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A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges. ↗
Indeed, "brute force" solutions are often characteristic of advanced cultures, not primitive ones. The Romans and their predecessors spent a long time figuring out how to build arches... and virtually all our buildings today use post-and-lintel construction, precisely what the arch was devised to replace. We have better materials and more money, and given that, arches are usually not worth the extra complexity. ↗
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We need – more urgently than architectural utopias, ingenious traffic disposal systems, or ecological programmes – to comprehend the nature of citizenship, to make serious imaginative assessment of that special relationship between the self and the city; its unique plasticity, its privacy and freedom. ↗
I must study politics and war that my sons may have liberty to study mathematics and philosophy. My sons ought to study mathematics and philosophy, geography, natural history, naval architecture, navigation, commerce, and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain. ↗
[The building] had been designed by an architect, so it bore little resemblance to any normal structure. ↗
But it is doubtless true, and evident from [the] Scriptures, that the essence of all true religion lies in holy love; and that in this divine affection, and an habitual disposition to it, and that light which is the foundation of it, and those things which are the fruits of it, consists the whole of religion. ↗
