Re: [asa] Re: Ages of the patriarchs

On 2/23/07, dickfischer@earthlink.net <dickfischer@earthlink.net> wrote:
>
> Hi Iain, you wrote:
>
> >>Interesting take. So the MT is garbage, right?<<
>
> No, if your information is flawed your conclusions are flawed. Plus, what
> does it signify? If there is a pattern in the numbers, therefore they were
> all manipulated? If there is a pattern in the numbers therefore they must
> be true? If there is a pattern in the numbers therefore we have proof that
> God himself dictated the numbers? In other words, tell me what a pattern
> proves and why.
>

It appears you didn't read my post properly. I clearly explained that the
presence of the pattern justified the conclusion of intentionality on the
part of the author. Try developing your listening skills, rather than
twisting what I said. It's extremely aggravating to have words put into
ones mouth like "proof that God himself dictated the numbers". I never said
that.

Here's what I know about numbers games. Say you had a sporting event and
> the stadium seated 100,000 patrons. Let's say that the tickets were mailed
> out all over the world and that at game time all filed through a gate. When
> the tickets are collected the numbers on the tickets are read into a
> computer in the order that the fans filed through the gate. The number
> sequence turns out to be 1 to 100,000 in perfect numerical sequence. What
> are the odds? What's your conclusion? Manipulation? A miracle?
>
> Now let's say the number sequence appears to be random in accordance with
> what we would expect and the computer records that particular sequence.
> Whatever the sequence of numbers turned out to be, the odds are just as
> great that that particular sequence would occur as the afore mentioned 1 to
> 100,000. Except that now you aren't thinking it was anything exceptional.
>
>

The only way we could attach some significance to a number sequence is if we
> had advance warning that IF such a sequence occurs then it would signify
> thus and such. After the fact proves nothing.
>
> See, you don't have to be a mathematician, just smart.
>

[Emits long sign of sheer exasperation].

 If I've explained this simple argument to the list once, I've explained it
1000 times. (There's a nice non-literal use of numbers for you!)

Here comes the 1001st attempt.

Yes, it's true that the perfect numerical sequence is just as unlikely as
any given random one. No one's disputing that. But that isn't the relevant
probability calculation. In order to get a handle on the real odds that you
have to worry about, I did a small experiment to simulate your thought
experiment.

First I generated a file of 1000000 numbers in perfect numerical sequence.
Next I generated a file of 1000000 numbers containing all the integers from
1 to 100000 but permuted into random order.

I then used a file compression utility (such as WinZip) to compress both
files.

The ordered file compressed down to 113845 bytes, or 910,760 bits.

The randomly permuted file compressed down to 314370 bytes, or 2,514,960
bits.

The two numbers 910,760 and 2,514,960 are called in statistics the
"description length". To download the disordered file over the internet
would take over two and a half times as long as to download the ordered one.

Why did the ordered sequence have a description length about a million and a
half bits shorter than the disordered sequence? The reason is simple - the
file compression utility detected more evidence of structure and pattern in
the ordered sequence.

How many possible sequences are there that would have a description length
of 910,760 bits? Clearly there are 2^910760. How many would have a
description length of 2,514,960. Clearly 2^2,514,960. So the odds of
getting a sequence like the ordered one with its short description length is
2^910,760/2^2,514,760. That is around 1 in 10^(500,000).

So if you told me that there's nothing special about the football crowd
turning up in perfect numerical sequence because that sequence is as likely
as any other, I think I'd be justified in saying you're nuts because the
odds are 1 in 1 followed by half a million zeros!

The description length principle is not some esoteric principle - it applies
to any area of statistical modelling. Ever seen a scatter plot with a trend
line on it? Do you know how the slope and offset of the trend line are
calculated? It is done by choosing the values that minimize the sum of
squared differences of the data points from the trend line. This has
immediate implications in terms of transmitting the data over a channel. If
you transmit just the raw data, you might have values that are between 1000
and 10000, and have to transmit four digits per data item. But if you fit a
trend line and there IS a real trend in the data, all you'd have to do was
transmit the slope and offset and then the differences, which might be, for
example between 10 and 100, so you'd only have to transmit two digits per
data item. So you have halved the description length. However, if the fit
was very poor (there really was no trend), then the differences would still
be large.

It should be clear now why your football stadium argument is, to use one of
Pim's favourite terms, scientifically vacuous.

Iain

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Received on Fri Feb 23 04:18:32 2007