How mathematics built the modern world
worksinprogress.co
worksinprogress.co
> The pioneers of the Industrial Revolution valorized precision...
This phrase to me is the key of the whole thing. They weren't excited about what we would recognise today as maths. They wanted accurate manufacturing and measurement.
That does naturally dovetail into improved mathematical technique, but I think it is incorrect to say that math is the driver here. Precision is the driver. That has remained true to today by the way (most precise manufacturing? semiconductors).
Right. What the author doesn't really pick up on is how engineering developed. Before 1800 or so, science and math were not routinely used by people who built stuff. Edison tended to deride mathematical theorists, although he hired some.
Early navigation and astronomy required math, but that was mostly measurement, not design. The first thing that really required math in the engineering was the steam engine. It's possible to build a steam engine with no understanding of thermodynamics, but it will be a really crappy steam engine. Watt's early engines were about 2% efficient. Carnot, in 1824, published "Reflections on the Motive Power of Fire", which, for the first time, addressed engine design in terms of heat, pressure, efficiency, heat transfer, etc. Around the middle of the 19th century, Joule and Kelvin finally got a decent mathematical theory for heat engines. Engine designs improved substantially and efficiencies went up. At last, direct use of math in engineering was really paying off.
Early electrical work was trial and error. Sort of. Edison publicly derided theorists, but he had some on his payroll. When AC came along, more theory was needed. Now calculus was required. Westinghouse and Tesla got involved, and generators, motors, and transformers started working much better. (I've pointed out before that Tesla's real contribution was that he figured out how to get AC electric motors started.) Good motors require electromagnetic fields in strange shapes, and intuition fails for that. You need math.
It is completely possible to build stuff without any math whatsoever if the community of builders copies what they did last time, makes minor adjustments when it doesn't work and keeps an oral history.
Of course, the constructions will be overengineered, not really of industrial volume and the community will believe a lot of things that are not true. And any attempts to be innovative will usually be expensive disasters.
Don't forget all the unstable buildings fell down a long time ago and we don't remember them.
All magic is supposed to work on this principle: one starts with a real-world problem, applies some ("sympathetic") correspondences to arrive at a magical representation, and manipulates that representation ("pins in the voodoo doll") in order to apply it and result in a real-world action.
However, mathematics seems to be the only* subset of magic where the (in the case of mathematics: Galois) correspondence back to the real world proves effective!
* marketers and politicians may disagree
He. Whenever people make claims that violate [math + the laws of physics], invariably it's those people who prove to be at fault. Leading to a favorite of mine:
"Math combined with laws of physics are more reliable than people."
In other words: where possible, measure & do the math! What you find = reality (aka truth). Claims from people saying something else, can then be safely ignored (okay.. up to the point where measurements or the math itself is found to be in error).
@roenxi: I agree that the precision obsession is central and not about super advanced math. However, it's clear that it does require explicit quantification, and it was not done in the middle ages say. Also, the era does not only see the rise of manufacturing (where precision is key), but also Newtonian science, accounting, financial markets, and better navigation and cartography. When trying to explain these things jointly, you land in the diffusion of the calculating paradgim.
@Animats: We don't give it a lot of space, but we do mention that practical engineers used little math: "Before the Industrial Revolution, however, aspiration often outran achievement. Many of Leonardo’s machines were famously unworkable, and while Ramelli’s machinery book was popular, practitioners remained unimpressed. Before the Industrial Revolution, men of practice often saw mathematicians as frivolous." When you discuss the type of math that was important, I also think that you aim a bit too high. Calculus is useful, but a lot is just really getting the most out of simple arithmetic.
@082349872349872: We're not claiming that it works for other things than math. Clearly the strateg works because there is mathematical structure in the world....
@ecshafer: Isn't this strengthening our point? Yes, during this era of broad spectrum of activities were conducted by "mathematical practictioners" which blended a lot of disciplines. That suggests math as a unifying glue. Also, we don't neglect trial and error and practical skills. That's the whole point of the industrial revolution section: "the Industrial Revolution required that basic mathematics and a quantitative outlook reached the class of people actually engaged in production". But trial and error was nothing new. Mathematized production was.
@303uru: I don't deny these points; there's always complexity. But if a single factor accounts for a lot of things, it should be noted.
The Industrial Revolution was fueled by more than just mathematical advancements; it was equally driven by empirical experimentation, practical innovation, and socio-economic factors. Innovators like James Watt relied heavily on trial-and-error and hands-on experience, not just mathematical models. Technological breakthroughs such as the spinning jenny and power loom stemmed more from mechanical ingenuity than from direct mathematical applications. Moreover, the rise of capitalist economies, availability of investment capital, and political stability played crucial roles in facilitating industrial growth. These elements, combined with a consumer culture, suggest that the revolution was as much about socio-economic transformation as it was about a mathematical paradigm shift.
Additionally, the revolution cannot be seen solely through the lens of mathematics, as it underplays the significance of scientific understanding and multidisciplinary collaboration. Scientific theories in physics, chemistry, and biology provided essential underpinnings for technological advancements. The development of efficient steam engines, for example, was closely tied to the understanding of thermodynamics. Furthermore, the Industrial Revolution was a result of collaboration among mathematicians, scientists, and craftsmen, blending theoretical concepts with practical applications. The evolution of education, encompassing both mathematical and practical skills training, also played a pivotal role in preparing the workforce for industrial challenges. Thus, the revolution was a multifaceted phenomenon, influenced by a blend of practical experience, scientific knowledge, and socio-economic developments.
I recently read "Lost in Math" by Sabine Hossenfelder and I'm seeing some similarities here. Hossenfelder's book critiques modern theoretical physics, particularly its reliance on aesthetic criteria such as beauty and simplicity in maths, which she argues can lead physicists astray from empirical science. The idea that the most elegant or beautiful mathematical equations are the best or most accurate representations of the physical world has almost become comedy.