in recent times of thought i have come up with the notion that infinty and infinitely larger sets are nothing more than a flawed theorem.
We start with a circle. Within this circle there is an endless number of points we could pick out. Then if we draw another larger circle around the
first we find another endless set of points larger than the first.
But how can this be you say. . . How can there be and endless number larger than an endless number. . . the answer is there is not.
Before i start my explanation please note that this is conjecture based on conjecture
Modern quantum theory has taken quite well to the notion that there is an indivisble unit of space-time. maybe smaller than the planck length maybe
not. The point is however that there is this unit. If you could zoom in close enough you would see space-time become grainy.
Lets just use the planck length as our unit of measure.
inside the circles we created earlier theres is a finite number of planck length 1 dimensional objects that both the smaller and larger circles can
While the larger circle contains a larger number both are very finite.
The problem people come across with infinity is that they use the point as their unit of measure. This is a flawed concept. Of course there is no
limit to the number of points
that any given circle can contain. To understand this allow me to define the point.
in geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of
neither volume, area, length, nor any other higher dimensional analogue. Thus, a point is a 0-dimensional object.
An imaginary concept like a point can not be used to measure the extent of the space inside a real object like our circle. So when we replace the
point with the planck length or the length we may discover to be the smallest unit of space time we can dismiss the notion of infinitim out of
Now i know people will say oh but space is infinite and there is an infinite number of places for an actuall planck scale object to exsist. This
notion is incorrect if we assume space has an indivisible unit.
This idea comes from the notion that if space-time is infact grainy that it is built up from one grain to a pile of grains to a mountain to the entire
bulk space any given universe occupies due to quantum fluctuations happening in succesion (over time).
If this is the case then even the "bulk-space" (hyperspace if you like Dr. Kaku) has a finite volume. Inside a finite volume there is a finite
number of this smallest unit. So now the entire universe is no longer infinite.
So from here peole will say well then the growth of the universe is infinite and there is no limit
to its growth so its growth is infinite.
Not so fast. If space time is grainy and built up by quantum fluctuations then both its growth rate and size become measurable and no longer
Finally we come to the argument that whatever the "bulk" is growing into must be infinite. The solution to this is that we arent expanding into
anything. Its a very difficult concept but one that imo must be true. There is nothing beyond the bulk all that exsists is the bulk. There is no
beyond space-time. While space time may grow larger it is not growing into a larger volume outside itself.
So if we throw out the philisophical nonsence about but you can always divide further (which in fact you can but its meaningless because reality ends
at the indivisble unit of space-time) we find that a more reasonable scientific line of thought that says infinity is just an excercisein futility.
The fact that you can divide endlessly any unit of human measurement shows not proof of infinity but shows only proof that number theory isn't
perfect. The universe is perfect and until we can find the correct way to describe it the maths will always have little ghosts like infinity,
endless sets (continuum hypothesis), and incompleteness. Ifinty doesnt show anything other than a lack of human understanding.
hope that wasn't to confusing
[edit on 17-7-2009 by constantwonder]