What do you think about pi - should it exist?

[us38]

Though I doubt there is a last decimal place to be calculated to, who for sure is to say there is not one.

Pi is transcendental, therefore irrational, and therefore does not repeat or terminate.

 

[AnonymousCoward23]

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.

And I think you've missed basic math classes.
Look at, for example, Wikipedia's definition for Countable Set and Uncountable Set. There is a difference between countable and uncountable infinite.
Given infinite time, you can count pi. But you cannot count the number of points on a circle, not even in infinite time.
This is not about pi having a "very last decimal place", this is about pi being countable and the number of points on a circle being uncountable.

 

[necroforest]

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.

Wow. Well, for starters, pi has been mathematically proven to be irrational (meaning it has no terminating or repeating decimal expansion; i.e, infinite) since the 1700's I believe (maybe before then). There's no need to guess whether or not their's a last decimal place, since it's been proven that there isn't!

 

[Nathan Poe]

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?

Yes. You've forgotten that words are also symbolic.

So, words such as "DNA," "atom," and "George Bush's credibility"* are symbols which are far greater than the things they symbolize. I guess these words shouldn't be allowed to exist?

* sorry, couldn't resist!

 

[Gottservant]

Yes. You've forgotten that words are also symbolic.

So, words such as "DNA," "atom," and "George Bush's credibility"* are symbols which are far greater than the things they symbolize. I guess these words shouldn't be allowed to exist?

* sorry, couldn't resist!

Don't knock Bush's credibility, he's the only elected Christian leader I know of. Who else would defend Earth's freedom from despots who have no respect for diplomatic relations?

Interesting point, although you ignore the fact that the things you mention can be committed to memory, hence their size is not an issue; I wonder if there is really any reason why atoms should be studied...


Back to topic, I have to say that people's discussion has been fascinating. I have two points to make, the first is scriptural. Jesus says in Matthew 12:33

"Either make the tree good and its fruit good, or else make the tree corrupt and its fruit corrupt; for the tree is known by its fruit. "​

"What does that have to do with pi?" you ask? Well, it means that something like pi means that you are forced to make a decision. Either make pi finitely countable, which would be good, or make all countable numbers uncountable, which would be bad. The point is that a number cannot be infinitely countable and acceptable.

The second point I would like to make is about infinites. Bear in mind that this is an opinion, but I do not think that a proof is enough for us to accept that countable infinites are less than uncountable infinites because we accept infinites by faith, so proof doesn't apply. You could say that you could count more of a countable infinite than you can of an uncountable therefore countable infinites are more "infinite" (although that would be in a qualitative sense more than quantitative)!

In all, I have to agree that we are just talking about representation; the one thing that sets me apart from people who try to claim that I do not understand that something is merely a representation, is that I am being practical. Say you are just relaxing counting pi and a baby is drowning nearby, if you can be happy with a smaller approximation before you look up, you are more likely to save the baby - that's what I'm talking about!

 

[Mysticus]

And I think you've missed basic math classes.
Look at, for example, Wikipedia's definition for Countable Set and Uncountable Set. There is a difference between countable and uncountable infinite.
Given infinite time, you can count pi. But you cannot count the number of points on a circle, not even in infinite time.
This is not about pi having a "very last decimal place", this is about pi being countable and the number of points on a circle being uncountable.

Essentially both descriptions are of infinity. To consider one set to be countable and the other to be uncountable is a reference to how infinity is being expressed. Yes I know that there can be infinitely repeating decimal versus an infinitely non-repeating decimal and so on, but my point is that both express and embody the same nature... being infinite.

 

[Mysticus]

Wow. Well, for starters, pi has been mathematically proven to be irrational (meaning it has no terminating or repeating decimal expansion; i.e, infinite) since the 1700's I believe (maybe before then). There's no need to guess whether or not their's a last decimal place, since it's been proven that there isn't!

I agree, yet I also tend to avoid absolutes in my use of language due to changes in our knowledge regarding the nature of systems being always possible, and even likely.

 

[necroforest]

I agree, yet I also tend to avoid absolutes in my use of language due to changes in our knowledge regarding the nature of systems being always possible, and even likely.

