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# Does the number π really exist? watch

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1. (Original post by Implication)
Numbers are abstract concepts that we apply to the real world. It doesn't make sense to ask if they "exist".

If you want a physical application, it is the ratio of a circle's circumference to its diameter.
It doesn't make sense to ask if they "exist" ? Why not? Abstract concepts don't exist? Such ratio is the abstract concept? And the ratio exists?

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2. Given that it's defined using a circle and circles don't really exist in nature, I think it's a good question.
3. (Original post by StarvingAutist)
Erm, yes...

http://en.wikipedia.org/wiki/Pi
Wiki doesn't give me the answer. It didn't tell me the "real value of Pi ". Just approximation.

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4. (Original post by KeepYourChinUp)
Why are you always asking ridiculous questions? You're not a philosopher you're just asking stupid questions as if they have some sort of meaning.
Grow up! Don't beat around the bush, please. It's not about stupid question or answer.

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5. (Original post by skunkboy)
A constant? Why a constant? Is it really a constant? And if it's not a number, what exactly is it? I'm not close-minded.

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Yes it is a constant. The ratio of a circle's 2 radius to it's circumference is always pi therefore it is constant. Out of interest to what level do you understand maths? The great philosophers in history would study the topic they want to philosophise about intensely before trying to question it, since you are asking if pi is a constant when it clearly is and apparently think you have to know all the decimal places to define a number it seems clear that you have not studied the definition of a number before asking these questions.

Edit for the typo.
6. (Original post by HJ M)
I don't think it's a stupid question at all, it branches into philosophical questions about knowledge, its nature, its sources and questions such as how do we know pi really exists? A great place to look when answering this question specifically would be Descartes when he was exploring certainty and doubt, his Meditations and the quest for certainty. I suggest you look at Descartes yourself because he explored similar questions about knowledge and 'how do we know' questions.
its people like you who make philosophy look like a useless wishy washy subject.
7. Pi exists and is proven to exist. I can show you a proof but since you clearly are not a student of mathematics, it is beyond your understanding. Take it from the experts it exists.

It is simple physics, the constant Pi has to exist in order for the world to exist and function. You enquired if Pi was a number, yes it is, it is an irrational number, which differs from say naturals or rationals.

You may be equally confused by a number defined as the square root of 2. If you construct a right angled triangle with the non hypotenuse sides being 1, we see that by Pythagoras the hypotenuse must be equal to square root of 2, which like Pi is also irrational and cannot be represented as a fraction (or what you think of as a 'normal' number). Yet this number clearly does exist, just like Pi.

I am sorry that your confused, but this is not your field, and you do not have the credentials to discuss these matters, as I would not have when discussing ideas in your field.

If you have anymore questions, please do not ask them in the future, you are making your self look bad here.
8. (Original post by skunkboy)
Grow up! Don't beat around the bush, please. It's not about stupid question or answer.

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How about negative numbers, do they exist? What about complex numbers? I guess you disagree that 0.999 repeating = 1?

Do you know what is equal to? I really think the OP just doesn't understand numbers in all fairness. GCSE Bitesize is great for basic mathematics.
9. Circles exist; they can be manufactured by humans, or they can be found in nature. pi is defined to be the ratio of the circumference of a circle to the diameter of that circle, so, if circles exist, then pi exists.

The question is meaningless until you define existence, though. Is existence being able to be expressed as a decimal with a finite number of digits? Then, from the manner in which we have defined existence, pi, the square root of 2, and all other irrational numbers do not "exist". Is existence not being able to be written down accurately on paper with simple instruments? Then pi, e, and the transcendental numbers do not "exist".

Ultimately, numbers can't really exist on their own - we can use them to count things, and the we count exist, but the numbers with which we count do not. Mathematics is an abstract field of study, after all.
10. (Original post by skunkboy)
Wiki doesn't give me the answer. It didn't tell me the "real value of Pi ". Just approximation.

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So? Pi is clearly a number, and it is very real and very important.

If it wasn't a number, how could it be in any way useful? Sure, it's not algebraic, but it has many applications. I'll just remind you:

11. (Original post by skunkboy)
It doesn't make sense to ask if they "exist" ? Why not? Abstract concepts don't exist? Such ratio is the abstract concept? And the ratio exists?

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I'm just saying that the question is meaningless until you define "existence". Abstract concepts don't have physical existence by definition.

Can you see a pi in real life (please no lame jokes )? No. But can you see a 2 in real life either? No. Can you apply pi to concepts in real life? Yes. Can you apply 2 to concepts in real life? Yes. Can you apply them both to the same concepts? Not necessarily.
12. Even the rational numbers don't exist, we can merely construct examples with the number tacked on to some referent in our heads. It doesn't have to be something as crude as "two apples plus four apples" but we do think "two ones plus four ones", since one is the multiplicative identity, so you can say that psychologically speaking it allows us to attach an abstract referent to numbers so we can do sums in our head.

So the rational numbers are things we can identify by conceptualising them in terms of how many ones they are, creating a ratio out of them, hence the name. Of course you can also express them as ratios like 5/2, and even think of them that way psychologically without reducing them to a ratio over 1, but since "2" has already been constructed in terms of 1 it's fine.

