Marais: Pi = Infinity(?)

Pi. π. 3.14159. A mathematical constant; an infinite number – the ratio of a circle’s circumference to its diameter. Records of its use date back to Babylon and Egypt, as early as 1900 BCE, and both civilizations developed approximations within 1% of pi’s true value, and the number has proved infinitely important to both maths and science – whilst it’s use can be as simple as helping to calculate the diameter of a circle in a maths class, or for laying foundations to a circular building, we have been able to use the number for far greater purposes: in calculating the circumference of the earth, for example.

The most interesting thing about pi, however, is its irrational nature: it can never be expressed as a ratio of two integers – thus, it’s decimal representation never ends, and it can never settle into a permanent repeating pattern. As of late 2011, scientists have extended pi’s decimal representation to THIRTEEN TRILLION digits. That amount alone is incomprehensible to all but the most skilled mathematicians – I can’t begin to comprehend its enormity.

But here’s the rub: is pi truly infinite? If so, what possible information does the number hold? And if not, what impact would that have on every aspect of the scientific world?

If pi is a infinite, non-repeating decimal, then the implications are simple – every single possible number combination that could ever exist, exists within pi. If you were to convert into the number into ASCII (American Standard Code for Information Interchange; this translates figures into text) you could find any and all possible data within it – the name of every person you will ever meet, love, hate and the birthdays; the manner of your death, and the exact time and date it will take place; answers to any and all questions that could possibly be asked; even the entire works of William Shakespeare in exact order of publication: letter by precisely placed letter. The implausibility of this is obvious, but such is the incomprehensible nature of infinity that we can never truly understand what pi holds – buried within pi is the eighth Harry Potter book, the name of the thirteenth month, and details on how to build a time machine. All information that does or could ever exist is held with this number, but this, however, is reliant on one key principle: that pi does remain irrational.

If, as previous mentioned, we ever found a recurring pattern in pi, buried somewhere after 20 trillion digits of non-recurring chaos, then maths as we know it would fall apart – all calculation based around our approximation of pi would be wrong, albeit by a fraction of a decimal place. It is, however, tiny, minute miscalculations like this that make up the foundations of maths and physics – such a discovery would revolutionise both topics. On top of this, theories regarding it containing all possible information would be proved incorrect, and whilst this may again see trivial, it would reform the boundaries of infinity – whilst 20 trillion digits may seem an incomprehensible number, it would hold much less “information” then it’s previously assumed “infinite” form.

It is, however, hypotheses like this that build up the foundations of science – all previous data indicates that pi is infinite and will continue to prove itself to be, just like all previously acquired data indicates the existence of gravity; of our planet’s place in orbit around the sun; of the length of time homo sapiens have existed since their evolution from homo erectus. And if, one day, our theories about pi were proved wrong, then scientists would see it not as a setback, but an incentive to work out the truth. After all, we’ve been proved wrong before. But that is another topic for another day.

Conclusion (TL;DR): Pi, as far as we know, is an infinite number, and a non-recurring one at that, thus containing all possible information.

Until next time,

Marais

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