What do you think about pi - should it exist?

[Eudaimonist]

Sure but it's not that the number is infinitely large, but that it's irrational. In other words, it doesn't fit our number system with complete precision because our system is a rational system designed for counting.

I think that a lot of people don't realize this. Our decimal system is a purely human invention. It's a tool designed to fit our mental ability to count. Of course it has some relationship to reality, but it shouldn't be confused for reality.


eudaimonia,

Mark

 

[Mysticus]

Infinites are expressed in all sorts of manors throughout nature. And the shape of a circle exhibits neither a beginning nor an end.

 

[Mysticus]

I think that a lot of people don't realize this. Our decimal system is a purely human invention. It's a tool designed to fit our mental ability to count. Of course it has some relationship to reality, but it shouldn't be confused for reality.


eudaimonia,

Mark

The same goes for any language, yet it is the only and best means we have to define and describe reality, not only to ourselves but to others.

"The Tao (Way) that can be spoken is not the Eternal Tao (Way)."
-Lao Tzu

 

[MoonlessNight]

Pi is the counterexample to us living in a discrete (or should I say, digital) world. Of course that's assuming that the circles we see are circles, and they probably aren't. But it seems logical to us that they could at least potentially exist, or do exist at least as relations drawn up by us (say the perimeter of a search that looks at everything within a one mile radius).

 

[Blackguard_]

Let me put it another way. Numbers are symbolic; now, pi is so long that the area it takes up is greater than any circle you could hope to symbolize the circumference to diameter ratio of. How can a symbol be considered symbolic if it is greater than that which it represents?

Do you see the problem now?

Letters are symbolic too, and the ratio symbolized by that infinite string of digits is also symbolized by the much smaller Greek letter π and the letters p and i when Latinized.

Problem solved.

But seriously, the number is only greater in terms of physical size which or course is not the only measure of greatness.

A symbol is always inferior because it is not the thing it represents. A string of digits is not the ratio of diameter to circumfirence in a circle, but a way of representing it, and imperfectly as pointed out.

 

[quatona]

Let me put it another way. Numbers are symbolic; now, pi is so long that the area it takes up is greater than any circle you could hope to symbolize the circumference to diameter ratio of. How can a symbol be considered symbolic if it is greater than that which it represents?

Do you see the problem now?

pi takes much less space than the number it symbolizes.

Now, as for the issue that the ratio between radius and circumfence is not a simple one of whole numbers:
Whilst I understand that you religious guys blame a lot of regrettable things on man, I don´t seem to understand how anyone (except for the creator of everything, if you believe in such) can be blamed for the fact that pi is an infinite number.

I wonder how that is a "should" question, anyways. Let´s say, for argument´s sake, that pi shouldn´t exist. What would be the consequences and implications of this? Should "pi" be added to the profanity filter?

Gravity - should it exist?
Humans - should they have wings?
Words - should they have any meaning?

 

[necroforest]

Actually if you assigned one digit of the numerical representation of Pi to each point within a circle, you would find them to be equal. Or we can represent the value of Pi exactly by simply assigning a symbol to it, which, indeed we have done.

Actually, no you can't. There are "more" points on the circle than their are digits in pi. (Mathematically speaking, the points on a circle are uncountable while the digits in pi are countable).

 

[IzzyPop]

Actually, no you can't. There are "more" points on the circle than their are digits in pi. (Mathematically speaking, the points on a circle are uncountable while the digits in pi are countable).

Both would be infinite. They would be equal.

 

[us38]

Both would be infinite. They would be equal.

There's a huge difference between countably infinite and uncountably infinite. Not to mention that infinites are rarely equal. f(x)=x and g(x)=5x both approach infinity as x approaches infinity, but g(x) only equals f(x) when x=0. For x>0, g(x) is always greater than f(x).

 

[IzzyPop]

There's a huge difference between countably infinite and uncountably infinite. Not to mention that infinites are rarely equal. f(x)=x and g(x)=5x both approach infinity as x approaches infinity, but g(x) only equals f(x) when x=0. For x>0, g(x) is always greater than f(x).

Ack...I'm barely into my first cup of coffee and you pull this out? My head is going to spin for the rest of the day...

