity into account (e.g. for food), then rotations around the "up" axis can be counted as duplicates, while other rotations might result in a catastrophical loss of hull integrity.
demofox@hungryjoe @mogwai_poet yes, but a Newton is fruit and cake
Khleedril@hungryjoe @mogwai_poet But the mirror image of a sandwich is a wichsand. I'm doing science here.
Marc B. Reynolds@mogwai_poet Nah. Choice of coordinate system is arbitrary.
gkrnours@mogwai_poet ok but the symetry say they are mostly the same. Taco A and Taco B are taco. I'll accept that toast up and down are two different things. One is a pizza, the other is hope and dream turning into sticky floor
marble 弹珠@mogwai_poet but if I cut the sandwich in half, will I have two halves of one sandwich, or two sandwiches?
Jo Shields@mogwai_poet @mcc "Cube Rule" is deeply flawed anyway. My own personal test of sandwichdom is the "Earl Rule", i.e. "can I eat this one handed, whilst playing euchre with my Regency-era chums, without losing my eye contact with them (which might risk missing a tell) and without messing up the felt of my fancy gambling table"
A Snickers is a sandwich. A thick milkshake is a sandwich. A hot dog is only a sandwich if it is light on condiments. Cheetos are too messy to be a sandwich unless eaten with chopsticks.
val@mogwai_poet not if the filling is a flan and sticks to the top or walls
kira :3@mogwai_poet the minus world of cube-based food configurations
Jesse Morris@mogwai_poet This implies that a taco is twelve different types of food depending on how it's oriented. That's a prospect that I think is worth investigating empirically.
@aubilenon Is a slice of pizza you hold by the crusty end a different kind of food from a slice of pizza that you hold by the pointy end? I'd argue yes
@mogwai_poet I don’t think it matters how you hold it so much as what end goes into your mouth first, and in which orientation
mcc@aubilenon @mogwai_poet do we unlock new categories of food if we draw the mouth facing the opposite direction
@mcc @aubilenon Lately I've just been smashing meals against the back of my head and yeah, it's a totally different experience
@mcc @mogwai_poet Well I'm considering the mouth to be the anchor for the camera PoV. Obviously I'm simplifying things, because rotation is actually continuous but I only examine discrete 90º increments. Furthermore, I’m a traditionalist, so I didn't consider the more avant garde methods of eating. This is a new field of research, and the possibilities are nearly unbounded!
miunau
JP
Kenneth Finnegan@aubilenon @mogwai_poet That bottom right one.
The Uberduck@aubilenon @mogwai_poet to be fair, I think some of these can be collapsed. In no other context do we consider the orientation of the eater to the food when preparing it, nor do we change food designation based on rotation around the vertical axis. Gravity alone provides a privileged vector.
A pizza should have three rotational isotopes (what's the actual math word for this?), not six.
@uberduck @mogwai_poet These diagrams are simplified and as such elide gravity, friction, etc. The mouth is the fixed point around which camera is oriented, and how the taco relates to the mouth and tongue _does_ affect the culinary experience. _You_ may find, for instance, the first two on the second row interchangeable, but for someone who's right- or left-mouthed, they can make a big difference. Don't assume everybody's ambilingual just because you are!
@aubilenon @mogwai_poet I'm not saying the eating experience is the same across rotational symmetry. I'm just saying that even at the fanciest restaurants they won't have a different word for the slice of pie 90 degrees from the one you ordered.
@uberduck @mogwai_poet The famous none pizza with left beef is a mild counterexample. It's still a pizza, but that's okay, these can still be tacos.
juv3nal@mogwai_poet so the sushi in the diagram is clearly a roll, but does that make nigiri...toast?
Ben Aveling@mogwai_poet Rotation does not create a new shape. Bending does not create a new shape.
Because, topology.
Taco is toast.
Stretching does not create a new shape.
Because, topology.
'bread bowl' is toast.
