[hinkley]

There's a way to grind mirrors optics for optics with polishing stones that aren't even flat to the naked eye. Basically the system arrives at tiny tolerances via the process of using the system.

And there's way to make three perfectly flat sharpening stones by starting with three raw pieces of natural sharpening stone, just by alternately rubbing the three stones together until they flatten each other out.

Paul Sellers can teach you how to flatten a large board without a planer. He also has videos on how to get a wood plane perfectly flat using a large sharpening stone (which can be made as above or with float glass).

And if memory serves, you to make something perfectly round you first need something perfectly flat. Once you have something perfectly flat and something perfectly round it's off to the races.

Edit: "The Origins of Precision" is a half hour well spent https://www.youtube.com/watch?v=gNRnrn5DE58

[jmholla]

Do you have links to the other videos about the other things you said besides the creation of something perfectly flat? I saw that covered in the Origins of Precision but was left wanting on the lens making and board flattening. It seemed to be more historical and less practical, from the perspective of bootstrapping things.

[hinkley]

I think the same channel covered mirror grinding but I'm very fuzzy on that. Paul Sellers is all over Youtube. He's practically the elder statesman of hand tool woodworking. The video I'm thinking of, he's planing a board that is too big to go through a hobbyist's planer, so that one always made the most sense to me. Rob Cosman's might be easier to find, like https://www.youtube.com/watch?v=GGuGFGAQTxE

Flat boards require a flat plane, and like chisels, the tolerances on a new plane are fairly loose. Partly down to thermal contraction (from running the production line too fast? I've never gotten a straight answer). So the first thing you do with both is grind them truly flat, and you need a reference surface for that, like float glass or a diamond stone. Common protocol is to use the diamond stone only to flatten sharpening stones, and the sharpening stones to flatten chisels, and the chisels to flatten mortises. Basically diamond stones are very accurate but too expensive to have sufficient grit ratings and longevity

This is not the one I'm thinking of, but it's a taste:

https://www.youtube.com/watch?v=Cl5Srx-Ru_U

Right angles can be achieved by a process of iterative refinement. A square is two flat surfaces that are used to adjust two other flat surfaces, and they are only at right angles when 90.0º + 90.0º = 180.0º. So if you reverse the square or make two identical squares, they should touch along their entire length. If they don't then they're not square. Alternatively you can apply a square multiple times and check if the 1st and 3rd plane are perfectly parallel. Or if the 1st and 4th plane intersect at the same point, which also increases your accuracy by 4x by multiplying the error. I've seen this demoed by fine woodworkers squaring up a table saw for instance.