So, to answer this we have to answe “what is a machine?”
A machine is an object with multiple moving pieces that give you an advantage in a task. That advantage could be increased strength, speed, precision, or the ability to do the task over and over again for a fraction of the effort.
As an example, a hammer.
A hammer that you can hold in your hand is not a machine. It is limited in the amount of force it can apply by your strength and technique.
But if we take the idea of a hammer, and make a machine out of a much larger hammer head on a pivoting arm, with a counterweight on the far end of the arm so the hammer moved freely around the pivot, we have created a machine that can hit much harder with much less effort, and with some practice this can also deliver that harder hit with greater precision, since the mechanical arm moves in fewer directions than your human arm.
You start out creating something that is bad, but better than not having anything.
The thing you made, makes it possible for you to make a new things, better than the thing you just made. The new thing is still bad, but not as bad.
The new thing can now do the same again. Make a newer thing that is better than itself.
You are basically making something that enable you able to make something better.
Sometimes that means making something which’s only purpose is to make a better thing of something else.
The biggest thing is that improvements are easy early on, and you don’t need “modern perfection” for it to help a whole lot. The first years with steam engines, were a massive improvement compared to not having. Even though the first steam engines weren’t all that strong nor efficient.
Geometry, optics, and abrasion.
Rub two surfaces together. The high spots of one will get rubbed off by the high spots of the other until they come into perfect intimate contact everywhere.
There are only three geometric surfaces that remain in contact everywhere as you slide them across each other: planes, spheres, and cylinders. So now you can make perfect flat sheets, spheres, straight edges and circles just by rubbing things together.
Once you have a straight edge, other tricks from geometry allow you to divide a line perfectly in half, draw perfect triangles and squares, etc. The law of similar triangles allows you to build things like the [pantograph](https://en.m.wikipedia.org/wiki/Pantograph) and other tools that can duplicate a shape at half the size and twice the accuracy.
Light travels in an (almost) perfectly straight line. So just by lining up objects visually (e.g. a gunsight), you can create perfectly straight lines of arbitrary length, and generally do all the geometric tricks above to create and copy shapes on very large or very small scales. If you need better precision than the human eye, you can use the rubbing trick to create spherical lenses, and thus magnifying glasses, microscopes and telescopes.
Light is a wave, with crests and troughs less than a millionth of a meter apart. Two light waves can be made to interfere, canceling each other out if the crests of one line up exactly with the troughs of the other. If those waves are reflected from two different surfaces, this lets you measure the distance between them to within a fraction of a wavelength of light — a precision of tenths of millionths of a meter!
I saw a guy cut a thread on a guide rod with nothing but a small file in his hands. Shit worked perfectly. And to be honest, it doesn’t need that much precision to create the rudimentary mass production machinery. Then, so long as your initial machinery is consistent, you can use it to manufacture more precise instruments, and so on and so forth. This is how we’re not stuck on some arbitrary level of precision and keep making more precise tools using their previous, less precise iterations.
Nothing is perfectly flat/plumb/level – that’s an important piece of it. They’re just as flat/plumb/level as we need them to be for our purposes. So as tools got better, craftsmen got better at both making things with tighter tolerances and measuring those tolerances. Both of those things tend to go hand in hand – as our ability to make things with more precision increases we need increasingly sensitive tools to let us know how precise we’ve made them.
It’s not like we didn’t possess machining abilities before the industrial revolution. Simple tools like latest, stone grinders, chisels and hand planers have been used by craftsmen for hundreds/ thousands of years.
The difference is that industrial machines do the same work, but fast, and now more precise. The first industrial machines weren’t any more precise, just faster.
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