Sunday, 4 May 2014

Who is Hippasus?

Kenji Yoshino wrote an excellent book called, A Thousand Times More Fair: What Shakespeare's Plays Teach Us About Justice (2011). Though Yoshino writes from the perspective of a legal/Shakespearean scholar his insights into Shakespeare's plays are linked to our times and his analyses are unparalleled in the grand tradition of literary criticism.

Another literary critic that I admire is the great Canadian, Northrop Frye (July 14, 1912 – January 23, 1991) who wrote:

The axiom of criticism must be, not that the poet does not know what he is talking about, but that he cannot talk about what he knows. To defend the right of criticism to exist at all, therefore, is to assume that criticism is a structure of thought and knowledge existing in its own right, with some measure of independence from the art it deals with. (Anatomy of Criticism, 1957).

Frye pretty much lived the ideas he formulated above as given testimony in an anthology of essays and memoirs called, On Education, all of which can rightfully be said to have achieved "some measure of independence from the [subject] it deals with" beautifully. To wit:

It is impossible to teach the humanities properly if we think of them as ornaments or graces of ordinary social life. They have their laws and disciplines like the sciences, and must be taught as impersonally as the sciences, despite their emotional and aesthetic connections.
(The high school student) is becoming aware of an underlying conflict in his situation. On one side of him is his ordinary social environment, the world of his television set, his movies, his family car, advertising, entertainment, news, and gossip. On the other side is the school, and perhaps the church, trying to dislodge him from this lotus land and prod him into further voyages of discovery. ...

The school has only five hours a day in which to fight the influences which keep soaking into the student from the rest of his experience, and which usually command an authority that the school cannot command. As a rule, therefore, the world of technology and rhetoric wins out, whether the student goes on to university or not. ...

The education theories generally called progressive tried to abolish this conflict by making the school the agent of society. Education thus became a matter of social adjustment to the world one must live in. But this world, in itself, provides no real standards or values. It stands for immaturity and a cult of youth, for social values rooted in entertainment and advertising, and for emotions rooted in the erotic. Besides, the world, unlike nature, always betrays the heart that loves her. It changes very rapidly, driven on by forces that the socially adjusted cannot comprehend, and can only cope with by the fixations of prejudice and stock response. Thus understanding the world, if made the goal of education, is forced to become an acceptance of the world, and that in turn becomes increasingly an acceptance of illusion. The forms of illusion are familiar: there are the illusions of slanted news, and the illusions of entertainment....

(The student) should understand what he must do to live in his society; but he must understand too that that society has no criteria for judging itself or one's actions within it. The criteria (or at least the secular criteria) can come only from the arts and sciences, the co-ordinated vision of the greatness and accuracy of human imagination and thought. 
("The Critical Discipline", from On Education)

I would encourage anyone who's interested in the subject of education to read this collection of his works.

-I call Frye "a great Canadian" because I'm not normally into Canadian literature much. This "tradition" - if it can called that - has had the unfortunate fate of having to live in a hostile environment in much the same way that a planet in a dual star system (America and Europe) may be subjected to the tidal forces of such conflicting gravity wells. The other Canadian great that I admire is Timothy Findley but it takes a titan to overcome such environment.

Now, who is Hippasus?

Hippasus is said to have been a student of Pythagoras, and attributed the discovery of irrational numbers. Apparently, Hippasus left no extant text to testify to his time in the ancient world, and is only mentioned by writers like Aristotle. Lost into the mists of time, Hippasus is said to have written a text called, Mystic Discourse, ostensibly to discredit his master. But it makes little sense as legend would have it that he was sentenced to death by Pythagoras and thrown off a boat and drowned.

I let Simon Singh (Fermat's Enigma, 1998) take over:

For Pythagoras, the beauty of mathematics was the idea that rational numbers (whole numbers and fractions) could explain all natural phenomena. This guiding philosophy blinded Pythagoras to the existence of irrational numbers and may have led to the execution of one of his pupils. One story claims that a young student by the name of Hippasus was idly toying with the number √2, attempting to find the equivalent fraction. Eventually he came to realize that no such fraction existed, ie, that √2 is an irrational number. Hippasus must have been overjoyed by his discovery, but his master was not. Pythagoras had defined the universe in terms of rational numbers, and the existence of irrational numbers brought his ideal into question. The consequence of Hippasus's insight should have been a period of discussion and contemplation during which Pythagoras ought to have come to terms with this new source of numbers. However, Pythagoras was unwilling to accept that he was wrong, but at the same time he was unable to destroy Hippasus's argument by the power of logic. To his eternal shame he sentenced Hippasus to death by drowning. (Fermat's Enigma, pp. 49-50)

Dogma of any kind - including religious dogma - disturbs me greatly and, in fact, gives me disquieting moments of reflection. Society may "have no criteria for judging itself or one's actions within it" but like Frye claims time and again as those before him, I believe a liberal arts education is the best and only hope to make life worth living.

To those who persist in asking "what profit from an arts degree or the 'soft' sciences?" I say, the ability to analyse and articulate ideas and concepts beyond the bounds of arbitrarily defined and prescribed dataset, the ability to reflect phronetically on questions like:

1. Where are we going? 2. Is this development desirable? 3. Who gains and who loses, and by which mechanisms of power? 4. What, if anything, should we do about it? (


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