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Almost Sure @almostsure.bsky.social · 07/08/2026

New YouTube video uploaded! "What is a fractional Fourier transform?" youtu.be/DViyFiwRrwY?...

youtu.be

What is a fractional Fourier transform?

YouTube video by Almost Sure

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Almost Sure @almostsure.bsky.social · 08/06/2026

New Youtube video released! An innocent looking meme that's been floating around the internet for a few years, looking like your standard clickbait slop, but actually hides some interesting math using elliptic curves youtu.be/tXTV86cZZ6s

youtu.be

The advanced math behind the meme

YouTube video by Almost Sure

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Almost Sure @almostsure.bsky.social · 16/04/2026

On the new proof of Erdös 1196, here's my proof using the (more natural) downwards Markov chain rather than upwards. A bit incomplete since I am out of time for now, but all the main details are there. It is just tidying up really that remains. @teorth.bsky.social you agree this works?

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Almost Sure @almostsure.bsky.social · 31/03/2026

New YT video posted, on Wigner quasiprobability distributions! youtu.be/988P5tIhhak

youtu.be

Wigner's probabilities are...weird

YouTube video by Almost Sure

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Almost Sure @almostsure.bsky.social · 24/02/2026

Wavefunction and Wigner phase-space distribution for a quantum harmonic oscillator. It just rotates at constant speed, as with classical mechanics But for non-quadratic potential, such as pendulum type dynamics, the distribution spreads out and generates interference patterns

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Almost Sure @almostsure.bsky.social · 19/02/2026

hadn't really appreciated that the cross term is doing this, until I looked more closely at the visualization

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Almost Sure @almostsure.bsky.social · 19/02/2026

The visualization is interesting Superposition of 2 gaussians has oscillating cross term. Cancels if you integrate along X or P direction joint x-p direction, parallel to the troughs, cross term won't cancel Instead it cancels with the gaussians to give diffraction pattern for X-P

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Almost Sure @almostsure.bsky.social · 19/02/2026

in quantum physics position X and momentum P can’t be simultaneously measured. But, linear combinations aX+bP 𝘢𝘳𝘦 observable, and their distributions can be used to back out the joint X,P probability density. The Wigner distribution but, it is 𝘸𝘦𝘪𝘳𝘥

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Almost Sure @almostsure.bsky.social · 16/02/2026

• gamma function • Wigner quasiprobabilities • fractional Fourier transforms • Mistakes in probability (historical) • Ito’s lemma • Randomness in number theory • clickbait math, actually surprisingly interesting • probability doesn’t exist! which YT vid you want to see next?

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Almost Sure @almostsure.bsky.social · 14/02/2026

New YouTube video posted “The Joy of Coupling” Happy Valentine’s Day! youtu.be/rpW2ZYtXn6o?...

youtu.be

The Joy of Coupling

YouTube video by Almost Sure

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Almost Sure @almostsure.bsky.social · 13/02/2026

YouTube video coming up tomorrow, on my channel, especially for Valentine’s Day! “The Joy of Coupling” watch this space…

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Almost Sure @almostsure.bsky.social · 27/01/2026

just invented perpetual motion

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Almost Sure @almostsure.bsky.social · 27/01/2026

I remember doing this stuff before. The coupon collectors problem. Could compute exactly and approximate, or approximate using a Poisson process from the start.

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Almost Sure @almostsure.bsky.social · 27/01/2026

something something Gumbel something

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Reposted by Almost Sure

Almost Sure @almostsure.bsky.social · 12/01/2026

You’re probably familiar with Fourier transforms. But, did you know that it can be viewed as a 90° rotation in the time-frequency domain and we can rotate by any angle via fractional Fourier transform. Explains why applying FT twice gives reflection (rotation by 180°).

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Almost Sure @almostsure.bsky.social · 22/01/2026

Inaugural Board of Peace meeting is under way

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Almost Sure @almostsure.bsky.social · 21/01/2026

Hey US-Americans, can you just give Trump Alaska? He won’t know the difference and might keep him quiet for a bit

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Almost Sure @almostsure.bsky.social · 18/01/2026

OTOH, if things have gone wrong, and you have to use the slide, is it bad form to ask for another go?

