People sometimes ask why theory is so important, and recently I've been reading John D. Clark's wonderful book Ignition!: An Informal History of Liquid Rocket Propellants, and I've started thinking rocketry and chemistry provide a good example.

Chemistry turned manufacturing new rocket propellants from a continuous problem into a discrete one.

In the early days of rocketry, when we were trying to figure out which rocket fuels we could use, we had three requirements:

It needs to make our rockets go
It needs to have a melting point below
It needs to be storable within rockets without corroding everything or spontaneously blowing up

1 is obvious, while 2 and 3 come from military preparedness reasons. You want your rockets to be able to launch in colder regions year-round, and you don't want to be refueling your rockets every time you need to launch them, so the fuels ought to be storable within the rockets themselves.^[1]

There are two actions you can take to find a liquid possessing those three properties

Mix a chemical which has 2-out-of-3 of the properties with a bunch of other chemicals until you get the 3rd property
Invent a new chemical

And really you do both of these, so you invent a new chemical and then mix it with a bunch of stuff to try to get all the different properties you want.

So why do I say chemistry turned a continuous problem into a discrete one?

Well, the first action is a discrete one. At minimum you just loop through all the different combinations of liquids and do binary search to discover their optimal ratios.

If that sounds tedious and boring, well, it was tedious, but these are rocket scientists during the '50s dealing with some of the most destructive chemicals in the world. Some of the properties of these chemicals sound like literal witchcraft, and results could range from causing a test site to smell like sulfur for decades, to accidentally melting all the metal in the building you're working in, to just straight up blowing yourself up. So boring it sounds not.

Like the rocket scientists, the chemists too were methodical. You see, there are a finite number of elements, and a small number of remotely reasonable elements you could use, either because of technical reasons (it must be derivable from petroleum), or because... well... be honest, have you ever seen an explosive compound not made up of hydrogen, oxygen, carbon, nitrogen, or possibly sulfur?^[2]

Further, the search space is pretty easy to search through, you have a carbon backbone, and you take your time replacing the carbons with other elements that may fit, exchanging single bonds for double or triple bonds, sticking on other carbons backbones, or turning the backbone into a ring.

This sort of search was only possible because of the time and effort spent making a solid underlying theory for chemistry.

Imagine you were an alchemist trying to solve this problem. You don't know about molecules, you don't know about (the correct) elements, your process would basically be to mix everything you can think of together at varying heats and pressures, perhaps occasionally distilling some of your mess off.

There are a near infinite number of things you could possibly vary, and (in your view) a continuous range of possible liquids you may get, with minimal unifying properties, and no clean way to enumerate what you could possibly hope to get given the input liquids. Your results may not even generalize to someone following all your steps but in a copper cauldron instead of an iron one!

For all the complaints about every rule in chemistry having 10 exceptions, how atoms stick together and that they stick together in particular shapes to form unique molecules with different but perhaps related properties is hard and firm, and turns many of your problems into simple discrete searches.