title: Can any finite bit string be found in pi within a reasonable amount of time?
body: <p>So, a while back I read a joke that went something like this:</p>
  
  <blockquote>
    <p>"Never compute pi in binary - because it goes on infinitely and is random, it theoretically contains every finite bit string. So, you will then possess all copyrighted material in existence and be liable for some serious fines."</p>
  </blockquote>
  
  <p>This is obviously meant to be humorous, but it got me thinking. If every finite bit string exists in a binary representation of pi, would it be possible to use this as a method of transmitting data?</p>
  
  <p>For example, let's say I wanted to transmit a bit string that could be interpreted as an jpeg image. Instead of sending the information directly, I would find its location within the digits of pi, and simply send the location of the first bit within the digits of pi, as well as the lengths of the string.</p>
  
  <p>This seems pretty straightforward to me, but the obvious hurtle here is that the probability of finding this string within even the first several trillion digits is remarkably small. So, it could end up taking an immense amount of time to find. </p>
  
  <p>My thinking is that several machines could be dedicated to searching for large files within pi, and then creating an index of all of their start locations. So, each computation would only need to occur once and then that information could be transmitted extremely quickly from then on.</p>
  
  <p>So, what do you think? Is this at all feasible, or would these computations take far too much time?</p>
  
  <p>Thanks for reading! I apologize if I have overlooked any posting guidelines, this if my first question in this forum.</p>
  
  <p>EDIT:</p>
  
  <p>Thanks for your quick responses, folks! I figured there was error in my reasoning, nice to know why!</p>