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Can all books be found somewhere within the number Pi?

31 pointsby jkbycabout 10 years ago

9 comments

brudgersabout 10 years ago
The idea of encoding a book as a string is incoherent once we look at it with intellectual rigour. How are images in illuminated manuscripts or graphic novels encoded? What does &quot;all books&quot; even mean? Are we talking about each individual artefact past present and future or some idealized representation of each: e.g. is my current copy of <i>Catcher in the Rye</i> encoded separately from the copy I was assigned in 10th grade English class?<p>It&#x27;s all a matter of interpretation.We can just as easily choose a different arbitrary encoding and claim to have found all the books in π. There&#x27;s no need to make things complicated. We are free to pick any interpretation we want once we are claiming that numbers represent books. Let:<p><pre><code> B = {b1, b2,...bn} </code></pre> Such that it contains the set of all books. And let:<p><pre><code> def Find-books(num) if 3.14 &lt; num &lt; 3.15 then return B else return &quot;all the books not found&quot; </code></pre> The article assumes that there is some natural way of encoding books. But digits of π are not Unicode or Ascii characters. Though we can interpret a digit or string of digits as such, that encoding is arbitrary not a property of the natural or mathematical world.
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plikan13about 10 years ago
Yes, but the number which indexes the position in PI where your book starts will probably be longer than the book itself.
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BuildTheRobotsabout 10 years ago
Theoretically, everything can. And there&#x27;s a FUSE implementation: <a href="https://github.com/philipl/pifs" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;philipl&#x2F;pifs</a>
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axblountabout 10 years ago
The question is: is pi a &#x27;normal&#x27; number? It&#x27;s an open question. Note that it&#x27;s not particularly difficult or illuminating to generate a normal number, example: 0.(binary digits of 1)(binary digits of 2)...(binary digits of n)...<p><a href="http://en.m.wikipedia.org/wiki/Normal_number" rel="nofollow">http:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Normal_number</a>
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a3nabout 10 years ago
Disclaimer: I don&#x27;t know what I&#x27;m talking about.<p>My dim understanding of the issues leads me to consider a conflict. Pi is more or less considered to be more or less random, or some flavor of random, notwithstanding known patterns of Pi. &quot;Random,&quot; to me, sounds a lot like &quot;unorganized.&quot;<p>A book is definitely organized. A larger book is highly organized (entropically speaking). So while you probably can find the same sequence of words in a two-word or ten-word or other small book in Pi, at some point you get a book that&#x27;s too highly organized to appear in Pi.<p>However, Pi is also infinite, so it&#x27;s infinitely possible to find any sequence. (This sounds really hand-wavy to me).<p>But since Pi is infinite, then isn&#x27;t it also infinitely unorganized?
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danbrucabout 10 years ago
Maybe it could be more efficient to go the other way round - instead of searching in the digits of pi kind of invert the BBP formula [1] and try to calculate the position of what you are looking for. But because the BBP formula involves rounding this is certainly not a simple task and I have really no idea if anything could be gained.<p>[1] <a href="http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Bailey%E2%80%93Borwein%E2%80%93...</a>
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gchokovabout 10 years ago
Theoretically, you can also find all books in a random N-long number as well. Just keep on generating.
antavianaabout 10 years ago
At which digit of Pi can I download the code used by the author of the blog post?
hurinabout 10 years ago
It&#x27;s been argued about a lot - with far brighter people unable to come to agreement than the author of this blog.<p>The reason the linked article in itself is quite worthless is because it trivializes the question from philosophy of mathematics to <i>oh pi is random let&#x27;s calculate probability</i> - but obviously that has nothing to do with the real problem.