(and I did say imagine, not visualise).
Because Euclidian geometry doesn’t work with quantum physics, that’s why! 
But you are, Justhink. You are denying the existence of pi based on its infinite decimal place. Unless you’re using an infinite measuring tool, the portion of pi which doesn’t exist is not relevant. You can use pi to measure the area of a circle out to a billionth of an inch if you needed it to be that precise. How does the inability to calculate the infinite decimal point of pi preclude its usefulness? Are you a recently self aware super computer for whom the latest calculations of pi are too imprecise for your delicate circutry? Can you provide a useful calculation of the area of circle without using pi?
It is really the infintesimal thickness that gets me. I don’t think we can imagine infinitely large or small or divisible etc, after reading Hume. Actually, I thought this before Hume, but it was cool to have him flesh it out. You know, no use reinventing the wheel.
But my disagreement would then come from a sort of Humian perspective on the way we obtain ideas, and that is, through perception [this will be a very rough sketch, I’m afraid]. We cannot imagine things we have not actually sensed, or are not constructions of things we haven’t sensed (like a unicorn). A point, for instance. Dimensionless and utterly unimaginable. But, not unoperable. For we can, and have, imagined extended objects, and so we also have come up with the sort of abstraction “length” (however, note that in imagining “the length of a rod” it could be said—and has been said, and I will say—that you simply imagine a rod, and of course all rods have length (though this is not some special property of rods given a priori)). And we can then say: let the length be zero. And is this a problem? Of course not! But we haven’t imagined it; one doesn’t imagine nothing. Nothing, to the mind, is—as it were—like imagining my house without me in it. An empty container, perfectly imaginable, even in the abstract.
But the ideal—the ideal line of infinite divisibility and extension, the ideal circle with constant and precise diameter, the ideal number derived thereof (well, pi, of course)—is not there in our mind just because we speak the word, or operate with a symbol. The symbols go places we seemingly cannot, and it is this that fascinates us.
So, in a sense, we have an infinitely divisible line, or an ideal circle; but, we don’t have it in mind. That is, we don’t, and cannot, imagine it.
There is such a thing as a line of infinitesimal thickness in our experience though; visualise the circle as disc of solid, uniform material (material that, for the sake of convenience is just ‘stuff’, with no structure), the circumference is the boundary between the material of the disc and empty space.
The boundry? The infintesimally thin part where we perceive neither disc nor space? And what is it that we are perceiving, if all that is in front of us is the disc and the space?
Pick any spot outside the circle and draw a line from it to the ceter of the disc. Is this line’s length the sum of the three segments {center to boundry}, {width of boundry}, {boundry to spot}? Suppose I say it isn’t that, there is no boundry, and so I remove it from the calculation.
Does {center to boundry}, {boundry to spot} describe the same thing? What is missing? What have you perceived here that I have not?
Exactly. In science there is this little concept of significant figures. All this means is that, to be honest, you cannot report more figures than the most uncertain one. Let’s say I’m calculating the temperature of an ideal gas. I know R to, say, the fifth decimal place , n to the 5th, v to the 5th, but I only know the pressure to be 1x10^5 Pa. Therefore, having only one significant digit, the best I can report the pressure is to one significant figure. If I get a T of say, 235 K, I have to round down to 200. That’s not very accurate, but it is honest because that’s the best I can do based on the limitations of my worst piece of equipment.
Pi’s the same way. Just because it doesn’t repeat, even though we’ve calculated it to 1.24 trillion places doesn’t mean we can’t use it. You will never have an instrument so precise that it can give you 1.24 trillion significant figures, so an approximation is good enough. You don’t even have to take it into account for significant figures, it’s a constant, same as r or g or h or the fact that there’s 1000 mL in a 1 L.
Well the boundary has no measurable thickness and yet we are able to perceive it. In any case, this discussion is a sidetrack; if the line that describes the circle must have thickness, let us say that we will measure to the inner or outer edge of it; same difference - we’re still talking about a circle.
Agreed; if the (1.24 trillion)+1[sup]th[/sup] digit and all digits following it are 9, it has no impact on the first ten significant digits; it doesn’t make pi equal 3.15…
If you could perceive it, you could measure it. Or do you suppose that our eyes are infinitely more powerful than our instruments of science?
Justhink, I feel sorry for your math teachers.
And your economics teachers.
And your science teachers.
Even your philosophy teachers.
Maybe not your Literature teachers though. 
For one, I want to make very clear (as if I haven’t already) that I see a concept with pi that strikes me as being exceptionally analagous to the concept of the Biblical God.
With the Biblical God, I cannot in all sane-ness deny the existence of a concept such as “God”. The question becomes, is the concept meaningul? If so, how? If not, why?
Is it truly meaningful for me to attribute existence to God, rather than simply not doing so? If God is an infinite set under which all aspects of reality form, God contradicts God in every concievable means we humor the logic even necessary to make the claim.
It’s not a denial of the infinite here, it’s a denial of one single entity ultimately being able to represent a contradiction and exist!
We’re not even positive what sentience is, and we really don’t have much evidence for omni-science, as it proves incompatable with sentience. In the same sense, we’re not really positive what a ‘thing’ is with regards to a finite diameter, and we don’t really have much evidence that such a thing is meaningful in the context of a ‘one-sided’ ‘other-object’ such as a circumfrance.
