The Beauty of PI

“Pi, the ratio of the circumference of a circle to its diameter, and this is just the beginning; it keeps on going, forever, without ever repeating. Which means that contained within this string of decimals, is every single other number. Your birthdate, combination to your locker, your social security number, it’s all in there, somewhere. And if you convert these decimals into letters, you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, everything we ever say or do; all of the world’s infinite possibilities rest within this one simple circle. Now what you do with that information; what it’s good for, well that would be up to you.”

– from “Person of Interest, Season 2, Episode 11

I was watching this episode casually – but this statement did intrigue me. If true, I would have wished for my math lessons back in school to let me explore things like this and provide information beyond the pure presentation of facts… spark my imagination! Make me want to challange and discover! Let me experiment!…

So let’s see how much truth the statement up there holds: yes, Pi is an irrational number which means it cannot be expressed as a/b. Pi never ends… and it never infinitely repeats… so far, the statement above is correct. Wether it contains all possible combinations of digits somewhere within is beyond my knowledge to say… but one thing to keep in mind is that no matter how many digits we compute for Pi, the chance of finding a specific complex pattern in the digits known today is unbelievably small – but if Pi never ends and never repeats itself, somewhere in there…

So let’s try and find my birthday in Pi – 14.07.1972 – and I am looking for the representation in the German date scheme: 14071972. And hey, it is in there… starting at the 10.266.360 decimal digit. (see http://www.subidiom.com/pi/)

Let’s try something else – let’s search the string “Pi” itself. Obviously, Pi only contains decimals and a string is not a decimal. But we can find a way to convert a string into a decimal (actually, we can find multiple ways to do so).

We could simply fall back to the ASCII Code where each character is represented by a number: “P” is 80 (decimal), “i” is 105 (decimal). So looking for the ASCII representation, we could be searching for “80105” (and would find it at the 18.098th digit).

So how about my name, Andreas. You can use an online ASCII Calculator to make your life easier (http://www.branah.com/ascii-converter) and so, my name would be represented as “65 110 100 114 101 97 115” decimal. Now, this already is a complex pattern and I am not lucky enough to find “myself” in the first 2 billion digits of Pi. But shorter names like “Tom” (at decimal 16.524.559) and “Sam” (at decimal 4.246.411) and “Max” (at decimal 5.245.782) can be found.

However, if I take a different coding scheme (counting a letter’s position in the alphabet where A=1, B=2 and so on), “Andreas” comes out as “1 14 4 18 5 1 19” and this sequence is present at decimal 1.593.228.194…

Germany does not have a social security number but we have a tax number – I don’t tell you mine but it is an 11-digit number. Again, no luck – pattern too complex for just the first 2 billion digits. So let’s try at which point I get lucky… and that happened faster than I though: I only had to take off the last 2 digits (make it a 9-digit number) to find the beginning of my tax number in Pi.

And so it goes on:

  • all my (4-digit) PIN numbers for credit cards are in there (na, I am not going to tell you where!),
  • my bank account number is in there (send me money to the digits starting around decimal 548.684.250),
  • my wife’s birthday is in there (somewhere around digit 108.242.600), actually all of the dirthdays of all of my family members I tried are in there.
  • my telephone number (without area code) is in there, and
  • my cell phone number (without provider code) is in there

As you can see – as long as the pattern is relatively small (less than 10 digits), your chances of finding it within the first 2 Billion digits is relatively good. And given that Pi goes on forever, we would just need more digits (actually, many more digits!) to find almost anything you are looking for… somewhere.

By the way, Pi is also nice to create passwords and PINs: just come up with a number (say your birthday) and take the numbers of that particular digit as password or PIN: taking 10 digits starting at position 14071972 gives me “1109437165”. You could look it up almost anywhere you are (given you have a Smartphone) and you would of couse NOT use your birthday but some other “secret” number as starting point for your sequence…

So even if the discussed scene is more poetic and dramatic than maybe mathematically correct it still sparks imagination – it makes people curios. And maybe that is exactly the initiator someone needs to start thinking and exploring…

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