Wow! Great suggestion. Whether to count coconut milk as milk is a decision I had not yet had to make.
My thinking at the moment is that I probably would not. It seems like further research would reveal a whole new region in the upper left, clustering with Dan Bing, of "asian milkless crepes."
Something like a Dutch baby (German pancake) qualifies as dark breakfast (4 eggs 1/2c flour 1/2 c milk
What dimension would you add to make a tetrahedron?
I would add sugar.
Egg nog is listed on the triangle as away from flour, but it is extremely high in carbs. When I was a kid, I loved egg nog and a couple of years ago I decided to purchase some. I liked it so much I drank the whole half gallon in a day. That night I had horrible painful bloating and looked at the ingredients label to find "sugar", "cane sugar". "corn syrup", and "high fructose corn syrup".
It's not so much that it's high in carbs, it's extraordinarily high in fat. Its main ingredients are egg yolks and heavy cream along with the sugar. What you're describing is like eating an entire cheesecake or drinking a pitcher of melted premium ice cream. The bloating is from the enormous amount of fatty calories that are slow to digest. Not really about the sugar. (And of course it has sugar, it's essentially a dessert drink.)
My money is on the amount of lactose in all that dairy. There's a lot of lactose in a half gallon of nog.
Right? I felt bloated just thinking about drinking a half gallon of nog.
I can barely get through an 8 oz glass of that stuff. Wow.
They are delicious, similar to noodles but I eat them cold with a dry chutney and a great breakfast.
These look great, squarely in my breakfast wheelhouse, definitely eggy, but with - well, I guess what I now know as a hint of darkness. Thanks for sharing.
I've been meaning to go to Sri Lanka..
Going to share my advice to people going to Sri Lanka (other than what food to try and where) is to not focus on beaches (which are mostly pretty average) and go to the mountains and ancient cities which are unique and amazing.
Hoppers are not only Sri Lankan - also found in parts of South India and I think in some places in SE Asia.
Same. When I was on a bit of black beach I looked on the internet and found quite a few boats had shed oil along there. Everything else was good though.
FYI, You may not have to travel to Sri Lanka to try one.
I've tried their Kings X restaurant, and while their food is delicious, and the decor is also really nice, its not particularly authentic, and I felt its a bit overpriced (tbf its an extremely central location). I don't live in London so can't suggest a better alternative, but I'm sure there are much more authentic restaurants.
> the decor is also really nice, its not particularly authentic, and I felt its a bit overpriced
That describes all of the restaurants in the Kings Cross newly built area. They are all different cuisines, but they all fit.
sadly, they don't open for breakfast.
I wonder if this is why I've missed them? I've lived within a few hundred metres of their Soho place for the best part of the last decade.
The Egglish Muffin.
And is a decidedly superior breakfast.
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This article doesn't do it justice, but the Womelette at the short-lived Royal Canadian Pancake House in NYC lived in the dark abyss.
It wasn't just an omelette on top of a waffle (and both of them the size of a medium pizza). As you strayed from the edges toward the center it became difficult to see where the waffle ended and the omelette began.
Such a shame they went out of business.
A bit of a tangent, but I just want to say how, as a Canadian, I'm getting a lot of joy reading about this restaurant. It's a hilarious facsimile of a Canadian restaurant for a couple reasons:
- There's nothing Canadian about a pancake house. We love pancakes but they aren't really ingrained with our identity. Maple syrup on the other hand, is EXTREMELY important to a lot of Canadians. Serving table syrup instead of real maple syrup is an affront. I found a Reddit thread[1] where a user espouses "tons of free syrup" you were given at RCPH. That's NOT a good thing if you ask me!
- In Canada (and I assume other British Commonwealth countries) you aren't legally allowed to have "Royal" in the name of your business without Royal consent from the Governor General of Canada[2]
Just a bit of Canadiana sparked by your comment I thought I'd share. I always get a kick of the small but conspicuous cultural differences between Canada and USA. They give me that Ingluorious Basterds "number 3" moment.
The article you linked claims "any type of omelette", but the vast majority of omelettes[*] are semicircles, not circular, right? You'd have to cook the top and bottom separately or mostly separately to get a circular one. Hm.
[*] of course, here I mean proper omelettes, which are an egg shell around ingredients, not scrambled eggs with ingredients mixed in.
In my experience if they're semicircular it's because they're folded over on themselves. Not sure what that has to do with cooking (or not) both sides.
Your ingredient mixing distinction doesn't reflect what I've encountered. That seems to have more to do with the nature of a given ingredient or alternatively with presentation or other concerns specific to a given recipe.
Yeah if you wanted "cooked separately and also circular" you'd need to make a two omelette sandwich. I've yet to encounter that at a restaurant.
Blending an omelette and a waffle should be totally doable; I've made waffle frittatas before and they turned out great.
It sounds like you're kind of a little up and to the right of the Ugandan Rolex[1]. This sounds like some hideous method of gangland killing, but is in fact a tomato omelette rolled up in a big fresh chapati. Nothing to stop you using any other variety of omelette and indeed I've had excellent results with cheese ones.
Haha. I'd suggest that what's missing in the um "latent space" here, is that the triangle should be a pentagon involving some form of bacon/sausage, and some form of potato.
This cracked me up, because I had a fantastic dream the other night where I had a tour through a donut factory. But the best thing I had (in the dream) was something I'd never tried before, never seen, and which I intend to make at the earliest opportunity. It was slightly salty french fries, buttered and coated in sugar and cinnamon, like cinnamon toast. Bang on. Makes a lot of sense too, if you think about it. Definitely would fit in the "dark breakfast" polygon.
[edit] the potato and bacon theory also comes from what ends up deliciously mixed on your plate at the end, which along with syrup and ketchup is also an integral part of any egg/flour/milk breakfast.
> It was slightly salty french fries, buttered and coated in sugar and cinnamon, like cinnamon toast. Bang on. Makes a lot of sense too, if you think about it.
The closest existing food I know to this are churros, which can be truly excellent when made well. In places like Barcelona, they dip them in chocolate sauce.
I support your experiments in potato-based churro analogs!
Yeah meat is another dimension, as is potato. So we're up to 4 dimensional breakfast latent space. I hate to think what's in the dark breakfast black hole of that 4 dimensional latent space...
I feel like there's a lot of unexplored area in the carb-soaked-in-egg category that French Toast fits into. The major analogues being chiliqiles and matzoh brie. I recently did something like french toast bites where I cubed some sourdough bread, soaked it with egg and fried it up with small pieces of bacon mixed in. But what if you did that with a glazed donut? Or a waffle?
[edit] just also why this post touched my heart - I think form is as important as ingredients whenever you're dealing with relatively few ingredients. I have a breakfast I particularly love making that's just hash browns, egg and cheese. But the trick is, you griddle the hash browns, then flip them and smash them on griddled cheese, then crack an egg on top while the cheese fries and flip the whole thing again. The result is a crispy potato pancake where one side is fried cheese and the other is embedded fried egg. The same 3 ingredients, but it can be held in hand and it's got the perfect balance in each bite.
you can just french toast anything you have laying around in your fridge or kitchen. they can't stop you.
i've done the french toast pizza and it wasn't bad. not sure if it was worth the effort. maybe there's an ideal type of pizza or combo of toppings that makes this spectacular. either way it's worth trying once just to say you did.
theres a japanese recipe for fried sweet potatoes with brown sugar/caramel sauce
Isn't a basic soufflé gonna fall somewhere in the dark breakfast territory?
so, a pentagon, you say. hmmm. Yes, or more properly a pentacle, a protective glyph around the sacred meal.
yes, a much better vector space. Thank you, Noduerme, you are one of the faithful.
I'd add oil as another dimension - sunflower oil, olive oil, butter, lard, whatever.
In Malaysia, a common breakfast is roti telur + teh tarik which is close to the dark breakfast region. It's like paratha, with an egg, and milk tea.
It is difficult to put milk into food. Why not just drink it? Alternatively, can we drink eggs and flour?
Cheese is another variation for milk. What about grilled cheese and eggs? Or some variation on Mac and Cheese?
You can also consider other dimensions like vegetables and spices. According to this plane, shakshuka is pure egg. Add spices to milk and you have chai. Add eggs to chai and you have cursed eggnog.
Egg paratha is a common Indian dish. The dough can be made with flour and water, but is traditionally made with flour and milk.