 

[Mysticus]

Actually, no you can't. There are "more" points on the circle than their are digits in pi. (Mathematically speaking, the points on a circle are uncountable while the digits in pi are countable).

There are infinite points on a circle and apparently infinite digits of pi... counting is simply taking measure, which can be applied to both aspects.

 

[AnonymousCoward23]

There are infinite points on a circle and apparently infinite digits of pi... counting is simply taking measure, which can be applied to both aspects.

Actually, no. You can count the digits of pi, but you can not count the number of points on a circle.

Draw a circle in a coordinate system and you'll get 2 points for each coordinate along the x-axis. The number of values on that axis correspond with the number of real numbers, which means you have 2 points for each real number.
You can't count the real numbers (look at Cantor's diagonal argument for proof).

Therefore, the number of digits in pi are infinite, the number of points on a circle are uncountable infinite.
Therefore, there are "more" points on a circle then there are digits in pi.

(Sorry to any mathematician if I botchered anything, I'm a computer science student, no mathematics one)

 

[necroforest]

There are infinite points on a circle and apparently infinite digits of pi... counting is simply taking measure, which can be applied to both aspects.

Why is there only an "apparently" number of digits in pi?

 

[Gracchus]

Actually if you assigned one digit of the numerical representation of Pi to each point within a circle, you would find them to be equal. Or we can represent the value of Pi exactly by simply assigning a symbol to it, which, indeed we have done.

That does not make Pi infinite as it is always between 3.1 and 3.2. You seem, Gottservant, to be confusing the number with its representation.

Interestingly enough, the ratio of circumference to diameter of a circle on the surface of a sphere ( call it Rho) as measured along a great circle on the surface of the sphere,, can range Pi < Rho < Infinity as the diameter ranges from zero to half the circumference of the sphere.

Actually, no you can't. There are "more" points on the circle than their are digits in pi. (Mathematically speaking, the points on a circle are uncountable while the digits in pi are countable).

OOPS! My bad. I don't know what I was thinking.

 

[Tynan]

Let me put it another way. Numbers are symbolic; now, pi is so long that the area it takes up is greater than any circle you could hope to symbolize the circumference to diameter ratio of.

Pi is not 'long'.

Pi takes up no 'area'.

How can a symbol be considered symbolic if it is greater than that which it represents?

Do you see the problem now?

No?

I think you are seeing Pi as a figure written on a piece of paper in ink and not what it actually is, this is of course an abstraction.

 

[Fear]

We can work together to eliminate Pi.

 

[AnonymousCoward23]

...I'd rather eliminate pies...

 

[quantumspirit]

Actually if you assigned one digit of the numerical representation of Pi to each point within a circle, you would find them to be equal. Or we can represent the value of Pi exactly by simply assigning a symbol to it, which, indeed we have done.

That does not make Pi infinite as it is always between 3.1 and 3.2. You seem, Gottservant, to be confusing the number with its representation.

Interestingly enough, the ratio of circumference to diameter of a circle on the surface of a sphere ( call it Rho) as measured along a great circle on the surface of the sphere,, can range Pi < Rho < Infinity as the diameter ranges from zero to half the circumference of the sphere.

Please, don't confuse Gottservant any more. He'll just take it as another strawman, which he believes to be valid arguments.

 

[Mysticus]

Actually, no. You can count the digits of pi, but you can not count the number of points on a circle.

Draw a circle in a coordinate system and you'll get 2 points for each coordinate along the x-axis. The number of values on that axis correspond with the number of real numbers, which means you have 2 points for each real number.
You can't count the real numbers (look at Cantor's diagonal argument for proof).

Therefore, the number of digits in pi are infinite, the number of points on a circle are uncountable infinite.
Therefore, there are "more" points on a circle then there are digits in pi.

(Sorry to any mathematician if I botchered anything, I'm a computer science student, no mathematics one)

I think you may have missed my point. So you are saying that you can count all the digits of pi... good luck, I think some super computers are working on it as well.

 

[Mysticus]

Why is there only an "apparently" number of digits in pi?

I say "apparently" because, unlike AnonymousCoward23, I have noticed that no one has ever produced a complete calculation of pi to the very last decimal place. Though I doubt there is a last decimal place to be calculated to, who for sure is to say there is not one. Therefore I would say apparently the precise calculation of pi is infinite.