Math

Type Mechanics

Hadi published on
49 min, 9726 words

Type Mechanics

Did you ever wonder if Quantum mechanics is not following Constructivity's principles, then why it works, at least in the calculation level! I mean the "shut up and calculate" approach of the Copenhagen interpretation worked, right? Notice it's mostly referring to the gaps between the computations that don't have comprehensive explanation rather than the computation of the Quantum mechanics. After all, nobody has problem with the calculation part, since they are constructive and boring!

Anyway, I hope it'll be clear for you in the end of this post why it even works! The Type Mechanics is inspired by Matrix Mechanics of Heisenberg, and also its predecessor the Statistical Mechanics. I would say that this is the third major reversion of this concept. Obviously, there are some differences, which will probably help us to decide how to experimentally validate them.

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Matrix Fast Fourier transform(MFFT)

Hadi published on
22 min, 4307 words

Matrix Fast Fourier transform(MFFT)

Matrix multiplication lies at the heart of modern machine learning, powering everything from neural networks to transformer models. Its optimization can dramatically impact the performance of AI systems, potentially reducing training times from days to hours. Let's explore how we can make this fundamental operation more efficient.

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The Inner product

Hadi published on
30 min, 5909 words

Inner product

Did you ever come to the point to ask yourself what's the Inner product between a vector and a Bivectors? If you did, you may noticed soon that it doesn't have any meaningful answer yet. I got interested into this problem back when I was studying Mathematical Physics course in my bachelor degree. I wrote my finding to my professor. "wooow! You defined a higher dimensional Levi-Civita-Symbol", he saied. But my invention was much useful than that! This post is the details of that invention. If you know about vectors, and bivectors, etc. I encourage you to read to the end, because this tool is simple and super useful.

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