Roti Telur is basically Egg Paratha. Indian migrants brought Paratha to Malaysia and Singapore, and it underwent some "localization" to suit the local palate, including being drenched in palm oil as it is cooked on the flat griddle. Sure fire way to clog your arteries, if eaten on a daily basis.
The palm oil makes the difference. Not exactly drenched, but just enough for the crispy Mallard reaction.
It's a little simpler than the given recipe too. Just a regular paratha, crack an egg directly onto it, then cook on a griddle.
There is prior art in the grilled cheese and eggs area: Denny’s Moons Over My Hammy.
For a continental vibe see the french "Croque Madame"
Is that different than a "Croque Monsieur"? For whatever reason I've been watching Jacques Pépin videos recently. The crust on his "Croque Monsieur" is incredible.
We can certainly drink eggs, Rocky had a few in the morning before he went to punch hanging frozen meat.
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It has been speculated that over half of the breakfast in the universe is dark breakfast.
Others say we underestimated the importance of a small quantity of eggs and proposed a modified theory that doesn't need dark breakfast.
Can be confirmed by the fact anytime I eat a diner breakfast I feel more full than can be justified by the weight of the food alone.
By mass, sure - but have you considered delectability?
Even though it's not delectable by current methods, we can observe dark breakfasts effects on the movement of dietary bodies.
On the darkest day of the year, the dark breakfast can be balanced on its edge.
There's a lot more dark breakfast in the winter time.
If you add baking powder and butter, that dark breakfast recipe is very close to crepes.
My crepe recipe - cook on medium heat pan:
Blend on low: 4 eggs- 3/4 cup whole milk, 1/2 stick of melted butter, and 1/4cup to 1/2 cup plain flower, 1 heaped tbsp of baking powder, 1/2 tsp salt, vanilla optional and to taste
Looks like very close to the dark breakfast recipe
Interesting, we could add in an 'arm' from the pancake local group, heading out from American pancakes, via traditional English pancakes (approx 1 cup of whole milk, 2 eggs, 3/4 cup of flour) to Crepes.
I guess the only difficulty there is we English don't eat those for breakfast, and really only make them on one day of the year. Which I missed this year!
Dammit, we're going to be having a belated pancake day here soon...
As an Englishman that has been transplanted to another country, I find myself making them more in Germany than I ever made them back home.
But that's because my wife requests it.
It would never occur to me to up the egg ratio so high to reach into that void though. My wife manages to mess up the proportions every time though, so maybe we'll unwittingly explore that region one day.
Someone else may have said this but strictly speaking breakfast is something like a cone in a vector space, unless you want to explain to me how to eat negative eggs.
> unless you want to explain to me how to eat negative eggs.
I'm sure there's a good joke in there involving trans-dimensional vegans, but I'm still on my first cup of coffee.
Are you telling me this dimensional vegan is trans.
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Chicken maybe? It would represent an egg that did exist, but now doesn't.
Also, in the other direction in space time, it's an egg that could have been, but now won't.
In the breakfast space, I'm afraid, chicken is orthogonal to eggs.
The vectors containing the weights of each ingredient live in the positive orthant (x >= 0).
When you divide by x by sum(x), the resulting vector p has p >= 0 and sum(p) = 1. That new sum constraint is how you get the simplex.
Easy. Start eating two eggs a day. Then one day, eat three eggs taking the extra egg from tomorrows two spare eggs left in the carton.
Maybe the axes are actually logarithmic so 0 is 1 egg, 1 is e eggs, -1 is 1/e eggs, etc.
There’s a guy in overalls in a Brooklyn bistro who used to scramble them but that was very late-summer 2025 and you’ll get funny looks for asking about them.
I think I will attempt to just eat the negative eggs because at least I recognize, and can define what both "negative" and "eggs" mean. Can't say the same for literally half the words in the OP's graph.
I think it is all normalized into positive vector space [0, 1] using min-max.
What is menstruation but negative egg entering the body?
These are a Barycentric Coordinate System, so the weights on the targets are normalized, must sum to one, and must be positive.
Barycentric coordinates are the local coordinate system inside a simplex. A simplicial complex is what you get when you glue multiple simplices together along shared k-faces for k = 0 … n -- vertices (0-faces), edges (1-faces), triangles (2-faces), tetrahedra (3-faces), and higher-dimensional faces -- to form a larger state space.
It's not possible to have negative eggs, but you can apply the same machinery to many other things, like facial animation mesh blend shapes (Apple ARKit, Blender Blend Shapes and the FaceIt plugin, Unity SkinnedMeshRenderer, etc), where weights are often allowed to be overdriven >1 or even underdriven <0 for exaggerated or monstrous effects.
(Eric "Irk" Hedman designed and created the character animations and objects in The Sims 1, and as you can see is extremely skilled and delightful to work with! Hire him if you need professional high quality creative artwork and animation, and can pay him in bananas: https://erichedman.artstation.com/projects/8wJDgw )
Faceit: Facial Expressions And Performance Capture (Blender):
ARFaceAnchor.BlendShapeLocation:
Identifiers for specific facial features, for use with coefficients describing the relative movements of those features.
My breakfast recipe this morning, thanks to this article:
- 1/4 c. milk
- 1/2 c. flour
- 4 eggs
- 1/3 c. sugar
- some salt
- cinnamon
- cloves
- nutmeg
- poppyseeds
Did the first two cakes without baking powder, turned into something between a crepe and a tortilla. Did the last two cakes with baking powder and they were just a very squishy pancake.
Going against the spirit of TFA here, but I believe you can eat anything at any time of day, and my favorite breakfast tends to be regular food. Chili, soup, pasta, baked potatoes. Something warm, filling, and usually involving salt. I do sometimes have something more traditional, like oatmeal, but it's not as satisfying. I also sometimes have oatmeal as my final meal of the day if I'm hungry but already a bit tired, as it's more calm than something like spicy chili.
I really wonder why breakfast is the way it is, because since it's the first meal of the day, you'd think a big breakfast (e.g. dinner) would make sense as you need the calories during the (work)day. But maybe breakfast is relatively light because a lot of people have some digestive issues or sensitive stomachs in the mornings.
Circadian rhythm. In many people their liver releases a bunch of glucose right before waking, something diabetics term the "dawn effect" and need to control for. This helps get the metabolism going first thing in the morning (at least, in non-diabetics) and delays the need for caloric intake until later in the day. This effect is easily witnessed if you check your blood glucose before bed and when you rise in the morning: for example earlier in the week mine was around 5.4 mmol/L (normal) at bed time and 8.6 mmol/L (high for fasting blood glucose) before breakfast the next day.
A normal person will need caloric replenishment during the day, especially later in the day before (typically) an 8 to 10 hour fast during the night.
So, small proteine-heavy breakfast, large balanced dinner in the evening with a smaller balanced mid-day meal in the middle.
It depends on whether you're making the breakfast, or someone else is making your breakfast.
Light breakfasts are popular if you have to make it yourself
Eating a lot of food is tiring and you have plenty of energy stored from the previous day(s) food.
That is not what we are talking about.
Also, amazing article, haven't laughed that hard all day!
The recipe at the end sounds a lot like the crepes I'd make in college. It was pre-WWW and I had no idea what I was doing but it seemed to work. The one thing I had going for me in college was a Costco membership. 25lb bags of flour, gallons of milk, and flats of eggs.. all cheap. I'd barter with roommates for crepe toppings (sour cream and jelly usually).
A soufflé would fit some of the void. It has some flour in the bechamel.. whipped egg whites etc.
I feel like excluding French toast is a serious faux pas here!
Breakfast burritos are also at least as important as quiche (as in, neither are as tasty without addins - just like omelettes).
Agreed, he’s added criteria for excluding French toast to fit his narrative. Gaslighting the world away from us French toast lovers.
And don’t get me started on breakfast burritos, top 10 food that’s just ridiculous if you’re ordering it after 3pm?
Eastern European pan-fried cottage cheese fritters (mix and fry 150g cottage cheese, 5 tbsp flour, 1 egg, 3 tbsp sugar, salt) are great. That's all I have to say.
Quark works better than cottage cheese, if you don't have access to tvorog
Oh, I do frequently have biscuits and gravy topped with fried eggs, though the biscuits and gravy would definitely pull it further towards the flour end of the spectrum, maybe not quite in the dark region.
Also, hollandaise is pretty integral to eggs benedict, I've had lots of variations but the traditional with poached egg, canadian bacon, english muffin, and hollandaise is really by far the best.
