Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty," - that is all
Ye know on earth, and all ye need to know.
Russell observed that philosophy would be much easier had mathematics never existed. He is absolutely right. It would be much, much easier. It would also be easier had the organ music never existed, or if a lot of other true and beautiful things never existed – and for this reason most of our philosophy pretends that such things do not exist. Mathematics is said to be operations on logical tautologies while music is self-expression of the artist constrained by sound technology. The denial can take more sophisticated forms, but the gist is always the same. There is no Truth that is Beauty, and Beauty that is Truth, there are only many subjective opinions and aesthetic judgments, from which the consensus emerges, with or without the help of the Only Right Way of reaching this consensus. Of course, this outlook is barbarian.
The barbarians of the Dark Ages were not bad people, nor were they completely lacking the notions of truth and beauty. They did have these notions, often very elaborate ones. They were not particularly bloodthirsty or stupid. They were curious about the world, but this curiosity was satiated by conquest rather than inquiry. You do not have to be stupid or uninquisitive to destroy the foster-child of Silence and slow Time with a mighty blow of a club. The notion that was missing was not of truth and beauty. It was this very notion that truth IS beauty and beauty IS truth. If that was felt, it was not said, and if it was said, it was not acted upon.
Even their greatest refinements were of this disconnected sort. For example, algebra. Greek geometry is true and beautiful, and its truth cannot be separated from its beauty. Medieval algebra was true, but there was no beauty in manipulation of symbols. The same goes for trigonometry or logarithms. These are very useful things, but rather unexciting ones. It is amazing how long it took to reintroduce beauty back to mathematics, and mathematics took off only when that happened. Before it happened, there were just occasional sparks. Solving cubic and quartic equations in radicals is boring and unimportant. Understanding which properties of polynomials do not allow solving higher algebraic equations in radicals leads to the things of great beauty and truth. It is this double pursuit that makes mathematics, music, or art meaningful.
Barbarians do not get it. Their art is the craft that is not aiming at the discovery of truth. The Truth. The old-school barbarians were unpretentious about it, but their modern successors have mended their ways. Now they call their craft “self-expression,” as if expressing one’s artistic self could possibly interest the others. Barbarian art is skillful and wonderful in its own flashy way, but it is thoroughly barbarian. The same goes for barbarian science. Building a warship requires practical knowledge which is better be true, so the boat would not sink. The boat may even look lovely, decorated with all these skulls thoughtfully arranged on the mast poles. But the purpose of making the boat is not searching for Beauty, it is pillage or (at best) Wanderlust. The goal is still the conquest. It may be given an inspiring name, like “the Conquest of Nature.” The barbarians always battle with something or struggle for something. That’s because they have no idea what to do with the beauty or truth they occasionally find. If they find something beautiful, they carefully scrape truth out of it, put it on a pedestal and worship it. When they find truth they do their best to reduce it to algebra that is more suited to a computer than a human being.
The depth of this denial is seen in little things as much as in big things. I’ve been reading a lot of discussions among the aspiring barbarians as to whether mathematics should be taught to their children. Some learned barbarians observed that there was no need for such idle pursuits; there should be specially selected and raised barbarians that are, by the incomprehensible act of nature, uncommonly skillful in this craft; the rest of the barbarians should be taught more socially valuable skills. Then there were barbarians telling that mathematics is practically useful, being the very language of the barbarian science. Other barbarians found more convoluted barbarian uses for mathematics, such as that it teaches barbarian truths. Like logical deductions, consistent thinking, or the important for any modern barbarian fact that some things can’t be true no matter how badly desired to be true and how plausible it might look. Lastly, there were barbarians claiming that mathematics teaches barbarian beauty. Just look at all these beautiful symmetries and connections. We can’t deny our barbarian children this beauty, can’t we? The thinking, in all of its forms remains recognizably barbarian: it is not even registered that mathematics teaches that truth is beauty and beauty is truth. The silent form, - dost tease us out of thought as doth eternity – no, no, please, do not. There is no barbarian use for such teachings. So be it. Whether this barbarian mathematics needs be taught to barbarian children in barbarian schools is for the barbarians to decide. On the final count, their decision does not matter. What matters is their intent of becoming barbarians.
Barbarians would not be barbarians without having their own theories about their condition. Some of these theories are clever, but the approach is always barbarian: the condition is thought to arise from not knowing some barbarian truth or indifference to some form of barbarian beauty. It is never about what barbarianism truly is, which is lacking faith that beauty is truth, truth is beauty, and that is all ye know on earth, and all ye need to know.
What makes a barbarian a barbarian?