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Actually, it is a reference to The Simpsons.
Never into a simple fraction or even a fraction involving roots of numbers, but it does have nested fraction representations.
@Neko Majin C
A fellow devotee to the Book of Kings or Indiana resident, I see.
+1
Besides, unless you really need it, we don’t need to know PI in his entire expressions.
|| For the curious, Celestia might be trolling Twilight ||
Edited
Because it causes existential debates.
Lumino right now as you go:
I’ll probably stick to assuming that Celestia is being a troll, because all Celestia ever does is cause trouble for Twilight, but fair’s fair.
Last point and I promise to stop.
Your examples of scientific misconceptions (fire is a light element, the Earth is flat) are very old. Since the arrival of the modern scientific paradigm, roughly around Newton’s time, new scientific discoveries have not broken old scientific knowledge, but rather extended them. Newton’s mechanics are not true on the atomic level, but they work exceedingly well for macroscopic objects traveling at much less than lightspeed, and applying a “many slow particles ensemble” approximation to quantum mechanics yields Newtonian mechanics.
Suppose we were to witness talking ponies, unicorn telekinesis, and pegasus cloud-sculpting. Hypotheses with varying levels of likelihood include “we are being deceived by a clever faker,” “a local phenomenon is enacting these effects through unobserved means already known to physics,” or “a heretofore unknown physical force exists that these beings are harnessing.” The last would imply an extension of the Standard Model, not a revision to its underlying mathematics. I personally like E8 as a possible particle lattice, but there is room for new symmetry.
Between the two possibilities for this comic, “Celestia is trolling her student, who has a little too much faith in Celestia’s intellect,” or “circles in Equestria are a different shape than they are in our world,” the former seems to me by far the more likely scenario. Giving too much credence to nonscientific explanations weakens someone’s ability to seek the scientific ones. Scientific knowledge is not a skyscraper built on sand; it is far too useful a tool to abandon lightly.
Eloquently put. My point of order can be summed up like this.
This is a world where creatures have the ability to, with their minds, move enormous celestial bodies and mitigate the effects that those bodies would have on their surroundings. Where they can shift density to physically push and pull water vapor, or indeed make themselves (and constructs) lighter than air without their bodies falling apart. Where, at the most mundane, some can strike with enough force to shatter boulder which, under our laws of physics, would shatter their own body to dust.
We are quite simply looking at a world where the laws of physics do not apply as we know them, and since math (like physics) is based entirely on observation, we can’t take it as a given either. If Celestia says the last digit of Pi is 2, I’ll believe her.
-Lumino
Actually, you’re not even quoting LuminoZero’s position correctly.
You are wrong about irrationality proofs. It is perfectly possible to prove (contingent on all our other mathematical knowledge) that pi is irrational, without having to find an “end.” There are many such proofs.
Here is such a proof for the square root of 2. The square root of 2 is irrational because if it were not, then sqrt(2)=a/b for some integers with no common factors. That is just the definition of “not a rational number.”
So then it would be true that 2=a2 / b2. That is just the definition of square root of a thing: “if you square it, you get the thing,” along with “squaring both sides of a true equation remains true.”
So it would be true that 2b2 = a2. That is just multiplying both sides of an equation by the same thing.
But 2b2 and a2 are both integers. So you would be saying that two integers are equal even though one of them (a2) has an even number of 2s in its factorization (twice the number there are in a) and the other (2b2) has an odd number of 2s (twice the number there are in b, plus one more).
And that is impossible because prime factorizations are unique, and if you disagree with that then you literally disagree with the definition of number, in which case arglebargleflergh.
Lumino, if I understand their posts, is perfectly fine with all of that argument. They are simply pointing out that all of this, is, indeed, contingent on all of our mathematical knowledge. It may be the case that the Zermelo-Fraenkel axioms contain an inconsistency. It is possible that a subtle logical error has lain unnoticed in all of the many proofs of the irrationality of pi for hundreds of years. It is possible that there is a region of space or some observational regime in which the axioms of mathematics turn out to be an unjustifiably inaccurate approximation of physical reality.