How about a Sauce Mornay?
béchamel (roux + milk) + egg yolks + cheese
So eggs with white gravy? I think I’ve had that combo and it was pretty banging.
Even easier - egg sandwich using a basic milk bread.
Add crawfish and you're really talkin
This is amazing - and somehow channels both Douglas Adams and Randall Munroe at the same time...
Thank you! Two of my favorites. I'm honored.
Frankly I'm surprised Randall Munroe hasn't done this. (I assume he hasn't because nobody has linked to it.)
This is the greatest text I have read in the last 10 years, it kept getting better as it went along.
So that blurry eye vision I get in the morning could be from gravitational lensing from dark breakfast?
Surprised not to see “breakfast pasta” aka Carbonara. Wheat in the noodles, egg and cheese sauce.
Or pasta as a cereal, in a bowl with milk.
This whole thing is simply missing all milk based diary products like cheese, yogurt, white cheese, etc. When that is included then there is no gap or any mysterious quadrant.
Posts like this are why I read Hacker News.
My Egg McMuffin will never look the same!
What sort of projection is this that turns a 3-dimensional space into a triangle!
While you are technically correct, since any triangle is a simplex, this is not relevant to this visualization.
For this visualization: get positive quantities in 3D space, normalize to 1, now you have dot on a triangle on 1-sphere in a positive octant. Project triangle into 2D space a this is your visualization.
2-sphere, I believe you mean to say.
It's easy, if you normalize it so that it sums to one, it drops a dimension, and becomes an equilateral triangle.
"IHOP Transgression" cracked me up. There's a restaurant in my town that does the same thing and I hate them for that reason. And like IHOP, what they call an omelette is actually a frittata.
The Irish full breakfast (fry up) includes soda bread, often fresh baked. That with the eggs likely puts it in the "Dark Breakfast" sector. Other sorts of full breakfast may also end up there, there's no true fixed set of ingredients in a full breakfast so any egg-heavy variety can end up in the "dark" sector.
Is the "Dutch Baby" in the pancake group some alternative name for "flensjes" that I'm not familiar with? It's a thin dessert variation of Dutch pancakes that has relatively high egg and milk ratios compared to flour.
Dutch Baby or German Pancake is probably right in that abyss.
Very eggy, with some flour/milk. It's essentially a souffle, puffs up to like 6" high in the oven. Tasty with maple syrup, powdered sugar/lemon, or just butter.
> Confusion continues because: People who live in the Hollands are called Hollanders, but all citizens of the Netherlands are called Dutch as is their language.
> But in Dutch they say: "Nederlands sprekende Nederlanders in Nederland" which sounds like they'd rather we call them Netherlanders speaking Netherlandish.
> Meanwhile, next door in Germany, they're "Deutsche sprechen Deutsch in Deutschland". Which sounds like they'd rather be called Dutch.
Cold pizza dead center.
Cold pizza + eggs, but then we're just in "egg & cheese sandwich" territory which is one obvious "dark breakfast".
It would be remiss not to also mention The Cube Rule
You can tell a non-US-southerner wrote this because there's not a biscuit to be had here.
WHERE ARE THE BISCUITS???
I sympathize with the author, I've had similar thoughts about snacks. We need more non-sweet snacks. Ideally something that tastes good, is not too salty, is healthy and satisfies your cravings.
Nuts (in the culinary sense) and cheese are good for that - a mini-cheeseboard with a couple of different bits of cheese (maybe 20-30g of each), a handful of cashews and walnuts, and maybe a dab of fig jam or membrillo on the side.
Tasty, nutrient-dense, surprisingly filling. Great as a mid-afternoon snack, or add some fruit and a bit of bread or some oatcakes to make it into a decent lunch.
South African food actually has this in abundance, biltong is like beef jerky but better in almost every conceivable way - not to mention all the other variants of it for example dry stix, droevors, etc.
Not to say we don't also have other sweet snacks, but compared to other places I've been nowhere quite has the same level of "savory" snacks
That's a hard one.
In terms of beverages alcohol-free beer gained popularity in recent years because it's not sweet, has half the calories of juice/soda yet actually carries some taste.
If I were to imagine something fitting this description, it would have to be something you have to chew for extended periods of time.
Congratulations. You've reinvented the souffle.
No egg banjo*? That sounds like it would sit close to, if not in, the abyss.
Might choux hit that dark breakfast abyss? They aren't breakfast per se, but it might show that you can do things with those proportions.
Eggs benedict calls from the abyss, humanities' metabolic Voyager 1, speeding into the unknown.
Are we counting butter as milk? Because hollandaise sauce is an emulsion of egg yolk, butter, and lemon juice, so no milk directly unless we count butter.
Isn't it something like pancake with more eggs?
The real question is why this isn't already a dish.
Breakfast is just generally milquetoast then?
Aggakake or oeuf au lait.
3 eggs, 2 cups milk, 1 cup flour. Makes a nice flan/pudding consistency. Eggy and delicious.
Aggakake is on the chart!
What about eggs eggs and milk breakfast? (Omelette with cheese). Plenty of protein and little sugar
> IHOP omelettes include pancake batter.
Wait what? I've never heard of such a thing.
Does that make them better in any way? Or strictly worse, but cheaper?
Edit: looked it up and apparently they still use 3 eggs but the batter makes it super fluffy (like 2x) so the omelette looks enormous.
It’s a landmine for low carb gluten free people
What about french toast? I feel like there is a lot of egg in it, might place it near the bottom of the abyss.
French toast isn't plotted because the recipe doesn't customarily start with flour, but if you do plot it it ends up in the lower middle. If you have exceptionally eggy challah, then you might be able to push it into the abyss, but really exceptionally eggy, like 1:1 egg to flour by weight.
Things made of flour? I think they were explicitly covered. Perhaps "Flour" should have been more generally "Grain-based" to cover oatmeal and rye bread. Maybe add potatoes for a "starches" category.
What it's missing is fish, fruit, preserved meats (bacon, ham, sausage, black pudding?). It's very culturally biased to typical North American breakfast choices.
pizza
A Japanese Souffle Pancake might be in the Dark Breakfast realm.
I'm sorry, but I can't take seriously any topic in breakfast that leaves out the Taj Mahal of breakfast: stuffed French toast. I know there is reasoning for it but its inexcusable. Its like leaving Miracle Max out of a discussion of best physicians because he's fictional.
There's also no mention of the fourth leg of the breakfast triad: maple syrup.
It's what they ate on the Red October
Colombia's bandeja paisa.
I think it would make sense to include pudding - it's basically milk with a bit of flour. It's important to include because it shows that there are foods beyond Pancake Local Group that aren't just liquid milk.
One important property of pudding is that unlike pancakes, the space of pudding isn't "chaotic and fractal" because whether you add just enough flour to make it somewhat sticky or so much that you can cut it with a knife, it's still pudding. This means that if we take flour-heavy pudding and somehow add shitload of eggs, we should be able to venture into the Dark Breakfast area. I have a pudding recipe that calls for egg yolks, but I feel like this isn't a good lead. Still it proves further how flexible "pudding" is.
Going back to pancakes, there's one funny variation. "Naleśniki" with cottage cheese and cream (or yoghurt). Cottage cheese and cream are basically milk with extra steps, which means that the entire dish becomes mainly milk. This means that the Pancake Local Group actually stretches much closer to the "milk" vertex than your diagram suggests.
If I were to prepare something that passes as food and sits in the Dark Breakfast Abyss, I'd try scrambled eggs on the thinnest bread I could reasonably make. Something like "scrambled eggs taco".
I am humbled by the genius of this article.
This is the kind of creative thinking that makes HN great. Using the framework of dark matter detection to explore unobserved breakfast possibilities is both hilarious and oddly rigorous. The breakfast phase space is clearly under-explored.
Egg scramble fluffed with milk plus slice of toast might qualify
So basically omelette with matzo
An omelet wrapped in a paratha with a caffe latte to drink looks like the obvious answer... You can also play with the crust to filling ratio of a quiche...
How about doughnut with just the right amount of custard filling? Or perhaps a brioche with the right amount of French vanilla ice cream/gelato? A classic egg and cheese sandwich in your desired proportions?
While a delightfully funny article it also touches on something I’ve thought about many times before: just how uniform basically 99% of all (American) restaurant breakfast menus are. It’s really quite extraordinary in some ways how these menus are nearly entirely interchangeable from on to another. They might have very small tweaks and of course the ingredient specifics aren’t exact (specific butter brands, slight proportion differences)but by and large you could predict with almost perfect accuracy every single item that a typical breakfast menu in the US might have.
