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1234567890

360 Posts

Posted - 25 Feb 2004 :  20:33:38  Show Profile  Reply with Quote
quote:
Originally posted by rousejohnny

quote:
Originally posted by jrich

1234567890,

Does your finite divisible universe also require that matter have some smallest size? Is there a smallest particle?


JR



I have this question too, if there is a smallest particle the divisibility would have to be in interger multiples, or?

I like Jan's wave idea and thinking in terms of plasma. There would be an infinity of divisibility in the plasma (an aether) when homogenious and without dynamics. But, in order for dynamics to occur there would have to be defined multiples for interaction and complexity. There plasma would have to have or acheive differential charge as well in order for dynamics to occur.

So maybe both assumptions are correct, depending on the context of the debate.




Well, let's assume for a minute that the smallest particles are the electrons and positrons. If they are the smallest, then you can't divide them any smaller. But if you were to arrange them in space,
the resulting structures would be a composition of individual smallest particles and not fractional pieces of it.

Of course if you started out with the assumption that something is infinitely divisible, then it is. This however is not deducing infinite divisibility.

And as you, I think both assumptions are valid, but one excludes the other.

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jrich

USA
287 Posts

Posted - 25 Feb 2004 :  20:56:24  Show Profile  Reply with Quote
quote:
Originally posted by 1234567890
Yes there is since we assumed there to be. I really can't see how one can deduce through logic whether the universe is infinitely divisible or not. Those seem to be two mutually exclusive axioms.

You start with any finite quantity, how do you divide it into halves unless you assumed it to be divisible first? Likewise, if you start with the assumption that 1 is the smallest non-zero quantity, how can you divide it into halves without contradicting your starting assumption? What is 1/1?

You are correct that one cannot apply operations which contradict the assumption as that would be a form of logical fallacy. However, this does not mean that one cannot show that the assumption leads to logical or empirical contradictions. I provided such a proof in the previous topic on this subject last week. That was why I asked the question, to see if this ground had already been covered.

If assuming both finite or infinite divisibility in turn leads to contradictions, then it is a matter of personal preference since there is no way to scientifically distinguish them. However, when one assumption leads to contradictions and the other does not, then no matter our personal prejudices we must be accept the correctness of the logically consistent one. If one does not accept this then one is not practicing scientific, critical judgement and will not be taken seriously by most of the participants in this MB.


JR
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1234567890

360 Posts

Posted - 25 Feb 2004 :  21:12:15  Show Profile  Reply with Quote
quote:
Originally posted by Jan

Skarp,

quote:
I don't see the need for a medium


I stumbled a little bit over the wave issue and it just didn't come out right. What I wanted to say is that waves without a medium do not make much sense to me. I still see a wave as the collective motion of objects. But if everything is wave-like, then this would imply that there is no such thing as a smallest particle. For let the smallest particle be wave-like, then this particle must be the collective motion of other particles. Hence, a contradiction with the smallest particle assumption. There can be no smallest particle.



An ocean wave, overly simplified, is the collective motion of H20 molecules, which themselves are just an arrangement of units of "particles" we call protons, electrons and neutrons. So here we have a wave that is made up of indivisible units, if we assumed for a minute that the electron, proton and neutron are indivisible units. I mean we can actually "count" the number of these units that comprises a particular ocean wave frozen in space and time.

Does wave motion lead to infinite divsibility then? Only if you first defined a wave as an indivisibile "particle" then tried to show that by another definition of a wave, that waves are the collective motion of many particles, waves are not indivisible. I think all you have shown using this method is that both definitions have mutually exclusive meanings. It is not a logical deduction.

Well, perhaps you have also shown that the idea of matter-waves is quite vague in QM.






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1234567890

360 Posts

Posted - 25 Feb 2004 :  21:57:57  Show Profile  Reply with Quote
quote:
Originally posted by jrich

quote:
Originally posted by 1234567890
Yes there is since we assumed there to be. I really can't see how one can deduce through logic whether the universe is infinitely divisible or not. Those seem to be two mutually exclusive axioms.

You start with any finite quantity, how do you divide it into halves unless you assumed it to be divisible first? Likewise, if you start with the assumption that 1 is the smallest non-zero quantity, how can you divide it into halves without contradicting your starting assumption? What is 1/1?

