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Can someone help me find again an article I read in a philosophy journal which was an allegory/parable on this subject which imagined an island cut off from the rest of the world where the native discovered addition and multiplication but wrote the terms on the edges of shells, so in a circle, hence incorporating a tacit concept of symmetry.

When a native genius discovered subtraction, he was burned at the stake for saying that somehow 3 - 5 is not the same as 5 - 3.

Please don't tell me to post this in the math SE because I tried and it was banned there.

Obviously, this philosopher was making a very general point, not restricted to math, but applicable to all domains. It is not just about notation either but about categories (and about how notations shape our theories of categories.

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  • What is your question relating to philosophy?
    – Jo Wehler
    Commented Jul 26 at 11:48
  • My question is which PHILOSOPHER wrote this and where. Thank you.
    – Attila the Pun
    Commented Jul 26 at 11:56
  • I'm sorry that I can't answer your question. I didn't read for much of my life. Anyway, heard of Hippasus of Metapontum? Hint: sqrt(2).
    – Hudjefa
    Commented Jul 26 at 12:52
  • @keshlam, it is philosophy of mathematics but actually it is much more than that, it goes to the relationship between any sort of notation (not just mathematical) and what we are able to express or even conceive of.
    – Attila the Pun
    Commented Jul 26 at 16:56
  • Here's my guess: jstor.org/stable/3684920
    – J D
    Commented Jul 26 at 16:58

1 Answer 1

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Frame challenge:

This story does not sound very convincing. There are real-world cases you could use instead.

Newton's dot notation was fine for rates of change with respect to time, or some other single variable. Leibnitz' differential notation was more cumbersome but it did imply the rate of change as the limit of the ratio of two small differences. This made it easy to extend calculus to several independent variables, and then to several variables with dependencies. British mathematicians patriotically continued to use Newton's notion and fell behind.

Some feel notation is not important. A true statement is true in English, French or German. Provided we understand each other correctly, the language or the notation should not matter. But a good notation can help a lot.

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