Isa

fintech | ml | quant finance

[Isa @isssa0x]

Huntley Film Archives holds a nine minute sixties film where nobody explains anything out loud. The curve makes the point, not a voice off camera.

This is Mathematical diagrams, film 7751 from the Huntley archive. No narration, no face on screen, just ink, coordinate axes, and a rolling circle.

The first drawing shows a circle rolling along a straight line X, and the trace of a point on its edge draws an arch, a cycloid, a curve Galileo described and most people have only ever seen finished in a textbook, with no hint of where it came from.

Then the circle stops rolling along a line and starts rolling around another fixed circle instead, and the trace turns into a flower shaped figure with symmetric petals, an epicycloid, the same curve that describes the shape of gear teeth and the paths inside certain optical instruments.

The last drawing labels the centers M and M1 and the radius a, reducing the whole animation to three letters, each petal derived algebraically rather than drawn by eye.

The film sits in an open archive under number 7751. The picture is grey and grainy, there is no sound at all. The curve a circle traced sixty years ago is still the exact curve a CAD program draws today for a gear wheel.

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Isa @isssa0x]

Huntley Film Archives holds a sixties instructional film where a professor derives a formula that today gets handed to students in a textbook with no explanation of where it came from.

This is Maths Problems and Their Solutions, film 6767 from the British Huntley archive. A black chalkboard, a suit, no slides, a static camera the whole time.

He doesn't start with a problem, he starts with a set of identities: the distributive law, the difference of squares, the product of two two-variable binomials, the sum and difference of cubes. Six formulas in a row, each one derived, not handed over as a fact to memorize.

Then he takes the system ax+by=k, cx+dy=l, and instead of simply writing down Cramer's rule, he cross-multiplies both equations, subtracts one from the other, and derives x=(dk−bl)/(ad−bc) live on the board. The exact equation students usually memorize as a ready-made recipe appears here as a logical consequence of the two lines before it.

Then he moves to a triangle with sides 3, 4, 5, and uses the same habit, board, chalk, derivation instead of citation, to show where the Pythagorean theorem comes from for that specific case.

The film sits in an open archive of instructional footage under number 6767. Picture quality is low, sound is muffled. The method, deriving the formula instead of dictating it, hasn't aged a single day.

[Isa @isssa0x]

@fluixoo exactly, once you see the beauty in it, memorizing feels pointless

[Isa @isssa0x]

Huntley Film Archives holds a sixties instructional film where a professor derives a formula that today gets handed to students in a textbook with no explanation of where it came from.

This is Maths Problems and Their Solutions, film 6767 from the British Huntley archive. A black chalkboard, a suit, no slides, a static camera the whole time.

He doesn't start with a problem, he starts with a set of identities: the distributive law, the difference of squares, the product of two two-variable binomials, the sum and difference of cubes. Six formulas in a row, each one derived, not handed over as a fact to memorize.

Then he takes the system ax+by=k, cx+dy=l, and instead of simply writing down Cramer's rule, he cross-multiplies both equations, subtracts one from the other, and derives x=(dk−bl)/(ad−bc) live on the board. The exact equation students usually memorize as a ready-made recipe appears here as a logical consequence of the two lines before it.

Then he moves to a triangle with sides 3, 4, 5, and uses the same habit, board, chalk, derivation instead of citation, to show where the Pythagorean theorem comes from for that specific case.

The film sits in an open archive of instructional footage under number 6767. Picture quality is low, sound is muffled. The method, deriving the formula instead of dictating it, hasn't aged a single day.

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Isa @isssa0x]

@kocer_eth nothing beats a chalkboard and someone who actually gets it

[Isa @isssa0x]

McGraw-Hill wasn't the only one filming a lesson in the sixties better than half of what ships today. This one predates MIT's, and almost nobody has heard of it.

This is Patterns in Mathematics, part of the sixties Teacher Training in Modern Mathematics series. A man in glasses, a black chalkboard, no slides, no animation.

