The Hunt for Dark Breakfast

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.

josephjeon2• 5 months ago

Isn't it something like pancake with more eggs?

muzani3• 5 months ago

The real question is why this isn't already a dish.

efreak• 5 months ago

German pancake is mentioned in the comments (I don't think it was when you posted)

kazinator3• 5 months ago

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

scythe• 5 months ago

Have to wonder if yogurt counts, since I've had that for breakfast many more times than just milk or a latte

hspeiser• 5 months ago

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

moultano5• 5 months ago

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.

dheera• 5 months ago

What about vegetable-forward breakfasts? Completely not on this chart.

bigstrat2003• 5 months ago

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.

lucianbr• 5 months ago

nobody wants to break international law

I was with you up to this point, but my suspension of disbelief has its limits.

kenty• 5 months ago

Dietary fiber is clearly off charts for OP.

abakker• 5 months ago

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

josephjeon2• 5 months ago

Looks like very close to the dark breakfast recipe

Nursie2• 5 months ago

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...

xen0• 5 months ago

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.

noduerme4• 5 months ago

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.

kfarr• 5 months ago

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...

noduerme4• 5 months ago

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.

tenthirtyam• 5 months ago

I'd add oil as another dimension - sunflower oil, olive oil, butter, lard, whatever.

ekidd• 5 months ago

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!

noduerme4• 5 months ago

Speaking of Spanish food and sweetened french fries, I think berenjenas with miel de caña are a truly underrated breakfast competitor. And Spanish tortilla is also sort of a dark breakfast food... I make them to keep in the fridge. Although... heh. My fav thing to eat in Spain for breakfast are the small clams called almejas, sauteed in Manzanilla, with some crusty bread to soak up the boozy clam juice. Tragically, I became allergic to clams when I lived there.

mylifeandtimes• 5 months ago

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.

dnpls• 5 months ago

Isn't a basic soufflé gonna fall somewhere in the dark breakfast territory?

heeen2• 5 months ago

theres a japanese recipe for fried sweet potatoes with brown sugar/caramel sauce

https://www.okonomikitchen.com/daigaku-imo-japanese-candied-...

cadamsdotcom• 5 months ago

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

Fancy projection math is only for after coffee!

jonahx• 5 months ago

https://en.wikipedia.org/wiki/Simplex

Common for visualizing mixtures of three things!

vl• 5 months ago

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.

moultano5• 5 months ago

It's easy, if you normalize it so that it sums to one, it drops a dimension, and becomes an equilateral triangle.

JackFr• 5 months ago

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.

mikestorrent• 5 months ago

This is fantastic, I'm dying to eat a Womelette.

khafra• 5 months ago

Blending an omelette and a waffle should be totally doable; I've made waffle frittatas before and they turned out great.

ErroneousBosh• 5 months ago

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...

randallsquared• 5 months ago

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.

fc417fc802• 5 months ago

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.

skipants2• 5 months ago

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...

criddell• 5 months ago

If "Royal" is protected, the bar is pretty low:

https://www.canadacompanyregistry.com/catagory/Royal/

fyltr• 5 months ago

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.

01100011• 5 months ago

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).

jfengel• 5 months ago

Congratulations. You've reinvented the souffle.

muzani3• 5 months ago

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.

darth_avocado• 5 months ago

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...

jnaina• 5 months ago

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.

bathtub365• 5 months ago

There is prior art in the grilled cheese and eggs area: Denny’s Moons Over My Hammy.

psini2• 5 months ago

For a continental vibe see the french "Croque Madame"

acjohnson55• 5 months ago

Or the even more legendary Breakfast Dagwood https://violasmithcooking.blogspot.com/2009/08/breakfast-dag...

vasco• 5 months ago

We can certainly drink eggs, Rocky had a few in the morning before he went to punch hanging frozen meat.

purplezooey• 5 months ago

No mention of Eggs Florentine?

medi8r• 5 months ago

Breakfast is just generally milquetoast then?

zem• 5 months ago

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

kasitmp• 5 months ago

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

jacknews• 5 months ago

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.

csmantle• 5 months ago

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

aggakake• 5 months ago

Aggakake or oeuf au lait.

