Simon

code, ml, farm, and family.

[Kirk Borne @KirkDBorne]

“Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares”

473-page PDF download here:
https://t.co/8mQWClkE8p

[Python Programming @PythonPr]

Matrix Multiplication

[Mathematica @mathemetica]

Definite integrals calculate the area under the curve y = f(x) from x = a to x = b by summing areas of thin vertical strips of height y and width dx, yielding the exact value given by the formula Area = ∫_a^b f(x) dx.

The total distance traveled by an object with varying velocity over a time interval can be calculated using it.

[Mathematica @mathemetica]

Coordinates turn locations into numbers on the Cartesian plane using x for horizontal position and y for vertical from the origin.

The plane splits into quadrants by the signs of x and y. - Quadrant I shows positive x and y such as point P at (3, 4).
- Quadrant II has negative x and positive y at Q(-4, 2). - Quadrant III contains R(-5, -3) with both negative. - - - Quadrant IV features S(2, -5) with positive x and negative y.
The origin sits at (0, 0) where axes cross. To plot T(4, -3), start at zero then move right four units and down three.

It is used to plot data in charts for analysis or find exact spots in navigation apps.

[tetsuo @tetsuoai]

I animated how a neural network learns, from one neuron to backpropagation, simple math, no calculus required. Best 8 minutes you can spend if it has only ever been a black box to you.

[Q.E.D Insights @QED_Insights]

Spherical Coordinate system

[Infinite Logiz @Infinite_Logiz]

Differential Equations: The Math That Predicts the Future!

[Simon @Simchabenmoshe]

No <insert proper address), it is <insert your pronoun> who deserves the <action> more being so <proper compliment> about <person>’s accomplishments and we really <term of endearment> all the well wishes. On this fine day <insert date> we will always remember this <celebratory occasion>

[Tech with Mak @techNmak]

Tensors are everywhere in AI.

Images are tensors.
Audio is stored as tensors.
Embeddings are tensors.
Model weights are tensors.

But the word “tensor” is used in two slightly different ways.

In machine learning, a tensor usually means a multidimensional array of numbers.

A scalar has shape:
()

A vector might have shape:
(n,)

A matrix:
(m, n)

An image batch might have shape:
(batch, height, width, channels)

A language model may process activations shaped like:
(batch, sequence length, hidden dimension)

This is the practical meaning used by frameworks such as PyTorch, TensorFlow, and JAX.

It tells us how numbers are arranged and processed.

But in mathematics and physics, a tensor is not defined merely by having multiple dimensions.

The deeper definition is about transformation.

Choose a coordinate system, and a tensor can be represented by an array of components.

Change the coordinates, and those numbers may change.

But they must change according to a precise transformation law so that the underlying object still describes the same thing.

A vector is the simplest example.

Suppose a vector describes velocity.
Rotate the coordinate axes, and its numerical components change.

The physical velocity does not.
The coordinates changed.
The object did not.

Tensors extend this idea to more complicated relationships.

A stress tensor describes how internal forces depend on the orientation of a surface through a point.

A fourth-order stiffness tensor maps strain to stress.

A fourth-order compliance tensor describes the inverse relationship: stress to strain.

These objects must remain meaningful regardless of which coordinate system we use.

That is why saying “a tensor is just a multidimensional array” is useful in software, but incomplete in mathematics.

The array is the representation.
The tensor is the object being represented.

One more distinction matters.

Tensor order is the number of indices:
→ scalar: order 0
→ vector or covector: order 1
→ second-order tensor: order 2
→ piezoelectric tensor: order 3
→ stiffness tensor: order 4

Order is not the same as matrix rank.

And tensor-decomposition rank is another concept again.

Same word.
Different mathematics.

In AI, we often care about:
→ shape
→ axes
→ broadcasting
→ matrix multiplication
→ contraction
→ memory layout

In mathematics and physics, we also care about:
→ basis changes
→ covariant and contravariant indices
→ transformation laws
→ coordinate-independent meaning

Both uses are valid.

