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A place where a developer who likes solving problems writes sophistry

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@nicdunz @LucasBigandt @asikunaa Hi nic

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#NewProfilePic

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@nicdunz @krea_ai Hi nic

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@nicdunz Hi nic

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TBH Al is 100x smarter than y'all.

Isn't AGI already here?

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Halfway around the globe is about 20,000 km.
20,000 km / speed of light = 0.1s
Since my input has to go there and come back for a response, as a round trip, you get a 200ms ping.

Can't even play League at this ping.

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The speed of light is way too slow

Assume you're playing an FPS game with someone on the exact opposite side of the Earth.

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@RiotPhroxzon I believe solo queue should strictly be for solo players only. If you want to duo, you should play flex queue or normal games.

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@nicdunz Me too

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Looks like Gemini 3.7 Flash got some architectural improvements. Seeing that these upgraded algorithms will be applied to future Gemini models as well, yeah.

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When generalized to multivariable functions, T becomes the Jacobian matrix; and on manifolds, it becomes a linear map between tangent spaces.

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In single-variable functions, this linear map T is merely a one-dimensional operation of multiplying by a real number f'(x), which is why it simply looked like a "slope."

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When decomposing an expression into the form f(x+h) = f(x) + T(h) + r(h), the very definition of differentiation is the process of finding a linear map T such that the error term r(h) approaches zero much faster than h.

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If you only understand differentiation as the slope of a tangent line or the limit of a rate of change, you will inevitably hit a wall when you move on to multivariable analysis or differential geometry.

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This is because the moment variables become vectors, dividing by a vector is mathematically impossible.

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Once you get this perspective, the whole point of algebra—classification—finally makes sense. Instead of studying infinitely many groups one by one, you bundle together those that share the same isomorphic structure and treat them as a single entity.

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In abstract algebra, whether the elements are numbers, matrices, or functions doesn't matter at all. Algebra isn't about the identity of the elements—it's about the structure created by their operations.

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If two objects have the exact same structure and only differ in the names of their elements, algebra treats them as the exact same object. Isomorphism is the mathematical tool that bridges this.

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Geometry isn't really about the shapes themselves. It's about finding the invariants that hold up under a specific set of transformations.

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The essence of geometry is studying the properties that remain invariant under specific transformations.

The type of geometry you're doing is entirely determined by which transformation group you choose.

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Topology is the exact same thing. It's just a type of geometry that deals with invariants like the number of holes or connectedness, which survive no matter how much you stretch or squish things as long as you don't tear them.