The first nuclear bomb had a immediate impact on world affairs. The first steam engine did not. It took decades for the steam engine to transform civilization.

Why? Because of math.

The engineers at the Manhattan Project built a working nuclear device on their first try because they ran careful calculations. For example, they knew the atomic weights of different isotopes. By measuring the energy and velocity of different decay products and plugging them into you can calculate the theoretical maximum yield of a nuclear weapon. The limiting factor in going nuclear is (and always has been) uranium[1] and industrial capacity, not technical know-how.

The first commercial steam engine was invented in 1698 by Thomas Savery but the Carnot cycle wasn't proposed by Sadi Carnot until 1824 and the ideal gas law wasn't discovered until 1856.

Imagine building a steam engine 126 years before the discovery of the Carnot cycle. That's like building a nuclear reactor 126 years before . It's like building a nuclear reactor with Benjamin Franklin's knowledge of physics.

The early steampunks did not have statistical mechanics in their toolbox. They built their machines first. The science came afterward. The earliest steam engines were extremely inefficient compared to the earliest atomic bombs because they were developed mostly through trial-and-error instead of computing the optimal design mathematically from first principles.

Coal Mines

Mining was a big industry in eighteenth-century England. "Three-quarters of the patents for invention granted prior to the Savery engine [a steam pump] were, one way or another, mining innovations; 15 percent of the total were for drainage alone, as the shortage of surface coal became more and more acute and prices rose."

Water flows downward. Mines are underground. The deeper you dig your mine, the more likely you are to hit the water table. A mine full of water is unusable. A mine must be dry before you can send a miner down with his pickaxe.

Pumping water via animal power is expensive compared to coal pumps. "In 1742, a study was made of a 240-foot-deep coal mine in northeast England in which a horse-driven pump lifted just over 67,000 gallons every twenty-four shillings, while Newcomen's engine pumped more than 250,000 gallons using twenty shillings' of coal—a demonstration not only of the value of the engine, but a newfound enthusiasm for cost accounting."

I am skeptical of author William Rosen's implication that there was anything "newfound" about cost accounting in the eighteenth century. Double-book accounting was invented in Italy in the thirteenth century. Entrepreneurship is thousands of years old.

But putting steam engines next to coal mines does make economic sense. Steam engines (especially the early inefficient ones) require lots of coal. Coal is expensive to transport because locomotives haven't been invented yet. Even if 75% of the coal you mine goes into feeding your coal-powered water pump, the remaining 25% of coal is coal you wouldn't have at all if it weren't for the steam engine. "The coal-fired atmospheric engines designed by Newcomen and Calley burned so much coal for the amount of water pumped that the only cost-effective place for their use was at the coal mine itself…because the cost of transporting the coal to a steam engine more than a few hundred yards from the mine itself ate up any savings the engine offered."

Iron Smelters

To build steam engines, you need iron. Iron ore is common. It's more than five percent of the Earth's crust. But the iron in the Earth is iron oxide i.e. rust. To make iron oxide useful, you need to remove the oxygen. You can remove the oxygen from iron oxide by applying heat.

A wood fire isn't enough. You need a blast furnace. You need to pay attention to temperature-dependent phase transitions too in order to make good quality steel. But the process is simple enough you could do it in the Middle Ages. The earliest blast furnaces are attributed to the Han Dynastry in the first century AD.

A medieval blast furnace pumps air across burning charcoal. It requires lots of wood. "The production of 10,000 tons of iron demanded nearly 100,000 acres of forest, which meant that a single seventeenth century blast furnace could denude more than four thousand acres each year."

Abraham Darby invented a method of casting iron in sand. It didn't produce a high-quality product but it did produce a cheap product. Darby started a company. He sold lots of iron. He sold so much iron he ran out of charcoal. He had denuded the nearby forests in just a year.

Charcoal is made from wood. Pitcoal is more plentiful than wood but pitcoal smoke contains sulfur impurities which, when incorporated into molten iron, produce "a very brittle, inferior product."

