New Paradox for the "Principles of Physics".

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Mac]: unless one understands the math then one has no basis to object to its ultimate meaning.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

We agree. I could not have said this better myself.

But several people here, yourself included, I think, have never studied the math of infinities, which is standard math accepted around the world. So shouldn't we apply your statement to all those people?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>So lets scrap Relativity since it is purely mathematical with a physical understanding.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

If your premise were true ("relativity is pure math"), then I would agree with your conclusion ("scrap it"). However, relativity made physical predictions that have been tested to high precision and found to be valid. Only the physical interpretation of relativity (e.g., LR vs. SR flavors) is still in doubt.

In other cases, violations of physical principles are a sufficient reason for rejecting a theory. So logic, experiments, and observations are all reasons for scraping a theory. Disliking a theory or finding it inconsistent with one's personal philosophy are not good reasons to reject a theory.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[The discussion in "broken circle"] all seems very clearly stated. There is either an answer or there is not.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I answered your rephrased questions here. My objection is that your math claims have no physical counterparts, and do not obey standard mathematics. I object to making this Message Board a forum for debating whether the rule "2+2=4" is a good or bad idea, or any other debate about the value of standard math. Take those complaints to a math board with a math-interested audience. This is an astronomy board, and we take standard math for granted unless someone has a <i>very</i> good reason to do otherwise. Ignorance of the standard math of infinities is not a very good reason for rejecting an infinite or eternal universe.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote><BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[tvf]: I have great difficulty answering questions that are couched in confusing, ambiguous terms and make implicit, unacceptable assumptions. Your question assumes some connection between n/0 and reality. Where did that come from?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Again please be specific in your objections. What are the implicit, unacceptable assumptions?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Um... I just gave an example: assuming some connection between n/0 and reality.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Where do you in turn then make such statements that my view is based on miracles.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

In physical reality (as opposed to math), something from nothing requires a miracle.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I am also concerned here in as others have pointed out I am seeing a shift in your use of words. Initially you insisted that the Universe had existed for "infinite" amount of time. Now you are say in "Eternity" and claim the meaning is different.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

You should just read what I say and ignore what the others are claiming I said because sometimes they get it wrong. In this case, I did not suggest there is any difference between these two equivalent concepts. So your "concerns" are unwarranted. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>
TVF:

I answered your rephrased questions here. My objection is that your math claims have no physical counterparts, and do not obey standard mathematics. I object to making this Message Board a forum for debating whether the rule "2+2=4" is a good or bad idea, or any other debate about the value of standard math. Take those complaints to a math board with a math-interested audience. This is an astronomy board, and we take standard math for granted unless someone has a very good reason to do otherwise. Ignorance of the standard math of infinities is not a very good reason for rejecting an infinite or eternal universe.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The whole foundation of the MM model rests on the concept of infinity, I would think this would make infinity very relevant to
this discussion.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[123.. ]: The whole foundation of the MM model rests on the concept of infinity, I would think this would make infinity very relevant to this discussion.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Of course it is. I didn't suggest otherwise. My objection was to tutoring in standard math and number theory for those unfamiliar with it. If someone has the patience to do such tutoring, more power to them. But those unfamiliar with the math of infinities should not place that burden on others here, but should arrange to remedy the deficiency themselves.

And the math of infinities is relevant to this discussion. Most of the misunderstandings that have occured here arose because some people are unfamiliar with things like <img src=icon_infty.gif border=0 align=middle>+1=<img src=icon_infty.gif border=0 align=middle>. They don't even know what that relationship means. So grasping the significance of one-to-one correspondences between mathematical and physical infinities is simply beyond their present comprehension.

If there is enough interest by people willing to pay a reasonable tuition, we might be able to get someone to teach an online course in number theory. But what isn't going to happen is an explanation of the math of infinities (beyond a summary of the basics that I've already posted twice) typed out in these messages day after day over the next few months for the edification of those unwilling to pick up a library book.