Those of us on the other side of the discussion are simply pointing out that this is an excercise in navel-gazing. Given that your brain essentially does trigonometry to determine how to walk (you’re familiar with cosine and sine components of forces from the way they feel on your legs) and breathe (estimating pressure differentials in your lungs), such a world would be so unlivable and unrecognizeable that you might as well postulate that electrons orbit nuclei because the Flying Spaghetti Monster is pushing them around with His Noodly Appendage. Much less could you attempt any engineering in such a world. So we simply find the assertion as valuable as the equally unfalsifiable “brain in a vat” hypothesis – not a lot of good it could ever do you.
I’m glad you think so.
>It’s probably right, I have no doubt that it isn’t, but for anything to be proven, it must also be found to be true in practice as well.
I can’t even express in satisfying terms why or how this statement is not correct.
once again, you miss the point. The math proves that Pi is irrational in theory.
It’s probably right, I have no doubt that it isn’t, but for anything to be proven, it must also be found to be true in practice as well.
I’ll reiterate; The math adds up, the equating’s been done, but that doesn’t make it a fact.
But the worst part of all of this, is that I’m not even trying to argue with you. I agree with what you’ve said, but you have to understand that it doesn’t make either of us any more or less correct. We could be a mile off, or we could be right on the money, but you can’t know which it is until we have a real answer to point to and say ‘Look! I was right!’
You know what…? I really regret even trying…
https://en.wikipedia.org/wiki/Proof_that_CF80_is_irrational
I believe you misunderstand… What we’re all arguing over is really, all theoretical.
Pi is infinite.
No one is questioning that.
The issue that comes up is that, since it IS infinite, the only way to definitely PROVE it is irrational is by finding the end, which, by definition, would make it non-irrational.
Yes, the numbers add up.
Yes, the equations exist.
Yes, the equating’s been done.
But until you actually have the answer, you’ve proven nothing.
So, no, no-one is right, and yes, we should just agree to disagree.
Because honestly, the time I’ve spent typing this out, is wasted time I’ll never get back.
You can’t end an argument about whether pi is irrational by saying “neither side is right, let’s just agree to disagree”. That’s like saying “well we can’t decide whether or not the sun is hot so let’s just agree to disagree”.
I’m sorry, but you can’t get-out-clause irrefutible mathematical constants of reality. Your refusal to acknowledge their existence doesn’t make them not exist.
And now you are a part of the battle against insanity. Welcome!
-Lumino
Ahem
Actually, it’s been proven that pi is irrational. There are really simple logical arguments that demonstrate why pi is irrational.
Also, you can measure pi. It’s a rigidly defined mathematical constant. Quantifying it into numbers is the hard part, but even then only if you want incredible precision the likes of which isn’t really useful on a practical level outside of theoretical mathematics or other extreme scientific fields.
I understand BOTH sides of this argument, and I think you people need to realize: It’s a joke
And either way, neither side is wrong. It’s not always a case of right and wrong. You can’t prove yourself right, and you can’t prove anyone else wrong, because there is no answer. Infinity is infinity, and no amount of arguing is going to prove anything about something you can’t even measure.
So STOP. TRYING.
And, since math and physics are inexorably connected in OUR world, a difference in physics will cause a difference in math.
PONY SCIENCE.
-Lumino
…and yet we can measure the expansion of the universe and the presence of dark matter/dark energy via our current system. But, point, if we ever meet Cthulhu, or God in the flesh, then we may have to come up with a new way of measuring Him. Congrats.
Also, a signature? Really? We believe it’s you.
[Tryin to make a change :-](https://www.reddit.com/r/cringepics/comments/3ep29e/tryin_to_make_a_change/)
Water is wet, fire is hot, grass is green. Gravity is a thing.
I wouldn’t say it’s different on a fundamental level.
I don’t like having to repeat myself.
“Understanding math is kind of a cart before the horse problem. Reality doesn’t work because the numbers say so, the numbers work because that is what happens in reality. Much like all physics was birthed from observation, all math was born from the need to quantify what we observed.
When we observe things that are beyond the scope of our mathematical understanding, what then? It’s a big universe out there, and we may have to come to terms with the fact that our system of mathematics is a made-up system created by observing a highly localized set of rules.”
But yes, you know everything and this ONE system will hold over everything else (to spite the fact that no human designed system has done so). Hell, even the most basic concepts of Newtonian Physics break down if you go small enough. Assuming that everything we take as true will always be true is foolish.
For our current needs and uses, Pi is irrational. That is absolutely true. Doesn’t mean it always will be.
-Lumino