And I feel like that’s really a missed opportunity? Like even recognizing that of all meals breakfast is the most “comforting” and the one most likely for customers to want familiar, at the same time there are so many unexplored variants using the same ingredients (as this article shows!) that almost no restaurants will ever experiment with or offer. Lunch and dinner menus have massive variation in comparison!
The ones who walk away from omelettes.
That's a Pulitzer Prize for Poetry worthy reference.
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french toast was dismissed far too lightly, it's exactly what goes into the gap. also savoury bread pudding.
Applying Tom Ngo's Embedded Constraint Graphics to Direct-Manipulation Breakfast Selection (Direct manipulation over simplicial complexes using barycentric interpolation: they're not just for breakfast any more.)
The Breakfast Simplex is a space of recipes parameterized by {egg, milk, flour} ratios, normalized onto a simplex. Add butter or sugar and the dimension increases. Add prep method and you create adjacent regions. A breakfast buffet is a larger, possibly disconnected simplicial complex spanning multiple ingredient families.
That structure is exactly what Tom Ngo formalized and patented in Embedded Constraint Graphics in 1996 at Interval Research Corporation. I wrote about it when the patent expired in 2016:
When I asked Tom about applying ECG to other applications after the patent expired, he wrote:
>I am, of course, partial to the idea that gluing high-dimensional simplices at their edges and faces is an extremely general way to represent blending manifolds, in the same way that gluing polygons together has done us so much good in the 3D modeling space. I also think the >2 decades of progress since ECG have put us in a better position to do something really cool based on direct manipulation.
Golan Levin, Malcolm Slaney, and Tom Ngo used the ECG graphical editor to build the vector face cartoons for Mouther, simply by dragging eyes, mouths, and features directly on the drawing:
ECG defines example states at vertices. Compatible examples span simplices. The full state space is a simplicial complex. Interior points are barycentric blends.
When you drag something in screen space, the system maps that motion into the n-dimensional interpolation space and solves for blend weights via the Moore–Penrose pseudoinverse of the Jacobian matrix, the same linear algebra used in inverse kinematics.
You don’t indirectly adjust abstract sliders. You directly manipulate concrete outcomes. The solver recovers coordinates.
The same formulation applies to interpolating vector drawings, mesh blending, facial animation, pose spaces, and other example-based interfaces where states are meaningful and compatibility matters.
The same geometric intuition appears in large language models. Tokens and concepts are represented as high-dimensional vectors, and model activations are computed through weighted linear combinations in embedding space. Interpolating between embeddings corresponds to moving through that vector space via weighted blends, just in many more dimensions. ECG makes the simplices explicit and topologically structured, while LLM representations are implicit and learned. In both cases, behavior emerges from interpolation in high-dimensional spaces.
Apple’s ARKit already exposes facial expression as a set of named blend shape coefficients via ARFaceAnchor — values like mouthSmileLeft, jawOpen, and eyeBlinkRight driving a 3D face mesh in real time. Bring Mouther into 3D and you can drag the mouth corners upward to interpolate toward smiling targets, mapping that motion through the same barycentric machinery into blend weights instead of hard-coded sliders. This would make a great Blender plug-in for directly manipulating facial animation, to use with FaceIt!
Faceit : Facial Expressions And Performance Capture
Breakfast is a concrete instance. Pancake, crepe, and omelette define a simplex over ingredient ratios. Drag toward eggs and the egg weight increases. Drag toward milk and you move along that axis. Cross the egg-milk edge shared by the crepe simplex {flour, egg, milk} and the custard simplex {egg, milk, sugar}, and you move from thin batters into sweet custards without leaving the manifold. The Dark Breakfast region is simply an unoccupied part of a valid simplex -- suggesting adjacent, unexplored Dark Custard subspaces rather than forbidden states.
Simplicial complexes are useful UI primitives. They provide local linear interpolation inside zones and explicit global topology across zones. They scale to higher dimensions, while maintaining a user friendly 2D direct manipulation user interface. They encode constraints structurally instead of procedurally.
A pie menu can be viewed as a radial parameterization of a simplex. A direct-manipulation pie menu over ingredient space lets you drag in the direction of the crusts and fillings you want, with barycentric weights accumulating as you move.
The Design and Implementation of Pie Menus (Dr. Dobb’s Journal, Dec. 1991, cover story, user interface issue.)
An Empirical Comparison of Pie vs. Linear Menus (Jack Callahan, Don Hopkins, Mark Weiser and Ben Shneiderman.
Presented at ACM CHI’88 Conference, Washington DC, 1988.)
As a certified expert breakfast cook, I bristle at the idea that scrambled eggs includes any ingredient other than eggs or seasoning.
Also, while I know that omelette is technically the whipping of large amounts of air into what is otherwise scrambled eggs, it feels wrong to me that "omelette" is categorized as "pure egg singularity". Is an omelette worth the time and effort over scrambled eggs if it does not include bits of vegetables, meat, and/or cheese folded inside like a taco?
maybe Portugal’s Pastel de Nata falls in the dark zone?
It’s a baked custard (so plenty of eggs) in a pie.
I love the idea and the writing, but the execution seems off. Cake has a very well-defined spot and Weetabix doesn’t? More work needed
No mention of Eggs Florentine?
where's porridge?
Breakfast has way more dimensions.
I agree, that is an oversight.
Porridge is an extremely common breakfast here in Sweden. There is a huge number of different variations of it as well.
And then there is müsli, with and without yogurt / sour milk.
No jam and butter option when writing that long of a post on what to eat for breakfast is criminal.
I usually have egg on toast with plenty of butter. The combination sits squarely in the dark region I think.
I also get up early and it is often actually dark.
What about vegetable-forward breakfasts? Completely not on this chart.
That's because such breakfasts are forbidden by the Geneva Convention articles, section 23, subsection 8, paragraph 4. It's not one of the more well known provisions, but it does exist, and nobody wants to break international law.
> nobody wants to break international law
I was with you up to this point, but my suspension of disbelief has its limits.
Please allow me to introuce you to the sri lankan egg hopper (https://www.lavenderandlovage.com/2016/05/sri-lankan-egg-hop...) which lives squarely in the aforementioned dark abyss.
Wow! Great suggestion. Whether to count coconut milk as milk is a decision I had not yet had to make.
My thinking at the moment is that I probably would not. It seems like further research would reveal a whole new region in the upper left, clustering with Dan Bing, of "asian milkless crepes."
Something like a Dutch baby (German pancake) qualifies as dark breakfast (4 eggs 1/2c flour 1/2 c milk
What dimension would you add to make a tetrahedron?
I would add sugar.
Egg nog is listed on the triangle as away from flour, but it is extremely high in carbs. When I was a kid, I loved egg nog and a couple of years ago I decided to purchase some. I liked it so much I drank the whole half gallon in a day. That night I had horrible painful bloating and looked at the ingredients label to find "sugar", "cane sugar". "corn syrup", and "high fructose corn syrup".
It's not so much that it's high in carbs, it's extraordinarily high in fat. Its main ingredients are egg yolks and heavy cream along with the sugar. What you're describing is like eating an entire cheesecake or drinking a pitcher of melted premium ice cream. The bloating is from the enormous amount of fatty calories that are slow to digest. Not really about the sugar. (And of course it has sugar, it's essentially a dessert drink.)
My money is on the amount of lactose in all that dairy. There's a lot of lactose in a half gallon of nog.
Right? I felt bloated just thinking about drinking a half gallon of nog.
I can barely get through an 8 oz glass of that stuff. Wow.
Bacon. Or tomatoes.
Bacon
Giant string hoppers are far superior: https://www.hungrylankan.com/recipes/sri-lankan-string-hoppe...
They are delicious, similar to noodles but I eat them cold with a dry chutney and a great breakfast.
These look great, squarely in my breakfast wheelhouse, definitely eggy, but with - well, I guess what I now know as a hint of darkness. Thanks for sharing.
I've been meaning to go to Sri Lanka..
Going to share my advice to people going to Sri Lanka (other than what food to try and where) is to not focus on beaches (which are mostly pretty average) and go to the mountains and ancient cities which are unique and amazing.
Hoppers are not only Sri Lankan - also found in parts of South India and I think in some places in SE Asia.
Same. When I was on a bit of black beach I looked on the internet and found quite a few boats had shed oil along there. Everything else was good though.
