Re: The forgotten verses

From: gordon brown (
Date: Wed Jun 04 2003 - 15:59:22 EDT

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    I am with Vernon on this one. I don't know whether the explanation is the
    correct one, but I haven't seen a convincing argument against it. It seems
    too easy for people of today to look down on the ancients and declare them
    to be stupid. Thus the claims are often repeated that the Hebrews thought
    that pi was equal to three and that the Egyptians thought that the area of
    any parallelogram was the product of the lengths of two adjacent sides. I
    am skeptical that people whose constructions must have involved much
    geometric measurement would be so far off. Wouldn't it be better to assume
    that these people were intelligent and try to understand what they were
    really saying?

    Another issue in connection with II Chron. 4 is that verse 5 says that the
    sea could hold 3000 baths while the parallel passage in I Kings 7:26 puts
    its capacity at 2000 baths. There are several instances in the OT in which
    parallel passages differ on numbers. This seems to suggest that whatever
    method they used for writing numbers made it easy to miscopy them. This
    should be considered before jumping to the conclusion that the authors
    disagreed with each other.

    Gordon Brown
    Department of Mathematics
    University of Colorado
    Boulder, CO 80309-0395

    On Wed, 4 Jun 2003, Vernon Jenkins wrote:

    > Dave,
    > I'm currently digesting your response to my recent posting. For now, let me
    > just challenge your closing words, "I simply go by the text." - referring to
    > your belief that the Hebrews of Solomon's day believed pi to be 3 - a
    > deduction based upon the data provided by II Chronicles 4:2. But you surely
    > realise there is ambiguity here. All real cylinders have an inner diameter
    > (d, say) and an outer diameter (D, say); an inner circumference (c, say) and
    > an outer circumference (C, say). Does "...ten cubits from brim to brim..."
    > represent d or D? Does "...a line of thirty cubits did compass it round
    > about." represent c or C?
    > You must therefore agree that the data here provided is insufficient to
    > support your claim. It needs the additional information given in verse 5 of
    > the same chapter to bring the solution a little closer. Here we are told
    > "And the thickness of it (the cylinder wall) was an handbreadth..." (t,
    > say). A 'handbreadth' is defined as a measure of four fingers, equal to
    > about four inches, and a 'cubit' as the distance from elbow to to the tip of
    > the longest finger of a man - about 18 inches.
    > Clearly, pi may be determined as either of the ratios c/d or C/D, but not as
    > c/D or C/d. Thus, only by reading the 30 cubits as the _inner_ circumference
    > (c), and the 10 cubits as the outer diameter (D) do we make sense of the
    > data, thus:
    > d = D - 2xt = 10x18 - 2x4 = 180 - 8 = 172 inches
    > c = 30x18 = 540 inches
    > pi = 540/172 = 3.14 (which we recognise as a commonly used approximation
    > for pi).
    > There can be little doubt that the intrinsic ambiguities associated with
    > IIChr.2:4 are here satisfactorily resolved, and why anyone should, (a) have
    > believed the Hebrews incapable of detecting a 4.5% error in the value of pi
    > (by assuming it to be 3 rather than its true value), and (b) have assumed
    > that Egyptian knowledge of this constant would have stopped short of its
    > border with Israel, is really beyond understanding - unless, of course, the
    > principal motive was the undermining of the Judaeo-Christian Scriptures.
    > Vernon

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