Flummoxed by 7, He’s Still in the Game
Crispin Sartwell (Commentary, Aug. 21) has it right regarding the meaning of “seven.” I fell hopelessly behind in math when I skipped the third grade on reading ability alone, in the four-room school I attended during the Depression in the countryside near Tulare. I flunked algebra in high school and avoided all math as I struggled through Stanford; no mathematical demands were made of me at UCLA Law School.
In my 43 years in the practice of law I was called upon to compute the daily rate of interest, at the “legal rate,” on judgments I occasionally obtained for my clients. When I started out, the legal rate was--guess what--7%. Out there in the cold business world I was saved by a colleague who showed me how to use his calculator.
Now that I am retired, I recently had to figure out how to cover my 7-by-7-foot garden with 7 inches of manure. That one got me until I just dumped bags from Home Depot until it looked right. I kept getting stuck after 49. Coincidence? I think not.
Yes, there is something very, very strange going on with seven. I think getting to the bottom of it should be a prerequisite to getting out of kindergarten. If you don’t know math you are never, ever going to make any contribution to society, let alone succeed in life.
Edward M. Lynch
Venice
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Sartwell correctly points out that mathematics is largely a self-referential system, in the sense that most mathematical concepts (such as the number seven) are defined exclusively in terms of other mathematical concepts, but he incorrectly equates this with emptiness. An ordinary English dictionary, for example, is also entirely self-referential, since it defines English words exclusively in terms of other English words. A chess game is also entirely self-referential, since the placement and allowed movements of the pieces only have meaning in terms of the placement and allowed movements of the other pieces. What matters most are the relationships between these concepts, not necessarily the concepts themselves.
Circular reasoning need not be empty reasoning if the circle mirrors reality. Indeed, as Einstein pointed out so famously, the entire universe is a kind of self-referential system, without much in the way of absolutes: The speed of one object is defined only in terms of the speeds of other objects; the location of one object is defined only in terms of the locations of other objects, etc. Perhaps this is the fundamental reason why self-referential systems such as mathematics, language and games of strategy mirror aspects of reality so well.
Lance Menthe PhD
Physical Scientist
Rand Corp., Santa Monica
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Perhaps this is Sartwell’s “Modest Proposal” regarding mathematics education. I suggest that he try to live without all the products, services and useful knowledge that we enjoy from the application of mathematics. Let me count a few: 1) computer technology, 2) manufacturing, 3) transportation, 4) publishing, 5) medical science, and let’s not forget 6) problem-solving skills and 7) basic money-handling skills, which we learn from 8) mathematics teachers.
Sharon Kirk
Santa Ana