Sushi is different. It cannot be bent or stretched to be toast.
If Calzone is solid, then Calzone is toast.
If Calzone is hollow, then Calzone is a different shape.
And sandwich is not a shape.
It is two shapes.
Because, topology.
Taco is toast.
Stretching does not create a new shape.
Because, topology.
'bread bowl' is toast.
Sushi is different. It cannot be bent or stretched to be toast.
If Calzone is solid, then Calzone is toast.
If Calzone is hollow, then Calzone is a different shape.
And sandwich is not a shape.
It is two shapes.
Carlos Solís@mogwai_poet Sure there may be 64 categories, but many of these are functionally duplicate because of a simple trick called "rotational symmetry", or in lay terms, "just turn it around duh"
Shorty@mogwai_poet This thread is significantly bigger than it should be... Not that I'd complain about it 
w4tsn ~> 
@mogwai_poet except in space 🤪
Robin Neal@mogwai_poet 6 is a pie.
⁂ Fish Id Wardrobe@SudoCat @mogwai_poet Yes, and the one positive in this system is that a dish of filling with piecrust on top is NOT a pie. It's toast.
dubious moss [Viridi Vix]@mogwai_poet Why 64 when many of those 26 combinations are equivalent by rotation/reflection? Fair enough to the four unique missing shapes but the rest are redundant 
qnix@mogwai_poet 5 should be pizza
Jo@mogwai_poet
id go as far as saying there are only 3 types of food and all of them only differ in entropy: sandwich, salad, soup
try me ✌️
id go as far as saying there are only 3 types of food and all of them only differ in entropy: sandwich, salad, soup
try me ✌️
heislertecreator@mogwai_poet no. you figit panini grill. ::: Tim
lertsenem@mogwai_poet Not quite: I don't think we should count separately shapes which are symmetrical or just a rotation of one another. A toast upside-down is still a toast, you just have to scrape some of the jam from the ground.
Tiota Sram@lertsenem @mogwai_poet now this has me thinking that an upside-down open-face grilled cheese sandwich probably has very different mouthfeel than the same sandwich eaten right-side-up.
@mogwai_poet I can't accept that a hot dog is a taco.
Texty the Bard@mogwai_poet Then there's always the pie chart: what a particular combination of crust and filling is defined as based on type and location of the crust. Slump, buckle, Betty, crisp, etc.
emily, blinkenlight witch@mogwai_poet most of those are isomorphic though. if you rotate sushi 90 degrees around any axis, it's still sushi
the one missing one is floor+two adjacent vertical sides
Craig Timpany@mogwai_poet All y’all seem more preoccupied with enumerating the possibilities than doing the fieldwork of discovering L-toasts, scoops, and edible octants
@craigtimpany Luigi toast, Waluigi toast, Mr. L toast and Blue 7 toast
@mogwai_poet I dunno what half these are. We’ve strayed so far from devouring a simple organic mario
@craigtimpany Yeah I had to do research to complete the set 😂
Jouni Seppänen@mogwai_poet But surely food items stay the same when rotated. Burnside's lemma yields 10 distinct configurations. The illustration is missing the empty cube (a no-carb meal), the one with two adjacent faces (pita bread?), the one with three faces in a corner and the one you get by removing one side of the bread bowl.
plinth@mogwai_poet do all the isomeric differences matter at a macro level? One could argue "yes because of none pizza with LEFT beef" but left beef is rotationally identical to any other 1 sided beef.
Similarly top face toast and bottom face toast are identical in the jelly side up and down cases. Because of this, I think it's fair to eliminate rotational isomers.
Similarly top face toast and bottom face toast are identical in the jelly side up and down cases. Because of this, I think it's fair to eliminate rotational isomers.
Alex Markley@mogwai_poet If you allow for rotation, that might help with the classification. So for example, case 1 "Toast" might have a total of 6 variants. Five of them could be considered “Degenerate Toast" due to their inherent instability.