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.

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.

It has been speculated that over half of the breakfast in the universe is dark breakfast.

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.

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.

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.

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

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.

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.

Salzburger Nockerln seems to fit in that area. https://www.austria.info/en-gb/recipes/salzburger-nockerl/

I suggest that the forbidden breakfast is tantamount to an eggs benedict, but with the hollandaise sauce replaced by a roux.

Love how at at the milk apex, there is cafe latte. Of course, it couldn't just be milk, perish the thought!

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).

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.

What sort of projection is this that turns a 3-dimensional space into a triangle!

Fancy projection math is only for after coffee!

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.

It misses a lot of other breakfast options:

- croissants - muesli/porridge/oatmeal - cookies - toasts - bread & butter (nutella too)

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.

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...

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!

This is amazing - and somehow channels both Douglas Adams and Randall Munroe at the same time...

Colombia's bandeja paisa.

Congratulations. You've reinvented the souffle.

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.

Aggakake or oeuf au lait.

3 eggs, 2 cups milk, 1 cup flour. Makes a nice flan/pudding consistency. Eggy and delicious.

What about eggs eggs and milk breakfast? (Omelette with cheese). Plenty of protein and little sugar

Breakfast is just generally milquetoast then?

Isn't it something like pancake with more eggs?

What about french toast? I feel like there is a lot of egg in it, might place it near the bottom of the abyss.

Egg scramble fluffed with milk plus slice of toast might qualify

A Japanese Souffle Pancake might be in the Dark Breakfast realm.

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.

The ones who walk away from omelettes.

french toast was dismissed far too lightly, it's exactly what goes into the gap. also savoury bread pudding.

where's porridge?

Breakfast has way more dimensions.

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 jam and butter option when writing that long of a post on what to eat for breakfast is criminal.

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...

This reminded me of <https://xkcd.com/2893/>.

No mention of Eggs Florentine?

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.

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.