FYI, You may not have to travel to Sri Lanka to try one.
You can get them e.g. in London UK: https://www.hopperslondon.com/
I've tried their Kings X restaurant, and while their food is delicious, and the decor is also really nice, its not particularly authentic, and I felt its a bit overpriced (tbf its an extremely central location). I don't live in London so can't suggest a better alternative, but I'm sure there are much more authentic restaurants.
> the decor is also really nice, its not particularly authentic, and I felt its a bit overpriced
That describes all of the restaurants in the Kings Cross newly built area. They are all different cuisines, but they all fit.
sadly, they don't open for breakfast.
I wonder if this is why I've missed them? I've lived within a few hundred metres of their Soho place for the best part of the last decade.
The Egglish Muffin.
And is a decidedly superior breakfast.
This article doesn't do it justice, but the Womelette at the short-lived Royal Canadian Pancake House in NYC lived in the dark abyss.
https://www.eater.com/2015/1/26/7860903/amanda-cohen-royal-c...
It wasn't just an omelette on top of a waffle (and both of them the size of a medium pizza). As you strayed from the edges toward the center it became difficult to see where the waffle ended and the omelette began.
Such a shame they went out of business.
A bit of a tangent, but I just want to say how, as a Canadian, I'm getting a lot of joy reading about this restaurant. It's a hilarious facsimile of a Canadian restaurant for a couple reasons:
- There's nothing Canadian about a pancake house. We love pancakes but they aren't really ingrained with our identity. Maple syrup on the other hand, is EXTREMELY important to a lot of Canadians. Serving table syrup instead of real maple syrup is an affront. I found a Reddit thread[1] where a user espouses "tons of free syrup" you were given at RCPH. That's NOT a good thing if you ask me!
- In Canada (and I assume other British Commonwealth countries) you aren't legally allowed to have "Royal" in the name of your business without Royal consent from the Governor General of Canada[2]
Just a bit of Canadiana sparked by your comment I thought I'd share. I always get a kick of the small but conspicuous cultural differences between Canada and USA. They give me that Ingluorious Basterds "number 3" moment.
[1] https://www.reddit.com/r/newyorkcity/comments/1ajujhi/who_re...
[2] https://www.canada.ca/en/canadian-heritage/services/royal-sy...
If "Royal" is protected, the bar is pretty low:
https://www.canadacompanyregistry.com/catagory/Royal/
HA! I guess it's not as enforced as I expected.
The article you linked claims "any type of omelette", but the vast majority of omelettes[*] are semicircles, not circular, right? You'd have to cook the top and bottom separately or mostly separately to get a circular one. Hm.
[*] of course, here I mean proper omelettes, which are an egg shell around ingredients, not scrambled eggs with ingredients mixed in.
In my experience if they're semicircular it's because they're folded over on themselves. Not sure what that has to do with cooking (or not) both sides.
Your ingredient mixing distinction doesn't reflect what I've encountered. That seems to have more to do with the nature of a given ingredient or alternatively with presentation or other concerns specific to a given recipe.
Yeah if you wanted "cooked separately and also circular" you'd need to make a two omelette sandwich. I've yet to encounter that at a restaurant.
Blending an omelette and a waffle should be totally doable; I've made waffle frittatas before and they turned out great.
It sounds like you're kind of a little up and to the right of the Ugandan Rolex[1]. This sounds like some hideous method of gangland killing, but is in fact a tomato omelette rolled up in a big fresh chapati. Nothing to stop you using any other variety of omelette and indeed I've had excellent results with cheese ones.
[1] https://www.theregister.com/2015/08/23/post_pub_nosh_ugandan...
This is fantastic, I'm dying to eat a Womelette.
Haha. I'd suggest that what's missing in the um "latent space" here, is that the triangle should be a pentagon involving some form of bacon/sausage, and some form of potato.
This cracked me up, because I had a fantastic dream the other night where I had a tour through a donut factory. But the best thing I had (in the dream) was something I'd never tried before, never seen, and which I intend to make at the earliest opportunity. It was slightly salty french fries, buttered and coated in sugar and cinnamon, like cinnamon toast. Bang on. Makes a lot of sense too, if you think about it. Definitely would fit in the "dark breakfast" polygon.
[edit] the potato and bacon theory also comes from what ends up deliciously mixed on your plate at the end, which along with syrup and ketchup is also an integral part of any egg/flour/milk breakfast.
> It was slightly salty french fries, buttered and coated in sugar and cinnamon, like cinnamon toast. Bang on. Makes a lot of sense too, if you think about it.
The closest existing food I know to this are churros, which can be truly excellent when made well. In places like Barcelona, they dip them in chocolate sauce.
I support your experiments in potato-based churro analogs!
Yeah meat is another dimension, as is potato. So we're up to 4 dimensional breakfast latent space. I hate to think what's in the dark breakfast black hole of that 4 dimensional latent space...
I feel like there's a lot of unexplored area in the carb-soaked-in-egg category that French Toast fits into. The major analogues being chiliqiles and matzoh brie. I recently did something like french toast bites where I cubed some sourdough bread, soaked it with egg and fried it up with small pieces of bacon mixed in. But what if you did that with a glazed donut? Or a waffle?
[edit] just also why this post touched my heart - I think form is as important as ingredients whenever you're dealing with relatively few ingredients. I have a breakfast I particularly love making that's just hash browns, egg and cheese. But the trick is, you griddle the hash browns, then flip them and smash them on griddled cheese, then crack an egg on top while the cheese fries and flip the whole thing again. The result is a crispy potato pancake where one side is fried cheese and the other is embedded fried egg. The same 3 ingredients, but it can be held in hand and it's got the perfect balance in each bite.
you can just french toast anything you have laying around in your fridge or kitchen. they can't stop you.
https://www.youtube.com/watch?v=hB42iztkzVQ
i've done the french toast pizza and it wasn't bad. not sure if it was worth the effort. maybe there's an ideal type of pizza or combo of toppings that makes this spectacular. either way it's worth trying once just to say you did.
theres a japanese recipe for fried sweet potatoes with brown sugar/caramel sauce
https://www.okonomikitchen.com/daigaku-imo-japanese-candied-...
Isn't a basic soufflé gonna fall somewhere in the dark breakfast territory?
so, a pentagon, you say. hmmm. Yes, or more properly a pentacle, a protective glyph around the sacred meal.
yes, a much better vector space. Thank you, Noduerme, you are one of the faithful.
I'd add oil as another dimension - sunflower oil, olive oil, butter, lard, whatever.
In Malaysia, a common breakfast is roti telur + teh tarik which is close to the dark breakfast region. It's like paratha, with an egg, and milk tea.
It is difficult to put milk into food. Why not just drink it? Alternatively, can we drink eggs and flour?
Cheese is another variation for milk. What about grilled cheese and eggs? Or some variation on Mac and Cheese?
You can also consider other dimensions like vegetables and spices. According to this plane, shakshuka is pure egg. Add spices to milk and you have chai. Add eggs to chai and you have cursed eggnog.
Egg paratha is a common Indian dish. The dough can be made with flour and water, but is traditionally made with flour and milk.
https://www.thedeliciouscrescent.com/omelette-stuffed-parath...
Roti Telur is basically Egg Paratha. Indian migrants brought Paratha to Malaysia and Singapore, and it underwent some "localization" to suit the local palate, including being drenched in palm oil as it is cooked on the flat griddle. Sure fire way to clog your arteries, if eaten on a daily basis.
The palm oil makes the difference. Not exactly drenched, but just enough for the crispy Mallard reaction.
It's a little simpler than the given recipe too. Just a regular paratha, crack an egg directly onto it, then cook on a griddle.
There is prior art in the grilled cheese and eggs area: Denny’s Moons Over My Hammy.
Or the even more legendary Breakfast Dagwood https://violasmithcooking.blogspot.com/2009/08/breakfast-dag...
For a continental vibe see the french "Croque Madame"
Is that different than a "Croque Monsieur"? For whatever reason I've been watching Jacques Pépin videos recently. The crust on his "Croque Monsieur" is incredible.
https://youtu.be/2ZTOUyUBCz4
We can certainly drink eggs, Rocky had a few in the morning before he went to punch hanging frozen meat.
It has been speculated that over half of the breakfast in the universe is dark breakfast.
Others say we underestimated the importance of a small quantity of eggs and proposed a modified theory that doesn't need dark breakfast.
