There are two other possibilities that can exist... what has been termed "counterspace", negative space, and its temporal counterpart.
I think Larson's "primary magnitudes are absolute" postulate may need some clarification here, as the "magnitude" of -1 is UNITY +1. The polarity associated with it can be considered more of a direction than a magnitude. In counterspace theory, the negative spatial realm is associated with the involutive direction, rather than the evolutive one, particularly when dealing with scalar motion. "-1" is therefore "1" in an involutive aspect, where on the +Real axis, +1 is "1" in an evolutive aspect.
Looks like the "real" crossing of a logarithmic spiral, in polar terms:
This kind of curve shows up all over in living systems... except it is the full spiral, not just the intersection with the real/spatial axis. So you may be right--it may be the geometry producing the natural log, which is represented by the mathematical concept of integration.
It also seems to support the idea that PI is the "natural unit of rotation."
bperet
Sat, 03/28/2009 - 14:59
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Counter Sectors
There are two other possibilities that can exist... what has been termed "counterspace", negative space, and its temporal counterpart.
I think Larson's "primary magnitudes are absolute" postulate may need some clarification here, as the "magnitude" of -1 is UNITY +1. The polarity associated with it can be considered more of a direction than a magnitude. In counterspace theory, the negative spatial realm is associated with the involutive direction, rather than the evolutive one, particularly when dealing with scalar motion. "-1" is therefore "1" in an involutive aspect, where on the +Real axis, +1 is "1" in an evolutive aspect.
Gopi
Mon, 04/06/2009 - 10:32
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Natural Log
Might find this useful:
In lineland, the effect of the imaginary axes might change the magnitude in space via the natural log, in this recursive fashion...
Series = 1 - 1/2 + 1/3 - 1/4 + 1/5...
= ln (2)
So that is another origin of the natural log, without bothering about the integration aspect.
BE the change that you want to see in the world.
bperet
Sun, 04/12/2009 - 16:52
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Logarithmic Spiral
Looks like the "real" crossing of a logarithmic spiral, in polar terms:
This kind of curve shows up all over in living systems... except it is the full spiral, not just the intersection with the real/spatial axis. So you may be right--it may be the geometry producing the natural log, which is represented by the mathematical concept of integration.
It also seems to support the idea that PI is the "natural unit of rotation."