Posted on 12/03/2005 10:24:55 PM PST by sourcery
Doesn't the cube root of -1 = -1?
x=(-1+Sqrt(-3))/2 or (-1-Sqrt(-3))/2
These are the others cube roots. Multiplying by 3 gives the cube roots of (-27).
Does sqrt(-1) have two roots?
Ahhh, thanks!
"RA" uses them extensively on his work, IIRC.
in many cases, "it just can't" is a factual assessment, but an unsatisfying one.
The mathematical form of quaternions is very powerful for describing rotation. They were replaced by tensors in most physical applications that involve translation such as earthquake modelling, but they have their place. Translation could be viewed as rotation where the radius of rotation is infinitely long.
we perceive that we observe.
I agree that the human mind exists not in the "real" world but in its own cognitive synthesis, but overapplying this leads to Solipsism - a useless form of mental masturbation even in philosophy and mysticism.
assuming a non-solipsistic reality, real facts have real patterns which we conscious beings observe, recognise, and describe. Cases in point: Diurnal cycles, lunbar progression, tides, seasonal cycles, the surprisingly common incidence of close approximation of Fibonacci series and ratio in organic structures (including those long dead and fossilized before the first proto-primate flexed his thumb), etc...
the patterns and cycles existed and continue to exist independent from our observations, recognitions, and descriptions of them.
inquiry: does x**3 = x^3?
"lunbar"?
need... more... coffee
We DO need the cube root of -1. It's called "-1".
First nobody noticed mathematical rabbits, then they are everywhere. Need a set of observations form a perfect pattern? It appears not, since there is no perfection anywhere except in the pattern itself. Nature does not fit the patterns exactly. For example from astronomical things, what is the cause of the precession of the equinox? Wobble? What kind of pattern is that?
I thought we were discussing the cube root of negative one.
If this is so, wouldn't it be "x**3 + 1 = 0"?
um... who said a pattern has to be perfectly regular?
That's some convenient pet cat which only has 1026 atoms.
That's not a cat then, that's a thousand moles.
That is true enough, but a factual assessment of "it just can't" is always based on some rationale besides "it just can't".. :)
in any question-answer confrontation, if the querent asks "why?" enough times, the respondent will eventually be reduced to saying "because!"
there may or may not be ultimate answers in this sidereal universe - but it is unlikely that the human mind could encompas them or express them.
Yes, but when you reach the stage of "because!" the answer is not really "because!"; the real answer is: "because no one has ever observed otherwise and no one can think of any plausible way that it could be otherwise!"
They've been back for a few decades in guidance systems.
Thank you for posting this interesting article. I am fascinated by quantum physics. I always think the key to understanding it is just out of my range of vision, like an out of focus picture becoming clearer and clearer, can almost see it and then wham it's gone. I think it would be the greatest job in the world to study it! Probably would never go home.
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