New Paradox for the "Principles of Physics".

tvanflandern
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21 years 7 months ago #5446 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[JoeW]: What do you mean by a "real" world?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

The material, tangible, unique external reality.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Do you directly imply that a world where infinite time is reached is "unreal".<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Infinite time intervals are a concept. They are not material or tangible. But they do exist. Concepts exist, and accurately describe the real world, even if they are not a part of it. The set of all integers accurately describes things about integers, even though that set is not an integer and therefore not a member of itself. The concept of infinite time intervals exists and accurately describes things about the real world, even though it is not a material, tangible thing and therefore not itself a part of the real world.

I guess you could say that we finite beings can think about concepts, but not experience them. There is an uncrossable gap between the finite and the infinite.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Then, your infinite universe in time, mass, dimensions and scale is "unreal".<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

"Unreal" is a poor word because it seems to imply non-existent, which is untrue. The infinite universe exists as a concept, so it is not material or tangible and we cannot experience it. But we can think about it and recognize its existence.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Your postulate is that the universe exists for an infinite time, as of now. Then, infinite time has already been reached, unless your universe is not "real" and in a real universe this cannot happen. YOUR CONTRADICTION IS EVIDENT.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I realize these matters are subtle. But they are not self-contradictory. Having existed forever and coming into existence from nothing are quite different concepts.

I argued that, no matter how far into the future one goes from some fixed moment such as now, an infinite time interval will never elapse. The same holds true into the past. Infinite time intervals exist only as a concept, and we can think about them and their implications for the real world, but we cannot experience them. Time into the past is unbounded (the definition of infinite), yet the time interval between any two points in time is finite. We finite beings cannot experience infinity, but are limited to thinking about it.

You brought up a sand pile example, and I argued that you could never add an infinite number of grains of sand to it because, even if you never die, you can never get to or experience an infinite time interval. All intervals, however long, are finite. Correspondingly, in MM, scale is infinitely divisible and infinitely constructable. So forms of any size imaginable, however large, can and must exist. (Galaxies are just atoms on a super scale, and structures there are just atoms on an even larger scale, etc. forever.) Yet no form can be infinite in size, just as no individual integer is infinite even though the set of possible integers is unbounded.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>But you say that the universe has been around for an infinite time, has infinite mass, infinite dimensions and scale. Do you imply that in the way your universe exists there is no counting? If not, how do you conclude it is infinite? YOUR CONTRADICTION IS EVIDENT<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

As I said, it is difficult to imagine infinity. So we deal with infinite concepts in two ways: by analogy or by one-to-one correspondences. In this case, revert to the analogy of integers. Then your above statement reads:

"But you say that the set of all integers is infinite. Do you imply that, in the way this set of all integers exists, there is no counting? YOUR CONTRADICTION IS EVIDENT"

Quite obviously, when I switch to the integers analogy, your statement falls apart. By analogy with the universe, your original statement has the same flaw.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote><BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[tvf]: You cannot count to infinity, even if you live forever!<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

If the statement that "infinite time never elapses from a specific starting moment, even in an eternal universe", is not a contradiction in terms THEN WHAT IN THE WORLD IS A CONTRADICTION? YOU CONTRADICTION IS EVIDENT.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Switching to the analogy: When starting from any specific integer and counting forever, one never reaches infinity even though the set of integers is unbounded (infinite). Please show the comtradiction in that, or else show how the analogy is not valid.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[quote[[tvf]: * 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.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

You are contradicting your previous statements once more. We are not talking about infinite size but infinite sets. Your point is that infinite sets are concepts only. We are not adding grains, only accumulating grains and the resulting heap is the set, which is infinite and very real. You are becoming a victim of your contradictions. A set is a real thing. For example, three grains make a set. What you fail to understand is that sets result in new physical entities and an infinite heap of sand is a new entity made of infinite grains. A grain does not become infinite. ACTUALLY, YOU FAIL TO UNDERSTAND THAT THERE IS NO ISSUE HERE FOR THE FINITE BECOMING INFINITE. THIS IS A PROOF THAT ZERO BECOMES INFINITY. THERE IS NO HEAP OF SAND BEFORE ACCUMULATION STARTS, IT IS THE EMPTY SET=0. IN INFINITE TIME, THERE IS AN INFINITE HEAP, HOWEVER. YOUR CONTRADICTIONS ARE EVIDENT.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Hmmm. One can visually see your blood sugar dropping as you wrote this paragraph (the transition from normal text to all caps; increasing dogmatism; decreasing logical consistency).

You did not address (that I can see) my syllogism that preceded your response here. It just seemed to make you angry. Yet my syllogism plainly showed that, logically, one can never accumulate grains into an infinite heap, or count to infinity. Where, exactly, is the flaw in my syllogism? How did you bridge the gap between finite heaps and an infinite heap?

