A Mathematician's Apology

OK, I am going to violate course instructions by NOT blogging on a specific economic issue, but more of a bothersome topic I see a little too often.  This morning I was reading “Civilizations”, by historian Felipe Fernandez-Arnesto (FA),  a book for another class I am taking.  So far this is a fun book to read and in the intro FA does not hesitate to offer up some opinions.  For example, “History is a ‘humane’ discipline: it is too far steeped in tears and blood and affectivity and hatred to be anything else.  If it were a ‘science’ – in the old-fashioned sense of the word, a field of study governed laws,in which effects were predictable – I should find it uninviting.”  What got me going was a discussion early in the book of debates over the years on how to define “civilization” and attempts to enumerate them.  The author nails it when he states “Almost every theorist has proposed checklists of criteria which a society has to meet in order to qualify as a civilization.  All these lists are useless.”  

 

It seems that there is some innate drive to mathematize things, categorize, etc.  Is there some sort of romance of mathematics that drives scholars to wish to adapt mathematical-type arguments?  Thinking that a single definition of a term like civilization is possible (FA doesn’t make this mistake) and that one can create categories that make some sort of sense is so depressing.  It is the idea that taking on the mask of mathematics gives some legitimacy to an argument.  Mathematicians would probably be the last to see a reason or basis for this approach. 

 

David Harlan’s “The Degradation of American History” is another good book with a bunch of quotable quotes.  For example “… social scientists like to imagine themselves a community of inquirers held together not only by a common grievance over parking but by a common set of research procedures.”  It is always a definite thrill – OK, I am being sarcastic – to be involved in one of the wonderful debates over word usage and definition, etc.  I think mathematicians find it particularly humorous, since math builds fromm a VERY small set of simple statements (called Peano’s Axioms) into the entire field of mathematics.  Nothing is REAL in any sense of the word.

 

In 1940 G. . Hardy, one of the bright lights of early 20^th century mathematics from Cambridge, wrote a classic piece on the role of mathematics. 

http://en.wikipedia.org/wiki/A_Mathematician%27s_Apology has a good summary.  I think Hardy would have considered many of the attempts to “borrow” the beauty and stature of mathematics, as seen in many of the sociological works I read, and even some histories, to be vulgar.  And I think it is downright silly.  Language is so extremely imprecise that to think we can describe something as vague as civilization, or almost any other similar concept, precisely is fools play.

OK, rant over.  And I lied.  Here is a little topical economics for the class. Courtesy Dilbert, August 22, 2009

Comments

[Dianne Schmidley]

Wayne,
The way I see it folks who worship mathematics are like Catholics used to be...or at least what we thought before the Ecumencial Movement.

Our priest told the story of the Protestant who died and went to heaven and when he got there Saint Peter told him he could go anywhere in heaven he wanted. One day he was looking around heaven and noticed a closed and locked door. He heard a lot of laughing on the other side, and he asked St. Peter if he could go in that room because it seemed whoever was in there was having a great deal of fun. St Peter said, "No, that room holds only Catholics, and they think they are the only ones up here."

Thus my point is this. There is nothing mathmeticians can see, that others can't see....although each "philosopher" operates from his or her own worldview, as Foucault noted.

Furthermore, whatever has been said, Shakespeare said it best, so if we want to be wise, i.e., "understand," we should read Shakespeare's works, again and again....even the painful ones like 'Titus'(which I dispise). (Recall that Shakespeare wrote during the English Reformation.)

Take Hamlet for example. This play, like many of Shakespeare's plays is about revenge. Most, if not all, of the world's ills have to do with revenge.

When you finally realize you can never get revenge for a past wrong (not even if you are the Wicked Witch), and that two wrongs never make a right (try as they might, there is nothing humans alive today can do to make amends to past victims of exploitaion and/or murder without creating new vicitims), then you have reached true wisdom. Like it or not, this IS how it IS.

[Lindsey Bestebreurtje]

Your comment "It is the idea that taking on the mask of mathematics gives some legitimacy to an argument" made me think of O'Malley's discussion of the role of science in legitimizing racism. By connecting their ideas of hate to the "science" of cranial size and social Darwinism opponents of equal rights were able to stop the potential for equality during Reconstruction.

We want to feel like our ideas of legitimate and so we connect them with the things that we dont think people can argue against - math, sciene, religion. It is too overwhelming for people to think about all their beliefs and morals as relative so they connect them to the "real." To some extent I feel like this is a result to the standardization of daily life described by Chandler because of the improvements in technology.

Its all bullshit.

[Dianne Schmidley]

Leslie, you are so young to be so jaded.

The measurement of heads had to do with intelligence, and although some contemporary analysts look backwards and see race in everything, others (like Marxists) look back and see class.

Members of the elite, which included those whom we might call 'scientists' today tried to show that the justification for subjecting the many by the few had to do with supposed mental inferiority and this pertained to serfs, Slavs, slaves (root word is Slav), women and others.

Mathematics may have been used to mask this, but let us not throw the baby out with the bath water.

Antiquated ideas did affect science for sure. My favorite story is told by Clara Pinto, who shows how the discovery of what led to the human fetus (i.e., female egss and male sperm) was delayed by centuries by male scientists who persisted in believing males implanted seeds that grew into babies.

[essay]

Take Hamlet for example. This play, like many of Shakespeare's plays is about revenge. Most, if not all, of the world's ills have to do with revenge. Mathematics may have been used to mask this, but let us not throw the baby out with the bath water. To some extent I feel like this is a result to the standardization of daily life described by Chandler because of the improvements in technology.