Mathematical proofs are absolutes. If a mathematical theorem is proven, the only time that theorem is incorrect is if there was an error in the proof.

Essentially both descriptions are of infinity. To consider one set to be countable and the other to be uncountable is a reference to how infinity is being expressed. Yes I know that there can be infinitely repeating decimal versus an infinitely non-repeating decimal and so on, but my point is that both express and embody the same nature... being infinite.

I think your problem here is you're treating infinity as it was a number; i.e, x=infinity, y=infinity, therefore x=y; There is a *HUGE* (One could say infinite *snicker*) difference between a countable and uncountable set; It seems pretty obvious to me that you're not familiar with some of the more basic elements of higher mathematics (which is ok, since this stuff isn't taught until college level discrete math classes, which most people don't take), so I honestly don't know how to explain to you how wrong you are.

 

[artybloke]

Don't knock Bush's credibility, he's the only elected Christian leader I know of.

Umm, yah. And I am Marie of Rumania.

 

[Nathan Poe]

Don't knock Bush's credibility, he's the only elected Christian leader I know of. Who else would defend Earth's freedom from despots who have no respect for diplomatic relations?

Ask me again in 2008.

Interesting point, although you ignore the fact that the things you mention can be committed to memory, hence their size is not an issue; I wonder if there is really any reason why atoms should be studied...

I didn't ignore the fact; I just think it's irrelevent. The symbols are far larger than the things they symbolize. and Pi is not larger than what it symbolizes.

The number itself is infinite, the word which symbolizes it is two letters: Pi. The Greek letter which symbolizes the word is even smaller. Convenient, isn't it?

Back to topic, I have to say that people's discussion has been fascinating. I have two points to make, the first is scriptural. Jesus says in Matthew 12:33

"Either make the tree good and its fruit good, or else make the tree corrupt and its fruit corrupt; for the tree is known by its fruit. "​

"What does that have to do with pi?" you ask? Well, it means that something like pi means that you are forced to make a decision. Either make pi finitely countable, which would be good, or make all countable numbers uncountable, which would be bad. The point is that a number cannot be infinitely countable and acceptable.

Acceptable to whom? To you?

The second point I would like to make is about infinites. Bear in mind that this is an opinion, but I do not think that a proof is enough for us to accept that countable infinites are less than uncountable infinites because we accept infinites by faith, so proof doesn't apply. You could say that you could count more of a countable infinite than you can of an uncountable therefore countable infinites are more "infinite" (although that would be in a qualitative sense more than quantitative)!

What is a "countable infinite"? Could you give an example?

In all, I have to agree that we are just talking about representation; the one thing that sets me apart from people who try to claim that I do not understand that something is merely a representation, is that I am being practical. Say you are just relaxing counting pi and a baby is drowning nearby, if you can be happy with a smaller approximation before you look up, you are more likely to save the baby - that's what I'm talking about!

Say you are just relaxing reading the Bible and a baby is drowning nearby -- what then?

 

[necroforest]

I'll respond to a few of the above poster's comments.

The number we write as "pi" isn't infinite. Our representation of it in decimal (or any integer base, for that matter) is.

An example of something that is infinite that can be counted: The natural numbers:
1,2,3,4,5,6,7,8,9,10, etc.

Although there are an infinite number of them, we can define a process to enumerate them one-by-one, that, given infinite time, would enumerate all of them. (In fact, a set being "countable" means that it is either finite or has the same size as the set of natural numbers, which is where the term countable came from: The natural numbers are our basis for counting).

For example, the integers are also countable:
0,1,-1,2,-2,3,-3,4,-4

The set of strings on the alphabet sigma={0,1}:
0,1,00,01,10,11,000,...

The rational numbers (all numbers representable by a/b, where a and b are integers and b is not zero, or equivalently, all numbers representable by a terminating or repeating decimal expansion) are also countable.

 

[Eudaimonist]

Okay, I've finally decided that pi shouldn't exist. We should make it equal to three, for simplicity's sake.

And I've decided that 1+1 should equal three as well.

You will now adjust all your calculations accordingly.

 

[Sojourner<><]

Okay, I've finally decided that pi shouldn't exist. We should make it equal to three, for simplicity's sake.

And I've decided that 1+1 should equal three as well.

