Math To Save Us?

 I admit that math is far from my strong suit. Even less these past 15 years, since I seem to have lost my ability to do simple math in my head. When I was in pretrial detention, I knew I had had a breakdown of some sort when I could not add Scrabble scores. There was something lost.

However, I did learn - finally - algebra while in prison. Previously, my problem had been a disinclination to see its value, and I may not have paid as close attention to my teachers. I did do well in college with symbolic logic. That always left me wondering why I could not bend my mind around algebra. I had a better teacher or a more receptive mind in prison.

Quantum physics fascinates me. I just want that on the record. The sciences interested me at about the same time history interested me. If I had a better grounding in math, I would have gone into a different career.

All this explains why I read Gordon Gillespie's To better understand the world, follow the paths of mathematics  (Aeon Essays), and this may show why you should read the essay:

Ludwig Wittgenstein once said: ‘I want to show the colourfulness of mathematics.’ In that spirit, I placed mathematics at the centre of my project because, in my view, mathematics searches along more of these many paths than any other intellectual discipline. It is connected on a deep level both with the natural sciences and the humanities. It bridges the gulf between them, and it does so by putting certain metaphysical and epistemological dogmas into question, as will become clear in the following.

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These divergent understandings underpin the worldviews of each culture. Naive realists – primarily natural scientists – like to point out that nature existed long before humankind. Nature is ordered according to laws that operate regardless of whether or not humans are around to observe. So the natural order of the world must be predetermined independently of the human mind. Conversely, naive idealists – including social constructivists, mostly encountered in the humanities – insist that all order is conceptual order, which is based solely on individual or collective thought. As such, order is not only not independent of the human mind, it’s also ambiguous, just as the human mind is ambiguous in its diverse cultural manifestations.

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The best mediator of a conciliatory view that avoids the mistake of the naive realist and the naive idealist is mathematics. Mathematics gives us shining proof that understanding some aspect of the world does not always come down to uncovering some intricate causal web, not even in principle. Determination is not explanation. And mathematics, rightly understood, demonstrates this in a manner that lets us clearly see the mutual dependency of mind and nature.

For mathematical explanations are structural, not causal. Mathematics lets us understand aspects of the world that are just as real as the Northern Lights or people’s behaviour, but are not effects of any causes. The distinction between causal and structural forms of explanation will become clearer in due course. For a start, take this example. Think of a dying father who wants to pass on his one possession, a herd of 17 goats, evenly to his three sons. He can’t do so. This is not the case because some hidden physical or psychological forces hinder any such action. The reason is simply that 17 is a prime number, so not divisible by three.

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...But we can attribute at least one fundamental insight to Kant: mind and world are no separate spheres that must first be connected, so that the question arises as to how exactly this might be achieved. Rather, both depend on each other. Just as the world does not simply prescribe spatial, temporal and other structures that our mind then has to decipher, the mind is not free to impose any structure on the world at will. This is most impressively demonstrated by mathematics, which, despite the lack of empirical restrictions, does not fall into wild speculation.

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Mathematics provides the most impressive proof that a true understanding of the world goes beyond the discovery of causal relationships – whether they are constituted by natural or cultural forces. It is worth taking a closer look at this proof. For it outlines the bond that connects mind and nature in particularly bright colours. Kant understood this bond as a ‘transcendental’ one. The late Wittgenstein, on the other hand, demonstrated its anchoring in language – not in the sense of a purely verbal and written practice, but in the sense of a comprehensive practice of actions the mental and bodily elements of which cannot be neatly separated. In the words of Wittgenstein, ‘commanding, questioning, recounting, chatting are as much a part of our natural history as walking, eating, drinking, and playing.’

Reading the essay, I began thinking of conspiracy theories and Western theology. The conspiracy theorists want to explain causation. Western theology wants to explain God. Eastern Orthodox theology holds God is a mystery beyond our ken. My own opinion is to follow Hume on causation - things keep happening and there may be no connection from one to the other than experience, which is the mind making distinctions. 

Take the variety of the world as a thing of wonder and enjoy the spectacle. Once I did not, and it left me in a place where death felt like a soothing balm. Death has to be where all the bright voluptuous weirdness of our lives, our existence, our universe becomes a dry, shriveled grayness.

Too many books need read. There will be a pause here. Then back to my fiction.

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