Re: Infinity can not exist

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Date: 10 Jul 2004 05:09:16 -0700

Ann <aon2@hotmail.com> wrote in message news:<Pine.LNX.4.44.0407081319270.21684-100000@cicero.local>...
> Hi Chris,
>
> > On Thu, 8 Jul 2004, Chris Parker wrote:
>
> > I didn't mean to call you silly.
>
> I know, I quoted you jokingly, it might have sounded a bit rude but was
> in fact meant to be funny. And of course "I guessed that you take the
> concept of infinity for granted", it was clear from the start. Actually
> accepting the word 'infinity' is like with any other abstract
> construction: it starts as a game, at first it even seems rather
> convenient bearing in mind all the other infinitesimals, fluxions,
> infinite and universal sets that logically followed suit; and the next
> moment, however, we've already forgotten it were a game and took them
> for real, the question I posed was: Real where?
>
> Infinity exists where?
>

Infinity may just be a convenient phrase for denoting the logical
limits of human reasoning.It is most understandable in a geometric way
via the relationship between diameter,circumference and the Pi value
-

http://plus.maths.org/issue3/news/pi/pi.gif

A line generates a circumference and the relationship between the
length of the diameter (line) and length of circumference (circle) is
the nonperiodic decimal 3.1415....

A circumference always generates a center and the lenght from center
to circumference will always be half the original diameter.This new
discrete lenght (radius) can generate a new circumference and so on it
goes,diminishing without end,diameter generating circumference which
in turn generates a new radius half the original lenght and all held
together by the Pi value.

You conclude that you cannot reduce a one dimensional line to a zero
dimensional point within logical limits notwithstanding that
contemporaries achieve the sleight of hand and propose the difference
between line and point geometrically as a physical proposition.As a
circumference is always greater than a line drawn across the center
by a proportion of 3.1415.. there should be no objection to
determining a lenght half the original diameter and doing so without
end.

There is no reason to remain at the logical limits (infinity) longer
than is necessary ,by the same token there is no reason to impose
logical limits for the convenience of constructing concepts based on
faulty reasoning that implies a line can be reduced to a point or visa
versa.

To make this more human and less mathematical,what profit is there in
setting a logical limit to your own life within the greater life of
the cosmos,at what point does life begin and end and why would you
want to sever the ties between your existence and the great movement
that existed before you and will exist after you.While mathematics may
shrink from the idea of 'infinity' and retreat to a perspective that
the universe and all life within it had a singular knowable beginning
where everything gets scrambled,is it not more lovely to recognise as
the poet William Blake did -

If the doors of perception were cleansed everything would appear to
man as it is: Infinite. --William Blake, The Marriage of Heaven and
Hell

