You know, Steve, you are missing a great opportunity. Precision can be achieved without power tools, but it can't be achieved until you know what precision is and have a reliable means to measure for it. The Egyptians had a robust metrology and the math to back it up.
Yes they had some sort of natural geometry.
They understood fractional measurement and and had calibrated, government maintained standards. How precisly could they measure? I have no idea, but you should be checking it out, because if it turns out that they could measure with serious precision, then they could produce the artifacts, and "woo" would not be required.
You don't want to go down that rabbit hole as it actually throws up all sorts of theories. You o see a common geometry related to the Golden Ratio and other natural geometry.
But thats not really the point. Anyone can measure something and you don;t need a ruler. Just a piece of string. But its putting that geometry or maths into the 3D object.
With nothing but hand tools I could build you a lathe made mostly of wood, with a few small bits of iron, and no moving parts, no wheels required.
Yes and Chris King mentions this in the video. Iron wood could be used for bearings with whale blubber as the lubricant. I am not saying some sort of ancient lathe was made. But still we are talking about a pretty sophisticated lathe in a time where there was not even a potters wheel.
On that lathe I could turn a piece of metal to any reasonable degree of precision you required. I know I could do it because I have done it before.
If you listen to Chris King he goes into some detail on how a primitive lathe could hjave been made. In the end it starts getting complicated when you start to figure out how the lathe could cut the inside, uniform wall thickness and certain angles that require a fixed cutting point and tremendous pressure.
Or require high speeds due to a lack of pressure or have longer cutting arms which loose stability and with speed will move or break. Its a lot more complicated.
But if I did not understand precision and how to measure for it, backed up by the math, then I could not do it at all, even with the most modern CNC lathe going.
Yes I am sure the ancients could measure. We see the precision in many things. The base of the Great Pyramid of Giza is nearly perfectly level, with a deviation of about 2.1 cm (less than 1 inch). Theres lots of stuff like this which shows pretty good maths and geometry. I think the pyramid is also aligned to true north.
But its actually putting those numbers into 3D reality. Ensuring the base is level as its being built. All the complexity in achieving this. Especially for such an ancient time. The list of works even down to individual blocks with incoporated geometry and maths is long.
But sometimes its not the measure or maths but the witness mark itself. No matter what spin you put on it you cannot unsee what looks like a router cut or an arc cut from some preset planer cut into granite.
Thats got nothing to do with the measure and everything to do with what the tool was. That its cutting blade or shape cut the arc or routing cut. Or scooped out the granite in the shape of a shovel and left scoop marks.
Did the Egyptians make center lathes like that sooner than we know about? Who knows? Maybe they figured out something else. What we do know is that they had a sufficiently sophisticated concept of metrology that they could have done it.
Thats why I think we should be looking at the whole picture and all these signatures I have linked. Like you said we may be unsure of how they made the vases. But when we begin to collect other witness marks of machining you begin to see a bigger picture of methods that could cut super stright lines, shave off layers of granite, cut arcs in granite, rout hard stone, and even soften it.
Then you begin to think they had more ability than we think in working with hard stones and some primitive though pretty sophisticated lathe begins to look inadequate. That if they had devices that could slice off thin layers of granite then they could machine vases.