Wood is turned into charcoal by burning off the contaminants.

You can do the same thing to pitcoal. The result, called "coke", is less pure than charcoal but it'll do the job when you have exhausted your supply of wood. It helps to work out of Shropshire (which Darby did) where the coal is unusually low in sulfur to begin with. Darby shifted from wood to coke in 1710.

Darby completed the last piece of the industrial chain reaction. Steam engines are used to mine coal which is turned into coke which is used to smelt iron which is used to build more heavy infrastructure. Positive feedback loops explode. The more popular steam engines get, the more profitable it is to improve them.

The Military–Industrial Complex

Britain controlled the world's oceans in the eighteenth and nineteenth centuries. Naval superiority requires warships. Warships (even eighteenth-century wooden warships) require lots of iron. As late as 1750, Britain imported almost two thirds of its iron. The British government liked neither the monetary outflows nor their rivals controlling a critical strategic resource.

Darby's coke-fired furnace enabled Britain to produce coke domestically, even without trees, but the Royal Navy needed wrought iron of a higher quality than Darby's. An alternative process called "the stamp-and-pot system" produced wrought iron of sufficient quality but was too expensive (because it smashed lots of clay pots) to meet the demands of the Royal Navy. Purchasing agent Henry Cort was tasked with securing a scalable domestic source of quality wrought iron.

Cort's solution, called a "puddling furnace", separated the fuel from the iron.

Temperatures in the coolest parts of the ironworks were typically over 130° [Fahrenheit]; iron was transported by the hundredweight in unsteady wheelbarrows, and the slightest bit of overbalancing meant broken bones. Ingots weighing more than fifty pounds each had to be placed in furnaces at the end of puddler's shovels. Huge furnace doors and grates were regularly opened and closed by chains with a frightening tendency to wrap themselves around arms and legs.

Cort also invented grooved rollers which replaced hand-hammering iron ingots into bars and sheets. He patented it in 1783. That doesn't mean no one would have invented grooved rollers to shape iron if it weren't for the patent system granting a monopoly because Cort was not the only person to patent grooved rollers.

Not only had grooved rollers of a slightly different sort been patented by John Purnell in 1766, but puddling (under a different name) was included in peter Onion's 1783 patent. Other versions of puddling appeared in William Wood's patent of 1728, the 1763 patent of Watt's partner John roebuck, the 1776 patent of Thomas and George Cranage (who worked with Darby at Coalbrookdale), John Cockshutt's 1771 patent, and most telling, the four-stage technique that earned John Wright and Richard Jesson patent number 1054 in which the iron was "cleansed of sulphurous matter" inside of a rolling barrel.

All of which should serve as a reminded that while the industrialization of Europe was not a function of impersonal demographic forces, neither was it the work of a dozen brilliant geniuses. In any year, the lure of wealth and glory tempted at least a few hundred English inventors, but only a few achieved both.

I don't think author William Rosen proves that the industrialization of Europe was not a function of impersonal demographic forces. Britain's demand for iron was insatiable. Someone would have figured how to produce iron from coke if Darby hadn't. Someone else would have figured out how to produce quality wrought iron from coke if Cort hadn't.

Supply and Demand

Exponential growth in iron production required exponential growth in iron demand.

The Royal Navy was the largest customer of fabricated iron in the mid eighteenth century "but its ships were still made of wood, and driven by sails." Much of the wrought iron was going into steam engine components like boilers and cylinders but steam engines were still too inefficient to use for anything but mining coal.

Matthew Boulton calculated that if the coal demands of a steam engine could be reduced by half then steam engines could be used to pump water in tin mines. They could also power the the hammers and bellows of the the ironworks.

It is time to optimize these machines.

