26 November 2010
Nasser Saber and Algebra
Another recent and closely-related Saber entry discusses a neat algebra word problem. I'll give Saber's words for it: "A father is 48 years old; his son, 18. How many years from now will the father’s age be 3 times the son’s?"
I'm no great shakes as a mathematician, but I can handle this. Like a good student, I'll "show my work."
48 + x = 3(18 + x). Find for x.
48 + x = 54 + 3x
48 = 54 + 2x
-6 = 2x
-3 = x.
So we have learned that our question was badly worded. The two men have passed the point at which the father was three times as old as his son. They did so three years before the moment described in the question. Math corrects the false assumption buried in the wording of the problem.
Saber understands this, but I submit that he draws the wrong conclusion from it, and this again has everything to do with time preference. He seems to think that our intuitive sense of the passing of time is wrong, and math has here corrected it.
I disagree. Our intuition is that time only runs in one direction, so that there is no "negative year." That intuition is correct. It doesn't, and in a deep and true sense there isn't. We create various abstractions, and use those abstractions to do neat things. But if we let our tools tell us who we are, we have created a golem.
The mathematical tools let us write "-3 years," but they don't let us live three years in reverse and reach that younger age. Would that they could!
If you are a regular reader of these entries at all you know that I am about to quote William James. So here goes: "The essence of life is its continuously changing character; but our concepts are all discontinuous and fixed, and the only mode of making them coincide with life is by arbitrarily supposing positions of arrest therein."
Roughly that, I think, is one of Saber's key mistakes.
Knowledge is warranted belief -- it is the body of belief that we build up because, while living in this world, we've developed good reasons for believing it. What we know, then, is what works -- and it is, necessarily, what has worked for us, each of us individually, as a first approximation. For my other blog, on the struggles for control in the corporate suites, see www.proxypartisans.blogspot.com.