Subject: 5 most critical mathematical concepts

Posted by Henry Cole on 12/8/2010
In Reply To:5 most critical mathematical concepts Posted by George Richardson on 12/2/2010

Message:

Dear George,
The email you sent to Jay on Dec 3, outlining 10 mathematical concepts was really brilliant and basic and, for me, described a context for most of the mathematics we use today.
What I would add to that is the necessary historical discussion which locates some of the early developments. A great work is Lancelot Hogben, "Mathematics for the Millions" WW Norton, published first in 1937 which I imagine you know well. He carefully investigates, for example, the differences between the historical and arithmetic difficulties of adding smaller and smaller infinitesmels to the infinite series which represents the distances the Achilles and the Tortoise travel. Added to this are the difficulties the Greeks had in expressing numerically the series X + I + I/X
+ I/C + I/M + but the higher elements of the series become more difficult.
Division was difficult. So concluding that an infinite series had a finite sum was not possible and hence we were left with Zeno and a paradox based upon the inability to accurately calculate a dividend. The social culture imposes a limit on what the clever people come up with.
Another great and perceptive book of the same ilk is, of course, Dantzig, "Number the Language of Science" and the chapter in "The Decline of the West" by Spengler, called "The Meaning of Number."
I need to learn more about economics and plan to use your book on "Feedback Thought" as well as Nouriel Roubini, "Crisis Economics." I believe that your discussion of the feedback complexities will be of great use.