I look at the output of talking about God, as the same as the output of pi. There is no ‘right’ way to find for pi, and there always seem to be more or less efficient ways to calculate it and calculate it further and further – to this degree, the process itself is the variable!! “However you can get the process to conform to this wacky idea works just fine; just make sure that you know the process proves the wacky idea”
The creativity here is in the work required to harmonize something which is ultimately contradictory. It’s like a floating state for imagination attempting to make sense of delusion, because it’s convinced that it must, must, must prove the contradiction can exist in one single entity which can reference itself.
A persons means of locating pi is the equivilent of a specific religious sect, and the output is considered the word of God.
However, not all outputs are the same; as all of them are considered approximations by definition. It’s nice to think that one is more accurate than another, but is it really?
is 31/10 really any more sensical than another process, when the whole thing is just one big approximation anyways (as aknowledge within the system itself; just like in the Bible!).
Again, drawing this parallel:
It’s one thing to say that God exists somewhere where we cannot reach until death; an “imaginary number” to this degree.
It’s something else entirely when the component of this imaginary number which presumably distinguishes it from just a description of one of us, contradicts it’s capacity to actually be meaninful to any of us in such a means as to humor attention to it.
This is exactly what pi is doing IMO.
“Ok, so you can’t compare mathematics with the real world…
But even the imaginary values contradict each-other… that’s just plain stupid. That’s the definition of gullability, and necessarily setting yourself up for being a total whore of non-being; a toy for anyone and everyone’s consent, a robot. Why are you even responding to this thread, you’re contradicting your ability and purpose for doing so… If more, why should you matter to me, if you of your own mouth negate yourself? Did you not think I wouldn’t notice the contradiction?”
That’s basically what I see with the value of pi.
I don’t mind the concept of infinite value or finite values, but merging them so that they occupy one body and then forcing people to believe that this body exists in order to show evidence of humanity, is absurd IMO. You can’t have infinite self-reference finite. Once a person allows that, they destroy all purpose for logic and meaning, and evaporate any sense of standardization.
shrug
-Justhink
Just wait till you get into Calculus…
Enough “merging of finite and infinite values” to make your head explode.
Pi only an approximation that is useful in helping us find out the relationship (i.e. ratio) between a line drawn through a circle and it’s circumference. It has already been explained far better than I ever could do it earlier in this thread.
[quote[
If God is an infinite set under which all aspects of reality form, God contradicts God in every concievable means
[/quote]
I like this, too bad it’s buried in an incomprehensible rant.
That was meant to read:
You can’t have infinite self reference itself and also self reference finite at the same time in the same being.
-Justhink
Auf Englisch, bitte?
Pi is not infinite, it is finite. Its expansion in any base arithmetic is infinitely long. But who is saying we should be able to write it out?
Also, I am not sure how pi references itself. I have never seen a recursive definition of pi (though it might be interesting if one existed), only infinite series that converge on the value at varying rates.
I’m not saying you’re denying the infinite, I’m saying that you’re putting too much importance on a decimal place that has no practical applications. It’s not like when some math professor works pi out to the next million decimal places, scientists will think…‘oh yeah, now we’ll get those clear pictures of Pluto’. Pi has been worked out way past its useful precision. When we teach kids pi, we can honestly tell them that it can be used to figure out the most exact measurement they will ever need. It’s got nothing to do with religion. No one is asking anyone to believe that the infinite decimal place has some magic powers. And teachers aren’t making kids calculate circumference with pi out to the infinite decimal place, so you can relax.
I can’t believe we’re debating pi. Must be a slow news day.
Moderator’s Note: The point has already been made, but Justhink, please be more careful about throwing around words like “troll”.
Sheesh, now I know why I stay out of GD most of the time (the headaches)…
but still visit on occasion (these minds at work).
Look Justhink, God worked for society for very many years, up until, what? the Age of Reason? 17th century I think. (of course god still continues to work for some, but there’s plenty of threads on that). Science and reason replaced god in many ways for many people in the way they understood the world because it worked better. That’s all there is to it!
Pi works. It is not some arbitrary number that someone created simply to fill a gap in our knowledge, and it’s credibiltity does not rest on belief, for if it did, 6, 13, or 872 could all be substituted for it with equal results. It *should * continue to be taught in schools because nobody yet has come up with something better for doing the same thing. (And furthermore, how could someone not educated about the concept hope to spot flaws in it for the purposes of devising something better?).
Not to say that Pi is a theory (I don’t know, is it?), but by you’re reasoning should we abandon the teachings of all theories? Can a concept or idea still be useful even if it can’t ultimately be proven beyond a shadow of a doubt?
I think what Justhink is missing is that pi only exists in the realm of the perfect mathematics of the mind, meaning the ratio of a circumference to diameter only in our minds, the ration in the real world can never be pi because it is impossible to make a circle with perfect precision, at least not in the near future.
Using you’r reasoning, Justhink, circles do not exist either! I should say a circle is a faith based theory as well. A circle is the infinite set of points the same distance away from one central point. So those CDroms you see are not circles, they are an approximation of a circle…
And what is the deal with the “Bring Pie” joke? I don’t get it.