Can be confirmed by the fact anytime I eat a diner breakfast I feel more full than can be justified by the weight of the food alone.
By mass, sure - but have you considered delectability?
Even though it's not delectable by current methods, we can observe dark breakfasts effects on the movement of dietary bodies.
On the darkest day of the year, the dark breakfast can be balanced on its edge.
There's a lot more dark breakfast in the winter time.
If you add baking powder and butter, that dark breakfast recipe is very close to crepes.
My crepe recipe - cook on medium heat pan:
Blend on low: 4 eggs- 3/4 cup whole milk, 1/2 stick of melted butter, and 1/4cup to 1/2 cup plain flower, 1 heaped tbsp of baking powder, 1/2 tsp salt, vanilla optional and to taste
Looks like very close to the dark breakfast recipe
Interesting, we could add in an 'arm' from the pancake local group, heading out from American pancakes, via traditional English pancakes (approx 1 cup of whole milk, 2 eggs, 3/4 cup of flour) to Crepes.
I guess the only difficulty there is we English don't eat those for breakfast, and really only make them on one day of the year. Which I missed this year!
Dammit, we're going to be having a belated pancake day here soon...
As an Englishman that has been transplanted to another country, I find myself making them more in Germany than I ever made them back home.
But that's because my wife requests it.
It would never occur to me to up the egg ratio so high to reach into that void though. My wife manages to mess up the proportions every time though, so maybe we'll unwittingly explore that region one day.
Someone else may have said this but strictly speaking breakfast is something like a cone in a vector space, unless you want to explain to me how to eat negative eggs.
> unless you want to explain to me how to eat negative eggs.
I'm sure there's a good joke in there involving trans-dimensional vegans, but I'm still on my first cup of coffee.
Are you telling me this dimensional vegan is trans.
[dead]
Chicken maybe? It would represent an egg that did exist, but now doesn't.
Also, in the other direction in space time, it's an egg that could have been, but now won't.
Schrödinger’s egg?
More like Minkowski's egg in this case.
Now I want some chicken & waffles
https://en.wikipedia.org/wiki/Chicken_and_waffles
In the breakfast space, I'm afraid, chicken is orthogonal to eggs.
The vectors containing the weights of each ingredient live in the positive orthant (x >= 0).
When you divide by x by sum(x), the resulting vector p has p >= 0 and sum(p) = 1. That new sum constraint is how you get the simplex.
Easy. Start eating two eggs a day. Then one day, eat three eggs taking the extra egg from tomorrows two spare eggs left in the carton.
Maybe the axes are actually logarithmic so 0 is 1 egg, 1 is e eggs, -1 is 1/e eggs, etc.
There’s a guy in overalls in a Brooklyn bistro who used to scramble them but that was very late-summer 2025 and you’ll get funny looks for asking about them.
I think I will attempt to just eat the negative eggs because at least I recognize, and can define what both "negative" and "eggs" mean. Can't say the same for literally half the words in the OP's graph.
I think it is all normalized into positive vector space [0, 1] using min-max.
What is menstruation but negative egg entering the body?
These are a Barycentric Coordinate System, so the weights on the targets are normalized, must sum to one, and must be positive.
https://en.wikipedia.org/wiki/Barycentric_coordinate_system
Barycentric coordinates are the local coordinate system inside a simplex. A simplicial complex is what you get when you glue multiple simplices together along shared k-faces for k = 0 … n -- vertices (0-faces), edges (1-faces), triangles (2-faces), tetrahedra (3-faces), and higher-dimensional faces -- to form a larger state space.
https://en.wikipedia.org/wiki/Simplicial_complex
It's not possible to have negative eggs, but you can apply the same machinery to many other things, like facial animation mesh blend shapes (Apple ARKit, Blender Blend Shapes and the FaceIt plugin, Unity SkinnedMeshRenderer, etc), where weights are often allowed to be overdriven >1 or even underdriven <0 for exaggerated or monstrous effects.
Nouveau Art Pipeline Demo: Blend Shapes:
https://youtu.be/phM8Wnzs_-g?t=104
(None of Epstein's spiritually close friends and shameless guru confidants were harmed or embarrassed in this demo, alas.)
Eric Hedman - "Doppel" Character Modelling with Blendshapes for Animation (ARKit):
https://www.youtube.com/watch?v=6L7jtgRD5rs
(Eric "Irk" Hedman designed and created the character animations and objects in The Sims 1, and as you can see is extremely skilled and delightful to work with! Hire him if you need professional high quality creative artwork and animation, and can pay him in bananas: https://erichedman.artstation.com/projects/8wJDgw )
Faceit: Facial Expressions And Performance Capture (Blender):
https://superhivemarket.com/products/faceit
Unity SkinnedMeshRenderer:
https://docs.unity3d.com/6000.3/Documentation/ScriptReferenc...
Apple ARKit Tracking and visualizing faces:
https://developer.apple.com/documentation/ARKit/tracking-and...
ARFaceAnchor.BlendShapeLocation: Identifiers for specific facial features, for use with coefficients describing the relative movements of those features.
https://developer.apple.com/documentation/arkit/arfaceanchor...
My breakfast recipe this morning, thanks to this article:
- 1/4 c. milk
- 1/2 c. flour
- 4 eggs
- 1/3 c. sugar
- some salt
- cinnamon
- cloves
- nutmeg
- poppyseeds
Did the first two cakes without baking powder, turned into something between a crepe and a tortilla. Did the last two cakes with baking powder and they were just a very squishy pancake.
Going against the spirit of TFA here, but I believe you can eat anything at any time of day, and my favorite breakfast tends to be regular food. Chili, soup, pasta, baked potatoes. Something warm, filling, and usually involving salt. I do sometimes have something more traditional, like oatmeal, but it's not as satisfying. I also sometimes have oatmeal as my final meal of the day if I'm hungry but already a bit tired, as it's more calm than something like spicy chili.
I really wonder why breakfast is the way it is, because since it's the first meal of the day, you'd think a big breakfast (e.g. dinner) would make sense as you need the calories during the (work)day. But maybe breakfast is relatively light because a lot of people have some digestive issues or sensitive stomachs in the mornings.
Circadian rhythm. In many people their liver releases a bunch of glucose right before waking, something diabetics term the "dawn effect" and need to control for. This helps get the metabolism going first thing in the morning (at least, in non-diabetics) and delays the need for caloric intake until later in the day. This effect is easily witnessed if you check your blood glucose before bed and when you rise in the morning: for example earlier in the week mine was around 5.4 mmol/L (normal) at bed time and 8.6 mmol/L (high for fasting blood glucose) before breakfast the next day.
A normal person will need caloric replenishment during the day, especially later in the day before (typically) an 8 to 10 hour fast during the night.
So, small proteine-heavy breakfast, large balanced dinner in the evening with a smaller balanced mid-day meal in the middle.
It depends on whether you're making the breakfast, or someone else is making your breakfast.
Light breakfasts are popular if you have to make it yourself
Eating a lot of food is tiring and you have plenty of energy stored from the previous day(s) food.
That is not what we are talking about.
Also, amazing article, haven't laughed that hard all day!
The recipe at the end sounds a lot like the crepes I'd make in college. It was pre-WWW and I had no idea what I was doing but it seemed to work. The one thing I had going for me in college was a Costco membership. 25lb bags of flour, gallons of milk, and flats of eggs.. all cheap. I'd barter with roommates for crepe toppings (sour cream and jelly usually).
A soufflé would fit some of the void. It has some flour in the bechamel.. whipped egg whites etc.
I feel like excluding French toast is a serious faux pas here!
Breakfast burritos are also at least as important as quiche (as in, neither are as tasty without addins - just like omelettes).
Agreed, he’s added criteria for excluding French toast to fit his narrative. Gaslighting the world away from us French toast lovers.
And don’t get me started on breakfast burritos, top 10 food that’s just ridiculous if you’re ordering it after 3pm?
Eastern European pan-fried cottage cheese fritters (mix and fry 150g cottage cheese, 5 tbsp flour, 1 egg, 3 tbsp sugar, salt) are great. That's all I have to say.
Quark works better than cottage cheese, if you don't have access to tvorog
Salzburger Nockerln seems to fit in that area. https://www.austria.info/en-gb/recipes/salzburger-nockerl/
Love how at at the milk apex, there is cafe latte. Of course, it couldn't just be milk, perish the thought!
