8 ms·
I feel like this would make infinitely more sense to me if not for that singular "8" hiding close to the middle. Can anyone ELI5 what's going on here?
by pkfrank 11y ago
I feel like this would make infinitely more sense to me if not for that singular "8" hiding close to the middle. Can anyone ELI5 what's going on here?
- andrewstuart2 11y agoI may be wrong, but I believe it's some sort of math. Or wizardry.
- conistonwater 11y agoThe generating function for Fibonacci numbers is x/(1-x-x^2) = \sum_{n\geq0} F_n x^n, so you just let x = 1e-24. In this case it's x^2/(1-x-x^2) to make the fraction come out with numerator 1.
- userbinator 11y agoYou can see the pattern with smaller fractions too: 1/89 = 0.0 1 1 2 3 5... 1/9899 = 0.00 01 01 02 03 05 08 13 21 34 55... 1/998999 = 0.001 002 003 005 008 013 021 034 055 089...
- 0x0 11y agoPlease, leave the reddit jargon by the door.
- nothrabannosir 11y agoYes, and hurray for ad hominems, right? Why discredit the "eli5", just because it's from Reddit? What if it's a useful method to convey what you mean? We just can't use it now, because it's from Reddit?
- jklein11 11y agoI like where your head is at but I'm not sure this is an ad hominem. My understanding is that an ad hominem is an attack on a persons character[1] [1]https://en.wikipedia.org/wiki/Ad_hominem https://en.wikipedia.org/wiki/Ad_hominem
- nothrabannosir 11y agoThanks. The ad hominem is a counter-argument; you're discrediting an argument based on a person's character. So "jack is an idiot" is not an ad hominem; "that can't be true, because jack says it, and he's an idiot" is. I thought the guy meant: "I don't like it because it's from reddit." But ikeboy has it right: in this case, because reddit is not a person, it's a genetic fallacy, not an ad hominem. Which I didn't even know existed. And, of course, he didn't say that it was because of reddit, so it wasn't even that :)
- ikeboy 11y agoThe concept you're looking for is the https://en.wikipedia.org/wiki/Genetic_fallacy https://en.wikipedia.org/wiki/Genetic_fallacy, a broader form of ad hominem. Also, they didn't say it's bad because it's from reddit, the statement could be interpreted as saying that it's bad, and also that it's from reddit. Imagine http://laurencetennant.com/bonds/adhominem.html http://laurencetennant.com/bonds/adhominem.html applied to the genetic fallacy, and you'll see what I mean.
- oldmanjay 11y agoI'm all for not letting reddit jargon get a foothold here. Reddit culture is downright unlikeable since the entire reason that site seems to exist is to foster echo chambers and cliquish behavior. I'd prefer to keep any vestige of that out of HN. This site is a rare jewel in the sewer of the Internet and it's better that way.
- mineshaftgap 11y agoThis explains it well. http://www.quora.com/Which-is-the-Fibonacci-inverse-number http://www.quora.com/Which-is-the-Fibonacci-inverse-number
- svat 11y agoShort answer: the denominator is (10^48 - 10^24 - 1). Long answer follows. It's actually easier to understand if you work backwards and arrive at the expression yourself, by asking yourself: "If I wanted the number that starts like 0.0...000 0...001 0...001 0...002 0...003 0...005 0...008 ... (with each block being 24 digits long), how would I express that number?" Well, calling the Fibonacci numbers f_n (with f_1=0), that decimal expansion you want is sum (f_n 10^(-24n)) over n≥1. This is sum (f_n x^n) evaluated at x = 10^(-24). It is easy to work out (especially if you know the trick already) that sum (f_n x^n) = x^2 / (1 - x - x^2), which at x = 10^(-24) gives that the number we want is 1/(10^48 - 10^24 - 1), which is exactly what 1/999999999999999999999998999999999999999999999999 is. This may be more interesting if you consider more examples: * if we want the number 0 . 0001 0002 0004 0008 0016 0032 0064 0128..., then it is sum (2^(n-1) 10000^(-n)). We can calculate that sum(2^(n-1) x^n) is x/(1-2x), which at x = 1/10000 becomes 1/9998. And indeed 1/9998 = 0.0001000200040008001600320064012802560512102420484096... Similarly, * if we want the number 0 . 000 001 002 003 004 005 ..., then it is sum ((n-1) 1000^(-n)). And sum ((n-1) x^n) is x^2/(1-x)^2, and putting x = 1/1000 in it gives 1/999^2 = 1/998001, and indeed 1/998001 = 0.000001002003004005006007008009010011012013014015016... Basically whenever sum (a_n x^n) has a nice form (aka the generating function of the sequence), you can plug in x = 1/(some power of 10) and get such pretty decimal expansions. (Edit: Formatting, and the "short answer" at the top.)
- bglazer 11y agoThis is a great response. Thanks for taking the time to write this.
- deleted 11y ago[deleted]
- ghosthamlet 11y agoare you a master of math?
- username3 11y agoIs any of this useful for compression?
- 11y ago