Mathematical Musings

Originally posted by Nonpartisan on 06/11/07

I’m reading Strandsofpearl’s novel on mathematics (written in French), and she mentions the empty set.  Being a historian and a closet philosopher, I of course began to muse about said empty set and what it means for historical inquiry.  (Keep reading, it gets better, I promise.)

Simply put, the empty set occurs when you divide a set of numbers into all its possible subsets.  For instance, the set {1,2,3} can be divided into the following subsets: {1,2,3}, {1,2}, {1,3}, {2,3}, {1}, {2}, {3}, and the empty set, which is {}.

That’s enough math for now — on to the philosophy.  In life, we are born in a sense with an “empty set” of life experiences — that is to say, we have a life to fill with a series of expeiences from the set of all possible experiences.  To be sure, this ultimate experience set is curtailed in some ways by the circumstances of our birth — a child born in Africa, for instance, will never be President of the United States — or by our genetic material.  And every decision we make during our lives further eliminates, consciously or unconsciously, some potential experiences from addition to our set.

But to some degree, our lives are measured by how far we’ve come from the empty set — how many experiences we’ve had or accomplishments we’ve achieved, how full our lives have been.  In this sense, we’re all seekers, looking for not just answers but experiences with which to enrich and ennoble our lives.

As historians, we are often called, like it or not, to judge the value of historical figures; we make such a judgment even by the simple act of choosing which figures to examine.  And as a political historian, my instinct is to glorify and study those individuals throughout history who have achieved the most exalted elements in their life-set — Presidents, party leaders, political movers and shakers, great orators, people who can move mountains with their voices.  But what if the true measure of a worthy historical subject is not how important her life was, but how full her life was?  What if fleeing from the empty set is the greatest measure of the value of a life?  What if nothing is?  In any case, how are we to make such a judgment?

Meh.  Perhaps Kevin’s right — historians don’t often make good philosophers.


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