2
- THREE FUNDAMENTAL CONSTANTS
Abstract
1.
Background
To make
this page largely self-contained the following appendices are
provided:
Note: The
term characteristic value (hereafter, CV)
denotes a numerical attribute of every Greek or Hebrew word, or
group of words, that has its origin in one or other of the
alphabetic schemes of numeration introduced by these peoples
during the centuries preceding the Christian era.
2.
The primary universal constants
In mathematics,
the sciences, and engineering, the two most widely known (and
used) dimensionless constants are . Both are transcendental
numbers, ie neither can be defined exactly by the ratio of two
integers, nor by any algebraic process.
The first is most famously involved in
the mensuration of circle and sphere, and has been known from
ancient times. Its value is 3.141592654... - commonly
approximated by the simple fraction 22/7, or 3.142857... (error:
+ 0.04%). Leibniz discovered that it was possible to express this
number precisely as an infinite alternating series involving the
reciprocals of the odd integers, thus:
The second is of a
more recent vintage (18th century). Known also as 'Euler's
number', it occurs naturally in any situation where a quantity
increases at a rate proportional to its value, such as a bank
account producing interest, or a population increasing as its
members reproduce.
Like , this constant can also be
expressed precisely by an infinite series involving integers,
thus:
Here,
the denominators are the factorial numbers, 1,
1x2, 1x2x3, and so on.
Its value is 2.718281...
The fine
structure constant ()
is also dimensionless and is related to in a very specific way, and indirectly
also to . However,
it is in a different league from these. It measures the strength
with which subatomic particles interact with one another and with
light, and is fundamental to our continuing existence. is defined as the
square of the coupling constant - found by
experiment to be close to -0.08542455. The latest CODATA
recommended value for
is 0.007297352568, with an uncertainty of 24 centred on the
last two digits. It follows that only the first 8 significant
digits are 'safe'. [For further information, see The fine
structure constant, a 20th century mystery, by James G. Gilson.]
3. The
derivation of from the
internal structure of Genesis 1:1
The
Bible's first verse comprises 7 Hebrew words formed from a total
of 28 letters. Hitherto, attention has focused particularly on
the sums of the word CVs in total and in part. Now, however, it
is the word and letter products that
occupy centre stage. Observe that, although each word CV is the
sum of its letter CVs, the product of the latter bears no clear
and obvious relationship to the former. Essential features of
this analysis involve the two verse ratios
Writing
the product (R1 x R2) in standard mathematical fom, an accurate
value for is revealed.
The
details may be found here.
4. The
derivation of from
the internal structure of John 1:1
The number
of words in this verse is 17, comprising a total of 52 letters.
Again,
writing the product (R1 x R2) in standard mathematical form, an
accurate value for is revealed.
The
details may be found here.
5. The
derivation of from
the concatenation of verse characteristic values
Here are the 8 most
significant digits of the fine structure constant
= 72973525 [ x 10^(-10)] (recall that this
represents a square) -------- (i)
- The
7 Hebrew words representing Genesis 1:1 total 2701 (the
CV of the verse).
2701 ^ 2 = 7295401 = 72954010 [ x
10^(-1)] ------------- (ii)
Clearly, if we ignore the matter
of scaling (involving the respective powers of ten), (ii)
is a reasonable approximation of (i). In fact, (ii) - (i)
= -19515, and the error in estimating is -0.027%, or 1
in 3739. However, if we now concatenate the CV of Genesis
1:1 with that of John 1:1 we obtain the 8 digit string
27013627, and find
- 27013627
^ 2 = 72973604 [ x 10^(7)] -------------- (iii)
-
- This
slightly overestimates - the difference in the mantissa fields
being 79 and the error, therefore, +0.0001% - ie about 1
in 900,000.
Further
details may be found here.
6. Two significant biblical
statements
Notwithstanding
the great time interval between their respective inceptions, it
is clear that there exists a strong textual bonding between
Genesis 1:1 and John 1:1. Here are the translations as they are
found in the King James Bible:
- "In the
beginning God created the heaven and the earth." and
- "In the
beginning was the Word, and the Word was with God, and
the Word was God."