With pi you can't understand what it means in terms of ratios. It is simply meaningless to try to give it a numerical value, unfortunately because of the way we are taught counting, we think numerical values/rationality is the acid test for being a "proper number". We can only understand what pi means in terms of geometry, i.e. imagining a circle.

And you might say, but we can't really understand it, because we can't see exactly how long the circumference is compared to the radius. But that's a numerocentric view. Pi means we can construct any circle geometrically. Measuring the lengths in various circles and putting them into a big table and looking at patterns is a numerical approximation of what is much more simply described in geometry by just constructing a circle. You may then say yes, but what about circles of different sizes? But the inclusion of axes in a geometric construction is just another way of trying to measure numerically. A circle drawn on an axis-less background represents all circles, and uses pi as its base, just as the numeral 1 represents all sets that have one object in them.

The Greeks knew about irrational numbers and prioritised geometry in their mathematics to investigate them on their own terms. But the Islamic world was more into algebra, an outgrowth of basic arithmetic. When they tried to use the Greeks' ideas they kludged them into algebra.

Since Europe took its mathematical notation, including number forms, from the Muslims, we got this kludge as part of the package, including misleading abstract symbols like π which could never represent a numerical constant. The symbol for infinity is another such.
13. (Original post by scrotgrot)
Even the rational numbers don't exist, we can merely construct examples with the number tacked on to some referent in our heads. It doesn't have to be something as crude as "two apples plus four apples" but we do think "two ones plus four ones", since one is the multiplicative identity, so you can say that psychologically speaking it allows us to attach an abstract referent to numbers so we can do sums in our head.

So the rational numbers are things we can identify by conceptualising them in terms of how many ones they are, creating a ratio out of them, hence the name. Of course you can also express them as ratios like 5/2, and even think of them that way psychologically without reducing them to a ratio over 1, but since "2" has already been constructed in terms of 1 it's fine.

With pi you can't understand what it means in terms of ratios. It is simply meaningless to try to give it a numerical value, unfortunately because of the way we are taught counting, we think numerical values/rationality is the acid test for being a "proper number". We can only understand what pi means in terms of geometry, i.e. imagining a circle.

And you might say, but we can't really understand it, because we can't see exactly how long the circumference is compared to the radius. But that's a numerocentric view. Pi means we can construct any circle geometrically. Measuring the lengths in various circles and putting them into a big table and looking at patterns is a numerical approximation of what is much more simply described in geometry by just constructing a circle. You may then say yes, but what about circles of different sizes? But the inclusion of axes in a geometric construction is just another way of trying to measure numerically. A circle drawn on an axis-less background represents all circles, and uses pi as its base, just as the numeral 1 represents all sets that have one object in them.

The Greeks knew about irrational numbers and prioritised geometry in their mathematics to investigate them on their own terms. But the Islamic world was more into algebra, an outgrowth of basic arithmetic. When they tried to use the Greeks' ideas they kludged them into algebra.

Since Europe took its mathematical notation, including number forms, from the Muslims, we got this kludge as part of the package, including misleading abstract symbols like π which could never represent a numerical constant. The symbol for infinity is another such.
What exactly do you mean by "exists"? If you mean it occurs in nature, then does any number really exist? I've never seen a number 3 floating around. If you mean is pi a real number, then yes it is as I proved on the last page.
14. I would call it more of a constant than a number. It's value that I can recall so far is 3.1415... my memory is poor. I do know however that the millionth digit after the decimal point is 1. Pi is a strange and wonderful thing.
15. Tips to guys: ask your girlfriend this in bed, it will do wonders I promise *-*
16. You know the first link says "But John Adam, a mathematics professor at Old Dominion University and the author of Mathematics in Nature: Modeling Patterns in the Natural World, said that no perfect circle can occur in nature "since a perfect circle is a geometrical idealization.""

Also there are no perfect circles in nature and thence, the points about pi being related to the structure of DNA are wrong.
17. (Original post by KeepYourChinUp)
Just because great philosophers have asked a question, doesn't make the question anymore meaningful. There are some people who think that by asking completely random questions that makes it philosophy.

Why is our sun the size it is, why not some other size?
Why are there 8 planets.
How high does one have to go before they're classed as being in the sky.
If a tree falls and nobody is around to hear it, does it make a sound?

They're just stupid questions. Sure we can sit here and waste our time debating nonsense but it's about as pointless as the questions themselves.
I agree some questions are stupid, but there are other questions that superimpose those questions and like I said the OP's question relates to knowledge.
18. (Original post by Implication)
The fact that he focused on pi makes me think it isn't some deep question about Descartes' method of doubt and is more about his inability to understand irrational numbers. In fact, I'm not sure how easy it is to extend Descartes' method to abstract concepts like numbers anyway.

As per my last post, the question is completely trivial when one bothers to define existence and completely meaningless before then.
I agree it isn't a philosophical, but there is another interesting question about knowledge which is philosophical that links to this question and for some people is worth exploring.
19. (Original post by rickfloss)
its people like you who make philosophy look like a useless wishy washy subject.
look?
20. (Original post by rickfloss)
its people like you who make philosophy look like a useless wishy washy subject.
That's your perspective, in my view it demonstrates that it is indeed an important subject which extends into our everyday lives and it also demonstrates the difficulty in answering these fundamental questions, which come about from these 'simple' questions, to do with knowledge, the mind, religion etc. and why we must take a philosophical approach to them.

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