Almost Sure

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?

Land line
analogue tape
analogue clock
real life

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)

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

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.

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!

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)

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°).

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?

“jones dual” to avoid confusion

The hat really made a difference!