I suggest that those who want to understand infinities should make that effort. It's a fascinating, mind-bending subject, sure to keep the attention of anyone with even a mild aptitude for math. I've already recommended Gamow's "One, Two, Three ... Infinity" as an excellent self-teaching book. I read it while still in high school. Introductory calculus texts usually cover basic manipulations with standard infinities because they are needed in differentials and integrals.

OTOH, those who don't care to make the effort should stick to cosmologies that do not depend on infinities in the way that MM does. The reason is simple. The MM depends on one-to-one correspondences between certain mathematical and physical infinities. No one has yet learned how to comprehend infinities in other than the most cursory ways without this type of correspondence analogy. It follows that no one here is going to really understand the answers MM offers to these basic questions about the nature of the universe without understanding the math of infinities as a prerequisite. -|Tom|-

To all: Note the nice set of math characters our webmaster has kindly provided just above the message composition box. Just click on any needed symbol such as <img src=icon_alpha.gif border=0 align=middle>, <img src=icon_beta.gif border=0 align=middle>, <img src=icon_pi.gif border=0 align=middle>, <img src=icon_integral.gif border=0 align=middle>, <img src=icon_lessequal.gif border=0 align=middle>, <img src=icon_sum.gif border=0 align=middle>, <img src=icon_aleph.gif border=0 align=middle>, or <img src=icon_infty.gif border=0 align=middle>. The symbol immediately appears at the end of the message you are typing. (Alert: If you are replying, it will appear at the end of the quoted text.) You can write some basic math into these messages using these symbols. The infinity symbol has been useful on several occasions for this discussion. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>
I suggest that those who want to understand infinities should make that effort. It's a fascinating, mind-bending subject, sure to keep the attention of anyone with even a mild aptitude for math. I've already recommended Gamow's "One, Two, Three ... Infinity" as an excellent self-teaching book. I read it while still in high school. Introductory calculus texts usually cover basic manipulations with standard infinities because they are needed in differentials and integrals.
<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

What a clever attempt to undermine the main issue of the discussion by attacking the participant's educational level. Wee, let me tell you TVF: as far as I can see by reading the messages posted by the participants, all have a very good grasp and understanding of the mathematical concepts discussed. I find it very disturbing you thinking they don't.

What the participant cannot see is how infinity can be relevant to a model of reality. The logical fallacy you have just made, an "appeal to ignorance" cannot undermine the simple fact that you have not demonstrated in any way, acceptable to intellectual individuals, how a world can be infinite in time, dimensions, scale and mass and at the same time avoid the many paradoxes of infinity.

To be honest and specific, in the tradition of good science, I'm asking TVF to provide answers to the following REAL paradoxes of an infinite universe:

1. Thermodynamic paradox.

If the universe has been for infinite time, then thermodynamic equilibrium requires that stars do not exist and everything has the same temperature.

2. Propability paradox

If a universe is infinite then everything that could happen would have to have already happen. Therefore, why isn't the case that cats haven't become fluent in English and get elected for Senate?

Let's get the ball rolling here by avoiding getting trapped in word games and logical fallacies and let's see how simple well known paradoxes can be answered by TVf without making all sorts of assumptions and circularities.

I kindly propose to the participant to quit talking about the math of infinity because that is a simple diversion technique. Come up with real paradoxes and see what answers you get. The type and quality of answers will determine whether an infinite universe model can withstand a sanity check.

JoeW,

Very good observation. I would start by simply stating that the appeal to historical authority is "NO ANSWER", it indeed implies the proposer lack the ability to argue his case from its own logical conclusion.

If one accepts the historial authority as the basis, one invokes "Our current view is absolutely correct and nothing can ever change".

Considering that things do change historically and that old concepts fall daily, it is the weakest of positions to assume.

If your premise were true ("relativity is pure math"), then I would agree with your conclusion ("scrap it").[unquote]

However, relativity made physical predictions that have been tested to high precision and found to be valid. Only the physical interpretation of relativity (e.g., LR vs. SR flavors) is still in doubt.[unquote]

Ans:The fact is the mere concept of Relativity in any form is still in doubt. All proported observation and/or experimental results have or can have alternate explanations. To reject change on the basis of CURRENT understand attempts to impose "Status Quo", science will not evolve and we will flounder in our ignorance.