Infinity is a Floundering Human Notion

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 contain.

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 hand.

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 infinite.

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

CW




[edit on 17-7-2009 by constantwonder]

reply to post by constantwonder


S & F Amazing Post.

I've held this very belief for a long time. I also believe that at any point in time, the universe and its contents could very well be assigned finite values. Human math is only correct if it is put into the right context. If there is something you're not accounting for, then your equation will turn out correct relative to the context you put it in but that may not accurately reflect the reality of the situation. The universe cannot be wrong or uncertain about its contents, only we can be wrong and uncertain about its contents.

Not only did you take on the infinitely small aspect, but you also took on the infinitely large number aspect. Points are indeed subjective as I myself tried to point out in a thread recently (among other things). At a certain point, there will be a number that has no use, and by that I mean there is a number that has no applicable real world value both on a macroscopic and microscopic scale.

Lets assume the smallest possible divisible factor is a unit of space-time. 1 (even .01) + the number of space time units doesn't have an applicable value as the number of space time units is the largest applicable value in the universe. This number can change over time and it has infinite (meaning more or less undefineable) potential but at no one point is the value undefineable.

I believe you will find the answer is within infinite Fractle based quantum mathematics and your pineal gland as active transceiver for your soul/spirit.

The Universe would appear to be made entirely of waves (Fractle based) and our brain a receiver to convert these waves into our surrounding reality, the same way a computer converts binary data (waves) into on-screen graffics (virtual reality).

When a persons soul/spirit is created (at 49 days after conception) the Pineal gland (third eye) is activated. At death a similar re-activation is recorded and the Pineal is the device used to transfer our soul/spirit into the next realm.

The Universe is an infinite 3-D Hologram based on Fractle quantum mathematics and our brains are 3-D Holographic interferometers, designed to decode the waves and 'create' what we 'see/hear/taste/touch/smell' around us.

Life as we know it is governed by time, a known factor that travels at 186 thousand miles per second. When the soul/spirit is unlocked by death or '___' the time we know disappears and an infinite Fractle based realm is apparent.

Utterly beautiful, truly infinite and completely timeless.

Regards.

reply to post by constantwonder


S&F

Excellent post. Very thought inspiring. I have also spent a lot of time pondering the concept of infinity, and it can really rack your brain.

I'd have to say that your thoughts make a lot of sense...

Originally posted by constantwonder

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.

Infinity denotes uncertainty, it isn't a real number in mathematics. Our universe is uncertain, we don't know how large it extends for the further things are, the more red-shifted they are, until they are too much red-shifted that they are no longer detected by our best instruments. There maybe much farther objects out there we simply can no longer see...

So the universe size is pretty much unknown. Infinity isn't certain so for now, it can be used to describe things that are uncertain as well.

I do not think that there is a "smallest piece" of space-time made by nature. That piece, the planck length unit, is made by us because we can't make the math work otherwise. It was introduced into physics because there was an infinity found in the vacuum. Through this they invented the renormalization so some of the math could work out. We should rather try to understand the dynamics of the universe than to falsley simplify it to calculate.

Nassim Haramein make some very good points on this subject in his lectures, I suggest you check them out.

reply to post by constantwonder

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.

Your post gets a star for this. I've flagged the thread too, because the general point you are making is both very important and insufficiently recognized by the general public.

You are quite right, of course. There are no infinite quantities in nature.

Reality is digital.

You seem to be using the common concept of "infinity" and not the definition that's used in math and space sciences:
en.wikipedia.org...

You seem to be describing Dedekind Infinite sets (formalized in math in the 1800's): en.wikipedia.org...

That's just one of the approaches to infinity used in math. I personally like the cardinals and ordinals and hyperreal numbers. The set theory is bizarre, too (as well as the alephs)... multiplying infinties and so forth.

They have practical real world applications and are shown to work well. You might enjoy reading further on this idea of Dedekind's that you've thought about.

Originally posted by Astyanax
There are no infinite quantities in nature.

There is no proof of this, simply because, it is fundamentally unprovable.

It would probably be more accurate to say:

Human beings cannot observe infinite quantities.

reply to post by spartacus mills

Nature is what human beings can observe, directly or inferentially.

If human beings cannot observe it, it doesn't exist.

Originally posted by Astyanax
If human beings cannot observe it, it doesn't exist.

Again, not provable.

We have five forms of sensory perception. Who's to say there aren't a myriad of other types of sensory perception that we don't possess?

Take for example, some other creature in nature that doesn't have auditory perception. From their point of view, sound doesn't exist. Does this mean sound waves themselves don't exist? Evidently not, because we are able to perceive them.

To imagine that the five forms of sensory perception that we have been blessed with are the be-all and end-all of what exists objectively in the universe is incredibly naive.

reply to post by spartacus mills

I said 'directly or inferentially.

We have more and better senses than any animal. We can see gamma rays and radio waves. We can smell better than a bloodhound. Our machines confer these sense upon us.

We can, further, infer what we cannot sense, such as the presence of dark energy in the cosmos.

Beyond what we can perceive directly, through the media of technology and by inference, nothing exists. This is un effet, which is French for 'a fact'. You will take the point of the relationship with the English word 'effect', I'm sure.

Originally posted by Astyanax
I said 'directly or inferentially.

Whether directly or inferentially, it doesn't matter. Any technology we create to observe phenomena in the universe will always be a derivation of, and limited by, the five forms of sensory perception which we possess. Our sensory perception is the only thing we can ever use to interpret whatever data we are presented with. If there is a kind of data that is completely incompatible with any of our five senses, then it would seem to us that it does not exist. But it can only ever be an assumption that it doesn't exist, and not proved. This is, as you would say, un effet.

We have more and better senses than any animal. We can see gamma rays and radio waves. We can smell better than a bloodhound. Our machines confer these sense upon us.

This is irrelevant and missing the point. I'm talking about a potential form of sensory perception that is completely and wholly different from that which we possess, not just one that is 'better' than another. Smell is smell, regardless of whether one is more sensitive than the other, they are of the same kind.

Originally posted by constantwonder

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.

[edit on 17-7-2009 by constantwonder]

Not so. There are exactly as many points in the smaller circle as their are in the larger circle. If you assume that you are using an infinitely precise measurement system for your points (and you have to, else you don't get an infinite set of points), then there will be exactly the same number of points in both circles.

What you're describing is area which is a spacial measurement. The number of points in any given coordinate system (in this case the coordinates system is bound by a circle) is a function of the precision of the measurements used to define the points e.g. 1 v. 1.000000000.