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