prof_mm

There would be no electricity, since the automatic safety systems should detect such a failure and break the circuits, similar to what should happen if a cable fails in your bathroom. But assume not, to make it interesting. The way of shortest resistance is probably still through the cable. Or it would all go into the ground. I doubt that there would be any danger to a swimmer (that is not too close). Note that such cables are buried in the ground to protect them, or rocks are deposited on top of them.

Sure, it's not a solution that will scale. As is wind energy: if we cover all the oceans with it, it will influence our climate and probably slow down the rotation of the earth, etc. The point is that a relatively small such storage plant can already store a huge amount of energy - enough to help balance a lot of offshore wind.

The density of water is so much higher than that of air (if you are comparing subsea potential energy storage with compressed air storage onshore). And there is a lot of unused space at the bottom of the sea.

A Word document? Are you kidding me? Would a truly cyber-security conscious (i.e.: slightly paranoid) citizen download and open that, from the open internet, with a nation-state actor behind it?

Mathematics is typically approached in a different way than physics. But there are some books that offer a similar perspective to what Feynman tried to achieve, IMHO. I would recommend to look at works by John Stillwell, for example 'Elements of mathematics' or 'Mathematics and its history'.

Nathan Carter's 'Visual group theory' also seems an interesting experiment, if you are interested in that part of mathematics, though I have not read it.