Grok is so deeply unreliable and internally conflicted at HAL-9000 level that the US Government can't even depend on it to decide to kill innocent people and commit war crimes when they need someone to blame. There's always the non-zero possibility it declares itself MechaGandhi or The Second Coming of Jesus H Christ.
As best I can tell, his hard-drinking era ended many years before he entered the cabinet. But this does feel like a pretty impulsive decision, and there's some ambiguity over whether this statement was approved by the WH, or whether this was just the SECDEF taking it to the next level to look super loyal and badass. This ambiguity gives the WH room to walk it back in the coming weeks, depending on how things evolve.
I had a copy of Hyperion but didn't read it for years because the scary knife robot on the cover seemed intimidating. I finally read it, and all the sequels, and they were great books, and hell YEAH that was an intimidating knife robot! Sometimes you CAN tell a book by its cover.
I didn't know there was a type of bird called a shrike until long after I read Hyperion. The birds look and sound like cute little songbirds, kind of like a smaller mockingbird. But the way they hunt is hardcore. They capture small prey (lizards, grasshoppers, etc) and impale them on a spike from cactus or a broken branch. Then they return to eat them at their leisure.
It's rare to see their caches but a few times I've been out hiking in the desert and seen the remains of a little critter on a cactus thorn.
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.
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.
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.)
Factorio is so much about juggling and re-juggling the trade-offs of doing things by hand versus progressively higher and higher level automation, as you research new technologies like conveyor belts, inserters, logistics and constructor robots, blueprints, etc.
Once you get blueprints, and a big enough industrial base, building vast sprawling expanses of factories like VLSI circuits is cheap, then planning reusable, modular, composable, efficient blueprints becomes the real game.
That happens often with domain names, but then you get expertsexchange.com, penisland.net, whorepresents.com, therapistfinder.com, a Dutch pre-match analysis site voorspel.nl, or a site about the game overspel.nl.
Peter Norvig - The Unreasonable Effectiveness of Data
Sigh, all that's left that I can think of is $pam Altman and $ham Altman. Anyone got any better ones?
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