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Your paradox is due to these contradicti

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tvanflandern
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21 years 7 months ago #5600 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

To all:

It is evident this discussion has stirred passions and seems to be bringing out emotional responses. Could the participants, including me, please get some constructive criticism from readers about the conduct of the debate. (People can be criticized without insulting them. "I think you are doing this wrong..." can be said without saying "Doing this is stupid...") Participants can comment too, but should do so after eating a meal and when in a relaxed mood. <img src=icon_smile.gif border=0 align=middle>

Here, I am not looking for comments on the merits of the arguments, who is winning or losing, or anything about infinity. In fact, stating your leanings will probably be taken as a bias by whomever you criticize. I am looking for criticism of conduct, style, technique -- basically, what are we (I?) doing wrong that is inflaming people to such a degree? How can we get the discussion back onto a productive track?

Comments by anyone with an insight on this they would like to share would be most welcome. But be specific. "You are not being reasonable" is argumentative and uninformative. Try to provide advice that can be translated into action.-|Tom|-

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JoeW
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21 years 7 months ago #5447 by JoeW

Replied by JoeW on topic Reply from

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

1. The interval between any two integers can never be infinite.
2. The total number of integers before and after any interval is infinite.

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

I must caution you that you're proposing an intuitive solution to Cantor's "continuoum hypothesis", that there is no line segment with an infinite set of points in such a way as for it not being equal to the whole segment and also not equivalent to the set of natural numbers.

In other words, is there a cardinality between that of natural numbers and line segments?

I'd like to inform you that the continuoum hypothesis is still an unsolved problem in mathematics. You simplified analogy leadz to well known contradictions in formal logic and beyond. That's what I was trying to point out to you. You analogy is actually the problem of the continuoum hypothesis itself. it is well understood these days that another axiom is missing to settle the issue. This is the reason I suggested before that you settle yourself in your theory this by using an axiom, otherwise by these analogies your are subject to contradictions, the least to say (actually it means you are not aware of basic mathematical issues).

Simple...

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tvanflandern
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21 years 7 months ago #5353 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote><BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[tvf]:
1. The interval between any two integers can never be infinite.
2. The total number of integers before and after any interval is infinite.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

[JoeW]: I must caution you that you're proposing an intuitive solution to Cantor's "continuoum hypothesis", that there is no line segment with an infinite set of points in such a way as for it not being equal to the whole segment and also not equivalent to the set of natural numbers.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

These infinities are clearly unequal. You mentioned this before, and I ignored it because I don't see the relevance. Here's a web site that seems to describe the Continuum Hypothesis more clearly than you did.
[url] www.wikipedia.org/wiki/Continuum_hypothesis [/url]
The short summary statement there is especially helpful:
"there is no set whose size is strictly between that of the integers and that of the real numbers."

I referred to the different levels of infinity before in my message about the arithmetic of infinities. But my statements that you referred to above, and the analogy I have been using for most of this discussion, involves the set of integers only. So how can the Continuum Hypothesis possibly be relevant? You must be objecting that I am using a discrete set (integers) as an analog for a continuous set (time, space, or scale). But why should it matter whether or not there is another set between these two, or even that the two infinities are unequal? Why should the levels of infinity matter at all to this discussion as it has progressed to this point? Our whole discussion has focused on the fundamental gap between finite and infinite at any level.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>In other words, is there a cardinality between that of natural numbers and line segments?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

This is an interesting question. But so is the four-color problem. But what relevance does it have here?

The problem I have is, because I'm not seeing any connection to the discussion, it looks like a diversion.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>I'd like to inform you that the continuoum hypothesis is still an unsolved problem in mathematics.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

This can only be relevant if the Hypothesis is relevant. How might that be?

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>You simplified analogy leadz to well known contradictions in formal logic and beyond. That's what I was trying to point out to you. You analogy is actually the problem of the continuoum hypothesis itself. it is well understood these days that another axiom is missing to settle the issue. This is the reason I suggested before that you settle yourself in your theory this by using an axiom, otherwise by these analogies your are subject to contradictions, the least to say (actually it means you are not aware of basic mathematical issues).<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

I think I'm familiar with the relevant concepts as they pertain to MM interests.

Summary:
* My arguments rest on an analogy between concepts in the universe and any infinite set.
* The unbridgeable gap between finite and infinite (of any order) is the basis for my conclusions.
* The fact that the infinity of integers is of a lower order than the infinity of real numbers does not seem relevant to the analogies I have used. Please show the relevance, if you see any. -|Tom|-

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1234567890
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21 years 7 months ago #5354 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...]: It's difficult to hold a reasoned argument with someone who keeps changing their definitions to suit their arguments.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Magoo (and later you) pointed out that I had been using "substance" inconsistently. I then realized that was true, conceded as much, and tightened up the definition. Would you rather I defended the inconsistency and made no change? Your complaint here strikes me as of the "damned if you do and damned if you don't" type.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>you either have a failing memory ... or you are only interested in being right, even if it is achieved through confusion or other tactics.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

We are discussing intellectual issues that have been debated by people throughout recorded history. Zeno's paradoxes generate considerable controversy to this day. Given the lack of consensus in the world at large, why do you make no allowance for people seeing matters differently?

