John,
Herewith my responses:
> Off line discussions on Vernon's claim lead me to try to summarize it in
> a way that may show more clearly why I do not think it is of
> significance. The claim seems to be as follows:
>
> 1. Assume the denary system is divinely inspired, based on arguments from
> nature in that humans and some animals have five digits on each
> extremity. Pandas, horses, etc. don't count.
I don't know if Vernon thinks so, but I do not think there is any historical
evidence that base 10 is because we have 10 fingers and thumbs. I have this
from a History of Maths Prof. A better system, surely would be base 6, when
with two hands, one for each base 6 "digit" , one could count to 55 base 6.
Alternatively, counting to 12 on the knuckle joints of the fingers would be
more efficient.
A more likely historical reason for base 10 is the Ancient Greek reverence
for the "Tetratkys", 10 represented as a triangle of numbers 1+2+3+4. It is
also a tetrahedral number, being the sum of the first three triangulars 1
+ 3 + 6. Such things were considered important by early mathematicians.
>
> 4. Assume a certain numeric equivalence between certain Hebrew characters
> and numbers and do the same for Greek.
>
This is historically proven. The Hebrew numerals appeared on Maccabean
coins in the 2nd century BC. I have a Hebrew Old Testament, where every
fifth verse is shown as the Hebrew numeric equivalent. The Greek system was
apparently invented by Pythagoras in the 5-6 cent. BC. You will find the
Greek system documented in JH Conway and R Guy's book "The Book of Numbers"
(pub 1996). This is an excellent text, available from Amazon. It has
nothing to do with religion, but concerns the history of maths, and leads up
to much modern research, all in very accessible form.
>
> 7. Claim from all this that God designed things that way.
>
For myself, I prefer to say "how do you explain it"?
>
> 1. Claims that the denary system is somehow "divinely inspired" seem to
> be based on wishful thinking, and not on any real grounds. If true, one
> would expect to find consilience with other natural facts or theological
> arguments; these are not present. The Babylonians got along, it seems
> with a system based on 12.
In fact the Babylonians used base 60, probably reflecting different
traditions using 12 and 10 together. The base 60 sytem obviously persists
in astronomy today, and in the way hours are divided into minutes and
seconds.
Computers do well with the binary system. I
> used to work with the IBM 650 computer which used a bi-quinary system. It
> was as reliable as any other in the 1950s.
I don't see the relevance of this point. No one is claiming that base 10 is
"more efficient" than any other. The base 60 notation of the Babylonians
was much more efficient for their purposes. Because 60 has many divisors it
enables many more fractions to be represented exactly than base 10. The
Babylonians used to calculate large tables of reciprocals. For example, 1/3
can be represented in the Babylonian system as 0,20 exactly, as opposed to
0.33333...
>
> 2. I'm not an expert on ancient texts, but I expect that variants of both
> Genesis 1 and John 1 exist. If true, the claimant would have a number of
> texts to choose from "until it came out right."
>
But they didn't go around hunting for the right text. It was the first one
they chose. But as I understand, there are remarkably few variants on the
OT text - between the three main versions of the Hebrew text of the
Pentacheuch, there are only six character differences, and none, as far as I
know, with Gen 1:1. I am not aware of any variances with John 1:1, apart
from the earlier dispute about the subscript iota. But arguing
probabilistically, one notes that the approximation to e is of order 10^-5,
so one would expect to have to search through 100,000 variant texts before a
match could be found, or have a choice of 100,000 interesting numbers that
it might come to. In practice there are only a few dozen "interesting"
numbers that might fit (like the Golden ratio, square root of 2,
sqrt(3)/2, and so forth). And e and pi are by far the most famous.
> 3. Direct dictation of any part of scripture "by God" is problemmatical.
>
I don't think Vernon ever claimed that scripture was directly "dictated" by
God. What is claimed is that Scripture is "inspired by God" (2 Tim 3:16).
Inspiration is not necessarily the same as dictation. Did the writers hear
the "voice of God" speaking the words, or did they write as an act of faith?
I would tend to assume the latter.
> 4. Direct numeric equivalences are a "fun" thing to do -- are they
> inspired? Maybe. I have never seen an analysis of any that was in the
> least convincing, and I've encountered many which were sheer balderdash.
I've no doubt that many are balderdash. I've seen many on the web that are
balderdash. I just don't happen to think Vernon's analysis is balderdash,
and you can't dismiss this one as balderdash on the basis that others you've
seen are balderdash.
> 5. There are thousands of possible mathematical transformations that can
> be tried. The one used is a simple one, of course; there are still many
> simple ones. Why THIS simple one? No answer.
>
Steven Hawking makes much the same point at the end of "Brief History of
Time". You have a "Theory of Everything", but there is still no answer to
the question of why the universe exists at all. What is it that breathes
fire into the equations? And why are the parameters as they are and finely
tuned so that complex life forms can arise? There is similarly no answer
but an appeal to the anthropic principle: "Things are as they are because
WE are". But why does any universe have to have us in it?
The only justification I can give for the mathematical transformation is
that the same formula was tested on John 1:1 after it had been applied to
Gen 1:1. The result of finding "e" was a complete surprise to us all.
> 6. There are thousands of possible "fundemental mathematical constants"
> that might have resulted.
Conway and Guy list about 24 they consider interesting. I think you are
exaggerating here. To get "thousands" there would be some really obscure
ones in there. I for one would not have been at all convinced if John 1:1,
for example had come out close to the mass ratio of the pion to the muon.
That would qualify for the big "so what"?
Yes, pi and e are among the most interesting of
> these. But neither pi nor e is subsequently tied to anything else
> theologically. Both are expressed approximately (of course, they have to
> be; I know that). But why to that particular degree of approximation? No
> answer.
I think the same applies here as in the "theory of everything" answer. I
don't discount physics just because it doesn't tell me the mass ratios of
the elementary particles. Maybe a "theory of everything" will predict all
these, but the impression I get is that physicists accept that there will be
unexplained "brute facts" in any theory.
The degree of approximation is good enough to put it beyond previously known
approximations to pi in antiquity, as far as I am aware. There is evidence
that the Babylonians knew about "e", and that some of their tablets express
some solutions of equations in terms of powers of (2,43) in hexadecimal
notation, which is 2.7166, far less accurate than the approximation for e.
>
> 7. Therefore, the claim fails, at least for this person. To establish any
> degree of credibility, the questions I have above need to be addressed.
>
I hope that I have at least made some attempt to address these in the above.
Iain.
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