Reading Typing Declarations

I find typing rules in theoretical computer science hard to read, and I just realized that it’s for a completely trivial reason: I subconsiously read “:” as having lower precedence than ⊨ and “,”, which is completely wrong, so I have to concentrate to group everything the right way.

The only reason I can think of for this is that way back when I learned Pascal, which allows declarations like “ x, y : integer”, which is somewhat like “:” being higher precedence than “:”.

End of Printed Britannica

This article from the New York Times has a startling statistic: sales of the print edition of the Encyclopedia Britannica have dropped from 120,000 in 1990 to 12,000 today. (The article says 8,000, but a later article says the whole print run of 12,000 sold out.) I knew that Wikipedia had seriously hurt the sales of encyclopedias, but I had no idea it was on the order of 90%.

When I was a kid, I had the Funk & Wagnalls encyclopedia. (They sold it at the supermarket, one letter at a time.) I remember vividly reading the article on algebra, where it had a big table of axioms, like “the commutative axiom,” and “the associative axiom.” I was fascinated to find out that someone had isolated a list of properties of numbers, and that these properties had names.