You will now adjust all your calculations accordingly.

lol. Well we could create a new number system with pi as the basic unit, but that would render all numbers formerly rational as irrational.

 

[AnonymousCoward23]

Don't knock Bush's credibility, he's the only elected Christian leader I know of.

Then I guess you don't know many leaders. Hint: there are more governments than the USA on this world...

Who else would defend Earth's freedom from despots who have no respect for diplomatic relations?

...And GWB has respect for diplomatics? Since when?

Interesting point, although you ignore the fact that the things you mention can be committed to memory

Only to a certain abstraction.

I wonder if there is really any reason why atoms should be studied...

Do you mean "at all" or "anymore"?

"What does that have to do with pi?" you ask? Well, it means that something like pi means that you are forced to make a decision. Either make pi finitely countable, which would be good, or make all countable numbers uncountable, which would be bad. The point is that a number cannot be infinitely countable and acceptable.

It's completely irrelevant whether you "accept" a mathematical reality.
"Uuuh, no, I don't accept that 1+1=2!"

And a word about your precious scripture: It claims that pi is 3, so I'd think it disqualified itself in that respect:

23 And he made a molten sea, ten cubits from the one brim to the other: it
was round all about, and his height was five cubits: and a line of thirty
cubits did compass it round about.

The second point I would like to make is about infinites. Bear in mind that this is an opinion, but I do not think that a proof is enough for us to accept that countable infinites are less than uncountable infinites because we accept infinites by faith, so proof doesn't apply.

"Uuuuuh, we take that 1+1 always = 2 by faith, maybe it's suddenly 3 after the 1000th time!"

No, we don't accept infinites by faith. The natural numbers are by definition infinite, you can always add one. Faith has nothing to do with it.
Equally, there's an infinite number of numbers between each two natural numbers, when you go into the real numbers.

You could say that you could count more of a countable infinite than you can of an uncountable therefore countable infinites are more "infinite" (although that would be in a qualitative sense more than quantitative)!

If you go by how much you can count of an uncountable and a countable set in infinite time, both sets are equal in that respect. Looking at it like that has no proper use, though.

Say you are just relaxing counting pi and a baby is drowning nearby, if you can be happy with a smaller approximation before you look up, you are more likely to save the baby - that's what I'm talking about!

Oh, if you want to be polemic, I can do that as well:
Who are you to go after that one baby, while in the third world two babies die every second!

but my point is that both express and embody the same nature... being infinite.

No. One is "normal" infinity, the other is a higher order of infinity. Please look up the aleph numbers.

 

[Mysticus]

Mathematical proofs are absolutes. If a mathematical theorem is proven, the only time that theorem is incorrect is if there was an error in the proof.



I think your problem here is you're treating infinity as it was a number; i.e, x=infinity, y=infinity, therefore x=y; There is a *HUGE* (One could say infinite *snicker*) difference between a countable and uncountable set; It seems pretty obvious to me that you're not familiar with some of the more basic elements of higher mathematics (which is ok, since this stuff isn't taught until college level discrete math classes, which most people don't take), so I honestly don't know how to explain to you how wrong you are.

I am not thinking of infinity as a number. I am thinking of it as a concept or a description of a nature. And though my education in the realm of higher mathematics could use some refreshing and elaboration, I am an undergrad student of biology and philosophy at the University of Alaska; a senior beginning this fall. The only reason I am even bothering to mention that is so you might understand that I am not some uneducated high school drop out and what I was referring to originally had nothing to do with sets of number being countable or uncountable or x equaling y, what I am writing about is more along the lines of the philosophical perspective in respects to infinities, all infinities are infinite. And if you feel like elaborating some on what you are trying to get across, I'm always open to some insight.

 

[Mysticus]

No. One is "normal" infinity, the other is a higher order of infinity. Please look up the aleph numbers.

While some alephs are larger than others, &#8734; is just &#8734;. -Wikipedia

"Infinity is just Infinity" is what I am talking about; a description of a nature. Between every integer the nature of infinity is exhibited regardless of the value of a particular integer while the potential for a less than or greater value being expressed is always possible, which is describing the potential for values to be infinite.

