I'm guessing there's just more heat trapped in the Earth from its formation than suggested by formation models. A factor of two error would not surprise me because we're dealing with a fairly complicated system (with convection, multiple states, heterogeneous fluids, &c.).

For me it was Jurassic Park...

"Turns out Pollock had a seriously deep intuition for physics."

It's not like I wanted to say the US is now doomed to utter ruin. I'm just wanted to say the US is going fall to a position like the other major powers like Japan, the UK, Germany or South Korea. Important but not the most important.

You wanted to know the US must do this. I answered that it was historical. If you think history doesn't matter, that's your misconception. Actually, I doubt you think that the past is "essentially irrelevant". I think you just want to be Right on the Internet.

No doubt, but unless they invent a time machine, they can't have the most developed economies 30 years ago. You're absolutely right that they will have the largest economies in the next 30 years.

I think the scientific results from HST, alone, justified the cost of the telescope itself and the shuttle program which serviced it. An argument can be made that it would have been cheaper to develop robots to do the work, but for whatever reason, we don't have that technology, yet.

It depends on what you mean by random. If you mean "uniformly distributed", then you would certainly chance upon a diagonal, but overall there would be no apparent structure (imagine TV static... back when there was such a thing).

Violating the parallel postulate seemed pretty abstract, too. It's a good thing for Einstein (and general relativity) that Riemann developed a whole theory around it.

As far as I understand, mass never comes into consideration. We have a set that consists of a continuum of points (for any given point in the set, and any given distance, there is another point in the set that is at most that distance from it). The theorem says that we can slice up this set and reassemble the pieces…

My first thought was that this was a reference to LOST and the Bad Robot school of TV science fiction.

Given the proximity to Independence Day, I hope you don't mind if I point out America's own imperfect but profound monuments to religious freedom (they are in the form of letters, laws, and judicial rulings):

Oh my science!

I was wondering that, too. Other reasons:

That's wonderful! Did you make that?

Flowers for Algertron.

I should have been clearer. I was hoping to get the point across that "math isn't just for mathematicians". Anyone can try these ideas out.

Obviously, I failed at clear communication. However, you failed at reading comprehension.

See ShayGuy's explanation of mathematical induction above.

This is just an algorithm, and there are many algorithms that provably halt on any input.