ocfnash

Thank you for sharing these memories.

I'd be very interested to hear any thoughts you might have about Jung Chang's book "Wild Swans".

I read this book a year or two ago and learned a lot from it, but I also learned that many people who grew up in China take issue with the author's account. I'd be grateful for any remarks you may be able to share.

Most viruses are bacteriophages, so I imagine bacteria would run wild!

I think it is worth comparing this problem with the question of the behaviour of a particle placed at the apex of a cone. I claim it is clear that in this case, the problem is clearly not well-posed because the apex is a singular point: the slope at the apex is undefined. The singular nature of the slope (first derivative) is the issue.

This "dome" is essentially the same issue just with the singularity buried one level deeper: you need to take second derivatives to see it. Indeed a planar cross section containing the vertical axis through its center is a graph of the equation $y^2 = |x|^3$ (up to constants) and this is not twice differentiable at $x = y = 0$. Newtonian mechanics is governed by a second order differential equation, so we need a C^2 regularity assumption to get uniqueness.

So for me there is not really any more philosophically interesting than the question about a particle balancing at the apex of a cone.

If you like these, you should try the Uncle Fred books. Of course almost everything by Wodehouse is a sublime masterpiece.

As a kid, the alliterative mnemonic we were taught was "current kills".

The computer did find the answers itself. I.e., it found "even integers" for P1, "{1,1}" for P2, and "2" for P6. It then also provided provided a Lean proof in each case.