Doing good engineering with bad mental models

One thing I find interesting is how much can be built without understanding the building blocks. For example, when I worked on flash memory, there was still a debate over the physical mechanisms that caused some things to work (https://twitter.com/altluu/status/1478877045715202050). It's been twenty years, so I suspect the questions then are now resolved, but we'd been making flash memory for twenty years at the time and we still didn't really know how it worked.

Another example is Roman architecture. If you read Vitruvius's ten volume work on architecture, De architectura, you'll see passages like the following:

> The reason why lime makes a solid structure on being combined with water and sand seems to be this: that rocks, like all other bodies, are composed of the four elements. Those which contain a larger proportion of air, are soft; of water, are tough from the moisture; of earth, hard; and of fire, more brittle.

> Therefore, if limestone, without being burned, is merely pounded up small and then mixed with sand and so put into the work, the mass does not solidify nor can it hold together. But if the stone is first thrown into the kiln, it loses its former property of solidity by exposure to the great heat of the fire, and so with its strength burnt out and exhausted it is left with its pores open and empty. Hence, the moisture and air in the body of the stone being burned out and set free, and only a residuum of heat being left lying in it, if the stone is then immersed in water, the moisture, before the water can feel the influence of the fire, makes its way into the open pores; then the stone begins to get hot, and finally, after it cools off, the heat is rejected from the body of the lime.

>  Consequently, limestone when taken out of the kiln cannot be as heavy as when it was thrown in, but on being weighed, though its bulk remains the same as before, it is found to have lost about a third of its weight owing to the boiling out of the water. Therefore, its pores being thus opened and its texture rendered loose, it readily mixes with sand, and hence the two materials cohere as they dry, unite with the rubble, and make a solid structure.

Fundamentally, Romans were trying to reason from the concepts of "the four elements". This isn't something that's "a little" wrong, like how classical mechanics is only roughly correct, or even the Ptolemaic view of the galaxy which, despite putting the earth at the center of the galaxy, could actually predict the apparent movement of celestial bodies in the sky with decent accuracy with enough epicycles.

The four elements model doesn't really have predictive power and one can have a similar understanding of the world by just deleting the model from one's brain.

BTW, I believe the last quoted paragraph above is referring to a lime kiln, which facilitates the reaction CaCO_3 + heat -> CaO + CO_2. Removing water from the limestone (calcium carbonate) isn't really "the point" of the reaction, although moisture will, of course, be removed by heat.

A somewhat related quote is:

> Therefore, when different and unlike things have been subjected to the action of fire and thus reduced to the same condition, if after this, while in a warm, dry state, they are suddenly saturated with water, there is an effervescence of the heat latent in the bodies of them all, and this makes them firmly unite and quickly assume the property of one solid mass.

There will still be the question why Tuscany, although it abounds in hot springs, does not furnish a powder out of which, on the same principle, a wall can be made which will set fast under water. I have therefore thought best to explain how this seems to be, before the question should be raised.

> The same kinds of soil are not found in all places and countries alike, nor is stone found everywhere. Some soils are earthy; others gravelly, and again pebbly; in other places the material is sandy; in a word, the properties of the soil are as different and unlike as are the various countries. In particular, it may be observed that sandpits are hardly ever lacking in any place within the districts of Italy and Tuscany which are bounded by the Apennines; whereas across the Apennines toward the Adriatic none are found, and in Achaea and Asia Minor or, in short, across the sea, the very term is unknown. Hence it is not in all the places where boiling springs of hot water abound, that there is the same combination of favourable circumstances which has been described above. For things are produced in accordance with the will of nature; not to suit man's pleasure, but as it were by a chance distribution.

> Therefore, where the mountains are not earthy but consist of soft stone, the force of the fire, passing through the fissures in the stone, sets it afire. The soft and delicate part is burned out, while the hard part is left. Consequently, while in Campania the burning of the earth makes ashes, in Tuscany the combustion of the stone makes carbuncular sand. Both are excellent in walls, but one is better to use for buildings on land, the other for piers under salt water. The Tuscan stone is softer in quality than tufa but harder than earth, and being thoroughly kindled by the violent heat from below, the result is the production in some places of the kind of sand called carbuncular.

It's pretty wild what Romans were able to build with a mental model of building materials that was completely wrong.