New Paradox for the "Principles of Physics".

tvanflandern
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21 years 7 months ago #5717 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[JoeW]: Can you describe then a mechanism which would limit the formation of an infinite physical form in a universe that is infinite in any conceptual sense, nevertheless, finite in every form.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

There is no such thing as an "infinite physical form", just as there is no such thing as an infinite integer. All forms are finite in size and duration. The set of all forms, like the set of all integers, is infinite. Likewise, the possible size of a physical form is unbounded, just as the size of integers is unbounded. At the same time, every physical form and every integer is finite.

One cannot make an infinite physical form by combining finite forms for the same reason that one cannot make an infinite integer by combining finite integers.

It only seems paradoxical on first hearing. But with some thought, one can see that it isn't. Familiarity with the standard mathematics of infinities is a big help in understanding this.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>except if there is a mechanism to limit formation of such a form.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

One cannot combine finite objects to make an infinite one. No matter how many are combined, the result is still finite. (No matter how many integers are added, the sum is still finite.) The finite cannot become infinite.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>I understand that "the finite cannot become infinite" postulate prevents an already finite form from becoming infinite but what about already existing infinite physical forms.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

No "infinite physical forms" exist. The set of all physical forms is a concept, not a material, tangible thing.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>How does the use of infinity in MM prevent the existence of infinite physical forms in infinite time?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

No prevention is needed. It is impossible, physically and logically, to combine any number of finite things and get an infinite result. Yet no bound can be placed on how large a finite form can result because the number of finite forms is infinite (unbounded).

If you added together all integers, the result would be infinite. But that requires adding an infinite number of integers, which makes it a concept, not a physical possibility. Such a thing cannot be done in reality because everything material and tangible is finite, and only concepts (such as adding together all integers), but not material, tangible things (such as actual integers) can become infinite.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>It seems to me that if your answer is that infinite physical forms in infinite time are not allowed then you are missing another postulate. Simply by saying that "the finite cannot become infinite" does not account or accomodate for that possibility.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I see no need of another postulate. Concepts may be infinite. Material, tangible entities must be finite. The set of all material, tangible entities is a concept, even though it is part of reality. It is not "physical", meaning material and tangible. It exists, but as a concept, not as a physical form.

The set of all integers exists as a concept because integers are unbounded. Yet one can never find a physical counterpart of the set of all integers, such as an infinite line marked with integers every inch. That too exists only as a concept. All real lines are finite line segments.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>keep in mind that by assuming infinite dimensions, mass and scale, finite arithmetic does not apply any longer. Your answer must be justified using infinite arithmetic. Attempting to justify claims of the infinite using finite arithmetic is a fallacy of "huge" proportions. Recall that inf+inf = inf, whereas in finite arithmetic inf is a variable and inf+inf=2*inf. That makes a "huge" difference.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Of course. All the above is obvious. Infinite arithmetic applies to infinite entities, such as the set of all integers. Finite arithmetic applies to finite entities, such as members of that set.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>It is well known in mathmematics that an infinite set is a proper subset of itself and can be equivalent to one of its subsets.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

True enough. For example, the infinite set of all integers and the infinite set of odd integers are mathematically equivalent because they can be placed in a one-to-one correspondence. But nothing in what you just said applies to finite entities.

For the obvious reason that different arithmetic rules apply to infinite and finite entities, they cannot both belong to the same set without terminating most arithmetic relationships applicable to certain subsets.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>It is therefore not clear that in the universe of the MM even standard mathematics can be used, such as finite arithmetic, functions, derivatives and integrals.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

In MM, there is no mixing of finite and infinite entities. Standard rules apply to both because they are always separate. Your "paradoxes" arise from trying to combine finite and infinite entities into a common set. In MM, that is not legitimate because no simple set of arithmetic rules could apply to such a combined set.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Laymen are often intrigued by the use of the term infinity in a cosmological model and are skeptical of finite models of the world but scientist take the exactly opposite view due to the unresolved paradoxes that infinity poses.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I suppose you would define "scientist" as someone who agrees with you about this claim. <img src=icon_smile_big.gif border=0 align=middle>

In MM, you are seeing a resolution of the paradoxes (note: not contradictions) infinity poses. You may or may not see that, ot may or may not accept it. We are discussing your objections. Nonetheless, an argument that something has never been done before is different than an argument that something cannot be done, even in principle. Your argument is of the former type, not the latter. -|Tom|-

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1234567890
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21 years 7 months ago #5342 by 1234567890

Replied by 1234567890 on topic Reply from

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[123...]: you stipulated further that substances were not irreducible, that they were infinitely divisible. Under this stipulation, your analogy fails since now every form is a substance so that every form must be eternal. And if they are eternal, they can't also be finite.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Forms are made of substance. They are not the same thing as substance.