Have to wonder if yogurt counts, since I've had that for breakfast many more times than just milk or a latte
I suggest that the forbidden breakfast is tantamount to an eggs benedict, but with the hollandaise sauce replaced by a roux.
If it's forbidden, it is rather "eggs interdict".
The eggs had better be deviled, too.
https://en.wikipedia.org/wiki/Deviled_egg
Vile eggs need de-viling, otherwise not.
Oh, I do frequently have biscuits and gravy topped with fried eggs, though the biscuits and gravy would definitely pull it further towards the flour end of the spectrum, maybe not quite in the dark region.
Also, hollandaise is pretty integral to eggs benedict, I've had lots of variations but the traditional with poached egg, canadian bacon, english muffin, and hollandaise is really by far the best.
How about a Sauce Mornay?
béchamel (roux + milk) + egg yolks + cheese
So eggs with white gravy? I think I’ve had that combo and it was pretty banging.
Even easier - egg sandwich using a basic milk bread.
Add crawfish and you're really talkin
This is amazing - and somehow channels both Douglas Adams and Randall Munroe at the same time...
Thank you! Two of my favorites. I'm honored.
Frankly I'm surprised Randall Munroe hasn't done this. (I assume he hasn't because nobody has linked to it.)
This is the greatest text I have read in the last 10 years, it kept getting better as it went along.
So that blurry eye vision I get in the morning could be from gravitational lensing from dark breakfast?
Surprised not to see “breakfast pasta” aka Carbonara. Wheat in the noodles, egg and cheese sauce.
Or pasta as a cereal, in a bowl with milk.
This whole thing is simply missing all milk based diary products like cheese, yogurt, white cheese, etc. When that is included then there is no gap or any mysterious quadrant.
Posts like this are why I read Hacker News.
My Egg McMuffin will never look the same!
What sort of projection is this that turns a 3-dimensional space into a triangle!
Fancy projection math is only for after coffee!
https://en.wikipedia.org/wiki/Simplex
Common for visualizing mixtures of three things!
While you are technically correct, since any triangle is a simplex, this is not relevant to this visualization.
For this visualization: get positive quantities in 3D space, normalize to 1, now you have dot on a triangle on 1-sphere in a positive octant. Project triangle into 2D space a this is your visualization.
2-sphere, I believe you mean to say.
It's easy, if you normalize it so that it sums to one, it drops a dimension, and becomes an equilateral triangle.
"IHOP Transgression" cracked me up. There's a restaurant in my town that does the same thing and I hate them for that reason. And like IHOP, what they call an omelette is actually a frittata.
The Irish full breakfast (fry up) includes soda bread, often fresh baked. That with the eggs likely puts it in the "Dark Breakfast" sector. Other sorts of full breakfast may also end up there, there's no true fixed set of ingredients in a full breakfast so any egg-heavy variety can end up in the "dark" sector.
Is the "Dutch Baby" in the pancake group some alternative name for "flensjes" that I'm not familiar with? It's a thin dessert variation of Dutch pancakes that has relatively high egg and milk ratios compared to flour.
Dutch Baby or German Pancake is probably right in that abyss.
Very eggy, with some flour/milk. It's essentially a souffle, puffs up to like 6" high in the oven. Tasty with maple syrup, powdered sugar/lemon, or just butter.
6 Eggs, 1 C flour, 1C milk.
https://www.allrecipes.com/recipe/36900/german-pancakes-ii/
No (1). I believe that it's "Dutch" in the same sense as "Pennsylvania Dutch" (2) - i.e. an American version of "Deutsch", actually German.
1) https://en.wikipedia.org/wiki/Dutch_baby_pancake
2) https://en.wikipedia.org/wiki/Pennsylvania_Dutch
obligatory CGP Grey https://youtu.be/eE_IUPInEuc?t=74
> Confusion continues because: People who live in the Hollands are called Hollanders, but all citizens of the Netherlands are called Dutch as is their language.
> But in Dutch they say: "Nederlands sprekende Nederlanders in Nederland" which sounds like they'd rather we call them Netherlanders speaking Netherlandish.
> Meanwhile, next door in Germany, they're "Deutsche sprechen Deutsch in Deutschland". Which sounds like they'd rather be called Dutch.
Cold pizza dead center.
Cold pizza + eggs, but then we're just in "egg & cheese sandwich" territory which is one obvious "dark breakfast".
It would be remiss not to also mention The Cube Rule
https://cuberule.com/
You can tell a non-US-southerner wrote this because there's not a biscuit to be had here.
WHERE ARE THE BISCUITS???
I sympathize with the author, I've had similar thoughts about snacks. We need more non-sweet snacks. Ideally something that tastes good, is not too salty, is healthy and satisfies your cravings.
Nuts (in the culinary sense) and cheese are good for that - a mini-cheeseboard with a couple of different bits of cheese (maybe 20-30g of each), a handful of cashews and walnuts, and maybe a dab of fig jam or membrillo on the side.
Tasty, nutrient-dense, surprisingly filling. Great as a mid-afternoon snack, or add some fruit and a bit of bread or some oatcakes to make it into a decent lunch.
South African food actually has this in abundance, biltong is like beef jerky but better in almost every conceivable way - not to mention all the other variants of it for example dry stix, droevors, etc.
Not to say we don't also have other sweet snacks, but compared to other places I've been nowhere quite has the same level of "savory" snacks
That's a hard one.
In terms of beverages alcohol-free beer gained popularity in recent years because it's not sweet, has half the calories of juice/soda yet actually carries some taste.
If I were to imagine something fitting this description, it would have to be something you have to chew for extended periods of time.
Congratulations. You've reinvented the souffle.
No egg banjo*? That sounds like it would sit close to, if not in, the abyss.
* https://en.wikipedia.org/wiki/Egg_sandwich#Fried_egg_sandwic...
Might choux hit that dark breakfast abyss? They aren't breakfast per se, but it might show that you can do things with those proportions.
Eggs benedict calls from the abyss, humanities' metabolic Voyager 1, speeding into the unknown.
Are we counting butter as milk? Because hollandaise sauce is an emulsion of egg yolk, butter, and lemon juice, so no milk directly unless we count butter.
Isn't it something like pancake with more eggs?
The real question is why this isn't already a dish.
Breakfast is just generally milquetoast then?
Aggakake or oeuf au lait.
3 eggs, 2 cups milk, 1 cup flour. Makes a nice flan/pudding consistency. Eggy and delicious.
Aggakake is on the chart!
What about eggs eggs and milk breakfast? (Omelette with cheese). Plenty of protein and little sugar
> IHOP omelettes include pancake batter.
Wait what? I've never heard of such a thing.
Does that make them better in any way? Or strictly worse, but cheaper?
Edit: looked it up and apparently they still use 3 eggs but the batter makes it super fluffy (like 2x) so the omelette looks enormous.
It’s a landmine for low carb gluten free people
What about french toast? I feel like there is a lot of egg in it, might place it near the bottom of the abyss.
French toast isn't plotted because the recipe doesn't customarily start with flour, but if you do plot it it ends up in the lower middle. If you have exceptionally eggy challah, then you might be able to push it into the abyss, but really exceptionally eggy, like 1:1 egg to flour by weight.
It misses a lot of other breakfast options:
- croissants - muesli/porridge/oatmeal - cookies - toasts - bread & butter (nutella too)
Things made of flour? I think they were explicitly covered. Perhaps "Flour" should have been more generally "Grain-based" to cover oatmeal and rye bread. Maybe add potatoes for a "starches" category.
What it's missing is fish, fruit, preserved meats (bacon, ham, sausage, black pudding?). It's very culturally biased to typical North American breakfast choices.
pizza
A Japanese Souffle Pancake might be in the Dark Breakfast realm.
I'm sorry, but I can't take seriously any topic in breakfast that leaves out the Taj Mahal of breakfast: stuffed French toast. I know there is reasoning for it but its inexcusable. Its like leaving Miracle Max out of a discussion of best physicians because he's fictional.
There's also no mention of the fourth leg of the breakfast triad: maple syrup.
It's what they ate on the Red October
Colombia's bandeja paisa.
I think it would make sense to include pudding - it's basically milk with a bit of flour. It's important to include because it shows that there are foods beyond Pancake Local Group that aren't just liquid milk.
One important property of pudding is that unlike pancakes, the space of pudding isn't "chaotic and fractal" because whether you add just enough flour to make it somewhat sticky or so much that you can cut it with a knife, it's still pudding. This means that if we take flour-heavy pudding and somehow add shitload of eggs, we should be able to venture into the Dark Breakfast area. I have a pudding recipe that calls for egg yolks, but I feel like this isn't a good lead. Still it proves further how flexible "pudding" is.