You are correct that one cannot apply operations which contradict the assumption as that would be a form of logical fallacy. However, this does not mean that one cannot show that the assumption leads to logical or empirical contradictions. I provided such a proof in the previous topic on this subject last week. That was why I asked the question, to see if this ground had already been covered.

If assuming both finite or infinite divisibility in turn leads to contradictions, then it is a matter of personal preference since there is no way to scientifically distinguish them. However, when one assumption leads to contradictions and the other does not, then no matter our personal prejudices we must be accept the correctness of the logically consistent one. If one does not accept this then one is not practicing scientific, critical judgement and will not be taken seriously by most of the participants in this MB.


JR



I assume you are referring to your argument regarding to touching spheres where the intermediate space directly above and below the
point of contact would be smaller than the diameter of each individual sphere? One obvious answer would be that at that distance, there are no spheres. Again, all the arguments leading to infinite divisibility appear to arise from a particular geometry , which carries with it a set of assumptions. If you start out with different assumptions, you get different results. And you can't say one is self contradictory unless you interpreted it using a different set of assumptions. It's like you can't say the shortest distance between two points is not a straight line leads to contradiction unless you used Euclidean geometry.



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jrich

USA
287 Posts

Posted - 25 Feb 2004 :  22:25:16  Show Profile  Reply with Quote
quote:
Originally posted by 1234567890

quote:
Originally posted by jrich
You are correct that one cannot apply operations which contradict the assumption as that would be a form of logical fallacy. However, this does not mean that one cannot show that the assumption leads to logical or empirical contradictions. I provided such a proof in the previous topic on this subject last week. That was why I asked the question, to see if this ground had already been covered.

If assuming both finite or infinite divisibility in turn leads to contradictions, then it is a matter of personal preference since there is no way to scientifically distinguish them. However, when one assumption leads to contradictions and the other does not, then no matter our personal prejudices we must be accept the correctness of the logically consistent one. If one does not accept this then one is not practicing scientific, critical judgement and will not be taken seriously by most of the participants in this MB.


JR



I assume you are referring to your argument regarding to touching spheres where the intermediate space directly above and below the
point of contact would be smaller than the diameter of each individual sphere? One obvious answer would be that at that distance, there are no spheres.

Then give me another example of a particle geometry that does not violate the assumptions of smallest object and smallest distance?
quote:
Again, all the arguments leading to infinite divisibility appear to arise from a particular geometry , which carries with it a set of assumptions. If you start out with different assumptions, you get different results. And you can't say one is self contradictory unless you interpreted it using a different set of assumptions. It's like you can't say the shortest distance between two points is not a straight line leads to contradiction unless you used Euclidean geometry.

One must be very careful not to introduce hidden assumptions. However, assumptions impose their own requirements and necessarily define constraints on the problem. These requirements and limits are not assumptions in themselves, but are part of the original assumptions. It makes no sense to talk of smallest anything except in the context of some goemetry. Every geometry will have the equivalent of "smallest", so this can be generalized to any geometry.


JR

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1234567890

360 Posts

Posted - 26 Feb 2004 :  05:40:53  Show Profile  Reply with Quote
quote:
Originally posted by jrich

Then give me another example of a particle geometry that does not violate the assumptions of smallest object and smallest distance?
JR



Well, Astro has been trying to figure this out so read his examples.
But take a look at this photo


There are obviously smaller distances in between the "spheres" in the photo than the diameter of the spheres themselves, but does this fact change the size of the pixels on your monitor, which represents the smallest area resolvable by your monitor? No, it just means that the spheres are larger than the smallest pixels possible. Does the fact that the spheres in the photo exist lead to the "logical deduction" that there are an infinite number of pixels on your monitor or do their existence make impossible the existence of minimum sized pixels on your monitor?

I don't think so or you wouldn't be seeing the picture on your monitor. Minimum physical quantity is a property of existence,
the fact that we exist and take up a certain amount of space proves this. It is not a mathematical deduction that can be shown to be contradictory using some set of axioms.