The cube-square law was first published by Galileo Galilei in 1638. The cube-square law is the idea that the when you scale all three spatial dimensions of an object up by its volume increases by a factor of but its surface area increases only by a factor of . The heat capacity of a boiler is proportional to its volume but the heat loss rate of a boiler is proportional to its surface area. A large well-designed steam engine ought to be be more efficient than a small similarly-designed steam engine. A steam engine designed to operate at one scale may not function at all when you scale it up or down.

The brasssmith-turned-scientist James Watt (after whom the unit of power is named) realized that the square-cube law could cause a steam engine to fail when miniaturized. "Watt needed to calculate exactly how much heat was being lost in the Newcomen design, and that meant converting general theories about theme into precise measurements, which were, to be kind, thin on the ground at the time, even for such elementary benchmarks as the boiling point of water." You cannot use 100°C because the Newcomen engine operates in a vacuum.

William Cullen discovered[2] in 1756 that water boils at a lower temperature in a vacuum. That was a new discovery at the time. Watt began his experiments in 1777. People didn't even know how much water expands when it boils. Estimates ranged from 2,000× to 14,000×. Watt measured a ratio of 1,849× and independently discovered the concept of latent[3] heat.

By quantifying the efficiency of a steam engine in terms of heat loss, Watt could identify precisely identify the Newcomen engine's efficiency bottlenecks. If you've ever tried to optimize a machine (or software) then you know that most losses come from a tiny number of bottlenecks. Accurately identifying bottlenecks is a prerequisite to effective optimization. Quantitative measurement is a prerequisite to accurately identifying bottlenecks.

William Rosen argues that James Watt was incentivized by Britain's patent system. "Eighteenth-century Britain wasn't any more hospitable to their brilliant innovations than anywhere else; but it was a lot more hospitable to innovators who couldn't afford to invest years of their lives with no hope of material gain." James Watt figured out that the problem with the Newcomen engine was heat loss in the cylinder. He eventually solved the problem in 1765 by inventing a separate condenser and earned patent #913.

Watt was not a businessman.

I would rather face a loaded cannon than settle an account or make a bargain.

―James Watt

Watt's financier John Roebuck tried to sell (part of) the intellectual property related to Watt's engine to visionary progressive[4] businessman industrialist Matthew Boulton but Boulton turned Roebuck down. Roebuck went bankrupt. Boulton bought the patent rights for the firesale price of £630[5] and joined forces with Watt to start their own company Boulton & Watt.

Cornwall copper mines were about to shut down because they couldn't operate without steam pumps and coal prices had increased so high they could no longer afford to run Newcomen-style engines.

Unfortunately for Boulton & Watt, the patent on the separate condenser patent was about to expire in 1783 but the company predicted they would need until 1800 to break even on the investment needed to perfect the Watt engine. Boulton arranged for an Act of Parliament, the "Fire-Engine Act of 1775" to extend his patent protections.

Economists still debate whether the 1775 patent extension promoted or inhibited innovation in steam technology; even the strongest critics concede that if it did retard innovation, it did so for at most a decade, which seems modest enough in the great sweep of history.


Did patent rights help advance technology? I don't know for sure. Roebuck (who owned the original patent) went bankrupt. I get the impression Roebuck and Boulton spent a lot of money on litigation (as did the Wright brothers).

I think patents have a net-negative effect on innovation. My personal experiences interacting with the patent system as an entrepreneur have been hell. For example, I once built a product and then, after I shipped my product, a competitor (who did not have a working product at the time) revealed that they had secretly filed a patent upon which they felt my company had infringed. But the alternative to patents is the secrecy of guilds, which might have nasty effects on society too. Except the earliest patents didn't even make the techniques public.

[Baron] Dudley had discovered "the mystery, art, way, and means, of melting iron ore, and of making the same into cast works or bars, with sea coals or pit coals in furnaces, with bellows"—but the actual process remained, well, mysterious…. He did not…describe how they did it, and the patents of the period are even vaguer than the genealogies.

Patents might make more sense in heavy industry and biotechnology. I'm not saying they do. Just that they might. If the steam engine industry really was on life support than the British government intervening with industrial policy was the right decision.