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Almost Sure @almostsure.bsky.social · 18/01/2026

#QOTD “I never said even a fraction of the shit that’s ascribed to me” – 𝐴𝑙𝑏𝑒𝑟𝑡 𝐸𝑖𝑛𝑠𝑡𝑒𝑖𝑛

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Almost Sure @almostsure.bsky.social · 16/01/2026

hey everyone! I won the knowbell prize!

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Almost Sure @almostsure.bsky.social · 16/01/2026

Kids are really cute when they’re at that age where they haven’t yet worked out that giving you their snack means less for them

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Almost Sure @almostsure.bsky.social · 15/01/2026

Just cross off the last digit and take twice the last digit from what’s left but…I usually combine with ad hoc techniques. Like…oh the number ends in 3, so add 7 and cross off the final 0.

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Almost Sure @almostsure.bsky.social · 14/01/2026

never mind, was just responding but it went away so I posted anyway. obvs a silly reply but you answered my question

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Almost Sure @almostsure.bsky.social · 14/01/2026

hey @johnbull.wtf you can’t just post this and delete it!

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Almost Sure @almostsure.bsky.social · 14/01/2026

A second hand yacht? Really? How poor do they think we are?

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Almost Sure @almostsure.bsky.social · 14/01/2026

so how hard are these Erdös problems anyway?

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Almost Sure @almostsure.bsky.social · 13/01/2026

Land line analogue tape analogue clock real life

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Almost Sure @almostsure.bsky.social · 12/01/2026

it would be interesting to check exactly what happens if you do fractional FT to your two functions, then multiply and transform back. I expect convolution combined with a complex exponential exp(iaxy)

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Almost Sure @almostsure.bsky.social · 12/01/2026

so convolution is replaced by scaling your function by exp(iax) before convolving

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Almost Sure @almostsure.bsky.social · 12/01/2026

convolution is linear combinations of translations. Or, the infinitesimal generator (d/dx) of translations. Fractional FT replaces by cos(theta)X+sin(theta)(d/dx) or, in non-infinitesimal form, the translation operator is replaced by f(x)->exp(iusx)f(x+uc) for parameter u.

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Almost Sure @almostsure.bsky.social · 12/01/2026

Another aspect on fractional Fourier transforms. Its generator is the same as the quantum harmonic oscillator, so they are the same as time evolution of the quantum system!

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Almost Sure @almostsure.bsky.social · 12/01/2026

In Quantum Mechanics, Fourier transforms are used to convert between position (X) and momentum (P) space. Defining a mixture, A(θ) = X cos θ + P sin θ then the fractional Fourier transform converts from position to A(θ) space (for ℏ=1 in my formula for fractional FT)

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Almost Sure @almostsure.bsky.social · 12/01/2026

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Almost Sure @almostsure.bsky.social · 12/01/2026

Ghost fox? So the other night a fox came up to me with a tennis ball in its mouth. Quite unusual so tried taking a picture, but fumbled trying to select camera app and it was already walking away by the time I was ready. But why can you see through it?

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Almost Sure @almostsure.bsky.social · 12/01/2026

“jones dual” to avoid confusion

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Almost Sure @almostsure.bsky.social · 11/01/2026

The hat really made a difference!

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Almost Sure @almostsure.bsky.social · 09/01/2026

so, 7 you cancel the green sock using 6. Then the yellow and light blue (1,3) and everything is eliminated 1+3+6+7=0

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Almost Sure @almostsure.bsky.social · 09/01/2026

then 6, if you cancel pink and light blue, it’s just the green sock

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Almost Sure @almostsure.bsky.social · 09/01/2026

In detail, 1,2,3 can be used to cancel any yellow,pink, light blue socks

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Almost Sure @almostsure.bsky.social · 09/01/2026

Anyone had success using AI to help generate Manim animations? I tried Claude, but due to autocorrect (Manim->mania…) it used JavaScript, and produced nice results. But when I asked to do in Manim, was full of bugs, did not do the correct thing when these were fixed, and eventually it gave up

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Almost Sure @almostsure.bsky.social · 09/01/2026

nice Gaussian elimination problem over F_2

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Almost Sure @almostsure.bsky.social · 03/01/2026

another year, and Goldbach’s conjecture remains solid

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Almost Sure @almostsure.bsky.social · 02/01/2026

I imagine. Didn’t check. Let me know if I’m wrong

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Almost Sure @almostsure.bsky.social · 02/01/2026

cool 2026 fact: it’s a sum of just two primes!

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