I'm wondering whether it is known whether the 227 days in Life of Pi symbolical is for pi or that the symbolism I see (as a mathematician :)) is pure coincidence.
I think that it is symbolic for pi because pi ~ 22/7, which is quite well-known.
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I found this interview with Yann Martel, from which two of his answers in particular jumped out at me:
I chose the name Pi because it's an irrational number (one with no discernable pattern). Yet scientists use this irrational number to come to a "rational" understanding of the universe. To me, religion is a bit like that, "irrational" yet with it we come together we come to a sound understanding of the universe.
I wanted an Indian animal. At first I had an adolescent Indian elephant. But that was too comical. Then a rhino, but rhinos are herbivores and didn't see how I could keep a herbivore alive for 227 days in the Pacific. So finally I settled on what now seems the natural choice, a tiger.
The first quote tells us that the author had the concept of rationality and irrationality, and the connections as well as the contrast between them, in his mind while writing the book. This sounds similar to the rational approximation 22/7 for the irrational number pi, and makes it more likely that this was indeed an intentional reference.
The second quote suggests that the length of time was somehow significant. Why, instead of changing the animal to one more likely to survive for 227 days, did Martel not instead change the time period to one a rhino was more likely to survive?
Which brings me to (IMO) the most compelling argument: why specify the number of days at all? It seems quite strange and unrealistic that Pi or anyone else would even be able to keep track of the days during that surreal voyage; "several months" would surely be a more reasonable way of describing the period. But no, it's stated as exactly two hundred and twenty-seven days. Why bother to give a precise number at all, unless it's somehow significant? And given that it's significant, exactly what its significance is then becomes obvious, tying in with the title and the name of Pi.
If this is a coincidence, it's one hell of a coincidence.
This is one of those situations in which Chekhov's gun is your friend. If it weren't significant, why would the author have mentioned a specific number of days? While some books do get into gritty details like that with no particular stated reason - many fantasy books, for example - Life of Pi isn't that kind of book. It's pretty safe to assume that if the author makes a point of a seemingly arbitrary number, it's not really arbitrary at all.
So 227 days is almost definitely from 22/7, which is approximately pi.
It's highly doubtful that it was a coincidence. Most of the sources I looked at on the internet acknowledge that it was intentional, although in the book, Pi is named for the French word for swimming pool. However, the fact that he is named after 3.141592.... (close to 22/7) does at many new facets to his character. I think the 227 days on the boat adds to the metaphor of the infinite, the allegorical figure that Pi is and all he represents.
I could not find a quote by the author, so I think this is up to the individual reader. However, it doesn't seem like this could be a coincidence.
The fraction 22/7 was often used as an approximation to pi, and is often used when first teaching children the basics of geometry and arithmetic, so it seems pretty certain that Yann Martel put in this bit of numerology on that basis.
Yann's rationale for choosing Pi as the name of his protagonist, whilst interesting in describing his creative thought process, and symbolic of his way of seeing the world, seems at odds with the mathematical understanding of pi. Whilst pi is often called 'irrational' and has no discernible pattern in its digital expansion, this isn't the best way to understand pi; it's better and more simply understood from its definition as the ratio of the circumference of a circle to its diameter, which on the basis of geometric reasoning is easily seen to be an invariant of any circle - this is the sensible and rational way of looking at it. It's probably safe to say that pi was described as 'irrational' because it was not a fraction, that is as a ratio of two finite numbers; in fact it is - it's a ratio of two infinite integers (to make this actually precise one has to use the theory of limits, nevertheless the idea is easily understood).
ALT+227 on the keypad = π
Although I do not doubt that there may be some link between 22/7 being an approximation of pi and the title of the story, another simpler explanation is that in order to get the π as text (other than searching through font settings and symbols) is to use the ALT+227 combination.
No doubt the author would have needed to discover this considering his book uses that very same symbol on the cover. Coincidence? I personally feel it's more likely that 227 was chosen for that exact reason and not the "almost pi" equation.
As for why the ALT+Keypad combinations happen to have pi at 227, no doubt the original creators intentionally placed it there, and then set the rest of the Greek alphabet around it. Again, seems a bit too on the money for it to have been otherwise.