Formerly u/CanadaPlus101 on Reddit.

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Cake day: June 12th, 2023

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  • Alright, so I followed the same tack for a while, but the tricky thing is that a hyperboloid of one sheet is doubly ruled, which means you have to worry about secant lines corresponding in some way spuriously, just due to relation with the ruling lines. That inspired me to go in a different direction.

    To make a cone, you need the wiper/striker to be coplaner with the axis or rotation; otherwise, it will become a ruling line. This is both necessary and sufficient, given that we don’t particularly care about the exact cone. Furthermore, any two non-coincident intersecting lines make a plane, and gravity offers an easy way to produce parallel lines.

    You make a half-mould with a cavity that will look something like a speech bubble. The inner edge of the tail(?) will become half of the wiper, and the rest will become half of the upper beam. By reusing the mold, you can ensure the mated halves will be fairly symmetrical bilaterally, which means the center of gravity will be close to coplaner with the meeting point where the wiper forms. Some combination of filler or adhesive in between and a draw string around the outside seems like the best way to hold them together. True, that may introduce asymmetry, but with such limited tools compromises have to be made. The string or rope itself is relatively light, and with attention to detail it will still end up reasonably close to balanced.

    Now you have a rigid piece with a center of gravity (roughly) coplanar to the wiper. You can use the parting line to center awl points, which will also be (roughly) coplanar. Tho only configuration of the two rotating awl points involved and the rigid body’s center of gravity which can balance is the three of them all lined up along the zenith. So, if you can balance these two components, you’ve guaranteed that the axis of rotation is the zenith, the line from center of gravity to upper awl point is the zenith. Then, the zenith is in the plane of the wiper, and so the axis or rotation is coplanar to the wiper. QED, to whatever degree that applies to caveman work.

    The actual process would be very involved. The task is picky, the pieces are heavy and the top beam is probably made out of clay, which is physically delicate. The way to go is probably to sit them all in a frame with vegetation for padding, move the frame slightly away somehow, and then adjust the frame corresponding to which direction the assembly falls into the padding. It’s probably worth it to use knapped clay points for the rotating stake just to reduce sticktion. Experimentation is needed, but unfortunately I don’t really have a good place to do it.

    Once you’re done, easing the beam upwards and then fixing it tightly in place will allow you so start turning. There would still be some error, of course, both from the sources I mentioned and others, but that seems unavoidable. As long as the finished product is fairly close to a cone you can rotate the resulting bearings together dry in order to lap them to a tighter fit.


    In case you’re curious about the next steps, you need cones in the first place because clay shrinks when drying and firing. Two similar cones will continue to fit together after rescaling, but hyperboloids won’t. The plan then is to use the turned cone as a master for female cones, which will themselves be used to make matching male cones. The two bearings will be placed large ends together, and held on a thickened section of the wooden axle, and any stationary frame, by rope tension. The male cones will then protrude out due to being smaller, allowing clearance for the axle to continue on.





  • I’m not sure what you mean about the sombrero potential only being partially observed. It is a principle only, and you could observe it fully by simply making a sombrero shape and putting a ball in the middle and observing how it falls multiple times.

    You can see the model do that, but not the actual quantum fields. The transition is supposed to have happened irreversibly once in the instants following the big bang.

    The difference is that supply & demand is presented as a foundational and ubiquitous law to high-school students, whereas the sombrero potential is presented honestly.

    It was never taught where I went, but that could be. High school teachers should knock it off, if so. It seems to work exactly as theorised in most sectors, bulk commodities being a common example, but there’s definitely other sectors that are broken, some of which I mentioned.

    I’m a fan of regulation to address that. So are both orthodox and most heterodox schools, to various degrees.

    Either they don’t exist, or your story about that isn’t complete.

    I’m sure someone is dumb enough to try it, but I’m actually not convinced it’s widespread. In Canada, we literally just don’t have enough houses for a first-world nation of our population - which has been measured - and all of our tradespeople are swamped. (Sorry if I brought that up already, this has been a long-running thread)

    However I’ve never heard of a scientific discipline where there is an “orthodox” school, except in economics. It’s the orthodox school that I have a problem with. Supply & demand is just emblematic of that issue.

    Hmm, now that is a good point. There’s various small offshoots of anthropology and psychology, some of which are questionable (there’s people that still use Freud), but nobody really divides it up like that. Alright, you’ve sold me on economics probably having especially bad lab politics.





  • Yes, when bootstrapping, tuck in your bootstraps.

    To add a bit of detail, it comes down to circles being nice, simple geometric objects, and an assembly of metal with contact points being capable of way more accuracy than you’d first expect.

    Bootstrapping the first lathe is harder; most likely some historical elite master craftsman was able to make one freehand, and future ones derived from it. We still have the one Vaucanson made that way, although it sounds like it was a one-off. David Gingery wrote a book on the topic, but he still assumes you have a power drill and a ready-made threaded rod.







  • On this same note, insulation in general. We can only make something so strong, conductive, heat-resistant, light or hard, so we’ve internalised the expectation that there’s always practical limits. But insulative? There just isn’t one. That means that with an arbitrarily small source of energy - body heat is not only possible but typical - you can overcome unlimited external coldness. We’ve being doing this since before we were human, by many definitions.