I just explained that every infinitely divisible form is finite in duration, even though the substance (or atoms) from which it is composed are eternal. That is because the substance (like atoms) just moves on from form to form as time continues. The only contradiction I see here is in your denial of the properties of forms and substance. Specifically, forms are temporary and substance is eternal. Please explain in detail what is bothering you about this.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

The problem is your stipulation that substances are infinitely reducible. So if we were to use my example of an alkali combining with a halogen, you are saying that the alkali is not fundamental- that it is made up of infinitely smaller "atoms". If so, then there becomes no difference between your idea of form and substance. NO DISTINCTION. When you add two forms, they are still substance because substance is infinitely reducible. You end up playing a word game of sometimes calling the stuff substance but calling it a form on some other occassion.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
You yourself are a form. You are presumably temporary. Yet the atoms that make up your body were all "borrowed" from other forms, mainly from things you eat or breathe. Someday, those same atoms will be recycled again into some other form. This all seems perfectly routine.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

No, the atoms are infinitely reducible, you say. That means the atoms are made of something else, ad infinitum. So unless you are conceding my point- that substance is an irreducible form- you are using the word form and substance interchangeably and giving them separate properties.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Or using your beloved integer set analogy, it would be like if we started out with the whole integer set instead of only the odd integers. Here, no matter how you add the integers, 1 +3, 2+5, 3+7, etc., you end up with an integer that has the properties defined by being an element in the integer set. You end up with another integer. So if existence is a property of elements in the integer set, for example, no matter how you add the integers, you end up with another integer that must be eternal.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Um, the set of all integers is infinite, not "eternal". So your last sentence should read "no matter how you add the integers, you end up with another integer that must be infinite", which is obviously false.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Um, I opened the sentence with the qualifier "IF". IF this were true, than this is true. Aka, analogy. If "existence" were a property of elements in the integer set, and you defined existence
as eternal, every integer would exist forever.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
In an analogous way, when we add temporary forms made of eternal substance together, as happened to make your body, we get another temporary form (you).
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Again, this only works if substance were irreducible. If they are infinitely reducible, they become no different than form- they are forms. You obviously are not clear on this point since not too many posts before you were saying forms ARE substance. Well, the distinction to be made is that substance is an irreducible form. Irreducible is different than being infinitely divisible. The former is saying that they are not composed of anything other than themselves, the latter is a mathematical construct saying that any object can be divided into infinite like parts.

This discussion is getting pathetic, TVF. You take my idea, twist it in your own words and try to make it look like it is any different than yours. And you turn around trying to make me look like I don't understand it. LOL, you are a joke.

Clearly it is you who are confused with the distinction between substance and form since you keep changing the definitions from post to post. Well, I am done with trying to clarify your confusion.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>

I still see no hint of a problem here, yet see you struggling with this concept. I do not see why. But then, I didn't understand why you introduced the concept of "irreducible" because whether forms are irreducible or infinitely divisible makes no difference to this argument. -|Tom|-

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

LOL, how can I be struggling with a concept that I proposed? Idiot.
You are a hypocrite Tom. Everything someone else say is wrong, but when you start saying the same thing but using different words, they somehow become right.

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tvanflandern
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21 years 7 months ago #5343 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[Magoo]: How can we have an "Eternal" "substance" which is "non-existent", "non-physical", with no "material" properties, construct a physical "form". How can you construct something with physical material from something which has no physical properties.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Substance is "essence of matter or energy", is eternal, and exists as a concept. Forms are made of substance and are physical, material, tangible, finite, and temporary. [Note: Energy is just very small bits of matter moving at very high speeds. Converting matter into energy is just breaking up the matter into such small, high-speed bits. So there is no difference between "essence of matter" and "essence of energy".]

This is analogous to the set of all integers being infinite, while each integer is a member of the set of all integers but is finite. (Substance is infinite and eternal, yet each form is made from substance but is finite and temporary as forms change into other forms.)

I have probably created some confusion (unintentionally) by being inconsistent in my usages of "substance" and "forms". In most discussions, this distinction is not needed, so I just speak of substance and never mention forms. So sometimes I have spoken of substance interchangeably with forms to avoid making the distinction. But in this discussion, a careful distinction is important.

Other relationships:
* Substance is the collection of all forms.
* Forms are made from smaller forms, and ultimately come from substance.
* Forms are to substance as integers are to the set of all integers.
* If atoms were the basic ingredients of everything, then substance would be the set of all atoms and forms would be individual atoms or bodies made of atoms. -|Tom|-

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tvanflandern
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21 years 7 months ago #5344 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

123...:

I clarified the forms/substance distinction in reply to Magoo. I did introduce some confusion in this usage, which was my fault. However, that does not excuse your losing your composure and turning ad hominem. This is your first caution. Ad hominem remarks of the type below will not be tolerated on this Message Board.

