just deduce the domain from text similarity :o)

"Obey so they don't carry out their threat." may be prescribed by classical decision theory, but I wouldn't call it rational when it's bad for you to be known to do it. I just asked classical decision theory what decision theory to pick and I think it said "take action x such that, if you do x, and everyone had known since 15:53 UTC Mar 24, 2023 that you'd do x, you'd have done as well as possible.". So what deserves to be called "rational" may be to do what the person you wish you'd always been would do.

If the capacity is proportional to the depth of the tunnel and the mass of the weights, and the maximal mass of the weights is proportional to the depth of the tunnel, then wouldn't the capacity grow quadratically with the invested money?

Edit: You assumed that they can both fill most of the tunnel up with lead and move that up or down 500 meters. The volume that they can fill with that is thus only half of what you say.

Why is the maximal mass of weights proportional to depth? It's more proportional to diameter than anything else. There's a practical limit to how much weight you can hang. Sure if you make a 10km deep hole and a 3km deep weight you could store a lot of energy. But a 3km deep weight might not hold itself together.

If we have enough volume that we can't use the most dense possible weight for all of it, we can find cheaper weight materials by dropping the density constraint.

Couldn't you have the weight grip the sides of the tunnel with gears attached to a generator/motor (inside the weight) so the weight wouldn't rip itself apart? It would be the same machinery that ordinarily would operate the pulley at the top, just moved down into the weights (cause with this, you would need no more pulley). (To illustrate why it wouldn't rip itself apart, imagine gaps on the weight every 100 meters.)

Technically that would work fine. Economically, it's a disaster. McMaster prices are at least 2x what's available if you buy direct from a source, and if you were buying in bulk it'd probably get cheaper still. But this is cheap, cheap stuff for not that much weight. You'd need something I dunno, 100x-10000x stronger to do what you're talking about: http://www.mcmaster.com/#racks-and-pinions/=upn9xl

The appeal of the cables is that they're cheap. And they're cheap because they're easy to make (all things considered). Once you start applying sophistication to the design the price gets higher, and it's already too high from having to drill the hole.

1. Those 10% are per year, not per transaction. 2. This kind of inflation is one of many factors that is already incorporated into the market value of Bitcoins.

I think the statement you meant to remind us of is that NP is a subset of PSPACE.

According to the paper under discussion, the two statements are equivalent. Your version is probably more graceful, however.

That's from last year.

Maybe by "the same turbine" they mean the generator at the center, having swapped out the short blades shown on their site for a traditional set.

Doesn't look like it, neither in the photo nor the comparison table. Besides, I doubt that it's even built to allow that.

If the wind gets slowed by turning the turbine, shouldn't the output side funnel of the turbine be larger than the input side funnel to be able to hold more air? (So the additional wind coming in from behind doesn't have to waste its own kinetic energy pushing the front air out of the system)

I believe the output side should as wide as possible while still preventing turbulent flow, as would exist if there were no output tube.

Would turbulences be prevented if 3 radial blades (3 so the 45:15=3fold amount of air can pass without problem) divided the wind from the turbine into 3 funnels as large as the input funnel?