See subject. Some GQ poster–*you know who you are…*suggested it to me, indirectly.
Excuse me?
Well, yes. But I’m not asking if TriPolar is oxymoronic, but about the possible definitions of “polarity.” I’ve seen similar non-intuitive reinterpretations in mathematics of heretofore established usage.
It took me six months to get your username.
I’d think this might also depend on what you mean.
If it’s a charge-like question, the number of fundamental charges matters I think. In electricity and magnetism we have two charges. You can have an isolated electric charge and its electric field is a monopole. In magnetism (in the absence of monopoles) the dipole moment is the first term in the expansion of the magnetic field. I don’t know, but for the color charge with three basic colors, a tripole moment might be the first term in the expansion.
But I think you might be asking a question more like a rotating sphere has an axis of rotation with two poles. Is there any > 3 dimensional space in which you can have three poles for a rotating hypershpere? I’d think not. I’d think you could perhaps in a high enough dimensional space have more than one axis of simultaneous rotation, but I’d think poles would have to come in pairs. But I sure can’t visualize this at all. Nor can I do the math.
Maybe I’m being whooshed here but aren’t three poles the usual number to describe a location in normal three dimensional space? The old X, Y, and Z axes?
Yes, you have to define what you mean by ‘tripolar’, either:
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three poles, each of which has two opposing ends, like the x,y,z Cartesian coordinate system, or
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three opposing ‘states’ that a singular entity can possess, e.g., if there were a north, south, and hypothetical ‘west’ charge that an electron can have. Or like quarks can be up, down, or charmed.
Yes, #1 above. I should have been clearer by yards. And even “dimensional” is wrong, I think.
“Tri” states are interesting and all, but I was kind of feeling out a geometrical system in which “2”(==polar–>common, 3-D, two points by definitin) can be “3” (“polar”–>posited system).
A geometry for a vector makes sense for what I’ve called “3-states” must be simple: Cartesian space come to kind. This I understand, think, but I’m guessing needs a definitive proof, which probably has been out there since I don’t know when.
Perhaps I’m trying to square a circle. Three:two just isn’t going to wind up as 2:1, as millennia of music theorists have discovered when trying to get back to that multiple: an octave (latest definition) by keeping to Pythagorus’s demand for simple ratios such as 3:2 for the “mid point” of the bipolar pole defined as 2:1 – a pain if you want a closed musical scale across the board.
(To add for those inclined, in music theory the distance between the first occurrence of the “closest” you can get to a multiple of 2:1 is 3:2^12; the “distance,” known as the Pythagorean comma–which is hearable. That point of math being hearable is both BTW and of the essence, depending on who is thinking. Which is why the word “music” to the Greeks and continuing as part of the quadrivium does not mean “music” like Beethoven or the Beatles.
But all that is arithmetic. Excursus ended.)
Actually, I have done Pythagoran music theory, as a whole, a mis-service, trying to address the issue at hand in a simpler way. The 2:1 has been considered over times as a unison, 1:1, but not always–in which case the simpler way is that the two ends of the (bi) pole are 2:1 and 3:2. But here stuff gets hard, as to the implications. Let alone with how that Pythagorean comma obtains in different definitions and abstractions of tonal space.
I would say that tripolar referred to the spherical co-ordinate system in 4-space [r,phi[sub]1[/sub],phi[sub]2[/sub],phi[sub]3[/sub]], where the three unitary poles are othogonal from the origin to the planes defined by
[1,0,phi[sub]2[/sub],phi[sub]3[/sub]]
[1,phi[sub]1[/sub],0,phi[sub]3[/sub]]
[1,phi[sub]1[/sub],phi[sub]2[/sub],0]
Yes! Swish!
I don’t understand your comment. Perhaps someone else could do it justice. Perhaps it is as si_blakely said, with “rotation” being a mapping image.