From: Rich Blinne <rich.blinne@gmail.com>

Date: Fri Jan 11 2008 - 21:14:15 EST

Date: Fri Jan 11 2008 - 21:14:15 EST

On Jan 11, 2008, at 4:10 PM, Iain Strachan wrote:

*> Rich,
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*>
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*> I really can't see the point of this long recitation. I suppose you
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*> are trying to say that you can say something interesting about any
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*> number given sufficient ingenuity. But some of these are really
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*> obscure, and smack of clutching at straws. I thought I was a maths
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*> buff, but many of these I've never heard of. I'll give you that I
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*> know about 163 as a Heegner number (related to the fact that
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*> e^(pi.sqrt(163)) is extremely close to an integer - a subject of a
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*> famous April fool in Scientific American when it was claimed it WAS an
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*> integer). But many of them I've never heard of and I think you'd need
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*> to have done a maths degree probably to understand them! I mean what
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*> on earth is:
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*>
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*> 618 is the number of ternary square-free words of length 15?
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*>
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*> No idea, and what, by turn is the importance of the 15? What about
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*> ternary square-free words of length 14? It seems to me this is a
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*> pretty arbitrary property to pick out.
*

The number of ternary square free words of length 14 is 456. A

"square" word consists of two identical adjacent subwords (for

example, acbacb). A squarefree word contains nosquare words as

subwords (for example, abcacbabcb). The only squarefree binary words

are a, b, ab, ba, aba, and bab (since aa, bb, aaa, aab, abb, baa, bba,

and bbb contain square identical adjacent subwords a, b, a, a, b, a,

b, and b, respectively).

However, there are arbitrarily long ternary squarefree words. The

number s(n) of ternary squarefree words of length n=1, 2, ... are 1,

3, 6, 12, 18, 30, 42, 60, ... (http://www.research.att.com/~njas/sequences/A006156

), and s(n) is bounded by 6 * 1.032^n and 6 * 1.379^n where n is the

length of the sequence. (Brandenburg 1983)

And, you're absolutely right it is pretty arbitrary. But is it any

more arbitrary about the largest rep-digit triangular numbers? You do

get the gist of my argument that given any particular number you can

come up with anything that makes it special. In addition to this, I

was showing that Vernon's argument was circular. Namely, 666 was the

preferred variant because it was "special". But, it was "special"

because the text was 666. I know I drove the idea of "special" to

utter silliness but that's because I was making a reductio ad absurdam

argument. In essence I was noting how the idea of a number being

"special" is an eisegetical rather than exegetical one. Having

particular numbers in Scripture (particularly when all copies do not

agree on the number) in no way "proves" Scripture. The piling on was

to illustrate that such arguments about the meaning of numbers can go

on forever in keeping with Titus 1:8-9:

*> This is a trustworthy saying. And I want you to stress these things,
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*> so that those who have trusted in God may be careful to devote
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*> themselves to doing what is good. These things are excellent and
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*> profitable for everyone.
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*>
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*> But avoid foolish controversies and genealogies and arguments and
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*> quarrels about the law, because these are unprofitable and useless.
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*>
*

Note that this "list" is not original to me and it goes on well past

666. As a maths buff you will undoubtably find it entertaining

because it links to all the obscure properties mentioned previously.

It's at: http://www.stetson.edu/%7Eefriedma/numbers.html

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Received on Fri Jan 11 21:15:23 2008

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