Wednesday, September 17, 2008

Mmmmm Pi

On my way home from school today I was thinking about π and the arbitrary nature of things. Π is a pretty important number. It pops up over an over in mathematics concerning the relationship of things in nature. It’s also an irrational number. Strange that something so important would be irrational.

But why is it irrational, really? Yeah, it can't be reduced to a simple fraction and has all those non-repeating decimals, but really, what it all boils down to that π is 3.14 blah blah blah because we have arbitrarily assigned our number system to be based on 1.

What if π was our basic unit? How would that change things? If our number system were set up so that π=1, or rather that 1= the Circumference of a circle divided by its diameter. For one thing, circles would be a lot easier. It could be done. Or rather, it could have been done. Once upon a time when whoever was inventing numbers and math, what if they saw that π was an important number and decided to base the entire number system on that?

One only means one to us because that's what we believe. It's what we've been taught, that's the significance that has been assigned to that particular unit by society, by people. It could have just as easily been assigned to π. If π had been assigned as our basic unit, as 1, it wouldn't actually change the world we live in much at all. Ok, it was totally fuck math, but we'd be used to it by now, and we'd have a totally rational number to explain the relationships of circles.

I wonder though, if that's how we saw the world - where π was the basis of our number system, if we would See things differently? I think this is something to think about while staring at the ceiling and just letting my mind wander. It's kind of a mind-fuck. Sadly, I don't have time. I have to do stuff for school.


veganaron said...

Yeah, I have thought about it. If our most basic idea was that a circle was the basis of math. Time might no longer be a line but a circle... Yep it's my birthday and I had a little fun... :P

Anonymous said...

Time isn't a line ... Dr E said it was a curve.

The reason for 'one', of course, was that the system needed to fulfill its functions in commerce and architecture.

If we used Pi as the basic unit, everything that costs a dollar would cost $3.14. And there would be no penny, there would be a threepointonefoury.


mark teh rider said...


Just to spoil your fun -- of course the number 1, and our base ten numbering system is based on the fact that we have ten fingers, "digits." Hard to show your friend Grog how many chickens you saw by holding up a circle.

Anonymous said...

To Mark:

Unless you saw zero chickens.

Thank you Arab mathematicians!


Cassie the Great said...

Aaron- In some philosophies, time is non-linear. I'm thinking specifically of Taoism (which I need to look into more one of these days), but I'm sure there are others.

Rusty (the first time)- No. Because pi wouldn't be 3.14, it would be one.

Dad (Mark)- Stop raining on my parade! Grog would totally get how many chickens I wanted because he would understand circles too. Digits shmigets.

Anonymous said...

I said that. Einstein copied my work.

If it is one, there is no point in not using 'one'.

Yah Mark! Besides, Grog is a drink.


Shani said...

See, I've thought about this, and I had to come to the conclusion that we couldn't have established the system that way because it would feel like pretending that a curved line is straight - and, you know, those ancient landlubbers watched the ships sail out, they knew the world was flat.

And then my round brain sorta flattened out.

But, you know, you can always take solace in radians if you want to see pi get some respect.

Shani said...

And I totally meant to say they knew the world wasn't flat and couldn't pretend it was - see? Bad for the brain.

Cassie the Great said...

Ahhh radians. I remember those. I have to say I'm kind of glad my math days are over. Yay books!

veganaron said...

Cookies are nice.