[123...]: This discussion is getting pathetic ... you are a joke ... Idiot ... You are a hypocrite

Please get yourself back under control or take a time-out until you can. Your contributions have been of value up to now. -|Tom|-

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21 years 7 months ago #5658 by JoeW

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<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>

If you added together all integers, the result would be infinite. But that requires adding an infinite number of integers, which makes it a concept, not a physical possibility. Such a thing cannot be done in reality because everything material and tangible is finite, and only concepts (such as adding together all integers), but not material, tangible things (such as actual integers) can become infinite.

<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

This is where the paradox and contradiction lies. It is the combination of infinite time and members of an infinite set. I give you an example:

at T=0 there is a grain of sand

at T <--- T+dt a grain of sand is added, and so on.

at tine T there are T/dt=N grains of sand (I could make that an exponential growth but I keep it arithmetic for simplicity)

If the universe exists for an infinite time then as T goes to infinity N goes to infinity. Conclusion:

By a simple aggregation of finite in size substances (grains) in infinite time one will get an infinite heap of sand. Then:

1. Either the mathematics is wrong and the heap is constraint finite
2. or the heap is infinite and infinite physical forms exist
3. or the heap is finite because the universe is finite in time

So why are you telling me I cannot start accumulating grains today and in infite time from now I won't be able to get an infinite heap of sand? There are of course an infinite number of finite in size grains I can play with and time is on my side. What will prevent the heap from getting infinite? By you just saying it will remain finite and claiming common sense or worse making the logical fallacy of an "appeal to common sense", you are not proving anything.

Besides all, in an infinite universe there is plenty of room for an infinite heap of sand, simply because inf+inf is still equal to inf.

You will have to saw me how an infinite, in time, aggregation of finite grains will not produce an infinite heap, in a rigorous, scientifically accepeted way, since you have rejected the use of an axiom to prohibit infinite substances.

I'm not rejecting <img src=icon_i.gif border=0 align=middle>a priori[/i] the possibility that you will offer such proof and be nominated for a Noble prize in math and physics. I will be very happy for you and certainly Archimedes will feel alike, I'm sure.

Standing by...

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tvanflandern
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21 years 7 months ago #5718 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[JoeW]: By a simple aggregation of finite in size substances (grains) in infinite time one will get an infinite heap of sand.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Of course. I did not suggest otherwise. This is not different from counting integers one at a time. It takes an infinite time to reach infinity. But in the real world, no matter how far into the future you check the count, the count is still finite.

Infinite time can never be realized in physical reality. It exists only as a concept, just as the set of all integers being infinite exists only as a concept. One can never reach infinity by counting long enough. And the sand pile can never reach infinite mass by accumulating long enough. Infinite time elapsed after a process starts never arrives.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Then:
1. Either the mathematics is wrong and the heap is constraint finite
2. or the heap is infinite and infinite physical forms exist
3. or the heap is finite because the universe is finite in time<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Or 4. The heap is finite because an infinite time never elapses from a specific starting moment, even in an eternal universe.

You cannot count to infinity, even if you live forever!

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>So why are you telling me I cannot start accumulating grains today and in infinite time from now I won't be able to get an infinite heap of sand?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I am not telling you that. In an infinite time, an infinite heap can exist. But starting from a specific moment, an infinite time will never elapse, even in an eternal universe.

Time forward from any moment is unbounded, and therefore infinite. But finite beings, forms, and processes can never get to infinity. The finite cannot become infinite.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>By you just saying it will remain finite and claiming common sense or worse making the logical fallacy of an "appeal to common sense", you are not proving anything.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

When dealing with infinities, we must use analogies and one-to-one correspondences with other infinities because we are finite beings. The reasoning goes roughly as follows:

* One can add only finite increments to any finite quantity.
* No finite increment can ever convert a finite quantity to an infinite one.
* So no matter how many increments are added, the finite cannot become infinite.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>You will have to show me how an infinite, in time, aggregation of finite grains will not produce an infinite heap, in a rigorous, scientifically accepeted way, since you have rejected the use of an axiom to prohibit infinite substances.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

In an infinite time, the heap would be infinite. But an infinite time from now will never elapse. No matter how far into the future you look, it's still only a finite time from now.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>I'm not rejecting a priori the possibility that you will offer such proof and be nominated for a Noble prize in math and physics.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

How about offering that nomination again for something that is at least possible? I'll have a better chance. <img src=icon_smile_big.gif border=0 align=middle> -|Tom|-

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