The latest issue of Works in Progress has a choice essay out on how mathematics built the modern world. As a onetime major in the subject and longtime fan of the purest arena of human inquiry[1], an area that is simultaneously neither an art nor science yet instrumental and in another light composed of both:
Most of the significant inventions of the Industrial Revolution were not undergirded by a deep scientific understanding, and their inventors were not scientists.
The standard chronology ignores many of the important events of the previous 500 years. Widespread trade expanded throughout Europe. Artists began using linear perspective and mathematicians learned to use derivatives. Financiers started joint stock corporations and ships navigated the open seas. Fiscally powerful states were conducting warfare on a global scale.
There is an intellectual thread that runs through all of these advances: measurement and calculation. Geometric calculations led to breakthroughs in painting, astronomy, cartography, surveying, and physics. The introduction of mathematics in human affairs led to advancements in accounting, finance, fiscal affairs, demography, and economics – a kind of social mathematics. All reflect an underlying ‘calculating paradigm’ – the idea that measurement, calculation, and mathematics can be successfully applied to virtually every domain.
Today as mathematical intertwines into every aspect of human life through increasingly ubiquitous computation, studying the uses and impact of math provides an increasingly useful perspective. The Works in Progress essay details the basic formula for that "calculating paradigm" as follows:
Today that paradigm is more powerful than ever, although taking action in the real world can be incredibly difficult, particularly in the Western world where a thicket of rules and procedures make action in the world of atoms a tricky endeavor.
[1] A truth well put by no less than the estimable webcomic, XKCD.
Purity
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[2] The title of this short blog post is a reference to an essay of that name from decades ago. It's well worth a read if you have not already seen.