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

moultano5• 5 months ago

Aggakake is on the chart!

p0w3n3d• 5 months ago

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

bbminner• 5 months ago

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.

tsukikage• 5 months ago

Quark works better than cottage cheese, if you don't have access to tvorog

pbnjay• 5 months ago

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).

aunty_helen• 5 months ago

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?

petesergeant• 5 months ago

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

ccppurcell3• 5 months ago

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.

graypegg• 5 months ago

Chicken maybe? It would represent an egg that did exist, but now doesn't.

TeMPOraL2• 5 months ago

Also, in the other direction in space time, it's an egg that could have been, but now won't.

1659447091• 5 months ago

Now I want some chicken & waffles

https://en.wikipedia.org/wiki/Chicken_and_waffles

ccppurcell3• 5 months ago

In the breakfast space, I'm afraid, chicken is orthogonal to eggs.

porphyra• 5 months ago

Maybe the axes are actually logarithmic so 0 is 1 egg, 1 is e eggs, -1 is 1/e eggs, etc.

asdff2• 5 months ago

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.

moron4hire2• 5 months ago

What is menstruation but negative egg entering the body?

anon_cow1111• 5 months ago

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.

DonHopkins2• 5 months ago

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...

ccppurcell3• 5 months ago

I was just referring to one of the early sentences saying breakfast is a vector space. If you allow arbitrarily many (say) eggs so that two eggs and one egg are different breakfasts, you get a cone inside R^d. If you normalise and consider the ingredients as fractions of a whole (so that 1 egg and 2 eggs are both represented by the 1.0 egg breakfast) you get this simplex structure and the coordinate system you mentioned. But that's still not a vector space as there are not inverses in general. At best it can be embedded in R^d.

CoastalCoder• 5 months ago

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.

BigTTYGothGF2• 5 months ago

Are you telling me this dimensional vegan is trans.

tclancy2• 5 months ago

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.

felineflock• 5 months ago

I think it is all normalized into positive vector space [0, 1] using min-max.

getnormality• 5 months ago

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.

d--b• 5 months ago

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.

theoa• 5 months ago

Posts like this are why I read Hacker News.

My Egg McMuffin will never look the same!

xg15• 5 months ago

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

madcaptenor• 5 months ago

Frankly I'm surprised Randall Munroe hasn't done this. (I assume he hasn't because nobody has linked to it.)

moultano5• 5 months ago

Thank you! Two of my favorites. I'm honored.

pxtail• 5 months ago

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.

reedf1• 5 months ago

The ones who walk away from omelettes.

messe• 5 months ago

That's a Pulitzer Prize for Poetry worthy reference.

talldan• 5 months ago

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

haritha-j2• 5 months ago

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.

SideburnsOfDoom3• 5 months ago

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/

Quarrel3• 5 months ago

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.

haritha-j2• 5 months ago

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.

Quarrel3• 5 months ago

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..

graemep• 5 months ago

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.

hardlianotion• 5 months ago

And is a decidedly superior breakfast.

moultano5• 5 months ago

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."

batisteo• 5 months ago

What dimension would you add to make a tetrahedron?

hammock• 5 months ago

Something like a Dutch baby (German pancake) qualifies as dark breakfast (4 eggs 1/2c flour 1/2 c milk

SpaceNoodled• 5 months ago

I bet they would work with milk milk, though.

cyanydeez• 5 months ago

Is fruit not a 4th dimension in breakfast?

s_dev• 5 months ago

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.

jeej• 5 months ago

The Egglish Muffin.

opan• 5 months ago

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.

hilliardfarmer• 5 months ago

That is not what we are talking about.

Also, amazing article, haven't laughed that hard all day!

