Next live lesson + Tagging along with Matt Parker

Talking about holes ion tickets, in London up until the 60s, bus and trolleybus tickets were clipped by the conductor using a hole punch. The ticket had a grid of numbers on it and the hole was supposed to be aligned with the number corresponding to the bus stop where you got on. Also, the tickets were coloured according to their cost which was linked to the length of the journey. And, most exciting of all, bus tickets were a uniform colour but trolleybus tickets had a broad white stripe down the middle.

Awesome! Yes, that is one of the reasons I think the convention of writing it as e^X can be misleading.

3blue1brown

That's crazy!

3blue1brown

Other interesting trivia: The Apollo AGC project was restoring an non-flight AGC from MIT. They needed a program to get their hardware to boot, the MIT one had some test modules which wouldn't let it do a full simulated flight. So they literally just popped a module out of the one in the Computer History Museum, dumped the memory, and used it to complete the project.

Tom Moll

The Computer History Museum is such a fun local spot! I recently went to the Vintage Computer Fest that was held there and saw some original Apple protoypes and got to play with dozens of old working 8-bit / 16-bit computers

Tom Moll

I actually was just running into a problem regarding the exponential on operators recently for a project for my linear algebra class (on the use of linear algebra in quantum mechanics). And I was trying to show at one point that e^(A+B)=e^A e^B for any operators A,B, and I thought that I had shown it, only to do some reading on the topic to find that this identity is only ever proven if A and B commute. It took me a very long time to realize where I actually assumed that! But the main result was being able to derive the form of the Schroedinger equation.

Isaac Briefer

I worked on IBM's internal payroll program in the UK on a 1401 back at the end of the 60s. The one shown in the video here must be a very late model as the one I worked on wasn't solid state, but had actual valves (tubes) and required a lot of cooling. As I remember it we had only 16K of 16 bit words to play with in memory, and we knew what data was being stored in every byte!

the history of computing is a fascinating topic and rabbit hole to go down :)

The Great Quux