And I'm sure it is much more a function of the properties of space and matter and energy of motion than it is a function of the supposed existence of continuous functions in calculus.

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Jan

Netherlands
287 Posts

Posted - 26 Feb 2004 :  05:41:28  Show Profile  Reply with Quote
123,
quote:
Does wave motion lead to infinite divsibility then? Only if you first defined a wave as an indivisibile "particle" then tried to show that by another definition of a wave, that waves are the collective motion of many particles, waves are not indivisible. I think all you have shown using this method is that both definitions have mutually exclusive meanings. It is not a logical deduction.



It is clear we first must come to an agreement what constitutes a wave. For example, do we assume that a wave is the collective motion of objects? Secondly, do we interpret this collective of objects as a medium?
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jrich

USA
287 Posts

Posted - 26 Feb 2004 :  13:38:40  Show Profile  Reply with Quote
quote:
Originally posted by 1234567890

quote:
Originally posted by jrich

Then give me another example of a particle geometry that does not violate the assumptions of smallest object and smallest distance?
JR



There are obviously smaller distances in between the "spheres" in the photo than the diameter of the spheres themselves, but does this fact change the size of the pixels on your monitor, which represents the smallest area resolvable by your monitor? No, it just means that the spheres are larger than the smallest pixels possible. Does the fact that the spheres in the photo exist lead to the "logical deduction" that there are an infinite number of pixels on your monitor or do their existence make impossible the existence of minimum sized pixels on your monitor?

I don't think so or you wouldn't be seeing the picture on your monitor. Minimum physical quantity is a property of existence,
the fact that we exist and take up a certain amount of space proves this. It is not a mathematical deduction that can be shown to be contradictory using some set of axioms.

And I'm sure it is much more a function of the properties of space and matter and energy of motion than it is a function of the supposed existence of continuous functions in calculus.

The picture of the spheres is composed of pixels. Therefore, the spheres are not the smallest particle. A smallest particle could not be decomposed into smaller "pixels", therefore your representation of the spheres as the smallest particle violates the assumption. The pixels in your example are the smallest particle. Now suppose that the spheres are exactly one pixel in size so that they may not be further decomposed on the monitor. The smallest distance is then the distance between the pixels. In your pixel universe no pixels may touch, but if the pixels may not touch, how will the spheres touch? Are you saying that in your assumed finitely divisible universe contact is impossible? Does your pixel universe represent the real universe or is it only a close approximation?

I am not trying to "logically deduce" that the universe is infinitely divisible. That would be impossible because deduction doesn't work that way. What I am attempting to do is assume finite divisibility and using logical deduction show that a contradiction will result. I'm even letting you define the properties of the particles, such as their geometry and whether contact is possible lest you object to the ones I might choose.


JR

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1234567890

360 Posts

Posted - 26 Feb 2004 :  23:24:33  Show Profile  Reply with Quote
quote:
Originally posted by jrich

quote:
Originally posted by 1234567890

quote:
Originally posted by jrich

Then give me another example of a particle geometry that does not violate the assumptions of smallest object and smallest distance?
JR



There are obviously smaller distances in between the "spheres" in the photo than the diameter of the spheres themselves, but does this fact change the size of the pixels on your monitor, which represents the smallest area resolvable by your monitor? No, it just means that the spheres are larger than the smallest pixels possible. Does the fact that the spheres in the photo exist lead to the "logical deduction" that there are an infinite number of pixels on your monitor or do their existence make impossible the existence of minimum sized pixels on your monitor?

I don't think so or you wouldn't be seeing the picture on your monitor. Minimum physical quantity is a property of existence,
the fact that we exist and take up a certain amount of space proves this. It is not a mathematical deduction that can be shown to be contradictory using some set of axioms.

And I'm sure it is much more a function of the properties of space and matter and energy of motion than it is a function of the supposed existence of continuous functions in calculus.

The picture of the spheres is composed of pixels. Therefore, the spheres are not the smallest particle. A smallest particle could not be decomposed into smaller "pixels", therefore your representation of the spheres as the smallest particle violates the assumption. The pixels in your example are the smallest particle. Now suppose that the spheres are exactly one pixel in size so that they may not be further decomposed on the monitor. The smallest distance is then the distance between the pixels. In your pixel universe no pixels may touch, but if the pixels may not touch, how will the spheres touch? Are you saying that in your assumed finitely divisible universe contact is impossible? Does your pixel universe represent the real universe or is it only a close approximation?