He's not explaining arithmetic. He's showing that arithmetic hides a structure most schools skip past. He breaks 37 times 24 into 37 times (4 plus 20), works out 148 plus 740, gets 888. Same number, different path, and the gap between those paths is the entire lesson.

Then he takes 41 plus 41 plus 41 and shows it equals 41 times (41 plus 1 plus 1), which is 41 times 43, which is 1763. One sum written three ways, each way revealing a pattern in numbers that looked random at first glance.

A math teacher I studied under used to show this exact clip before introducing factoring, and said it was the one piece of footage that turned the distributive law into something he discovered rather than a rule from a textbook.

The film sits free in an open archive of instructional footage. The picture is grainy, the sound is thin. The method he's showing hasn't aged a single day.

[Isa @isssa0x]

@Mirelaa27 hope it was worth the extra time

[Isa @isssa0x]

McGraw-Hill wasn't the only one filming a lesson in the sixties better than half of what ships today. This one predates MIT's, and almost nobody has heard of it.

This is Patterns in Mathematics, part of the sixties Teacher Training in Modern Mathematics series. A man in glasses, a black chalkboard, no slides, no animation.

He's not explaining arithmetic. He's showing that arithmetic hides a structure most schools skip past. He breaks 37 times 24 into 37 times (4 plus 20), works out 148 plus 740, gets 888. Same number, different path, and the gap between those paths is the entire lesson.

Then he takes 41 plus 41 plus 41 and shows it equals 41 times (41 plus 1 plus 1), which is 41 times 43, which is 1763. One sum written three ways, each way revealing a pattern in numbers that looked random at first glance.

A math teacher I studied under used to show this exact clip before introducing factoring, and said it was the one piece of footage that turned the distributive law into something he discovered rather than a rule from a textbook.

The film sits free in an open archive of instructional footage. The picture is grainy, the sound is thin. The method he's showing hasn't aged a single day.

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Isa @isssa0x]

@0xDezo memorizing is just a workaround for not understanding it yet

[Isa @isssa0x]

@0xNoraa thanks

[Isa @isssa0x]

@fluixoo a good teacher makes even hatd stuff click instantly

[Isa @isssa0x]

James Simons, mathematician, from the lecture "Vibrating Strings: An Introduction to Fourier Analysis":

"The vibrating string equation is linear. That fact changes everything: if y1 and y2 are both solutions, any sum of them is a solution too. A string's motion that looks chaotic is always a sum of simple sinusoidal modes, each at its own frequency. Finding those modes is the entire problem."

this video explains the exact mathematical fact quietly sitting underneath every multi-factor alpha model, and it's freely available.

at the board it's simple. A string of length L, fixed at both ends, is described by the wave equation with boundary conditions y(0,t)=y(L,t)=0. Separation of variables gives an infinite sum of terms sin(nπx/L) multiplied by cosines and sines of time, each term one harmonic n. The string's actual motion, the one that looks messy, is just a superposition of these harmonics with different amplitudes Cn and Dn. No magic, the linearity of the equation guarantees any sum of solutions can always be decomposed back into its components.

Here's where it lines up with the graph engineering article on multi-factor alpha models. A stock's price, a column of noisy data, isn't one signal either, it's a sum of hidden components, each factor, each node in the graph, one mode with its own weight. A multi-factor model isn't inventing new math, it's doing the same decomposition Fourier did for the string, just with a basis that isn't sin(nπx/L) but a set of factors fitted to the market. The PnL on the output side is that same reconstructed sum of modes, just instead of the string's shape at time t, it's the portfolio's return.

the math is free and public, so is the lecture. what nobody can sell you is knowing the right basis to decompose a specific market into, rather than copying someone else's five factors. That basis is the model, and it's built over years, not one video about Fourier.

