Was pi invented or discovered?

[Anomalocaris]

Really? wake up!

Is universal gravitational constant discovered or invented, how about speed of light? Planck constant? Discovered or invented? Elementary charge?

You're conflating mathematics and physics. We're discussing the nature of the ration of diameter to circumference in a perfect circle. Are perfect circles found in nature? I'm not aware of any, though I do not necessarily doubt they exist. Does the concept of a perfect circle hold any meaning absent a consciousness capable of contemplating one? I'm not certain. How can you be?

No, I am not. No concept of perfect circle need exist at all, and still pi would fall naturally out of any thorough description of the actual effects of the physical laws in the real world.

Take for example, Given an initial inventory of radioactive elements at the core of the earth, how hot would the core be now? The answer involves dimensionless pi, like any dimensionless physical constant. Given an object of a mass and density attains isostatic equilibrium under its own gravity, what would its dimension be? Pi is there again. Given x amount of dough, how big of a pizza crust can you make? guess what, the answer involve that dimensionless constant again. Pi is all around you in every object that is round. What's more important, roundness is not a coincidence. Operation of laws of physics leads naturally to roundness at all scales of the physical world. So through analysis of the physical world would inevitably lead to discovery of this magical dimensionless, but far from theoretical or merely conceptual, constant pi

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Really? wake up!

Is universal gravitational constant discovered or invented, how about speed of light? Planck constant? Discovered or invented? Elementary charge?

Really Chuck.

Really.

[The Grand Nudger]

Fair enough, but the reason that they aren't perfect representations of said concept is that we have devised said concepts requirements in a way that excluded them. We could just as easily have defined a circle as a concept referring to the exact dimensions of the sun or ripples on a pond (or some equivalent ratio thereof). Had we done so, pi (not our pi, but thi sun pi we've never gone to the truoble of defining) would still exist, there would still be a relationship between the various dimensions ad ways of measuring the sun that yielded a guide as to what a circle was - and it would reside in the real world as filled with substance and material as the dimensions of any circle in our minds - based upon those relationships which exist in the real world and are contingent upon those properties of that world that we can detect - exemplified by the sun, as our prime example.

Our concept of a circle (and our determinations of what is or is not a cricle) have changed over time...but it's more than fair to describe our initial concept of a circle as something very similar to what a child today might point to when asked to show an example of a circle. The group of things the child singles out will not be circles as we now understand them, nor will the child leverage or likely understand pi, but they will still be circles, and the concept is still very useful in describing those things.

It shouldn't be surprising that a system refined for the systems sake begins to become divorced from what it was initially crafted to communicate. All that is required to show where a circle (or pi) resides in the world outside that system is for dimensions to exist, for an area to be singled out and the relationship between the borders of that area quantified in any way, if we single out a circular area, this will plainly demonstrate where pi resides and where it waited to be discovered in hard inches (if you will). Regardless of what we call that area (if not a circle) and regardless of the manner in which it is quantifed (if not the numbers and math you and I are familiar with). Whatever concept devised and whatever system leveraged to study this area will yield a result that is equivalent to our own. IOW, a rose by any other name.

[FallentoReason]

Fair enough, but the reason that they aren't perfect representations of said concept is that we have devised said concepts requirements in a way that excluded them. We could just as easily have defined a circle as a concept referring to the exact dimensions of the sun or ripples on a pond (or some equivalent ratio thereof). Had we done so, pi (not our pi, but thi sun pi we've never gone to the truoble of defining) would still exist, there would still be a relationship between the various dimensions ad ways of measuring the sun that yielded a guide as to what a circle was - and it would reside in the real world as filled with substance and material as the dimensions of any circle in our minds - based upon those relationships which exist in the real world and are contingent upon those properties of that world that we can detect - exemplified by the sun, as our prime example.

I think the way in which a circle is currently defined wasn't done like that so as to exclude physical objects from literally being a circle. It's kind of the same thing as the concept of a chair: we have small ones, big ones, wide® ones... but why would we arbitrarily chose one of the many representations of the concept to be the chair, just like you proposed we could have chosen the sun to be the representation of a circle? It seems to me that all of them (chairs & shapes resembling circles) have some intrinsic value that allows us to place them into the category of a chair/circle, and therefore it is correct for us to steer clear of physical manifestations of the concept by understanding the concept to be of a "pure" nature where it only exists in our minds.

Our concept of a circle (and our determinations of what is or is not a cricle) have changed over time...but it's more than fair to describe our initial concept of a circle as something very similar to what a child today might point to when asked to show an example of a circle. The group of things the child singles out will not be circles as we now understand them, nor will the child leverage or likely understand pi, but they will still be circles, and the concept is still very useful in describing those things.

Yeah absolutely.

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With a bit of imagination, I can tell you I just drew a representation of the concept of a circle, and in our everyday understanding of the world, you wouldn't call me out on it, but instead superimpose what you know a circle to be over my obviously imperfect circle. In practice, it will always work whenever we draw a circle in a diagram, blueprints or maths textbook provided that the person who sees it has an understanding of the concept. No, it's not a true circle, but it's a good enough representation of it that the message will get through to the other person that the concept is being dealt with.