I am not trying to "logically deduce" that the universe is infinitely divisible. That would be impossible because deduction doesn't work that way. What I am attempting to do is assume finite divisibility and using logical deduction show that a contradiction will result. I'm even letting you define the properties of the particles, such as their geometry and whether contact is possible lest you object to the ones I might choose.


JR



Can you see more pixels than the number of holes in the shadow mask of your monitor? How does the idea of these holes representing the smallest size possible on your monitor lead to contradiction then?
Can you divide these holes into smaller parts without changing the composite parts of your monitor, i.e., without changing the "universe" of the monitor?.The universe that comprises of the images on a specific monitor then is completely self consistent with the idea of a minimum distance and is incompatible with the idea of infinite divisibility. Any image appearing on your monitor can only be divided into integal parts of the smallest sized holes.




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jrich

USA
287 Posts

Posted - 27 Feb 2004 :  10:08:56  Show Profile  Reply with Quote
quote:
Originally posted by 1234567890
Can you see more pixels than the number of holes in the shadow mask of your monitor? How does the idea of these holes representing the smallest size possible on your monitor lead to contradiction then?
Can you divide these holes into smaller parts without changing the composite parts of your monitor, i.e., without changing the "universe" of the monitor?.The universe that comprises of the images on a specific monitor then is completely self consistent with the idea of a minimum distance and is incompatible with the idea of infinite divisibility. Any image appearing on your monitor can only be divided into integal parts of the smallest sized holes.

Obviously, a finitely divisible monitor screen cannot be infinitely divided without voiding the warranty But what is your point? I'm not arguing that a universe that is assumed from the start to be only finitely divisible can somehow be made to be infinitely divisible. Why do you keep putting up this straw horse? I am arguing that a finitely divisible universe must necessarily have properties which are incongruous with the properties of our universe. The question at hand isn't whether logically consistent finite universes may be devised, the question is whether a finite universe with the properties of our universe is logically consistent. Do you not see the distinction? Do you have no understanding of logical proofs?


JR

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1234567890

360 Posts

Posted - 27 Feb 2004 :  11:38:52  Show Profile  Reply with Quote
quote:
Originally posted by jrich

quote:
Originally posted by 1234567890
Can you see more pixels than the number of holes in the shadow mask of your monitor? How does the idea of these holes representing the smallest size possible on your monitor lead to contradiction then?
Can you divide these holes into smaller parts without changing the composite parts of your monitor, i.e., without changing the "universe" of the monitor?.The universe that comprises of the images on a specific monitor then is completely self consistent with the idea of a minimum distance and is incompatible with the idea of infinite divisibility. Any image appearing on your monitor can only be divided into integal parts of the smallest sized holes.

Obviously, a finitely divisible monitor screen cannot be infinitely divided without voiding the warranty But what is your point? I'm not arguing that a universe that is assumed from the start to be only finitely divisible can somehow be made to be infinitely divisible. Why do you keep putting up this straw horse? I am arguing that a finitely divisible universe must necessarily have properties which are incongruous with the properties of our universe. The question at hand isn't whether logically consistent finite universes may be devised, the question is whether a finite universe with the properties of our universe is logically consistent. Do you not see the distinction? Do you have no understanding of logical proofs?


JR



I've given examples about the finite properties of man made objects (such as the size of pixels on the monitor), and the discrete properties of natural phenomena, such as the angular momentum and spin angular momentum of the electron in the atom, and the discrete energy levels of photon emission and absorption as observed in spectroscopy. And I also finished convincing you with my logical arguments that a finitely divided universe can be logically constructed.

You on the other hand provided two imaginary spheres
that you defined as the minimum volume spheres which you then contradict yourself by constructing lengths smaller than the defined minimum length and you end up using that as proof that our universe is infinitely divisible.

Who's not understanding logical proofs here? Why don't you provide at least the minimal evidence that the smallest particles we know of are spherical?





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