Infinity…… Infinite? Or Finite?

Since you brought up the question of initial conditions and also TVF the mathematical wonders that predict cellestial movements I like to point out to you the very fact that our planetary system itself is considered a Chaotic system --a deterministic system that under certain initial conditions may result in chaotic motion---. If I recall, the King of Sweeden posed first this problem (Stability of our planetary system) in late 18th century and Poincare (Poincare maps) thought it solved it first but then realized he has made some error and, indeed, our planetary system is chaotic.

This means, that our mathematical predictions forward in time are severely limited by our models and, maybe, that some future conditions may result in unstable situations (such as planet allignements).

In chaotic systems, initial conditions determine system trajectories in an unprectictable way. Unless we are sure we are not sitting on the rim of the ball, then initial conditions do really matter.

As far as the line, since the ancients, there are two schools of thought and, in my opinion, still, no has won over the other.

The school of Thalis of Militious claimed reality is stationary and completely mechanistic, therefore we can define a line. The school of Efesos of Heraclitus claimed 'everything is in flux" and therefore, defining a straight line is just a creation of your own mind since in reality, as soon as you define it it dissappears. (You never enter the same river twice---Chineese say"

Patrick, at this level of thought, you cannot distinguish between philosophy and Science, simple because Science is Philosophy and vice versa. Answers depend on accepeted first principles and axioms. Very little can be proved.

Why not consider both zero and infinity as mathematical points rather than real? Neither one exists in the reality we all live in. Why all the fuss over this issue? There must be something I'm missing here and I wish I knew what it is.

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In order for infinity to exist does it require an initial starting point?
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Why would infinity depend on anything?

The proposed "zero" point would serve merely as a reference-point. Perhaps it may be called "the subjective," because it measures all thing in relation to itself, and not to the summation of all things ["infinity," or rather, "all things;" ie. "reality"].

Infinity does not have a predetermined reference point, otherise it would not be "infinity."

The forum will go in circles, unless the desire to question all things (ie. infinity/reality) prevails.

...a potentially infinite forum then.....?
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<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Patrick]: I don't see how the line could exist without someone or somethings perception of it.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

When you die, will everything cease to exist? Will everything that you perceived cease to exist? Will everything that you were the only one ever to perceive cease to exist?

Most of the universe is not being perceived by anyone most of the time. Doesn't it continue to exist at such times? Do parts of the universe never perceived by anyone not really exist?

In <i>Dark Matter...</i>, chapter 20, I wrote the following section that seems relevant here to avoid circular reasoning. I suspect Patrick will not agree with my conclusion, but perhaps will at least better understand why us "realists" think the way we do. -|Tom|-


B. About Truth and Reality

Like many words, the word "reality" has more than one meaning. Our efforts will be facilitated if we can agree to use the same meaning for this and other key words.

I therefore propose that we use "reality" for the unique, common, shared experience of the external world. Then the way individuals experience that reality would be called a "perception of reality," which is no longer unique. And a theory or model attempting to describe or predict reality would be a "description of reality."

With these definitions, the job of defining "truth" becomes less difficult. Let a true perception or description be one that agrees with this unique external reality, and a false perception or description be one that does not match reality. (Truth, of course, is not always determinable.)

This starting definition of reality makes an assumption, the truth of which may not be obvious: that such a single, unique, external reality does exist. Here is a justification for making this assumption.

(1) The process of reasoning or logic requires premises or assumptions. It is impossible to prove or derive anything without starting assumptions. Ordinarily the question of the existence or reality of everything lies outside the domain accessible by reasoning, because no prior assumptions are available. Such propositions are therefore knowable only by experience or observation.

(2) To observe and experience the external world, the tools available to us are our senses and our thought processes. But we already know that each of these is subject to occasional error. Not only can sensory input data be in error (as in the extreme case of hallucination, but more commonly, simple misperception), but even thought processes can be disordered (as in the extreme cases produced by drugs or mental illness, but more commonly from the influence of emotions).

(3) Given that our only means of perceiving and describing reality are occasionally flawed, we must provide a means to check each input and each thought for error, or else we will be unable to tell correct input and thinking from wrong.

(4) Some perceptions can be tested by looking for consistent input data from different senses, or a repetition of the original input data. But often such tests are not available or may be subject to the same error process as the original. So we must look to tests we can perform on the external world, and to the perceptions of others, to check up on our own thoughts and senses.

(5) In using tests of the external world and the perceptions of others to check for error in ourselves (a process called "reality testing"), we are implicitly making the assumption that there is a unique, common, shared experience available for this purpose. The alternative is to rely exclusively on our own senses and thought processes, which is illogical given all the evidence that these are occasionally faulty.

So although we cannot prove there is such a unique, common, shared experience that we can name "reality," we are logically compelled to make that assumption, because the alternative is known to lead to erroneous conclusions; whereas the assumption of a unique reality is not known to lead to any error.