Posted by: Alexandre Borovik | September 15, 2009

Aldous Huxley: A childhood story of mathematics

I have always been rather partial to plane geometry; probably because it was the only branch of mathematics that was ever taught to me in such a way that I could understand it. For though I have no belief in the power of education to turn public school boys into Newtons (it being quite obvious that, whatever opportunity may be offered, it is only those rare beings desirous of learning and pssessing a certain amount of native ability who ever do learn anything), yet I must insist, in my own defence, that the system of mathematics instruction of which, at Eton, I was the unfortunate victim, was calculated not only to turn my desire to learn into stubborn passive resistance, but also to stifle whatever rudimentary aptitude in this direction I might have possessed. But let that pass. Suffice to say that, in spite of my education and my congenital ineptitude, plane geometry has always charmed me by its simplicity and elegance, its elimination of detail and the individual case, its insistence on generalities.

(From Aldous Huxley’s essay “Views of Holland”, page 98 of Thomas R. Cook’s Essays in modern thought on Google books (http://books.google.ca/books?id=k1yrBlylOigC). With thanks to Dan MacKinnon.

He had not become a mathematician, but geometry had imprinted on Huxley as an aesthetic paradigm obvious from the description of the Dutch landscape that immediately follows his childhood recollections:
\begin{quotation}\small
My love for plane geometry prepared me to feel a special affection to Holland. For the Dutch landscape has all the qualities that make geometry so delightful. A tour of Holland is a tour trough the first books of Euclid. Over a country that is the ideal plane surface of the geometry books, the roads and the canals trace out the shortest distances between point and point.
[\dots ] I may be free to admire the farmhouse on the opposite bank of the canal on our right. How perfectly it fits into the geometrical scheme! On a cube, cut down to about a third of its height, is placed a tall pyramid. This is the house. A plantation of trees, set in a quincunx formation, surrounds it; the limits of its rectangular garden are drawn, in water on the green plain, and beyond these neat ditches extend the interminable flat fields. There are no outhouses, no barns, no farm-yard with untidy stacks. The hay is stored under the huge pyramidal roof, and in the truncated cube below live, on the one side the farmer and his family, on the other side (during winter  only; for during the rest of the year they sleep in the fields) his black and white Cuyp cows. Every farmhouse in North Holland conforms to this type, which is traditional, and so perfectly fitted to the landscape that it it would have been impossible to devise anything more suitable. An English farm with its ranges of straggling buildings, its untidy yard, full of animals, its haystacks and pigeon-cotes, would be horribly out of place here. In the English landscape, which is all accidents, variety, detail and particular cases, it is perfect. But here, in this generalised and Euclidean North Holland, it would be a blot and a discord.Geometry calls for geometry; with a sense of the aesthetic proprieties which one cannot too highly admire, the Dutch have responded to the appeal of the landscape and have dotted the plane surface of their country with cubes and pyramids.
Delightful landscape! I know of no country that it is more mentally exhilarating to travel in. No wonder Descartes preferred the Dutch to any other scene. It is the rationalist’s paradise. One feels as one flies along in the teeth of one’s own forty-mile-an-hour wind like a Cartesian Encyclopaedist—flushed with mental intoxication, convinced that Euclid is absolute reality, that God is a mathematician, that the universe is a simple affair that can be explained in terms of physics and mechanics

He had not become a mathematician, but geometry had imprinted on Huxley as an aesthetic paradigm obvious from the description of the Dutch landscape that immediately follows his childhood recollections:

My love for plane geometry prepared me to feel a special affection to Holland. For the Dutch landscape has all the qualities that make geometry so delightful. A tour of Holland is a tour trough the first books of Euclid. Over a country that is the ideal plane surface of the geometry books, the roads and the canals trace out the shortest distances between point and point.

[…] I may be free to admire the farmhouse on the opposite bank of the canal on our right. How perfectly it fits into the geometrical scheme! On a cube, cut down to about a third of its height, is placed a tall pyramid. This is the house. A plantation of trees, set in a quincunx formation, surrounds it; the limits of its rectangular garden are drawn, in water on the green plain, and beyond these neat ditches extend the interminable flat fields. There are no outhouses, no barns, no farm-yard with untidy stacks. The hay is stored under the huge pyramidal roof, and in the truncated cube below live, on the one side the farmer and his family, on the other side (during winter  only; for during the rest of the year they sleep in the fields) his black and white Cuyp cows. Every farmhouse in North Holland conforms to this type, which is traditional, and so perfectly fitted to the landscape that it it would have been impossible to devise anything more suitable. An English farm with its ranges of straggling buildings, its untidy yard, full of animals, its haystacks and pigeon-cotes, would be horribly out of place here. In the English landscape, which is all accidents, variety, detail and particular cases, it is perfect. But here, in this generalised and Euclidean North Holland, it would be a blot and a discord.Geometry calls for geometry; with a sense of the aesthetic proprieties which one cannot too highly admire, the Dutch have responded to the appeal of the landscape and have dotted the plane surface of their country with cubes and pyramids.

Delightful landscape! I know of no country that it is more mentally exhilarating to travel in. No wonder Descartes preferred the Dutch to any other scene. It is the rationalist’s paradise. One feels as one flies along in the teeth of one’s own forty-mile-an-hour wind like a Cartesian Encyclopaedist—flushed with mental intoxication, convinced that Euclid is absolute reality, that God is a mathematician, that the universe is a simple affair that can be explained in terms of physics and mechanics …

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Responses

  1. It is precisely for this reason that I have always regarded Piet Mondrian as a landscape painter. Flying low over The Netherlands is like looking at a Mondrian painting.


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