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In Darren Aronofsky's famous and mysterious film "Pi" there are many mathematical secrets. My question is about one of them.

When the film begins one can see the digits of the number Pi. But here something is wrong! The digits of that Pi are not exactly the digits of "real" Pi! Note the following difference:

The Real Pi = 3.14159265 358979323846...

Aronovsky's Pi = 3.14159265 263124534235...

It seems this is not just a simple mistake because "Pi" is a film about mathematics with a strong stress on numbers so every number in it has a particular meaning and probably is a sign for an implicit message. Furthermore many digits of Arnovsky's Pi are true so one who designed the title scene perhaps used a calculator to find exact digits of Pi and then replaced some true digits by fake numbers to produce this "Pi" which is so similar to the real one. Also there is no reason for a mistake in digits after 10th place when you know 9 digits exactly!

Question: What does this difference between the digits of these two "Pi" numbers mean? Is it a message?

enter image description here

coleopterist
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  • It might be an intermediate result obtained in the process of computing pi using a Taylor series or one of the other infinite series expansions commonly used for computing approximations of pi to a finite number of digits. I'm not sure if they would've gone to that extreme level of mathematical rigor just for the miniscule portion of the audience that might actually investigate this and "get it". – Matt Sep 22 '17 at 00:41

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No, I don't think that there is any message or meaning to the use of an inaccurate value of π. I submit that the inaccuracy is simply a result of laziness or small budget constraints. In the provided image, you can make out that Aronofsky's number has been generated (possibly) by his liberal arts college-going nephew who was familiar with the mysteries of Ctrl + C and Ctrl + V. If you compare lines 3 and 4, you can see that the digits 2858286858919431192301402971286501 are repeated on both lines. While I'm sure that there are repeating patterns in π, I dare say that this is not one of them. Other patterns can also be seen.

The movie isn't really mathematically sound which is unsurprising considering that it attempts to mix Math with religion. But that should also be apparent when one questions what it has to do with π in the *cough* first place. If my memory serves me correctly, the plot really deals only with the golden ratio (1.618…). IOW, the movie should have actually been titled Phi (φ) rather than Pi (π).

So, why is Aronofsky's Pi not Phi? :)

coleopterist
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    Yet it's a matter of three clicks in your favourite web browser to get a sufficiently accurate value for Pi, but I guess the situation might have been different back in 1998 or earlier. Sound explanation, though. But one might also ask if not this repeating pattern you noticed is a hidden message, but I guess one can ask that for any kind of inconsistency. ;-) – Napoleon Wilson Nov 19 '13 at 09:44
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    I guess it just hasn't been important enough for them to consider making it 100% correct, even though it's a central element of the story (somehow). This is just like all those movies about hackers getting your car to explode or your coffee machine to put poison into your cup of coffee. – Mario Nov 19 '13 at 11:11
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    Good observation coleopterist! But as a mathematician who is interested in cryptography this repeat in numbers can have another meaning too! It could be a repeated phrase (or sentence) in a paragraph which is coded by a Caesar cryptography system. Also there are many other signs which says "this film is designed very exactly!". For example when the main character enters a supermarket one can hear a voice in Arabic language. What is this? It is a part of Quran! Exactly the sentence 138 from the section 2 which says something about Jews! –  Nov 19 '13 at 12:51
  • @SaintGeorg :) But it would be interesting only if the pattern actually appeared in π, wouldn't it? Going by this random page, the chances of a repeating 34-digit pattern in the first 100M digits of π is virtually nil. It would have been cool if it were otherwise. But for me, the fact that π has no real role in the plot suggests that this was just an error. BTW, well done on spotting the discrepancy. Only a mathematician would have really noticed it ;) – coleopterist Nov 19 '13 at 13:16
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    @coleopterist "Only a mathematician would have really noticed it" - Haha, I'd doubt most mathematicians would notice a discrepancy in Pi at the 10th digit. It's rather that mathematicians are the only guys that would bother to even check this at all. ;-) – Napoleon Wilson Nov 19 '13 at 13:57