# What Are You Breaking Today?

January 11, 2013 3:28 amOnce in a while, when you read something, you get some surprises that kind of stay with you for quite some time. We spotted one such surprise recently when watching Taleb give an author talk at Google, on his book ‘Antifragile’. Here is the surprise from the book: Source

“Beginning in the distant past, consider ancient architecture. There is a tendency to believe that Euclidian geometry allowed for this. That the geometry came first, and the magnificent buildings followed in its wake (loc. 3959). As Taleb points out, though, this is not at all how it happened. As evidence of this, the author invites us to “take a look at Vitruvius’ manual, De architectura, the bible of architects, written about three hundred years after Euclid’s Elements. There is little formal geometry in it, and, of course, no mention of Euclid, mostly heuristics, the kind of knowledge that comes out of a master guiding his apprentices. (Tellingly, the main mathematical result he mentions is Pythagoras’s theorem, amazed that the right angle could be formed ‘without the contrivances of the artisan.’)” (loc. 3973).

Even the wondrous Roman aqueducts appear to have been created out of practical know-how, as opposed to applied mathematics. As Taleb explains, “we are quite certain that the Romans, admirable engineers, built aqueducts without mathematics (Roman numerals did not make quantitative analysis very easy)” (loc. 3968). Even later, by the time the middle ages rolled around, architecture and engineering were still advancing by way of practical experimentation, rather than the application of theory. As the author explains, “according to the medieval science historian Guy Beaujouan, before the thirteenth century no more than five persons in the whole of Europe knew how to perform a division… But builders could figure out the resistance of materials without the equations we have today—buildings that are, for the most part, still standing. The thirteenth-century French architect Villard de Honnecourt documents… how cathedrals were built: experimental heuristics, small tricks and rules… For instance, a triangle was visualized as the head of a horse” (loc. 3961-66).”

That is just so scary and surprising – all this amazing architecture – just by practical knowledge, and absolutely no knowledge that a corresponding theory could even be possible – Really? This is a high-impact argument from the book, one that could change the way you perceive things overall.

The message is clear: What are you breaking today?

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“before the thirteenth century no more than five persons in the whole of Europe knew how to perform a division…” – wow, seriously?

It’s funny, I have a Mechanical Engineering degree, but haven’t really used calculus since college. Trig I use all of the time though, as well as a lot of the concepts.