Okay, these are two totally unrelated topics, but I'm going to merge them into one post.  Madness!

First:

HAPPY PI DAY!

(photo stolen from a random Flickr person)

Be sure to have a slice today in celebration - after calculating its circumference and area.

Second:  I've seen this meme going around for a very long time, so I decided to finally participate. Under the cut, you will find a list of "The most significant SF & Fantasy books of the last 50 years (1953-2002)", courtesy of Backseat Driving. I've bolded the ones I've read and italicized the ones I own but have not finished yet.

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Looks like by this guy's criteria I have a lot of reading left to do.  Oh well.  I've already got my own list to get through first.  Are there any of these in particular that I should add to it?  I bought Le Guin's The Dispossessed recently, and if I like it I'll probably also read The Left Hand of Darkness.

Tags: books, math
Current Mood: geeky

This is a response to Don Lloyd's query on Catallarchy. Check this out, then check Don's post out first.

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All in all a fun little exercise in some algebra which I haven't had to do in a long time.

Update: Some bolded clarification in my write-up.

Tags: math
Current Mood: geeky

Math geekery ahead...

So, I wasted a ridiculous amount of time this week on Polymath's blog arguing mostly with math illiterates over the fact that .999... = 1.  As of right now, the comment count for that post and the three follow-ups comes out to 762, involving probably around 50 people.  Of course, this is probably because the story was farked.

It really is a very simple problem, and I've only ever had one math person I respect disagree with me on it (and that conversation was short, so I can't say why), but it seems to really offend many peoples' sensibilities for some reason.  There are so many different ways to prove it, however, that I really can't fathom how anyone can reasonably deny it.  So, since the doubters in polymath's comments couldn't find any way to really disprove his proofs, they began resorting to ever more bizarre claims - including denying that 1/3 = 0.333... and doubting the validity of all of mathematics because of this one break from their intuition!  I actually had to prove that "1/3 = 0.333..." to one commenter; I'm reproducing that proof in a cut here just because I couldn't format it correctly in the comments.

( proof )

One can actually use a very similar proof to demonstrate the point of contention; see "The real proof" here.  But one doesn't even have to go that far, because it's really simpler than any huge math proofs.  It has to do with the nature of real numbers.  See, real numbers are a continuous set - between any two real numbers, by definition, there are infinite other real numbers.  Between 0.1 and 0.2, for example, there are 0.100001, 0.100002, 0.199998, etc.  Between 0.999... and 1.000..., however, there are NO numbers.  If one subtracts 0.999... from 1, there is no number one can get other than 0.  So since there are no numbers between them, they are equal by definition.

Now, many people at this point resort to creating their own notation and try to posit that 1 - 0.999... = 0.000...1.  But this number is both incorrect notation and a meaningless figure - the ellipses indicate an INFINITE set of zeros.  How can you have a 1 at the end of an endless series?  You can't, otherwise the series would be finite.

Other people try to say that 0.999... approaches 1.  These people are thinking of asymptotic functions, such as f(x) = 1/x, wherein f(x) approaches but never actually reaches zero.  But this is a mistake, because 0.999... is not a function - it is a number.  A single number.  It doesn't approach anything; f(x) = 0.999... is just a horizontal line.

If you have a math background and you disagree with polymath's analysis or mine, I encourage you to comment on why you disagree.

Tags: geekery, math, rant
Current Mood: geeky