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?
New YT video posted, on Wigner quasiprobability distributions!
youtu.be/988P5tIhhak
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
hadn't really appreciated that the cross term is doing this, until I looked more closely at the visualization
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
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
• 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?
bsky.app/profile/almo...
New YouTube video posted
“The Joy of Coupling”
Happy Valentine’s Day!
youtu.be/rpW2ZYtXn6o?...
YouTube video coming up tomorrow, on my channel, especially for Valentine’s Day!
“The Joy of Coupling”
watch this space…
just invented perpetual motion
I remember doing this stuff before. The coupon collectors problem. Could compute exactly and approximate, or approximate using a Poisson process from the start.
something something Gumbel something
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°).
The Producers by Mel Brooks
Inaugural Board of Peace meeting is under way
Hey US-Americans, can you just give Trump Alaska? He won’t know the difference and might keep him quiet for a bit
“again! again!”
OTOH, if things have gone wrong, and you have to use the slide, is it bad form to ask for another go?
“do you even lift bro?”
#QOTD
“I never said even a fraction of the shit that’s ascribed to me”
– 𝐴𝑙𝑏𝑒𝑟𝑡 𝐸𝑖𝑛𝑠𝑡𝑒𝑖𝑛
that was sister sledge
Woke up to this sight
hey everyone!
I won the knowbell prize!
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
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.
never mind, was just responding but it went away so I posted anyway. obvs a silly reply but you answered my question
hey @johnbull.wtf you can’t just post this and delete it!
A second hand yacht? Really? How poor do they think we are?
so how hard are these Erdös problems anyway?