> > I guess that I take for granted the concept of infinity.
>
> > You do sound like a bit like a Constructivist, which is not a bad thing.
> > I know that they have gotten a bit of bad press, but Brouwer's
> > ideas are interesting.
>
> > I did not say that infinity exists, but that it is a concept (and a very
> > convenient one when dealing with things such as the set of natural
> > numbers, pi, e, etc).
>
> Totally agree with you (noticing the careful precision of your
> language:), though if you think about it, we cannot even COUNT
> 'things', or if we do that would be some 'imaginary' numbers (instead
> of the "real", "rational", "natural" ones, but clever names they have,
> who would dare question the reality of the "real number":) or money
> (again numbers:) or other hypothetical elements of "the set" or just
> 'straight' lines in the sand. That is why little children have problems
> with the concept of counting, for we could rarely find in nature two or
> more absolutely identical things to be added, subtracted or otherwise
> manipulated algebraically (they might have problems imagining the
> result too:).
>
> Instead, we usually imagine the objects were uniformly the same, that
> this talking 'animal' here (Chris) and that one (Ann) are two
> immaculate elements/members of the flock of sheep ('people') to then
> add them to produce the result of... the sum total of two... :). Maybe
> you've heard of the Greek Eleatics from 2500 years ago, like Zeno who
> almost proved that all measures, numbers and sets (including the
> sublime one of the "natural numbers":) are unreal ("numbers of the
> Beast":), do not exist independently (of our gorgeous brain:) in the
> external world. "Zeno was concerned to show that our understandings of
> time, motion, change, position, magnitude, unity, singleness, and
> plurality are incoherent; or that they result in contradictions."
> (http://www.gmu.edu/courses/phil/ancient/pzm3.htm)
>
> Many different mathematical universes are possible. When we
> accept or reject the Axiom of Choice, we are specifying which
> universe we shall work in. Both possibilities are feasible --
> i.e., neither accepting nor rejecting AC yields a contradiction;
>
> :) The "existence" of f -- or of any mathematical object, even the
> number "3" -- is purely formal. It does not have the same kind
> of solidity as your table and your chair; it merely exists in
> ==> the mental universe of mathematics.
>
> http://www.math.vanderbilt.edu/~schectex/ccc/choice.html
>
> To paraphrase you, "I did not say that infinity [does not] exist, but that
> it is a concept" that "merely exists in the mental universe of
> mathematics". And so do the numbers and all other mathematical objects,
> they need the support of the human mind, they badly 'need' us, go figure
> (you see, who would have thought; I mean, until very recently I was
> convinced that it was only us who badly needed them:).
>
> Best,
> Ann
>
>
> PS: Random quote generator:
>
> "Two things are infinite: the universe and human stupidity;
> and I'm not sure about the universe."
> Albert Einstein
>
>
>
> > On Thu, 8 Jul 2004, Chris Parker wrote:
> >> On Wed, 07 Jul 2004 Ann wrote:
>
> >> Hi Chris,
>
> >> "silly me" but it "seems to me" (the skeptic realist I am, not "the
> >> Constructivist":) that before we could "believe" or disbelieve the real
> >> "existence" of "infinity" you need to tell us "something" about your
> >> definition of existence and its whereabouts: in reality outside or
> >> within. Until then we may choose some point in the middle between "it
> >> does" and "it does not exist"--sitting and waiting ('indefinitely':)
> >> for the arrival of the overwhelming evidence that will finally force us
> >> to make up our gullible mind (i.e. fix it to the absolute 'truth', and
> >> stick to it to the bitter end:).
>
> >>> On Wed, 7 Jul 2004, Chris Parker wrote:
>
> >>> Or look at the Constructivists - L.E.J. Brouwer. They believe that if
> >>> something can not be constructed in a finite number of steps that it
> >>> does not exist.
>
> >>> This argument seems silly to me.
> >>> Infinity is not a measurable unit.
> >>> Infinity is an abstract concept.
>
> >> ... therefore, its reality is... outside or within? Come on, it must be
> >> easy, is 'infinity' a sublime product of the supreme mind (like all the
> >> words--"abstract" creations of Lord Logos), or is it something else
> >> entirely, or is it more, and how much more than a regular word. Or
> >> perhaps you could "construct" it for us, and it doesn't matter in how
> >> many "finite (or more:) number of steps" you do it, important is the
> >> experiment to last less than 'indefinitely'.
>
> >> I mean, people are impatient these days, few would like to be told to
> >> repeat some imaginary process 'forever'. We are just 'unprepared' to
> >> wait until the end of 'eternity' in order to witness the miracle (the
> >> actual "construction" or coming into existence of the 'infinitesimal'
> >> converging rapidly to the infinite loop, approaching but never actually
> >> reaching it:), you know why? Because...:), to experience anything it
> >> has to cross our path during our 'lifetimes' -- which happen to be...
> >> finite or infinite? (or more than 'finite' but less than 'infinite':)
> >> Best,
> >> Ann
>
> > I didn't mean to call you silly. I guess that I take for granted
> > the concept of infinity.
> >
> > You do sound like a bit like a Constructivist, which is not a bad thing.
> > I know that they have gotten a bit of bad press, but Brouwer's
> > ideas are interesting.
> >
> > I did not say that infinity exists, but that it is a concept (and a very
> > convenient one when dealing with things such as the set of natural
> > numbers, pi, e, etc).
> >
> > Chris

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