If I had to suggest where the “combination of four languages” idea came from, it would be from Homeric Greek (the language the Iliad and Odyssey were written down in). This was genuinely a complete mess, formed of a hodgepodge of different dialects.
From wikipedia:
“[Homeric Greek] is a literary dialect of Ancient Greek consisting mainly of an archaic form of Ionic, with some Aeolic forms, a few from Arcadocypriot, and a written form influenced by Attic.”
I’m not sure if this is a plausible explanation as I don’t have much experience using LLMs.
Richard Hamming’s “Methods of Mathematics Applied to Calculus, Probability, and Statistics” is a wonderful introduction to calculus from one of those rare individuals who mastered the interplay between applications of mathematics and its theory. It’s packed with insights from a true veteran. He aims to teach you to view and interact with mathematics as a living, breathing, occasionally messy but beautiful thing; and in my opinion he manages to do so with a rare humanity.
He was one of the gems of mathematical exposition. If you’ve studied any information theory you probably know his surname well. His other books are also excellent.
It begins with a lovely quotation: “every scientist owes a labour of love to his field”. His work embodies that.
There are lots of exercises, and it includes answers to enough of them for you to check you’re on the right track.
I feel like I may have misunderstood the point of the article because this seems like an obvious explanation to me. A pair of parentheses in Scheme tells the interpreter that it needs to open a new environment, evaluate the expression inside, and return the value. If there aren't parentheses, the evaluator will look up the value of the symbol in the current environment. These are very different things and, it seems to me, mixing them would make it unnecessarily difficult to pass named functions as arguments.
For example,
(map car '((a b) (c d) (e f)))
evaluates to '(a c e), while
(map (car '((a b) (c d) (e f))))
yields an error.
In this case, I don't want my interpreter to 'helpfully' add the parentheses in around car when it see it's a one-argument function that expects a list and the following expression is a list. And even if the interpreter is able to disambiguate it and thus avoid introducing errors, a huge benefit of the parentheses in Scheme is how easy is (as a human) to see the structure of your code at a glance. In my mind, introducing ambiguity here would only serve to undermine this while bring minimal benefit.