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| Joined: | Mon Nov 21st, 2005 |
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Anyone?
Nothing is something. Nothing is proven to be something when there is more than nothing.
When there is more than nothing the other thing takes up space, or displaces what was once nothing.
That is not easy to understand, but it works in my thinking, and that working now applies to the problem worked on in the earlier math problems concerning volume and surface area; comparing relative shapes.
So...I started thinking about surface area as a fictional skin, or a dimension of no substance, not thickness, this surface area non existence.
Then I imagined that single object that becomes the one thing that proves that nothing is no longer the one thing.
A = a time when there is nothing = there is no thing, and there is no things.
B = a time when there is now two things, = nothing is displaced in time and place with a thing, a shape, and the shape of the shape is not required in the following thinking.
The new thing that displaces nothing is a volume that can be imagined as a shape, such as a round sphere, or a square, or octahedron.
If the volume doubles and the new area displaced exists as an equal expansion of the original shape, expanding as another layer of uniform skin, rapping around the original shape, making the shape larger, then it is obvious that the shape is the same shape, and the volume is double, but the displacement of space is not shape that is twice the distance from one surface to the other extreme end of the surface, in the case of the sphere that measure is diameter.
In other words, double the volume is not double the diameter.
What happens when the volume is double again: the diameter grows even less compared to the first time the volume was doubled.
Suppose the time required to double the volume is one second (time according to our solar system) and each second the volume doubles, but each doubling of volume the diameter grows less each time.
How much time goes by in order to reach a doubling of the diameter?
If the same math problem is applied to a square, double the volume, rap the volume around the original square, measure the extreme end to end measure (corner to corner, or width, or height) and doubling of volume occurs each second, and then how much time is required to double the measure of length which is in that way a measure of displacement?
The first object is x amount of displacement. Doubling the first object displaces the same volume.
If it is a circle, and two circles cannot exist inside each other, then the displacement of the space that was once nothing (or space) is now occupied by the second circle, where once there was nothing, then there is one circle, then there is two circles.
If the second circle is not a skin around the first circle, then the second circle takes up an amount of room, or space, or displacement that is very large, and very large fast, compared to squares, because squares can fit next to each other precisely, leaving minimal room between the boarders of one square and another square.
Which shape reaches double the length faster when doubling the volume (as skin) at the same rate?
1.
Circle
2.
Square
3.
Octahedron
What happens to the rate of growth when doubling volume at a constant rate of time?
If, for example a circle doubles volume at the rate of one per second, and if the first diameter is 1, the second diameter is less than 1 one second later.
Diameter is 1.
Volume doubles in one second.
The diameter after one second is less than 1.
That is obvious.
Call the new diameter measure 1/x, which is less than 1, or 1 - x, or x < 1.
Volume doubles again in one second.
The diameter is less than 1/x, so there is now a rate of change in diameter, or a ratio of change between volume doubling and diameter increases decreasing.
What that looks like to me, an obvious observation to me, is that the increase in diameter reaches a very slow, and slowing, rate of increase compared to volume increases.
That looks like a rapid acceleration rate of acceleration whereby the rate of increase in diameter reaches nothing, or practically nothing, fast.
Diameter is already in decline after the first increase in volume less than 1.
Diameter is 1, a second later, volume doubles, but diameter does not double: diameter increases less than 1. Soon it will be such a small increase as to be imperceptible without eons of time going by?
How about the reverse?
Start with 1 volume.
The shape is a sphere.
Volume is reduced by half in one second.
Diameter decreases by how much?
Call the diameter reduction a measure of 1, and it will not cut the diameter in half when the volume is cut in half, but in the first second the measure of cutting of diameter is 1.
Now a second goes by and the volume is cut in half again.
The diameter is cut by a more than 1?
The original viewpoint was a problem I had with the concept of surface area, so the competitive solution to that problem was to create a layer of skin which had a thickness dimension to it.
If it takes eons for a sphere to grow at a rate of volume doubling, because the rate of growth of the diameter decreases to an ever smaller amount, then does the opposite mean that the increase in diameter becomes an ever larger amount going the other way?
No, the time factor at the ends of the scale are not the same.
Starting small going big is once second and eventually the rate of change in diameter is very small relative to increase in volume.
Starting big going small the rate of change is insignificant in one second, imperceptible, until the rate of change begins to be visible?