The prophecy in the pi decimals

I recently read this odd thing about pi, where decimals further down the line could be foretold.

It does sounds strange that something like that would be in there. (a) How can this work? and (b) why would anyone even discover this in the first place? Both are good questions. I can and will look into the first one (a) with this article, and for the second I can only say that it gives me a thrill of joy to look into such peculiarities (is that really a word? Yes, it is the plural form of peculiarity).

How can a number be foretold by iteself? Does pi really hold this information? I know the decimals of pi is irrational - neverending and doesn’t repeat itself, but this is something else.

The math in the prophecy

The mathematical exercise is to split and add up the first three sets of six decimals, like this:

3.141592653589793238462141592 + 653589 + 793238 = 1588419

It is within this sum that the hidden prophecy lies.

In a true National Treasure film style, you need to look at the first two digits of the sum 1588419, which is 15. At the position in the decimal queue where you stopped after grabbing the three sets of decimals, count 15 decimal spaces further down the line. Now, look forward at the next group of decimals. Yes, they happen to be the exact same as the remainder of the sum, which was 88419…

The adventure in pi-land continues

This could be the end of this this adventure, but no, not today. After I verified this simple mathematics using Python programming, my first thought was; Are there more? Actually, even before I verified it, that came to mind, and is the reason I chose to use programming to look at it. That way, with such tools, I could look further in more decimals of pi, programatically.

And so I did, with the first 160 million decimals of pi.

It turns out that this fortelling doesn’t happen all the time, but it happens.

At decimal position 62657, the sum of three sets of six sums up to 749177. I continue 74 number of steps and find the remaining digits 9177.

At position 112359, it adds up to 889990. Counting 88 decimals forward, I find 9990. Same with position 195074, 235899, 286767 and many more.

Does the fortelling parameters matter?

Well, if I change any of the parameters used to find these situations; like the size of the sets, the numbers of sets or the number that makes the position to look ahead.

If I change any of them, for example sets of seven and three move-ahead-digits, I find at decimal position 161090, the sum of three sets of seven sums up to 24498736. I continue 244 number of steps and find the remaining digits 98736.

Or at decimal position 22829, the sum of two 8-segments of digits sums up to 88635632. From this, I extract the first two digits 88 and continue that number of steps and find the remaining digits 635632. The prophetic digits without the first two: 635632 matches the digits at the new position: 635632.

So, is there just a coincidence based on some random inputs, and due to pi’s neverending and never-repeating decimal string, anything might be found there? Perhaps. Still a joyous adventure. :-)