A Non-Negative Reaction

Steven Strogatz has been writing a series of pieces for the NYT, paraphrasing from the bio blurb, describing math from "the basics to the baffling." I've been enjoying the weekly Monday articles... I haven't encountered anything really new, yet, which is a good thing, considering that today's piece is on negative numbers. I don't exactly remember what year I first encountered that concept, but I'm guessing second or third grade. Nevertheless, even though the concepts are elementary thus far, Strogatz has a fun and playful approach to his subject, and does a mesmerizing job of weaving in apparently unrelated topics and showing their relevance. In today's post, two examples of this are European international relations in the late 1800's to early 1900's and linguistics:

Actually, languages can be very tricky in this respect. The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive, but none in which a double positive makes a negative — to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.”

I have been telling this as a joke for years, with the punchline delivered by an anonymous student yelling "yeah, right." And I've come across descriptions claiming that the joke was based on an actual exchange, but I've never seen an authoritative statement of that fact. So the above tickled me.

I'm really looking forward to his reaching calculus- integral calculus especially. Everything up through algebra, geometry, trig and to a lesser extent, derivative calculus, just seems sort of intuitive to me. I didn't have to work at it very much, I just got it.

But when you start pulling extra dimensions out of nowhere, I get confused.