It shouldn't be surprising that a system refined for the systems sake begins to become divorced from what it was initially crafted to communicate. All that is required to show where a circle (or pi) resides in the world outside that system is for dimensions to exist, for an area to be singled out and the relationship between the borders of that area quantified in any way, if we single out a circular area, this will plainly demonstrate where pi resides and where it waited to be discovered in hard inches (if you will). Regardless of what we call that area (if not a circle) and regardless of the manner in which it is quantifed (if not the numbers and math you and I are familiar with). Whatever concept devised and whatever system leveraged to study this area will yield a result that is equivalent to our own. IOW, a rose by any other name.

I think the system itself kept improving to the point that it reached the "pure" understanding of a circle. Like the badly drawn circle above, I could try again to improve it. If I were living back in the days when e.g. sketching equipment had just been invented, I could have grabbed a compass and drawn as best I could a circle. Then for a while we could all go believing that that is a perfect circle because all points are at the same distance from the centre, but eventually we would realise that in fact I have drawn an infinite amount of circles because my pencil has a thickness i.e. there is a range of circles with radius r to r + t (where t is the thickness of the pencil). Bring if forward to today and our modern understanding of atoms would lead us to think a circle can never be but then when we bring in our understanding of atoms, we then can see that a circle can never be made in real life because any substance you use will have a thickness.

I don't know if this properly addresses your last paragraph. I wasn't too sure what you meant by the "system"...

[colossal123]

Exactly, people want to believe in Darwin's theory of evolution but when it comes to the reality of the belief everyone is steps back... because no 1 wants to be the 1 to say we should let children die in the hospital or blacks in Africa to finally die off and lets us stronger species survive... but they shouldn't bother you because according to Darwin, morals don't exist outside of cultures. especially to evolutionists...

[Aractus]

As a relationship between the circumference and diameter of a circle.

Again, not true. It could only be true for a perfect circle, which cannot be constructed. Think again. Pi can be used to calculate the circumference or area of a circle from the radius or diameter, or it can be used to calculate the radius or diameter or area from the circumference, etc. Pi is a transcendental number, a circle is a real object. A real object is finite, and thus not transcendental.

[pocaracas]

So you guys are arguing if a number was invented or discovered.
Was 1 invented or discovered?
Was 1024 invented or discovered?
Was 0.333333(3) invented or discovered?
Was e invented or discovered?
Was i (the imaginary unit) invented or discovered?
Was ∞ invented or discovered?

[Aractus]

∞, by definition, isn't a number.

[The Grand Nudger]

As a relationship between the circumference and diameter of a circle.

Again, not true. It could only be true for a perfect circle, which cannot be constructed. Think again. Pi can be used to calculate the circumference or area of a circle from the radius or diameter, or it can be used to calculate the radius or diameter or area from the circumference, etc. Pi is a transcendental number, a circle is a real object. A real object is finite, and thus not transcendental.

Yet we have no problem constructing them. Come now, a vast number of perfect circles exists anywhere we care to place them, as both the circle and pi are descriptions of a relationship between dimensions that we found it useful to define in a certain way. I'm not entirely sure what there would be to disagree with in the sentence you quoted, as this is how pi is defined. If pi is not a description of the relationship between the circumference and diameter of a circle please alert the mathematical community at your next convenience Aractus.

[Angrboda]

So you guys are arguing if a number was invented or discovered.
Was 1 invented or discovered?
Was 1024 invented or discovered?
Was 0.333333(3) invented or discovered?
Was e invented or discovered?
Was i (the imaginary unit) invented or discovered?
Was ∞ invented or discovered?

Yes. I'm going to interpret your questions as being sarcastically implied, and point out that the larger case of which this case is but a representative, the debate between Platonism and nominalism, is an important philosophical question. (Not assuming you consider philosophy important or not.)

While I'm certainly willing to steal a play or two from the playbook of mereological nihilism, I'm inclined to believe that things like pi emerge as a consequence of other truths (it is itself an analytical truth, derived from other a priori or a posteriori considerations), or is an emergent property of certain types of systems (in this case, specific neural networks) which compute idealizations of the properties of things as a useful shortcut in deriving behavioral solutions to the problem of survival. Thus we may have geometrical concepts which don't exist in the real world, but which can yield more consistently reliable consequences in terms of prediction if used in place of.... whatever we might use otherwise [and such computations based on idealizations are enormously more efficient, not even taking into account the properties of the computational infrastructure]. We have other, supposed, purely Platonic constructs; for example, our intuitive concept of folk psychology, the concept that a person has thoughts, beliefs and goals, is not something we actually encounter in our world [that of other people], but it is an eminently useful construct to use in predicting the behavior of people in our environment. (See, for example, Daniel Dennett, )

(ETA: Notice how, likewise, our folk psychological construct of mind can lead to unproductive predictive simplifications. The effect in psychology is a case in point. If we are reasonably competent and self-aware, we may innocently project that assumption onto someone who is not competent, nor aware of their incompetence, and quickly become frustrated trying to make sense of their behavior, when their behavior doesn't make sense in terms of our model of them as competent and self-aware.)

[pocaracas]

I'm thinking I've been called a "stupid ignorant", but with class.

I see your point.
pi and other special numbers have been derived.
As a number, they have always existed, so they were "discovered".
However, the concept which lead to that discovery was constructed by human intellect, so they would have been invented.