While reading Infinite Jest, I looked up a word in the dictionary only to discover that the example sentence in the definition on my Kindle was exactly the same sentence I had just read in the book. [more inside]
I just bought a B&N Nook Color, on which I'll read the NY Times and some Dickens and Trollope. I'd like to download and read "Infinite Jest" on it too, as I've not been motivated to read my five-pound paperback copy. But what's the simplest, cleanest way to flip back and forth between the IJ narrative and the notes on the Nook? Do you have a system? Can you keep both places marked and flip easily? Or what? (I'm pretty tech-phobic but trying to overcome.) Thanks.
Mathfilter: In Gelfand's exceptional Algebra text, he is talking about the formula 1 + x + x^2 + x^3 + ... = 1/(1 - x). He uses the Achilles racing the tortoise model when first introducing the formula. He discusses the case x = 10, whence 1 + 10 + 100 + 1000 + ... = -1/9. [more inside]
∞ focus at ∞ distance = out of focus? [more inside]
I saw a video from microsoft research which showed a new editor with like "infinite zoom" when viewing all source code files, like flash vector files - really cool. But i can't seem to find this video again! Does anybody know what it's called? Or a link?
Examples/terminology for media so compelling it drives you insane. [more inside]
What's the next polynomial in this series: x4+2x2+16, x8+40x6+1128x4+2560x2+65536, ? [more inside]
What's the sum of all integers? I remember from somewhere in the distant past of my math education that you can sum up all the integers and get a wide variety of different results. For instance, you can write the sum as S = 0 + (1 + -1) + (2 + -2) + ... where each pair cancels to 0, so S must be 0. But you can also write it as S = 0 + 1 + (2 + -1) + (3 + -2) + ... where each pair adds up to 1, so S must be infinity. With a little more work it seems like you could also get other answers. My question is: are these answers correct, or are all but one of them mistakes like the numerous "proofs" that 3=2? If they're all correct, how does it make sense that the same numbers can add up to different things when you get to infinity? If they're not all correct, what's the fundamental mistake?
Can anyone recommend any good recent articles or papers on whether the universe is infinite or finite? I've heard that scientists suspect that the universe is flat, which lends credence to the infinite-universe hypothesis. I've decided I don't know enough about this. Nothing too technical, please, though I'd prefer something more complex than an article from a newspaper science section.