Re: Small probabilities

I'll reply to a three posts to avoid replying several times.

Randy wrote:

 By all means, probabilities and statistics are vital in scientific
methodology, particularly in the areas you cite. I would suggest that this
is quite different from determining whether a unique event was
'intelligently designed." In this particular case, we know that many
surprising coincidences can occur and, in my opinion, we are not justified
in jumping to a conclusion of a deliberate supernatural message being
conveyed.
--------------------

Let's take a step back from Vernon's claim that this is a supernatural
message that is being conveyed & just try to establish whether the patterns
are intentional, or just a "surprising coincidence". I maintain that you
CAN use small probabilities under certain circumstances to determine if some
pattern was intentional, and this is the essence, as I understand it of
"specified complexity" - the pattern has to be sufficiently pre-specified
(ie you can't just say it's any old deal of bridge cards, but you have to
predict what the next deal happens - though both events have the same
probability, the predicted one is surprising because it was pre-specified).
Similarly a pattern that is sufficiently simple doesn't merit a "designed"
designation because there is in all probability a simple explanation.

I'll use arrangements of pieces on a chess board as an example.

If you walked into a room and found an empty chess board, then clearly this
is a specified pattern of chess pieces on the board and one of low
probability given all possible arrangements. But it is too simple to
warrant any design inference. The simple explanation is the board is left
there and no-one bothered to put any pieces out.

Now consider the board arranged with a random layout of pieces, as if a
child had been using the chessmen as toy soldiers (my son does this
occasionally). The position isn't legal, both kings are in check, there are
pawns on the first rank, or whatever. This position is complex, but not
specified - it's effectively random.

Now consider a class of chess position I'm very fond of trying to solve,
called "retrograde analysis". A whole lot of these positions can be found
at http://www.janko.at/Retros/. Typically you see a preposterous looking
position on the board, but are told it is legal. The purpose of the problem
is that you have to work out how the players got to this legal position by a
sequence of moves from the beginning of the game. It is often amazing how
much you can deduce about what went on previously in the game, which pieces
must have been captured by which pawns, which pieces are promoted pieces,
what the last move played must have been, and so forth.

Such chess positions are so bizarrely contrived (they can be arrived at by a
legal sequence of moves, but not a sensible sequence), that often they look
very little different initially to the random layout of pieces I described
that might have been set up by a child, or a monkey hitting a keyboard.

Suppose you went into a room and the chess pieces were set up in a bizarre
position that looked impossible. Your immediate impression would be that
someone who didn't know the rules of chess had set the pieces up in a pretty
pattern. But if you then analysed the position, and found that the position
was indeed legal, and that you could make all these deductions about the
contrived series of moves that would have been played to arrive at the
situation.

Would you not then be justified in deducing that the position had indeed
been designed by a very clever person who knew the rules of chess? And if
you were, what would be the basis of that deduction? I'd suggest it would
be low probability. The number of possible arrangements of chess pieces on
a chess board must vastly outweigh the number of arrangements of legal
positions, and that in turn must vastly outweigh the number of positions
that are suitable for retrograde analysis, where you can deduce e.g. what
the last several moves must have been.

Hence it is a small probability that determines design in this case. I'd be
interested to know if you agree, or if maybe this is a good illustration of
what Dembski means by "specified AND complex". Or would you perhaps say
that even if you found such a position set up on a chess board, that there
was no justification for concluding that the position was intentionally
designed that way?

Vernon's patterns, I would also say I believe to be both specified and
complex, and that it was justifiable to conclude intentionality (let's leave
open the question of whether it's a "message" for the moment).

Jim wrote (in part);

> Aside from my own skepticism as to the nature of the orderly derivations
> you present, just as a practical matter, the geometries and rationales
> you offer are sufficiently arcane for very few to even follow, much less
> accept on that basis as the evidence you offer.

I'm a little surprised that you should say the geometries are arcane and
difficult to follow. Triangular numbers are not a difficult concept. In my
kids' school in the maths classrooms, I've seen pictures of triangular and
square numbers that look much the same as the diagrams on Vernon's web-site,
geometric arrays of coloured circles etc. If it's presented in math classes
to kids, I can't see how you justify calling it "arcane". It is but a short
step to take an equilateral triangle and superimpose its inversion on itself
to give a six-pointed star, and note that the intersection of the two gives
a hexagon. (Everyone knows you get a six-pointed star by two triangles).
These three figures (hexagon, star, and triangle) form the backbone of
Vernon's geometries, and I really can't see why something that is little
further on from something taught to 12 year olds as part of basic math
education can be seen as arcane.

 Jim also wrote:

In the present discussion, it seems to me that the act of introducing even a
relatively small amount of structure into the letters/words of the basic
Genesis 1:1 scripture in consideration of numerical equivalences and
significances in Hebrew might alone be quite capable of creating a great
deal of collateral order and systematic structure in other representations,
such as those discovered by Vernon. I am not enough of a mathematician or
analyst to sort out whether this is in fact the case, but it sure seems
plausible. Just playing with that Sierpinski triangle algorithm the first
time is a mind-boggler. The Julia set is remarkable in its aesthetic appeal
(when graphed). Why should that even be? The idea of mapping the mathematics
into a visual representation is sort of incidental to the underlying
mathematics, but it is that (collateral) visual representation that captures
our interest.

My sense is that Vernon's gematrial discoveries could easily be another
example of unintended but beautiful collateral consequence that flows from a
relatively small amount of intentional gematrial ordering of the textual
elements of Genesis 1:1.

Me:

I believe I may have addressed this earlier. There is of course a large
amount of structure in written text, which allows probabilistic models to be
built that form the basis of speech recognition systems (Hidden Markov
Models). But these models exploit the temporal coherence of the letters,
e.g. that a 'q' is almost always followed by a 'u', etc. Higher order
models can be built up by e.g. computing the probability distribution of the
letter that follows every possible two-letter combination (digram), or
three-letter combination (tri-gram). It is then possible to use these
models in a "generative" fashion to generate synthetic text using a random
number generator. Such examples are found, I believe, in Claude Shannon's
original 1948 paper on Information Theory. The higher order models produce
outputs that are (of course) gibberish, but looking more like english text
(because of patterns of letters that we are familiar with) cropping up
repeatedly. However, these models are completely different from adding up
ALL the letters in a word, having assigned numerical values to them
according to the (apparently arbitrary) ordering of the letters in the
alphabet. Structure in the text arises, therfore from the sequence, not the
sum of the entire sequence, and there is no reason to suppose that the
entire sequence would give rise to the closely-knit set of multiples of 37
that Vernon has observed.

Incidentally 37 isn't a Vernon "discovery", the gematrial sum of the Greek
for Jesus as 888 = 37x24 was known about in the first century AD). 37 has a
long history of fascination for mathematicians and philosophers throughout
history (Plato was reportedly fascinated by it). The properties of it are
probably due to the fact that 37x3 = 111.

Best,
Iain

--
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After the game, the King and the pawn go back in the same box.
- Italian Proverb
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