 

[Mysticus]

Don't knock Bush's credibility, he's the only elected Christian leader I know of. Who else would defend Earth's freedom from despots who have no respect for diplomatic relations?

Interesting point, although you ignore the fact that the things you mention can be committed to memory, hence their size is not an issue; I wonder if there is really any reason why atoms should be studied...


Back to topic, I have to say that people's discussion has been fascinating. I have two points to make, the first is scriptural. Jesus says in Matthew 12:33

"Either make the tree good and its fruit good, or else make the tree corrupt and its fruit corrupt; for the tree is known by its fruit. "​

"What does that have to do with pi?" you ask? Well, it means that something like pi means that you are forced to make a decision. Either make pi finitely countable, which would be good, or make all countable numbers uncountable, which would be bad. The point is that a number cannot be infinitely countable and acceptable.

The second point I would like to make is about infinites. Bear in mind that this is an opinion, but I do not think that a proof is enough for us to accept that countable infinites are less than uncountable infinites because we accept infinites by faith, so proof doesn't apply. You could say that you could count more of a countable infinite than you can of an uncountable therefore countable infinites are more "infinite" (although that would be in a qualitative sense more than quantitative)!

In all, I have to agree that we are just talking about representation; the one thing that sets me apart from people who try to claim that I do not understand that something is merely a representation, is that I am being practical. Say you are just relaxing counting pi and a baby is drowning nearby, if you can be happy with a smaller approximation before you look up, you are more likely to save the baby - that's what I'm talking about!

Well not to get off the subject to far but what about GWB's behaviors and or policies makes you think he is a Christian? Is it because you might have heard him say something along the lines of "Oh... JC come into my heart?"

I would think that a lying politician associated with secret societies who wages war for corporate gains is far from "Christ like." And how can a capitalist who is more concerned with annual earnings for himself and corporate affiliates than he is about disrupting the environment be attempting to "protect Earth's freedom?" ---whatever that's supposed to mean.

And infinity is not excepted on faith, infinity is a description of the nature of a system. Something I found to be ironic is that you likely except your idea of the Big-Guy in the sky on blind faith, yet if you were to put some thought into it... would not the nature of this omnipotent, omniscient being be infinite and potentially Be the Universe IT'Self.

 

[Gottservant]

I've thought about it some more - pi - and I've come to the conclusion that the problem is something of a paradox. Let me explain. When you measure the circumference, you intersect a straightline with the circumference twice. But when you divide the circumference by the diameter, the instances of the diameter around the circumference do not intersect. To me that means the problem is like saying "a circle intersected by its diameter leaves an infinite remainder when its diameter is unable to intersect as it bends around the circumference". The reason this leads me to think of the problem as a paradox is that you can't measure a circle using the diameter without destroying the relationship of the diameter to the circle that makes the circle the circle (I am not that confident in this idea but I will state it as I have).

What I am saying is that the width of the circle is relevant to the final calculation of the problem and that you must calculate the diameter in identical ways to get a meaningful solution (if the diameter intersected with itself as it moved around the circle, your answer would change by at least 2 x value of the line you are using).

 

[The Nihilist]

I've thought about it some more - pi - and I've come to the conclusion that the problem is something of a paradox. Let me explain. When you measure the circumference, you intersect a straightline with the circumference twice. But when you divide the circumference by the diameter, the instances of the diameter around the circumference do not intersect. To me that means the problem is like saying "a circle intersected by its diameter leaves an infinite remainder when its diameter is unable to intersect as it bends around the circumference". The reason this leads me to think of the problem as a paradox is that you can't measure a circle using the diameter without destroying the relationship of the diameter to the circle that makes the circle the circle (I am not that confident in this idea but I will state it as I have).

What I am saying is that the width of the circle is relevant to the final calculation of the problem and that you must calculate the diameter in identical ways to get a meaningful solution (if the diameter intersected with itself as it moved around the circle, your answer would change by at least 2 x value of the line you are using).

Shouldn't you be posting a nonsense thread about how we can't evolve our way out of math?

 

[Patashu]

Pi is exactly 1 in base pi.

Btw, it's interesting to see how many different things in mathematics and physics involve pi, not just circles and spheres: http://en.wikipedia.org/wiki/List_of_formulae_involving_π

I don't think you could have a universe without pi!