[Isa @isssa0x]

@andreysuperior that's such a clean way to put it, most people just see noise

[Isa @isssa0x]

James Simons, mathematician, from the lecture "Vibrating Strings: An Introduction to Fourier Analysis":

"The vibrating string equation is linear. That fact changes everything: if y1 and y2 are both solutions, any sum of them is a solution too. A string's motion that looks chaotic is always a sum of simple sinusoidal modes, each at its own frequency. Finding those modes is the entire problem."

this video explains the exact mathematical fact quietly sitting underneath every multi-factor alpha model, and it's freely available.

at the board it's simple. A string of length L, fixed at both ends, is described by the wave equation with boundary conditions y(0,t)=y(L,t)=0. Separation of variables gives an infinite sum of terms sin(nπx/L) multiplied by cosines and sines of time, each term one harmonic n. The string's actual motion, the one that looks messy, is just a superposition of these harmonics with different amplitudes Cn and Dn. No magic, the linearity of the equation guarantees any sum of solutions can always be decomposed back into its components.

Here's where it lines up with the graph engineering article on multi-factor alpha models. A stock's price, a column of noisy data, isn't one signal either, it's a sum of hidden components, each factor, each node in the graph, one mode with its own weight. A multi-factor model isn't inventing new math, it's doing the same decomposition Fourier did for the string, just with a basis that isn't sin(nπx/L) but a set of factors fitted to the market. The PnL on the output side is that same reconstructed sum of modes, just instead of the string's shape at time t, it's the portfolio's return.

the math is free and public, so is the lecture. what nobody can sell you is knowing the right basis to decompose a specific market into, rather than copying someone else's five factors. That basis is the model, and it's built over years, not one video about Fourier.

[Roan @RohOnChain]

https://t.co/8HHG7saiut

[Isa @isssa0x]

@tonyprediction 🤝

[Isa @isssa0x]

@biektive the math never changes, just the marketing around it does

[Isa @isssa0x]

@tonyprediction this, the math is the actual skill, everything else is just tooling

[Isa @isssa0x]

@0xDezo glad you're info it, this kind of stuff doesn't get enough attention

[Isa @isssa0x]

@kocer_eth true, breaking price into frequencies is such an underrated approach

[Isa @isssa0x]

@kocer_eth my favorite kind of story honestly

[Isa @isssa0x]

James Simons, mathematician, co-author of the Chern-Simons form:

"We were chasing a specific 1948 theorem, Chern-Gauss-Bonnet, for a compact oriented Riemannian manifold. On the board it came down to one equation: the integral of the Pfaffian curvature form equals the Euler characteristic. The direct goal gave us nothing new. But when we lifted the problem to the sphere bundle over the manifold, a form appeared one dimension lower, whose differential vanished exactly where the manifold was parallelizable. That form had no name for ten years."

this video is the author himself rebuilding, step by step on the board, the exact moment a failed attempt at one theorem produced a different object, and it's freely available.

at the board it's simple. The 1948 Chern-Gauss-Bonnet theorem says the integral of the curvature Pfaffian over a compact oriented Riemannian manifold of even dimension equals its Euler characteristic. Chern and Simons were trying to understand what happens when that characteristic is zero, and lifted the construction to the unit sphere bundle S^(2n-1) over the manifold X. There they found a (2n-1) form TP_x whose differential equals the lifted characteristic form, and whose integral over the fiber equals exactly 1. That form is the secondary invariant, the hidden ingredient later named the Chern-Simons form.

For ten years the construction lived purely in differential topology, with no hint of physics. Only when Edward Witten and Albert Schwarz saw in it the exact structure for a topological quantum field theory did the form become the language of the fractional quantum Hall effect, anyons, and part of string theory.

the math is free and public, so is the lecture. what nobody can sell you is the willingness to lift a failed direct attempt one level of abstraction higher instead of calling it defeat. That step is the discovery, and it takes years, not one lucky guess.

[Roan @RohOnChain]

https://t.co/8HHG7saiut