Cthulhu_• 5 months ago

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.

have_faith• 5 months ago

Eating a lot of food is tiring and you have plenty of energy stored from the previous day(s) food.

yen223• 5 months ago

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

bregma2• 5 months ago

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.

asdff2• 5 months ago

Egg scramble fluffed with milk plus slice of toast might qualify

moron4hire2• 5 months ago

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?

fedeb95• 5 months ago

where's porridge?

Breakfast has way more dimensions.

VorpalWay• 5 months ago

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.

Tepix• 5 months ago

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.

Tade0• 5 months ago

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.

miningape• 5 months ago

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

roryirvine• 5 months ago

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.

DonHopkins2• 5 months ago

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...

paganel• 5 months ago

No jam and butter option when writing that long of a post on what to eat for breakfast is criminal.

pseingatl• 5 months ago

Colombia's bandeja paisa.

dghf• 5 months ago

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...

vanderZwan2• 5 months ago

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.

wiredfool• 5 months ago

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/

SideburnsOfDoom3• 5 months ago

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

meatmanek• 5 months ago

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.

vanderZwan2• 5 months ago

Than you for explaining. And I have to say, the other comment also makes me skeptical of the claim that it doesn't go into the abyss since it seems to have at least twice as many eggs as a regular pancake would have

madduci• 5 months ago

It misses a lot of other breakfast options:

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

bregma2• 5 months ago

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.

flerovium114• 5 months ago

pizza

impure• 5 months ago

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

Oarch2• 5 months ago

By mass, sure - but have you considered delectability?

mekdoonggi2• 5 months ago

Even though it's not delectable by current methods, we can observe dark breakfasts effects on the movement of dietary bodies.

tclancy2• 5 months ago

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.

BigTTYGothGF2• 5 months ago

There's a lot more dark breakfast in the winter time.

riskable• 5 months ago

On the darkest day of the year, the dark breakfast can be balanced on its edge.

GuB-42• 5 months ago

Others say we underestimated the importance of a small quantity of eggs and proposed a modified theory that doesn't need dark breakfast.

qingcharles• 5 months ago

Yes, Earth could be in a Dark Breakfast Local Minimum. Potentially there are worlds out there where all breakfasts are Dark and their scientists cannot even comprehend the idea of an Egg Singularity.

tbyehl• 5 months ago

"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.

DoneWithAllThat• 5 months ago

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!

mynegation• 5 months ago

So basically omelette with matzo

igrekel• 5 months ago

A soufflé would fit some of the void. It has some flour in the bechamel.. whipped egg whites etc.

crazygringo2• 5 months ago

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.

PcChip• 5 months ago

It’s a landmine for low carb gluten free people

Oarch2• 5 months ago

It would be remiss not to also mention The Cube Rule

https://cuberule.com/

moffers• 5 months ago

Surprised not to see “breakfast pasta” aka Carbonara. Wheat in the noodles, egg and cheese sauce.

xgkickt• 5 months ago

Or pasta as a cereal, in a bowl with milk.

Beestie• 5 months ago

I am humbled by the genius of this article.

brodouevencode• 5 months ago

You can tell a non-US-southerner wrote this because there's not a biscuit to be had here.

WHERE ARE THE BISCUITS???

d-us-vb• 5 months ago

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.

deeg• 5 months ago

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.

mekdoonggi2• 5 months ago

Eggs benedict calls from the abyss, humanities' metabolic Voyager 1, speeding into the unknown.

lambda2• 5 months ago

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.

SAI_Peregrinus• 5 months ago

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.

HoldOnAMinute• 5 months ago

This is the greatest text I have read in the last 10 years, it kept getting better as it went along.

mrbluecoat• 5 months ago

It's what they ate on the Red October

anal_reactor• 5 months ago

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".

fortranfiend• 5 months ago

Cold pizza dead center.

dfxm122• 5 months ago

Cold pizza + eggs, but then we're just in "egg & cheese sandwich" territory which is one obvious "dark breakfast".

dfxm122• 5 months ago

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?

awesomeusername• 5 months ago

So that blurry eye vision I get in the morning could be from gravitational lensing from dark breakfast?

The Hunt for Dark Breakfast

Related Stories