But when I picture myself as an eighteenth-century English inventor, the patent system appears (from my perspective) to be little more than legal cover for people with ties to Parliament to unfairly crush competition from small tech startups. If lawyers win business battles that means engineers lose. Engineers losing retards technological development. The "Fire-Engine Act of 1775" was rent-seeking by a hereditary aristocracy.

Matthew Boulton got what he wanted: a twenty-five-year extension.

The United States Declaration of Independence was signed in 1776.

  1. There are three basic types of nuclear weapons: uranium, plutonium and hydrogen. On the geopolitical stage, whether you have nuclear weapons is more important than what kind you have. Plutonium and hydrogen bombs are limited by a state's technical know-how. In this article, I am concerned with uranium fission bombs. ↩︎

  2. I'm using "discovered" as shorthand for "contributed to the scientific literature". I think mountaineers (and mountain-dwelling people) have been aware that water boils at a lower temperature when air pressure is lower. ↩︎

  3. Latent heat is the energy used to transform a liquid into a gas (or a solid into a liquid) at the phase transition temperature. When water condenses, it releases latent heat. ↩︎

  4. Boulton used no child labor. ↩︎

  5. For reference, Watt's annual salary as a surveying engineer in 1770 was £200. Roebuck testified that he had spent £3,000 on development. ↩︎

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The early steampunks did not have statistical mechanics in their toolbox. They built their machines first. The science came afterward. The earliest steam engines were extremely inefficient compared to the earliest atomic bombs because they were developed mostly through trial-and-error instead of computing the optimal design mathematically from first principles.

Of course they didn't have statistical mechanics in their toolbox! Gears-level models are capital investments, and you should only invest in things that might be valuable. You don't know that steam engines have value until you see them doing useful things, like pumping water out of coal mines. You don't know that streamlining steam engines has value until Matthew Boulton works out that it does. Only then do you do the legwork of iterated experimentation and modeling. The original steam engine was invented in the classical era, and it went nowhere because people used it solely as a party trick.

From Antifragile by Taleb:

One can make a list of medications that came Black Swan–style from serendipity and compare it to the list of medications that came from design. I was about to embark on such a list until I realized that the notable exceptions, that is, drugs that were discovered in a teleological manner, are too few—mostly AZT, AIDS drugs.

Practice precedes theory, with rare exceptions like the Manhattan Project. In an internship, I was semirandomly tinkering with my project, and found that applying [REDACTED] to the [REDACTED] led to a significant reduction in loss. In my written report and PowerPoint, I drew analogies between my methods and the human [REDACTED], implying that I was inspired by my theoretical knowledge of biology, instead of just happening upon [REDACTED] by chance. That was one of the few times I've done Actual Technological Innovation, and it wouldn't surprise me at all if most tech progress worked the same way: trial-and-error, then theoretical explanation.

The cube-square law was first published by Galileo Galilei in 1638. 

You write published which is good (!) because the cube-square law was surely known before Galileo. 

I contacted my friend Viktor Blasjo

Certainly much too trivial not have been noticed long before indeed. But I'm not sure about an unequivocal reference off the top of my head. Multiple Greek sources speak of scaling issues of catapults, e.g. how the diameter of the spring or rope of a machine should scale in proportion to the weight of the projectile. An example is:


(The same argument is given in Philon and Heron, pp. 41, 111 of Marsden, E. W. (1971). Greek and Roman artillery: Technical treatises. Oxford: Oxford University Press which unfortunately is not accessible online.)


I'm not sure if this amounts the law you mention exactly. But all of these sources are clearly interested in this because it leads to the mathematically interesting problem of cube duplication. So clearly the Greeks had thought a lot about scaling and this is the part preserved in the record because of its associated technical mathematical machinery.

Cort’s solution, called a “pudding furnace”, separated the fuel from the iron.

(From the quotes, sounds like this should be "puddling"?)

Fixed. Thanks.