if you click through to the linked Vannevar Bush article and scroll down there are a bunch of vintage ads around the prose that are kind of interesting. And some of the predictions have been well overtaken by events!
It is better stated that: since there are "so many more" irrational numbers than rational ones, if you were to pick a real number "at random," the probability that it would be rational is zero. The "many more" and "random" ideas are made precise in measure theory (and elsewhere).
When I was in high school my desk had a graffiti carved in it of the three most important numbers: 69, 2112, and 714. 2112 was the Rush album (which I liked), and I had to ask a friend about 714: he explained that it was the number printed on Quaalude pills (as if everybody knew that).
My own thought (I know there is a great deal of room for disagreement) is that the J6 crowd saw no consequences for the attempts to obstruct the Brett Kavanaugh confirmation and thought the rules had changed. One of them was shot in the neck, many others are still incarcerated two years later despite a clear constitutional right to a speedy trial. I'd rather the Capitol Police had just cracked heads at this point. You might think one protest was more justified than another, but the differential in response works to dissolve confidence in the fair application of the law. At any rate, the participants in J6 have been broken, so you're not likely to seen that again...yet I feel we could get another riot season provoked by police brutality at any time.
There is garbage and tent encampments thoughout much of my city, and I am told that nothing can be done about it. I've been invited to engrave something on my catalytic converter. I wonder what good that would do.
> Although widely held, the belief that merit rather than luck determines success or failure in the world is demonstrably false. This is not least because merit itself is, in large part, the result of luck. Talent and the capacity for determined effort, sometimes called ‘grit’, depend a great deal on one’s genetic endowments and upbringing.
Heads-I-win, tails-you-lose, or: since merit is mostly luck, you might as well choose your students at random. Show us how it works, Princeton!
I have done the translation from Scheme to Clojure which raises the possibility that some of the typing could be done gradually with spec; I haven't worked with typed scheme. There's a lot of code in the simplifier which is designed to work with S-expressions containing symbols. Changing them to work with an enriched type carrying unit information would be a big undertaking
I have been interested in doing this for a long time, and have thought about doing it in Haskell. It would be a lot of work, and some of the type decisions that would be needed would probably complicate the UX of the software (the automatic differentiation of functions of various shapes would make typing the D operator interesting; I think it would force all real-valued functions of a real variable to look like they were working in a vector space of dimension 1, or the inconsistency would be maddening). SICM's software also does a lot of "lowering" of types, so 0 (zero) is kind of a universal additive identity, but in a strongly typed system you'd need zeros of many different kinds and it might be that once all this was finished there was too much "wrapping" left visible and the scientific investigations in the SICM spirit would lose some of their charm. I guess that's a long-winded way of saying that there are lots of type puns in mathematical notation that are useful affordances even if they are slightly abusive.
(OT) I like iTerm for its smart select/copy behavior, mostly, but stopped using it about 3 months ago because I often caught it using immense amounts of RAM, slowing everything down on my 32Gb trashcan pro. I thought it might have something to do with the GPU, but it doesn't happen on Terminal.app, which is otherwise good enough, but I miss iTerm every time I have to cmd-C or adjust the span of a double click. Has anyone else observed the RAM trouble? Maybe I have a bad setting?
I lived in France for a few years and wanted to become fluent in the language. One part of my strategy was just to try to brute-force through some novels with the aid of a dictionary and a conjugation chart. I started with _Les Trois Mousquetaires_ but found the diction too difficult to slog through. I made it through _Le Petit Prince_, but I really clicked with Simenon's detective novels. Since it was a familiar, modern form, it was easier for my brain to fill in the blanks through context. The dialogue, especially, was realistic and quite to the point ("Ici c'est moi qui pose les questions" sticks in my mind).
So you get one free murder? No, the deterrent had to be there beforehand, so that our hypothetical killer who is certain she only wants to kill one person will be exposed to that deterrence. Even if she is not thereby deterred, the fact that the punishment is applied to her will have a deterrent effect on others contemplating a similar crime. Therefore the punishment has value even if there is no need to prevent the murderer from killing again. (Edit: you did point out that the omniscience allows you to know that there will actually be no deterrent effect but that's asking a lot :)
There is good news and bad news. The ODE integrators (etc.) in Apache Commons Math are great and work with unboxed types. In SICM, however, you'll be dealing with clojure functions generated by the system to map states to their time derivatives, and those states will be stored in "up tuples" and not native java []double. So copying must happen at state-derivative evaluation time. The system attempts to win back some speed by at least avoiding interpreting the state function. For the kind of explorations the book enables, it seems good enough. Also, you can "take your equations of motion out" of the system with ->JavaScript, and run that code in the browser with a suitable JavaScript integrator and that works too.