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 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.
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.
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.
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.
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.
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.
It's not possible to have negative eggs, but you can apply barycentric coordinates to many other things, like facial animation mesh blend shapes (i.e. ARKit, Blender Blend Shapes and FaceIt plugin, Unity SkinnedMeshRenderer, etc), and you can overdrive them >1 and even underdrive them <0 to get ridiculous effects:
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.
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.
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
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...
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.
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).
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.
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.
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
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.
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.
The concept of a 'Dark Breakfast Abyss' in the Breakfast Simplex is hilarious, but it got me thinking—maybe the reason we lack foods in that specific ratio of milk, flour, and eggs isn't because they'd destroy the world, but because they simply don't cook well conceptually. Like, an overly-battered omelette just turns into a gummy mess, not a crepe. It's fascinating how our culinary traditions naturally naturally sort themselves into these distinct mathematical vertices over centuries of trial and error.
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.
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.
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.
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?
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.
I've been meaning to go to Sri Lanka..
You can get them e.g. in London UK: https://www.hopperslondon.com/
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.
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.
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.
https://www.thedeliciouscrescent.com/omelette-stuffed-parath...
https://en.wikipedia.org/wiki/Chicken_and_waffles
https://en.wikipedia.org/wiki/Barycentric_coordinate_system
It's not possible to have negative eggs, but you can apply barycentric coordinates to many other things, like facial animation mesh blend shapes (i.e. ARKit, Blender Blend Shapes and FaceIt plugin, Unity SkinnedMeshRenderer, etc), and you can overdrive them >1 and even underdrive them <0 to get ridiculous effects:
Nouveau Art Pipeline Demo: Blend Shapes
https://youtu.be/phM8Wnzs_-g?t=104
(None of Epstein's close friends and guru confidants were harmed in this demo.)
Eric Hedman - "Doppel" Character Modelling with Blendshapes for Animation
https://www.youtube.com/watch?v=6L7jtgRD5rs
Faceit: Facial Expressions And Performance Capture:
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...
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.
[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.
- croissants - muesli/porridge/oatmeal - cookies - toasts - bread & butter (nutella too)
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
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...
Light breakfasts are popular if you have to make it yourself
Also, amazing article, haven't laughed that hard all day!
Breakfast burritos are also at least as important as quiche (as in, neither are as tasty without addins - just like omelettes).
https://en.wikipedia.org/wiki/Deviled_egg
béchamel (roux + milk) + egg yolks + cheese
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/
* https://en.wikipedia.org/wiki/Egg_sandwich#Fried_egg_sandwic...
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.
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
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.
Fancy projection math is only for after coffee!
Common for visualizing mixtures of three things!
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.
My Egg McMuffin will never look the same!
3 eggs, 2 cups milk, 1 cup flour. Makes a nice flan/pudding consistency. Eggy and delicious.
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...
Breakfast has way more dimensions.
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.
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?
It’s a baked custard (so plenty of eggs) in a pie.
not sure the proportions match.
I also get up early and it is often actually dark.
I was with you up to this point, but my suspension of disbelief has its limits.