Young machinist here. How did we make precise instrument from something supposedly less precise and how did we calibrate it? We have machines that can machine things within .0001 inches or less of tolerance. Wouldn’t that require the machine to be made with at least the same precision? This applies to the measuring equipment as well. In order for say a micrometer or CMM to measure down to .0001 or even .00001 of an inch, how did we ensure those firsts were accurate?
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It starts with making repeatable and consistent parts. Specifically screws/bolts that are interchangeable with each other. Every rotation of the handle moves the tool 1/4 inch etc. If you can make a set of consistent screws/bolts you can use the magic of fractions and gear ratios to make an even finer screw. Where one rotation of the handle is 1/64 of an inch and so on and so on till you get to the smaller fractions. Now instead of the handle turning the screw, have the screw turn the handle and replace the handle with a red arrow that points at some numbers that mean something.
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