Re: Anachronisms in LOTR

Raven wrote:
> "Stan Brown" <[EMAIL PROTECTED]> skrev i en meddelelse
> news:[EMAIL PROTECTED]
>
> > In article <[EMAIL PROTECTED]> in
> > rec.arts.books.tolkien, Douglas Eckhart
> > <[EMAIL PROTECTED]> wrote:
>
>
> > > Amazing guys the Greeks; they even came up with atomic theory (Atomism-
> > > where we got the word 'atom') first proposed by Democritus in 5th/6th
> > > century BCE, only to be proved as (substantially) correct in the late
> > > 19th/early 20th!
>
>
> > Democritus was nearer right than his contemporaries, but I don't
> > think it's fair to say that modern science proved him correct.
>
>
> > He was essentially guessing, just as his contemporaries were. The
> > big problem with Greek science is that nearly all of it was guesses,
> > with very little experiment to confirm or refute those guesses.
>
>
>    IIRC, Democrit used a faulty theory of mathematics to prove that there
> had to be some undivisible constituents to matter.  It's much the same
> mathematical fallacy that leads to Zenon's "paradox", in which the
> thought-experiment is made with Achilles racing a turtle, giving it a head
> start.  The theory "proves" that Achilles will never pass that turtle; he
> will get ever closer to it but never quite reach it.  Which is a paradox,
> since anybody knows from experience that Achilles will rather swiftly pass
> the armoured little reptile.
>    Let's say that Achilles runs ten times as fast as the turtle, and gives
> it a one mile head start.  When the great hero has run a mile, the turtle
> has progressed a tenth of a mile.  So Achilles runs that extra tenth of a
> mile but by then the turtle has plodded on for another hundredth of a mile.
> And so on.  Since "obviously" a sum of infinitely many numbers cannot be
> finite, the turtle will always stay ahead of Achilles.
>    Of course *we* enlightened people will realize that Achilles will reach
> the turtle after 1 1/9 of a mile, and then run on ahead of it, in accord
> with a billion experiments...


This is because 1 + 1/9 is equal to 11/9, or 
1.11111111111111111111111111111111111111111111111111111111111111111111111111111

which is 1 mile + 1 tenth of a mile + 100th of a mile ... etc.

The Greeks simply never understood irrational numbers.  Hence the name, 
irrational.  ;)  One philosopher when asked about this paradox, said 'I 
refute it thus!' and jumped up off the ground suddenly.

I wonder how many other things we think are 'irrational' today, but 
simply are the result of our own minds, ... I think in politics some say 
that social welfare is a zero sum game, i.e. to give to the poor you 
must take it away from someone else, ... but the reality might be way 
different.

Hasan