Infinity
- Thread starter Lithp
- Start date
Exactly, Gilbert. My subjective thought is applicable only to me, to nobody else.
My favourite math joke!
Q: What is the first derivative of a cow?
A: Prime rib!
Q: How long has Woden lived?
A: Forever
Contradiction: He'd have had to wait forever for today!
Q: What is the first derivative of a cow?
A: Prime rib!
Q: How long has Woden lived?
A: Forever
Contradiction: He'd have had to wait forever for today!
Objective reality is a manifestation of subjective thought. Reality is exactly what you believe it to be. Thus if you think the world is a dangerous and evil place, you will find no end of evidence to verify your belief. If you think the world is a wonderful place, you will have mostly wonderful experiences.
Hmmm. If you believe the rock I pick up is not hard, but as soft as a ball of cotton, would you then think in reality I couldn't bash a window to pieces?
Cliffy, there are two kinds of realities. What you are talking of are metaphysical realities. Thus is the world a good place or a bad place, is contraception good or bad, is Keynesian economics more realistic or is supply side economics, these are metaphysical realties. And here you are right; you will find evidence depending upon your point of view. Whatever your preconceived point of view, you will find evidence in support of that.
However, then there are physical realities. They do not depend upon our subjective thoughts (not in day to day world anyway, they do when one approaches relativistic conditions, when one approaches the speed of light). These are absolute realties, and a person denies them at his own peril.
Thus if you deny the reality of gravitation, and walk off a ten storey building, you are the only one who will get hurt (well, unless you land on somebody else). Or as Gilbert said, you may think a rock is as soft as cotton, but it still will smash a window to pieces.
So it is important to distinguish between metaphysical and physical realities.
However, then there are physical realities. They do not depend upon our subjective thoughts (not in day to day world anyway, they do when one approaches relativistic conditions, when one approaches the speed of light). These are absolute realties, and a person denies them at his own peril.
Thus if you deny the reality of gravitation, and walk off a ten storey building, you are the only one who will get hurt (well, unless you land on somebody else). Or as Gilbert said, you may think a rock is as soft as cotton, but it still will smash a window to pieces.
So it is important to distinguish between metaphysical and physical realities.
Imaginary numbers (or rather, complex numbers) form a higher order of infinity. Infinity of integers is Aleph Null, infinity of real numbers is Aleph One, and I think infinity of complex numbers is Aleph Two.
Is that right, Dexter? You seem to know more about this (you appear more enthusiastic anyway).
√-1 is much more complex than any integer.
I'm not really sure off hand, I'd have to look it up (and a quick look at Wikipedia doesn't resolve it), but I don't think so. The infinity of complex numbers is effectively the number of points on a two dimensional surface, which is Aleph One. Aleph One is also the number of points in a three dimensional volume, and possibly the number of points in a space of any finite dimension. I don't think anyone's ever demonstrated anything physically equivalent to aleph numbers higher than one.
And for Ariadne, the square root of -1, usually called i or j in most notations, is not an integer. One of the defining features of integers is that you can count things with them, which obviously you can't do with i. It's a most peculiar number in many respects, shows up all over the place in physics and engineering where you wouldn't expect it to have any reality. You can't, for instance, mathematically analyze alternating electric currents properly, or waves of any sort really, without it, because there's a deep connection among it, the base of natural logarithms e, and the sine and cosine functions in Leonhard Euler's elegant equation:
e^ix = Cos(x) + iSin(x)
I have now looked it up. I was partly right. Better than being partly wrong. :smile:
Aleph One numbers all the points in all spaces, up to an infinite space of Aleph Null dimensions. Aleph Two might be the number of points in an infinite space of Aleph One dimensions, nobody's been able to demonstrate that yet.