Going back to pancakes, there's one funny variation. "Naleśniki" with cottage cheese and cream (or yoghurt). Cottage cheese and cream are basically milk with extra steps, which means that the entire dish becomes mainly milk. This means that the Pancake Local Group actually stretches much closer to the "milk" vertex than your diagram suggests.
If I were to prepare something that passes as food and sits in the Dark Breakfast Abyss, I'd try scrambled eggs on the thinnest bread I could reasonably make. Something like "scrambled eggs taco".
I am humbled by the genius of this article.
This is the kind of creative thinking that makes HN great. Using the framework of dark matter detection to explore unobserved breakfast possibilities is both hilarious and oddly rigorous. The breakfast phase space is clearly under-explored.
Egg scramble fluffed with milk plus slice of toast might qualify
So basically omelette with matzo
An omelet wrapped in a paratha with a caffe latte to drink looks like the obvious answer... You can also play with the crust to filling ratio of a quiche...
How about doughnut with just the right amount of custard filling? Or perhaps a brioche with the right amount of French vanilla ice cream/gelato? A classic egg and cheese sandwich in your desired proportions?
While a delightfully funny article it also touches on something I’ve thought about many times before: just how uniform basically 99% of all (American) restaurant breakfast menus are. It’s really quite extraordinary in some ways how these menus are nearly entirely interchangeable from on to another. They might have very small tweaks and of course the ingredient specifics aren’t exact (specific butter brands, slight proportion differences)but by and large you could predict with almost perfect accuracy every single item that a typical breakfast menu in the US might have.
And I feel like that’s really a missed opportunity? Like even recognizing that of all meals breakfast is the most “comforting” and the one most likely for customers to want familiar, at the same time there are so many unexplored variants using the same ingredients (as this article shows!) that almost no restaurants will ever experiment with or offer. Lunch and dinner menus have massive variation in comparison!
The ones who walk away from omelettes.
That's a Pulitzer Prize for Poetry worthy reference.
french toast was dismissed far too lightly, it's exactly what goes into the gap. also savoury bread pudding.
Applying Tom Ngo's Embedded Constraint Graphics to Direct-Manipulation Breakfast Selection (Direct manipulation over simplicial complexes using barycentric interpolation: they're not just for breakfast any more.)
The Breakfast Simplex is a space of recipes parameterized by {egg, milk, flour} ratios, normalized onto a simplex. Add butter or sugar and the dimension increases. Add prep method and you create adjacent regions. A breakfast buffet is a larger, possibly disconnected simplicial complex spanning multiple ingredient families.
That structure is exactly what Tom Ngo formalized and patented in Embedded Constraint Graphics in 1996 at Interval Research Corporation. I wrote about it when the patent expired in 2016:
https://news.ycombinator.com/item?id=12572696
US Patent #5933150: System for image manipulation and animation using embedded constraint graphics
https://patents.google.com/patent/US5933150
When I asked Tom about applying ECG to other applications after the patent expired, he wrote:
>I am, of course, partial to the idea that gluing high-dimensional simplices at their edges and faces is an extremely general way to represent blending manifolds, in the same way that gluing polygons together has done us so much good in the 3D modeling space. I also think the >2 decades of progress since ECG have put us in a better position to do something really cool based on direct manipulation.
Golan Levin, Malcolm Slaney, and Tom Ngo used the ECG graphical editor to build the vector face cartoons for Mouther, simply by dragging eyes, mouths, and features directly on the drawing:
https://web.archive.org/web/20180717222910/http://www.flong....
ECG defines example states at vertices. Compatible examples span simplices. The full state space is a simplicial complex. Interior points are barycentric blends.
https://en.wikipedia.org/wiki/Simplicial_complex
https://en.wikipedia.org/wiki/Barycentric_coordinate_system
When you drag something in screen space, the system maps that motion into the n-dimensional interpolation space and solves for blend weights via the Moore–Penrose pseudoinverse of the Jacobian matrix, the same linear algebra used in inverse kinematics.
https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse
https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinan...
https://en.wikipedia.org/wiki/Inverse_kinematics
You don’t indirectly adjust abstract sliders. You directly manipulate concrete outcomes. The solver recovers coordinates.
The same formulation applies to interpolating vector drawings, mesh blending, facial animation, pose spaces, and other example-based interfaces where states are meaningful and compatibility matters.
The same geometric intuition appears in large language models. Tokens and concepts are represented as high-dimensional vectors, and model activations are computed through weighted linear combinations in embedding space. Interpolating between embeddings corresponds to moving through that vector space via weighted blends, just in many more dimensions. ECG makes the simplices explicit and topologically structured, while LLM representations are implicit and learned. In both cases, behavior emerges from interpolation in high-dimensional spaces.
Apple’s ARKit already exposes facial expression as a set of named blend shape coefficients via ARFaceAnchor — values like mouthSmileLeft, jawOpen, and eyeBlinkRight driving a 3D face mesh in real time. Bring Mouther into 3D and you can drag the mouth corners upward to interpolate toward smiling targets, mapping that motion through the same barycentric machinery into blend weights instead of hard-coded sliders. This would make a great Blender plug-in for directly manipulating facial animation, to use with FaceIt!
Faceit : Facial Expressions And Performance Capture
https://superhivemarket.com/products/faceit
Breakfast is a concrete instance. Pancake, crepe, and omelette define a simplex over ingredient ratios. Drag toward eggs and the egg weight increases. Drag toward milk and you move along that axis. Cross the egg-milk edge shared by the crepe simplex {flour, egg, milk} and the custard simplex {egg, milk, sugar}, and you move from thin batters into sweet custards without leaving the manifold. The Dark Breakfast region is simply an unoccupied part of a valid simplex -- suggesting adjacent, unexplored Dark Custard subspaces rather than forbidden states.
Simplicial complexes are useful UI primitives. They provide local linear interpolation inside zones and explicit global topology across zones. They scale to higher dimensions, while maintaining a user friendly 2D direct manipulation user interface. They encode constraints structurally instead of procedurally.
A pie menu can be viewed as a radial parameterization of a simplex. A direct-manipulation pie menu over ingredient space lets you drag in the direction of the crusts and fillings you want, with barycentric weights accumulating as you move.
The Design and Implementation of Pie Menus (Dr. Dobb’s Journal, Dec. 1991, cover story, user interface issue.)
https://donhopkins.medium.com/the-design-and-implementation-...
An Empirical Comparison of Pie vs. Linear Menus (Jack Callahan, Don Hopkins, Mark Weiser and Ben Shneiderman. Presented at ACM CHI’88 Conference, Washington DC, 1988.)
https://donhopkins.medium.com/an-empirical-comparison-of-pie...
As a certified expert breakfast cook, I bristle at the idea that scrambled eggs includes any ingredient other than eggs or seasoning.
Also, while I know that omelette is technically the whipping of large amounts of air into what is otherwise scrambled eggs, it feels wrong to me that "omelette" is categorized as "pure egg singularity". Is an omelette worth the time and effort over scrambled eggs if it does not include bits of vegetables, meat, and/or cheese folded inside like a taco?
maybe Portugal’s Pastel de Nata falls in the dark zone?
It’s a baked custard (so plenty of eggs) in a pie.
not sure the proportions match.
This reminded me of <https://xkcd.com/2893/>.
I love the idea and the writing, but the execution seems off. Cake has a very well-defined spot and Weetabix doesn’t? More work needed
No mention of Eggs Florentine?
where's porridge?
Breakfast has way more dimensions.
I agree, that is an oversight.
Porridge is an extremely common breakfast here in Sweden. There is a huge number of different variations of it as well.
And then there is müsli, with and without yogurt / sour milk.
No jam and butter option when writing that long of a post on what to eat for breakfast is criminal.
I usually have egg on toast with plenty of butter. The combination sits squarely in the dark region I think.
I also get up early and it is often actually dark.
What about vegetable-forward breakfasts? Completely not on this chart.
That's because such breakfasts are forbidden by the Geneva Convention articles, section 23, subsection 8, paragraph 4. It's not one of the more well known provisions, but it does exist, and nobody wants to break international law.
> nobody wants to break international law
I was with you up to this point, but my suspension of disbelief has its limits.
Dietary fiber is clearly off charts for OP.
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