Tag Archives: Donald J. Brown

On Being Given to Know

We may speculate, and it is interesting that we do speculate, on the following questions.

  1. What if we could upload books to our brains?
  2. What if a machine could tell us what was true?

It is interesting that we speculate, because I think the questions do not ultimately make sense—not the sense that seems to be intended, whereby something can be got for nothing.

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Interconnectedness

Note added January 13, 2019. This essay concerns a letter I once wrote about

  • teaching;
  • the infinitely large and small, as contemplated by Pascal in that one of the Pensées headed Disproportion de l’homme;
  • Zen Buddhism.

Since the ideas of Collingwood often dominate this blog, one may ask why they influence me. My old letter provides some evidence, since I wrote it before I had read anything by Collingwood but The Principles of Art.

The present essay has the first of this blog’s several mentions of the slogan verba volant scripta manent, which may not mean what we tend to think today.

The indicated pensée happens to allude to the definition of God as une sphère infinie dont le centre est partout, la circonférence nulle part; this definition is not taken up here, but it is in later posts, apparently without recollection of its use by Pascal.


When do our thoughts progress, and when do they only confirm what we have always thought?

In December of 1987, I was between college and graduate school. I was living with my mother in Virginia, doing some tutoring at my old high school, waiting for inspiration about what to do next. Inspiration did come in the course of the following year, when I was working at an organic farm in West Virginia. I was going to apply to graduate schools in mathematics or philosophy (earlier I had considered also physics); then, in a dream, I understood that I had to do mathematics. Continue reading

Learning mathematics

This is mostly reminiscences about high school. I also give some opinions about how mathematics ought to be learned. This article originally formed one piece with my last article, “Limits.”

I learned calculus, and the epsilon-delta definition of limit, in Washington D.C., in the last two years of high school, in a course taught by a peculiar fellow named Donald J. Brown. The first of these two years was officially called Precalculus Honors, but some time in that year, we started in on calculus proper. Continue reading

Limits

This is about limits in mathematics: both the technical notion that arises in calculus, and the barriers to comprehension that one might reach in one’s own studies. I am going to say a few technical things about the technical notion, but there is no reason why this should be a barrier to your reading: you can just skip the paragraphs that have special symbols in them.

Looking up something else in the online magazine called Slate, I noted a reprint of an article called “What It Feels Like to Be Bad at Math” from a blog called Math With Bad Drawings by Ben Orlin. Now teaching high-school mathematics, Mr Orlin recalls his difficulties in an undergraduate topology course. His memories help him understand the difficulties of his own students. When students do not study, why is this? It is because studying makes them conscious of how much they do not understand. They feel stupid, and they do not like this feeling. Continue reading