"Mark III: Can Man Build a Superman?"

(Aside: reading a lot of old articles about computing recently I find the use of the term "man" really grating. Not just because of the sexism (different time, yada yada), but also the grandiosity. It's also in the Xerox ad I recently posted.)

it's sad how humanity has lost the ability to write code to search for things. Whether it's Google, or Apple Music, or eBay, typing in exact substrings of the title of something is no longer guaranteed, or even likely, to find matching entries.

The thing that makes modern dimmers for lighting complicated is basically what Einstein got his Nobel prize for.

A propos of nothing: I often think of this work of art although I don't think it was on display last time I visited the Tate. It's a map of the US showing only the place names containing the word "Lost".

https://www.tate.org.uk/art/artworks/prendergast-lost-p78411

I regret not publishing more papers. I spotted my trick for computing Laplacians appearing in ML papers recently.

https://blog.sigfpe.com/2011/08/computing-errors-with-square-roots-of.html

This is actually how it is used - simulating stochastic processes such as diffusion where the infinitesimals are too large to discard.

I was a bit behind the times. I was astonished to find how easily you can just guess an ansatz, shape it with a neural net, and solve ab initio for the full wave function for a ground state of a multi-electron atom, with the energy computed to many decimal places. Small atoms and maybe even molecules on your laptop with no difficulty.

Eg. This and many other places
https://arxiv.org/pdf/2211.13672

Did you ever play my barrel game/puzzle?

https://dpiponi.github.io/barrels.html

The rules are

0. try to achieve the specified goal
1. you can tap on the circles to open and close the pipes
2. there are no more rules

I wrote it years ago and it wasn't originally for mobile platforms so open/close is a bit small. Sorry.

Anyway, it was very surprising to me you can make a puzzle out of equalizing water levels but it's an NP-complete problem IIRC.

Reading about the Bell Labs "Complex Computer" that used 450 relays to multiply complex numbers. Built in 1939 it could be used remotely over telegraph lines so it offered complex multiplication with up to 8 decimal digits as an online service. Took minutes for each multiplication.

https://gunkies.org/wiki/Bell_Telephone_Laboratories_relay_computing_devices

The sad thing about numpy.einsum is that the naming leads many to think that Einstein's innovation was to leave out sigmas whereas correctly used Einstein summation enforces a non-trivial type system that einsum blithely discards.

In principle I could probably retire now. But if I retired I'd end up still spending some time writing code to play with whatever interests me in the computing and adjacent world. So I may as well get paid for it.

But due diligence, I started looking at retirement. It seems more complicated than investments. You need to find an optimal strategy to withdraw from 401(k)s and other investments. A good way to optimise is in fact the very method I used to plan balloon trajectories years ago, solve the HJB equation.

And that's more or less why retirement would be a challenge at the moment. I'd be too busy solving equations...

If Biden was fighting this idiotic war the US media would be tearing it apart.

But I'm getting the hang of US politics now. A war is considered good if the government behind it is racist, homophobic, transphobic and misogynistic. It doesn't matter if oil prices are high or low or if the economy is tanking or any of that. If the government is suitably bigoted then the population are all behind it, otherwise these issues are just things to pretend to care about as a mechanism to bring back bigoted government.

I've written about various things you can do with functions of the differential operator D = d/dx.

For example, exp(aD) is a shift, because exp(aD)f(x) = f(x + a).

And exp(aD^2/2) is convolution with a Gaussian kernel, so a smooth or blur operation.

I've been meaning for a while to look at examples of the form f(X, D) where we mix D and X (where x is the "multiplication by x" operator).

I only realised today that exp(-iπ(X^2-D^2)/4) is a very familiar operation. It's none other than the Fourier transform. That was a big surprise to me!

There's a nice story here that I'll get back to one day so I'll just mention some key phrases here: That (X^2-D^2)/2 is the total energy of a harmonic oscillator like a pendulum. As a pendulum swings back and forth it exchanges kinetic energy for potential energy, ie. position for momentum. And in quantum mechanics, the wave function describes the position of a particle, and its Fourier transform describes the momentum. And similarly in the quantum case the time evolution is a back-and-forth between the original wave function and its Fourier transform. And exp(-iπ(X^2-D^2)/4) is basically the time evolution of such a system for 1/4 of a period.

(And I'm probably off by a factor of 2 or some phase factor... And a little care is needed with interpreting exp(-iπ(X^2-D^2)/4), especially when applied to functions that aren't square integrable.)