Dave

I am a very curious person that loves to break the limits of human imagination. Only good vibes and intelectual conversations about science or adult games.

[Dave @davidfitfet]

Queda alguien en el mundo findom que estuviera por 2022-2024???

[Dave @davidfitfet]

Hola!

Despues de mucho he decidido vover al mundo bdsm. Algunos y algunas ya me conoceis

Dave is back!!
(Estoy soltero otra vez)

[Kirk Borne @KirkDBorne]

An *online* short book "What Do Mathematicians Do? An Overview of Undergraduate Mathematics"

Accessible via the quoted post below by @burkov ⤵️

[Mathematica @mathemetica]

Philosophy of mathematics asks what numbers are and whether they exist beyond human thought.

This chart outlines the major schools.

- Platonism says mathematical objects exist independently of us.
- Formalism treats math as shuffling symbols under rules.
- Logicism grounds everything in pure logic.
- Intuitionism says math arises from valid mental constructions.
- Structuralism studies structures and relations.
- Fictionalism claims the entities need not literally exist; they just have to work.

Suddenly algebra feels like philosophy.

[Mathematica @mathemetica]

The four partials ∂u/∂x, ∂u/∂y, ∂v/∂x, ∂v/∂y, assembled into a single determinant, record the infinitesimal area distortion of a smooth map (x, y) ↦ (u, v).

A rectangle of sides dx and dy is carried, to first order, onto the parallelogram spanned by the images of the coordinate axes; the signed area of that parallelogram is exactly (∂u/∂x ∂v/∂y − ∂u/∂y ∂v/∂x) dx dy. The same quantity converts one double integral into another and vanishes at the points where the map ceases to be locally invertible.

Carl Gustav Jacob Jacobi gave the first systematic treatment of these functional determinants in 1841.

[Martin @martinmrmar]

Another good math channel on YouTube.. Joydeep Dutta 💪

[Mathematica @mathemetica]

A = UΣVᵀ

Every real matrix (square or rectangular, full-rank or singular) factors into a pair of orthogonal matrices flanking a rectangular diagonal of nonnegative singular values. The left and right singular vectors rotate the domain and codomain so that the linear map becomes a pure stretch along aligned axes; the singular values themselves are those stretches.

When the values decay rapidly the map is essentially low-dimensional, and the partial sum formed by the first k terms is the nearest rank-k matrix in every unitarily invariant norm. Beltrami obtained the square case in 1873, Jordan independently a year later.

One factorization therefore exposes geometry, numerical rank, and the most economical compressions of the data the matrix represents.

[Cliff Pickover @pickover]

Number of arrangements of a Rubik's Cube: 43,252,003,274,489,856,000. A gift for extraterrestrials.

[Kirk Borne @KirkDBorne]

MIT Advanced Data Structures course: https://t.co/EQtAOIndPI

Video lectures, lecture notes, problem sets, GitHub, and more

[Alfredo Canziani @alfcnz]

Tuesday I taught my first non-technical intro to AI.
Students: 😱😱😱
Today I went through it again.
Students: 😍😍😍
And after 75 minutes of lecture… they kept me in class for 45 minutes more, with all sort of questions, related and not. 🥹🥹🥹