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Comment Re:Hurray! (Score 1) 680

I just said "limits", and I didn't actually say anything about governments. I would not go as far as to say governments should force parents to have their children vaccinated, at least not for any current threats (if there were an extremely dangerous disease going around, with high likelihood of infection then maybe). Also, from what I've heard, governments often (usually?) do a horrible job of raising children.

I was actually addressing (as I thought the parent post was) the fact that the fundamental belief of Libertarians (of whom there are many in the US) is that self-interest trumps social interest. I was stating that I don't think this concept of "self-interest" can be applied to the vaccine issue in a clear-cut way. However I know that some Libertarians would say it does, because children have their parents' genes, and perhaps invoke Dawkins' "selfish gene" (I personally think this is a contrived pseudo-scientific argument and caring for a child has nothing to do with shared genes).

Comment Re:This is second place (Score 1) 1260

Except that I was counting non-mathematicians as well. A lot of people have difficulty grasping what is going on with 0.999... and what it means for that number to equal 1 (the idea that a number could have two representations in the same base goes over a lot of people's heads).

Yes, they do have difficulty. People who say that people who have trouble believing 1=0.999... are idiots are themselves having difficulty. 1 and 0.999... are different kinds of mathematical objects, hence in some sense they are not equal.

0.999... is not a "decimal expansion" of some number, but rather it denotes a sequence of numbers: 0.999, 0.9999, 0.99999, ....

The fact that "the real numbers can be defined as equivalence classes of Cauchy sequences of rational numbers" is probably not obvious to most of the people who think 0.999...=1 is obvious, and they would probably be surprised at how deep this area of mathematics is. See P-adic_number.

Also, one should not just casually accept the ideas of infinite series and sequences, because counter-intuitive things DO happen with them. There is no such thing as an "infinite decimal expansion" or "adding up an infinite number of numbers" -- those are just analogies, which may or may not mislead you in a given situation.

Comment Re:Sail Envy (Score 4, Informative) 277

Also, the paper was presented at an astrobiology conference. They are suggesting that an alien civilization is more likely to have built one of these than an actual Dyson sphere (because it seems possible with our own technology within the next 100 years, unlike a Dyson sphere), and they are wondering if we would be able to detect it using our current instruments and techniques. That's the focus of the paper, not the idea that we should actually begin building one.

Comment Re:Bizarre number choice (Score 1) 277

I think their point is that it scales up very well. The sail material is relatively cheap, and the main cost would be deploying it and getting the power back to earth, so it probably makes sense to use a really, really big sail. The bigger you make it, the cheaper it will be (per GW), much more so than any existing sources of power. Of course, that assumes the power transmission can also be scaled up, and they haven't figured out that part yet.

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