I imagine it would be possible to describe a spiral of sorts, by synchronising transverse frequencies of a propogated wave (unpolarised light, for instance)... but we would have to assume that the oscillations are perfect and unvarying, and ignore the fact that waves/particles are only really a representation of various aspects and effects that aid in our understanding; utilities to aid methodology. Can a vibration in space-time really describe a circle?
I read somewhere that an electron whizzing around a cyclotron could be considered to describe a perfect circle (on a page that also mentions rainbows, oddly enough). Whether this would bear-up under the closest examination is the question; does perfection have a tolerance, and how many planck-lengths variation could be tolerated in that path before it is no longer perfect? I assume a cyclotron has to have astoundingly fine tolerances to ensure any probability of an intentional collision between particles.
On a serious note - that last example strikes me as being closest to a perfect circle! Extrusion into the fourth dimension allows us to envisage a circle of infinite points; a single electron describing a (near perfect, perhaps) circular path, at any given unit of time occupies a 'point' on that path, and as time is arguably of infinite resolution, the number of 'points' describing the circle are functionally infinite!
Electrons (all leptons, in fact) are actually considered to be point-like; they have an effective size of nil. Again, this could be considered a methodological eccentricity (as the true nature of leptons is probably unimaginable; 'waves and particles' are functionally appropriate), but would theoretically confirm your assertion, WS, that 'points' exist in the real world!
Out of all this babble, back-tracking and self-contradiction, the only answer I can realistically conclude is that a perfect circle can exist only if the definition and context are adjusted appropriately. Mathematically it exists and this is not debatable, but beyond that, we get into the realms of theory, variable tolerances, finite numbers, and representative abstracts and devices.
I'm sure this is all relevant to Pi, and that it clears up the original question completely! (lol)
From: The Happy Hunting Grounds... Insane since: Mar 2001
posted 06-02-2009 17:07
It does make sense. A frequency is in the form of a Sine wave, which consists of a 360° pattern. Since I am trained in Radio Frequencies, it is part of the schooling that one gets (and you can measure this with an oscilliscope, btw).
A complete wave is 360°.
What I am wondering, is if the wave is perfect.
WebShaman | The keenest sorrow (and greatest truth) is to recognize ourselves as the sole cause of all our adversities.
- Sophocles
Again though - is a 'wave' actually and literally the reciprocating deviation of a particle from its path, or just the most convenient method of describing and predicting the behaviour of radiation? I would once have thought this a silly question, but the answer is not apparently simple. Is it more accurate to consider waves a property of the particle rather than representative of its path; more a pulsing than a wobbling?
So, if I send my electron whizzing around a cyclotron in an attempt to take a four-dimensional photo of a perfect circle, would I end up with a giant cog (a wiggly-lined circle) or a lightning ring, or simply a near-perfect circle..?*
*...even if the photo is granular and fuzzy, and poorly/imperfectly represents the path I've imaged with my magical camera.
quote: WebShaman said:
It does make sense. A frequency is in the form of a Sine wave, which consists of a 360° pattern. Since I am trained in Radio Frequencies, it is part of the schooling that one gets (and you can measure this with an oscilliscope, btw).A complete wave is 360°.What I am wondering, is if the wave is perfect.
..Aaah u r referring to a 2D representation of a Sine wave.....i was picturing a 3D wave...ok if u represent the sine wave on paper..why do u decide to start from a certain point say for instance Zero to do your measurements...isnt this just the half of already existing sinusoidal pattern.......so where does it start or end
quote:I was asking if a wave is perfect, WH. I myself have no idea.
Many surfers seek what you ask, WebShaman.
The only information I could find about 360° waves is that it's a hairstyle I probably couldn't pull off (nor would I wish to).
I would have to fall back on my assertion that nothing is perfect. Even if a wave were, I'm not sure how one would go about deriving a perfect circle from it that wasn't merely an interpretation.
I'll also have to admit that I myself have no idea.
quote: White Hawk said:
I would have to fall back on my assertion that nothing is perfect. Even if a wave were, I'm not sure how one would go about deriving a perfect circle from it that wasn't merely an interpretation.
....if only I cld change the subject of this thread to Nothing is Absolute...and have anyone try to prove otherwise
From: Cranleigh, Surrey, England Insane since: May 2003
posted 06-08-2009 18:39
Just my two cents:
1) One is the identity element for the integers under multiplication; this is really its fundamental property that we are considering here, and this is how it should be considered.
2) Pi has a couple of very interesting features: firstly, while its digits never 'end', the "don't end" in a very specific way: they never repeat, and thus pi is _irrational_, but also, it is not expressible as the solution of _any_ finite polynomial equation, and this is _transcendental_. Proving either of these last two facts, however, provides a mild challenge (undergrad maths has only shown me its irrationality, not even its transcendentality yet)
Wrayal
[edit] Also, I would contend, and I hope not too contentiously, that proofs are, essentially by definition, perfect. Given a rigorous set of axioms together with a derivation, they are perfect in a way I've found unique to Maths [/edit]
quote: wrayal said:
Also, I would contend, and I hope not too contentiously, that proofs are, essentially by definition, perfect. Given a rigorous set of axioms together with a derivation, they are perfect in a way I've found unique to Maths...
quote:...they are perfect in a way I've found unique to Maths.
Precisely; 'unique to maths', as nothing real is perfect.
Actually, I have trouble with the whole 'never repeat' thing. In order to make any sense of that, I would have to assume that a given sample size never repeats (say, no 30 digits ever repeat). Surely, once the sample size is small enough (say, two digits) you would find that Pi repeats quite frequently!
Even larger sample sizes must eventually repeat. If Pi is an endless string of numbers, there must be a point in the string that eventually repeats (finite combinations, infinite string). I suppose the meaning is that there is no looping or regular repetition.
Absolute is impossible, unless in retrospect; "the atomic bomb ABSOLUTELY exploded - we saw it, measured it, and got anice dose of radiation (that we also measured) while we burned another hole in the ozone layer".
Absolutely nothing cannot exist - ask a chemist what's in a complete vacuum, and he'll guess 'nothing' (typically, extremely rarified gasses, probably, but for the sake of argument, let's say that it's absolutely nothing from a chemist's point of view).
Ask a physicist, and (s)he'll tell you that a vacuum is absolutely teeming with matter/antimatter reactions, energy fields, countless passing neutrinos, etc, etc.
From: Cranleigh, Surrey, England Insane since: May 2003
posted 06-17-2009 15:59
binary: I daren't go into this when I don't know the material thoroughly, but go and look up a textbook on "set theory and logic" - this will demonstrate a *completely* rigorous and axiomatic approach.
White Hawk: yes, in sloppy use of the word 'repeat', you are indeed correct. But to Mathematicians it has quite a precise meaning: http://en.wikipedia.org/wiki/Recurring_decimal - one might also describe the numerical expansion as 'periodic' after some point. However, we shouldn't get too bogged down in the numerical expressions of numbers - they're really quite meaningless.
posted 06-02-2009 13:56
...so where does it start or end
