Category Archives: Mathematics

A New Theory About Primes

But it seems misleading to me. The title implies that an odd number could be the sum of two, three, four or five primes, but two and four are excluded because they will generate an even number, so isn’t it really saying that it can be expressed as the sum of either three or five primes? Anyway, nice proof.

[Via Geek Press]

[Update a while later]

D’oh! As the commenter notes, I’d forgotten that two is prime, and unique in it being an even prime.

NASA’s Irrational Approach To Risk

Bob Zubrin asks how much an astronaut is worth. I don’t think that this is historically accurate, though:

The attempted Hubble desertion demonstrates how a refusal to accept human risk has led to irresponsible conduct on the part of NASA’s leadership. The affair was such a wild dereliction of duty, in fact, that O’Keefe was eventually forced out and the shuttle mission completed by his replacement.

That’s not how I remember it. I recall at the time that I thought, and even advocated, that O’Keefe step down, because he had demonstrated himself unable to do the job, being traumatized by having to tell the Columbia families and friends on the tarmac at KSC that their loved ones weren’t coming home, which is probably what caused his timidity about Hubble. But I’m aware of no evidence that he was “forced out” over the decision. I thought that he simply wanted out of the job and took the best offer that came along. The administration would have been loath to remove an administrator, knowing how hard it is to find a good one. Someone should write a letter to the Reason editor on this. Bob either needs to substantiate this with a credible citation, or the magazine should run a correction. Because I think it’s wishful thinking on his part.

[Update a few minutes later]

Bad link, it’s fixed now, sorry.

[Mid-afternoon update]

While I criticized O’Keefe at the time, I didn’t actually disagree with the Hubble decision at the time. The problem that I saw with it was that it was based on irrational criteria. All the focus was on astronaut safety, and no one seemed to be considering how disastrous it would be if we lost another orbiter. NASA had no shortage of astronauts, but there were only three birds left in the fleet, and we would have had to complete ISS with only two, if the program survived at all. Add to that the fact that we probably could have launched an improved Hubble replacement for the cost of the repair mission, and the decision to do it was irrational in its own way, driven by an emotional attachment to the telescope that had shown so many wonders over the past decade.

The Minimum Sudoku Problem

has been solved.

Of course, this is for a nine-by-nine. There is nothing intrinsic to the sudoku concept that requires a nine-by-nine matrix, as far as I know. That’s just the size that utilizes the non-zero digits. Smaller ones would just leave out the upper numbers, and larger ones could continue by using letters, as in hexadecimal (though they would get increasingly tough to solve as size increased). People think that sudoku is about math because it has numbers in it, but it’s really just a logic puzzle. It doesn’t have to use numbers at all, but everyone knows them, so they make handy symbols. You could just as well use mah-jong tiles, or animals for a kid’s version.