I could complain that you have repeatedly insisted on statements or interpretations already ruled out. But I understand that the discussion has been lengthy and that I have used many different examples of the same idea to make my points, so some repetition of objections is inevitable.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Well, your present definition, that substance is "the collection of all forms", and that "forms are finite in duration", leads to creation ex-nihilo, I'm afraid. If forms are finite in duration, then they came from nothing and disappeared into nothing.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

This is a case in point of repetition of matters already corrected. I've pointed out several times that it is logically impossible for something to become nothing, and vice versa. Forms can only assemble or decompose into other forms. Nothing of importance to the argument (only to the terminology) changed when I agreed that substance was the collection of all forms and not the ingredients that make up forms. Forms are made of other forms through an infinitude of scales.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>you cannot eradicate the problem of coming into and out of existence of the forms.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Please cite an example -- any will do -- of a form coming from nothing or becoming nothing. If you have no clear, definite example, why do you insist this is a "problem"?

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>I think this is what you are trying to say: Substances are eternal and there are an infinite number of different substances.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

With the corrected terminology, this should read: "Substance is eternal while forms are temporary. The amount ('mass') of substance is infinite, and there are an infinite number of different forms made from substance, but each form is finite."

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>using the integer analogy, it is like saying that substances are the integers themselves and all elements in the integer set are eternal.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Forms are the analog of integers, and are finite. Substance is the analog of the set of all integers, and is eternal.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>But the interaction (operation) between integers, say 1 + 2, yields something other than an integer.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

No relationship between successive integers is required for my purposes. Each integer could be replaced with an identical apple. Integers and apples are forms.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>You are basically creating a new set that has finite properties out of the operation. This set is composed of elements produced from operation between integers (substances).<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Apples might be combined to make applesauce. Forms are made of other forms. But why create a new set? Relationships between set members are not needed for the analogy to work.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>I think it is possible to ask what came before substance. Or in terms of the integer set, what operations from which set that is as yet discovered leads to the existence of the integer set? Ad infinitum.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Certainly, it is possible to ask "What came before?" because in our experience with forms, which are temporary, there has always been an answer to that question. That is because forms change, so cause and effect apply. Substance, by contrast, never changes, is not an effect, and therefore had no cause and is eternal. Substance is therefore a concept, and not a material, tangible thing (a form). Forms come from substance just as integers come from the set of all integers. But a form is not substance (an integer is not the set of all integers), and substance is not a form (the set of all integers is not an integer). -|Tom|-

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

Dr. Flandern,

actually I'm having a ball with these discussions. I even like calling people names. It's fun. I don't do it in the real world of course but in the virtual world, you are supposed to vent a little. Sticks and stones... As long as it doesn't get too nasty... I don't think I have been nasty.

No, as you can see, in every criticism I've made, I've tried to offer a model for my thinking. I only got a little frustrated when you kept changing the definitions, and without realizing it yourself. I think you are probably a very busy man and this matter probably isn't the focus of your life as it has been mine these few days so I do apologize for being rude at least.

Anyways, a little ad hominem is healthy, imo.

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Atko
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21 years 7 months ago #5355 by Atko

Replied by Atko on topic Reply from Paul Atkinson

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
I will not be checking these boards any longer as I see no point in engaging into a debate of this kind, so there is no need for you to reply to this post. Try to understand that no one is attacking you but instead trying to help you.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>
JEREMY

LOL, this kind of post always means the poster has walked off in an angry huff and they can't resist coming back to see the results of their parting salvo. I particularly find the "no one is attacking you but instead trying to help you" hilarious. The multiple lines of capital letters and repetitions of YOUR CONTRADICTIONS ARE EVIDENT are a great example of how not to behave in a civilized discourse. I suspect JoeW will be back again to have at it again under another name. His style is so much like ATKO's one wonders if that was who he was to begin with.

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

LOL - Which style are you referring to? Last time I had an argument on this board was months ago, and I learned my lesson back then that this type of debate just leads to flared tempers and name-calling; besides which, I don't remember you taking part - unless, God forbid, you're a resurrected version of Patrick just coming back to haunt me? (just kidding <img src=icon_smile.gif border=0 align=middle>)
I'd be fascinated to see where I ever used capitalization (never done that before), but I must confess I've only skimmed this thread (too deep for me), so whatever the style is you're referring to is a mystery; maybe you can link some of the old threads I previously posted on and I'll take a look to see if I can improve myself.
<img src=icon_smile_wink.gif border=0 align=middle>

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