Blog RSS Feed
Fun With π
by
= 3.1415926..
The ratio of a circle's circumference to its diameter. An irrational and real number. Might we find meaningful significance hidden within the sequence?
First, step back and consider the increasingly acceptable notion of finding a level of order in chaos. Complex adaptive systems theory for example. Just look to nature. Patterns within systems. Branching trees and dendrites, migration processes, fish and flock behavior, and symbiotic relationships evolving over time. Seems to me there's something
interesting about all this math..
Back to π. If it truly is a normal number with infinite digits in the ration, travel far enough past the decimal and unmistakable patterns must eventually emerge. Not merely triangles and circles mind you, but everything from the complete works of Michelangelo to ancient maps of Pangea. How do I know? Simply because infinity means that any specified message will be found somewhere within the series.
Herein lies the fun.
Any intelligent lifeform with the propensity for mathematics must come to the same value of π regardless of how different their concept of space and time may be. Bringing us to seemingly disjointed and conflicting but ultimately relatable ideas of Science and..
Religion.
Creationism.
Intelligent design.
What?! How doth the scientist wax spiritual?
Just
think: patterns exist that establish themselves out of disorder. So could it be that a higher order of some kind constructed a universe ascribing to specified geometrical axioms that result in early trajectories forward? And what if these single points of origin determine not only where we came from, but where we are headed?
Perhaps there are no mistakes and everything is how it's destined to be when pondered on the appropriate scale.
Or, perhaps, I'm simply having fun with π.
7 Comments
+ Add Comment
December 24, 2007 4:37 AM
Traums
Perhaps the same "unmistakable patterns" emerge out of any infinite sequence of numbers!
Consider 'e'. The base of an exponential function changing at a rate equal to its own value. Hence possessing an uberpretty power series expansion. Used to express eigenfunctions of linear differential equations. Projects unit-vectors onto arbitrary axes on the complex plane.
i^i = e^(-pi/2) => One God?
December 26, 2007 9:32 AM
Old Bogus
How Biblical; string enough of anything together and anything can be proved. Or disproved, for that matter. Kinda like the I-35 "revelation". I think that was also found in the book of 'e'.
December 26, 2007 11:57 AM
bob koepp
"...infinity means that any specified message will be found somewhere within the series."
Where did that come from? And, does it imply that every infinite sequence carries exactly the same message(s)?
December 26, 2007 3:20 PM
L Zoel
Then again, pi has never actually been proven to be normal, and if you believe the ultra-finitists, it doesn't even exist.
December 27, 2007 12:28 AM
Alan Kellogg
Pi is an approximation, and only an approximation because we insist on using decimal notation to write it down. It is a very close approximation, but it is not exact. In real life the exact value of Pi depends on the exact size of the circle being measured. So that a circle 3 feet in diameter will have a value of Pi different than a circle 6 feet in diameter. The difference will be very small, but it will be there. At the scales we now work at this difference can be dealt with, but should we ever find ourselves working at a scale of thousands or even millions of light years it could become a huge problem.
December 27, 2007 1:39 AM
cvj
"Pi is an approximation..."
No it is not. 3.1415926 is an approximation. Pi is exact. And for all circles in flat Euclidean space, regardless of their radius, their circumference is 2 times Pi times their radius. No more, no less. The deviations you might be thinking of are to do with (perhaps) working in other, non-Euclidean geometries. Even if that were the case, that does not change the value of Pi, it is the relation between the radius and the circumference that changes.
-cvj
December 27, 2007 1:45 PM
Sheril Kirshenbaum
Bob asks:
"Where did that come from? And, does it imply that every infinite sequence carries exactly the same message(s)?"
It implies that infinity, being limitless, contains all sequences.
Or it may imply that this blogger has fun thinking about numbers, mathematics, and toying with ideas of complex adaptive systems theory... and she especially enjoys bringing readers along for the ride to see what they might contribute ;)
Post your comment