The pi lie (or quantum uncertainty)

Great Debates
1

What is up with this bizarre constant which cannot be expressed in a finite series completely with operators (as of yet anyhow)?

I’m referring to pi: This constant of the circle measuraments; the constant of angular measurements within the context of an abstracted circular shape (or rather any closed one sided shape).

There’s a funny thing about this pi:

For any given circle drawn, the number of circumfrances solvable within the line used to represent that circle are infinite.

This can be proven. How are we so sure we’ve determined a constant from a set of infinite variation for each expression? That seems a bit presumptious, doesn’t it?

How much more inductive can one get? It’s like standing on a pile of infinitely stacked needles and only selecting one needle at a time to prove that every needle in the stack is exactly the same, when we already know that the stack is infinite! We haven’t found anything to compare pi to; to translate it against, to set it apart from anything else.

If pi could only be compared against something esle, but it can’t; we already know that it only works when the circle isn’t there.
That’s not very rigorous logic! It’s no better or different than “the god of the gaps” - the bane of rational deduction. Yet we continue to use it, to teach it, to mark the intelligence of other individuals by ‘correctly’ answering a question on a test which disproves itself. Are we trying to create stupid people?

If the stack is known to be infinite, and the combinations of operators to discern this is hypothesized as potentially infinite; then why does pi work? Is the entire symbol irrational? Why do we bother with this symbol? Because it works? That’s not very satisfactory; all kinds of irrational things end up working because they confuse people about motive and intent. We as humans seem to be in a process of rationalizing everything so that we can communicate a purpose to be. Yet instead of pi being an open question for every student, it is taught as a closed asnwer; where students are graded upon their ability to force themselves into ‘buying it’.

Is it possible that students who fail a geometry or trig or calculus exam are brighter than those who ace it? By drawing the circle, are we making our students dumb in the sense that an observer effects the outcome of a photon no matter their best intention?

I suggest that we are. So, why continue to teach pi?

-Justhink

2

I like pi!

3

I suppose more to the point of the OP; is pi a religion?
I think it is. I think that the use of it necessitiates a corruption in logic which re-enforces the use of non-trasparency to achieve both an ends and a means. I think pi should be relegated to cult status, rather than a pinicle of intellectual rigor.

We already know that pi is going to need to be abstracted out in some other means; that it and all of the systems derived from it are cosmetic and necessarily a waste of time given the system which is bound to collapse this absurdity.

Is pi evidence of magic? Is that what we want to teach each-other? That something comes from nothing.?

-Justhink

4

Pi is significant only on surfaces with zero curvature (like flat planes). The ratio between a circle’s diameter and its circumference is not pi on a surfaces with positive (like globes) or negative (like saddles) curvatures.

5

Because you can round it off to whatever precision you require.

6

You can do the same thing with Bible passages to explain God.
We already know that the precision is meaningless because we’ve proven that the symbol only has this property because we’re missing something. When the meaning of pi or pi derived constructs is either proven or disproven, the precision won’t be an open question anymore. (i.e. what is the 1 trillionth value of the pi decimal? Who cares! The entire question is pointless IMO. We might as well be using oracles again to tell us all of our opinions.).

-Justhink

7

The proof that pi was transcendental was made in either the 1700’s or 1800’s. I have never seen it, but I wouldn’t call it any more presumptuous than other mathematical proofs I haven’t seen.

8

Justhink wrote:

It’s a ratio.

9

Euclid’s followers to Archimedes: When come back, bring pi.

10

And here is our totally on topic troll!

We can prove that the ratio interpretation is inaccurate from the infinite series which emerges when you physically draw the circle.
The precision only becomes infinite when the circle isn’t there any-more. This has historically been a scientific light-bulb! The purpose of which is to alert us that we’re using a cosmetic patch to explain away something which we can’t really explain… until we can explan it, which we know we can’t do. So we keep drawing circles to prove it to ourselves, even though we know that it renders the symbol meaningless.

You’re assuming (and we don’t know this) that pi IS a ratio.
I think there are excellent arguments to put forth that pi can never be a ratio.

-Justhink

11

Are we being whooshed?

12

(Slapping Justhink back and forth across the face) Snap out of it man!! Jeez. It’s just pi, guy. You can round off to whatever fraction of a unit is within the size of whatever you’re drawing your circle with. If your writing utensil is small enough that you have to round to the trillionth decimal, then you won’t be able to see the circle anyway.

13

Who is this we to which you refer?

14

Here you go. It’s pretty damn nasty, actually.

Justthink, you shouldn’t make the error that anything in pure mathematics necessarily relates to the real world. You’re welcome to come up with all the new definitions for pi you’d like to, but mathematicians will judge them based on how interesting the results are, and how consistent they are. Based on the axioms that mathematicians start from, and flowing logically from them, pi is no lie. And the axioms claim to describe nothing but themselves. People who try to read too much into them, on the other hand, come up with all sorts of complaints.

15

  1. Don’t call people “trolls”.

  2. When someone posts with a halfway decent response to your OP (as opposed to yet another joking reference to “pie”), it’s rude, as well as stupid, to call him a troll. What if he’s offended and decides not to come back?

  3. If he’s even slightly on-topic, why do you care whether he’s a troll or not? You seem to have picked up on his debate quick enough, that’s for sure. If he really had nothing to contribute, why are you rebutting him?

  4. http://mathforum.org/dr.math/faq/faq.pi.html

Looks to me like pi is a ratio.

Naw.

16

Justhink wrote:

According to SDMB guidelines:

"Do not publicly accuse someone of trolling at the SDMB. Use the “Report this post to a moderator” facility below the “trolling” post. Do not reply to the troll in any way in the thread, that will only encourage the troublemaker."

“Lord, my load is heavy.” — Lily Tomlin

Pi is defined as the ratio between a circle’s circumference and its diameter. Or are you defining it some other way for some wierd reason?

17

Duck! :smiley: My first almost-simulpost!

18

Wowzers! I was stating that calling pi a ratio was the most critical part of the debate and as such wholly relevant! As the idea that pi is a ratio has not been proven, and I didn’t think it could be as the very act of drawing a line or sculpting a sphere renders the symbol meaningless (even though we still use it for arcitectural purposes).

I was stating that: attributing any degree of arcitectural success on the use of pi is the equivilent of attributing my good luck to God, given this understanding of pi.

Apologies if my statement appeared derogatory, it was actually a compliment shrug

-Justhink

19

There is something we’re not getting about how this relationship is necessarily a delusional correspondance. I say ‘we’ with confidence, because pi cannot be expressed as a ratio, no matter how blue in the face one becomes repeating the existence of the definition over and over.

-Justhink

20

The word “irrational” has so many uses in a thread like this.