They simply answer different questions.

The computing view asks:
“How are the numbers arranged?”

The mathematical view asks:
“What do these numbers represent, and how must they change when the coordinates change?”

That is the cleanest way to understand tensors:
=> In software, a tensor is usually a multidimensional array.
=> In mathematics, it is an object whose meaning does not depend on the coordinates used to describe it.

[Daniel San @dani_avila7]

Claude Code subagents can nest 5 levels deep now

@bcherny announced it, and today I finally got to try it, Here's the full chain running end to end:

- main
- project-auditor // level 1
- structure-checker // level 2
- import-validator // level 3
- dependency-tracer // level 4
- style-sync // level 5

Each level runs in its own context window

Only the top-level summary returns to main, depth 5 is the hard cap, that agent can't spawn further

[Simon @Simchabenmoshe]

This is not a knock on bigtimeagen. Just that he is transcended to more of a social media icon. The future of coding and finding work with our skills is not his problem. But it is yours and it is ours. You’re a soldier on the ground. For now. But in this weird bizarro future we are heading I see you one day becoming the biggrifigen and I hope for you to escape the matrix as well sir 👍 but until then…. I will always choose the guy with prior coding knowledge, quality music taste and impeccable beanie selection talent, over the guy without. Keep at it.

[Simon @Simchabenmoshe]

Before bigtimeagen ever got his first award or his first viral sound bite….you were there “vibing” on twitch 10 years ago, before ai was a twinkle in anyone’s eye, you were rocking the beanie to phat beats and coding with style and flow. Yes the calculator was finally invented and we no longer have to do all of the math by hand that is true. Absolutely true. I would still rather hire the guy who did these calculations by hand for 20 years over the guy who thinks the Calculator is magic. Enough said. We will see where this future goes. Intelligence and knowledge may have lost some value these last few years, but it will still always have more value than those chuds out there with absolute zero. There isn’t a world that exist where the person who just knows how to use a calculator is valued equal/more than the person who understands the answers the calculator provides. We are good. The surface is changing beneath our feet. But we won’t trip up. Our dance moves are on point.

[Simon @Simchabenmoshe]

Before bigtimeagen ever got his first award or his first viral sound bite….you were there “vibing” on twitch 10 years ago, before ai was a twinkle in anyone’s eye, you were rocking the beanie to phat beats and coding with style and flow. Yes the calculator was finally invented and we no longer have to do all of the math by hand that is true. Absolutely true. I would still rather hire the guy who did these calculations by hand for 20 years over the guy who thinks the Calculator is magic. Enough said. We will see where this future goes. Intelligence and knowledge may have lost some value these last few years, but it will still always have more value than those chuds out there with absolute zero. There isn’t a world that exist where the person who just knows how to use a calculator is valued equal/more than the person who understands the answers the calculator provides. We are good. The surface is changing beneath our feet. But we won’t trip up. Our dance moves are on point.

[Simon @Simchabenmoshe]

@ClaudeDevs As a 20x max customer who uses maybe 6% a week but can’t bare the thought of lowering my plan out of fear of hitting limits. Uhhh, thanks, I guess

[Chris Griffing @cmgriffing]

If you have the time, please checkout our ProductHunt launch for our new ADE called Kepler

https://t.co/qQAQwjj2rM

[Mathematica @mathemetica]

Calculus defines the derivative as the slope of a function at a point and the integral as the area under the curve.

The left graph shows df(x)/dx at x=a as the slope via the tangent line touching f(x). The right graph shows the integral ∫f(x) dx from b to c as the shaded area under the curve.

GPS devices calculate current speed from position changes using derivatives and total distance from speed variations using integrals.

[Richard Palethorpe @jichiep]

privacy-filter.cpp performance Vs the PyTorch implementation. Approx between 1.6x and 18x faster:

[Cursor @cursor_ai]

We're excited to join forces with @SpaceX to advance the frontier of useful AI. Expect significant improvements to Cursor soon.

[Simon @Simchabenmoshe]

@haider1 @sbmaruf