Sunday, February 12, 2012

On re-creating the Renaissance education

So, I took today to work on my book and I've been reading a little of Leon Battista Alberti's "brief" treatise On Painting, and it immediately became apparent that in order to even follow this great man's thinking on the subject of painting, I am going to have to revisit mathematics, particularly geometry.

A few months ago, a reader kindly fulfilled one of my Amazon Wishlist wishes, and sent me all three volumes of Euclid's Elements. Many years ago, I took a remedial mathematics course and did quite well. I later discovered the reason for this. It was obvious from the layout of the course that its author had been a big fan of Euclid. All the proposals were laid out in my course in a logical and wondrously clear pattern from simplest concepts to greater and greater complexity.

By the end of this short course, I had discovered that not only was I not completely hopeless about maths, but there was in this Geometry business some elusive key to the secrets of the universe. Like a kind of map to God. It certainly became clear why the Pythagoreans worshipped mathematics like a god. This revelation is one of the key things I hope to lay out in my own book on re-creating the thought processes of the study of classical drawing and painting.

Book One of Alberti's treatise consists of over 6000 words on the mathematics behind perspective and composition. The work was, of course, intended for the sons of educated 15th century gentlemen who would have received Euclid as the beginning and end of their studies in mathematics and for whom Alberti's ideas were merely the application of these abstract concepts to a concrete form. But to us half-illiterate moderns, the damn thing is nearly incomprehensible. (And the edition I have found online has no pictures. This subject really does need illustrations!)

I think I'd better fetch my copy of Euclid from the office where it has very eruditely decorated my desk for some time.


What? People do Euclid as a hobby all the time, don't they? It's not weird.



Mark S. Abeln said...

You may also want to look up Boethius’ De Institutione Arithmetica, and closely related theories of musical harmony.

vox said...

Euclid is an awesome hobby to have! As is algebra, number theory, and mathematical logic.

But then I teach maths, so maybe this oddity about me is slightly - slightly - less bizarrely freaky.

(Not that bizarrely freaky is bad, of course)

Mark S. Abeln said...

Euclid, a hobby?

The ancients considered a knowledge of geometry to be nothing less than a stage in enlightenment, essential to breaking free from the chain of appearances and human opinion.

But yeah, I guess it can be a hobby.

I bet if you know geometry, you use it all of the time, even if subconsciously. It’s really obvious when someone doesn’t know it.

berenike said...

Detestable triangles.

Algebra, now that's the thing.

a Christopher said...

I've been known to enjoy a good algebraic geometry now and then. Resolution of singularities is a fascinating family of problems; but, O Berenike, what's wrong with triangles? (beautiful crystaline triangles!)

Here is a gem enlightened by algebraic considerations. And here is a counter-gem, which is a very fine indication that geometry isn't all about rulers and compases afterall, even if they're might handy.

One shudders to think of mentioning these without Morley's marvelous result.


Mark S. Abeln said...

Algebraic geometry is a perversion, an unholy hybrid foisted on us by the same Descartes whose Dualist anthropology has led to the modern malady of the culture of death and totalitarianism. From algebraic geometry comes the idea of a "frame of reference" which is one step towards moral relativism. A 3-4-5 triangle does not need a frame of reference to describe it, for it is a thing unto itself, invariable from any point of view. An algebraic approach to geometry often loses sight of the geometric principles.

That being said, algebraic geometry is very useful -- I was trained in physics and so used it all of the time.