Theos-Talk Archives (May 2000 Message tt00155)

    Aleister Crowley once said, in the introduction to one of his books, words
to the effect of, "Don't believe anything just because you read it in a book".
The book was simplifying a more complex idea.

    The that Mr. Seife was trying to put forward is that the rational numbers
are a series of separated points, and points take up no space, and that rational
numbers are extremely small that, compared to irrational numbers, the space they
take up on the number line APPROACHES zero. Note that, by the same logic, since
irrational numbers are also points on the number line, they also take no space,
either. But there are also an infinite number of rational numbers, and if
irrational numbers take up ANY space, then rational numbers must also take up an
infinite amount of space.

    That is why mathemeticians have come up with the concept of degrees of
infinity.

    Bart Lidofsky

Eugene Carpenter wrote:

> Gee Bart.  Charles Seife states clearly in his book that the rational number
> occupy no space on the number line and gives what seems to little ole
> uneducated me to be a good proof.
>
> Please see page 156 in ZERO, BIOGRAPHY OF A DANGEROUS IDEA.
>
> "How big are the rational numbers?  The take up no space at all. It's a
> tough concept to swallow, but it's true."
>
> Thanks for the feedback.  This is fun! Please help me understand how if one
> measures in radians one will have a rational number.  How can one ever
> measure and come up with an absolutely precise number?
>
> Gene
>
> -----Original Message-----
> From: Bart Lidofsky <bartl@sprynet.com>
> To: theos-talk@theosophy.com <theos-talk@theosophy.com>
> Date: Wednesday, May 17, 2000 9:17 PM
> Subject: Re: Theos-World Mathematics, Spinoza, Leibniz
>
> >Eugene Carpenter wrote:
> >
> >> This stuff about numbers is super cool.
> >>
> >> I have recently learned(Zero, Biography of a Dangerous Idea, by Seife)
> that
> >> rational numbers occupy zero space on the number line! The irrationals
> >> occupy most, if not all, of the number line!
> >
> >    Of course, the rational numbers also occupy an infinite amount of space
> on
> >the number line.
> >
> >> Also, all measurments in science, of matter, are irrational numbers!(same
> >> source)
> >
> >    Not if you measure in radians.
> >
> >    Bart Lidofsky
> >
> >
> >-- THEOSOPHY WORLD -- Theosophical Talk -- theos-talk@theosophy.com
> >
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>
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