For the
Christian, these writings are highly significant and informative
once the identity of "the Word" has been ascertained.
The matter is resolved in John 1:14 where we read, "And the
Word was made flesh and dwelt among us ...". Undoubtedly,
then, Jesus Christ = the Word.
These key
texts inform the reader of two significant things (concerning
which, there is today much controversy!):
The foregoing observations serve
to confirm these truths in a unique way.
7. A review of the , and evaluations
Let us
first observe that any estimate of or that is obtained as the ratio of two
integers must, necessarily, be an approximation. It is therefore
interesting, and undoubtedly significant, that the percentage
errors involved in the foregoing derivations, viz -0.0012 and
+0.0011, respectively, are small, of the same order of magnitude,
and of opposite polarity.
Concerning , we have observed this to
be a square. Appropriately, therefore, its derivation from the
concatenated verses Genesis 1:1 and John 1:1 has involved the
process of squaring, and the biblical estimate differs by a mere
0.00011% from its true value.
It is
appropriate that we derive a 'handle' on the kind of odds against
these results being chance happenings - bearing in mind the
fundamental nature and close relationship of the sources
involved. Here, again, are the first 10 digits of "estimate:
true value" for , and , respectively, with
matching significant digits underlined:
3.141554509
: 3.141592654, 2.718312812
: 2.718281828 and 0.0072973604
: 0.0072973525
Clearly,
if these figures are rounded , and are each seen to be correct to 5
significant figures. Based upon a random distribution of the
variables (a not unreasonable assumption in the circumstances), a
simple estimate of the combined probability of these events may
therefore be obtained as follows:
Since the
first digit in each case could have been any one of nine in the
range 1-9, and each of the remaining matching digits, any one of
ten in the range 0-9, each event is associated with a probability
of 1/90,000; and because they are independent and represent the
most significant of the physical constants, the final assessment
must argue heavily against them occurring fortuitously.
8.
Conclusions
Let us briefly
recap:
- The application of a simple
numerical procedure to the Hebrew letters and words of
the Bible's first verse (Gen.1:1) generates an
approximation of , correct to 5
significant figures (error: - 0.0012%).
- The application of
the identical procedure to the first verse of the Gospel
of John (which has much in common with Gen.1:1) generates
an approximation of , also correct to 5 significant figures
(error: + 0.0011%).
- The totals of the word CVs
for the same verses, when concatenated in the order in
which they appear in the Scriptures and squared, generate
the first 5 significant digits of (error: + 0.0001%).
- Given the
circumstantial evidence linking these two verses - both
textual and geometrical - it would be extremely
unreasonable to write off these coincidences as extremely
remarkable accidents; indeed, far more likely that they
are features of purposeful design.
Clearly, the planning
of these wonders must have preceded the writing of Genesis 1:1
(2nd millenium BC), the Hebrew alphabetic system of numeration
(c200 BC), and the writing of John 1:1 (c100 AD). Further, the
fundamental constants and could not have been known by man
before the 18th and 20th centuries AD, respectively!
Quite obviously,
therefore, what we have described here has to be viewed as a
purposeful supernatural act! And because the verses on which the
phenomena are centred speak of "Elohim" and "Jesus
Christ", it is not hard to deduce the identity of their
author.
The standing miracle
(for it is nothing less!) informs us as follows:
- The statements of
Gen.1:1 and John 1:1 were made by the same author (and
scientist); henceforth, their truth cannot be questioned
by any of rational mind.
- There are now
strong reasons for believing the whole of God's Word -
read literally - to be completely trustworthy.
- It is now clear
that God has therein provided empirical evidence of his
being and sovereignty; in this 'Age of Reason' - (and
gross apostasy!) - he is acting decisively so that none
should perish through ignorance or foolish presumption.
Return to Homepage
Vernon Jenkins MSc
2003-11-28
Acknowledgements
The author is grateful
to all who have been involved in this project, viz Peter Bluer,
Stephen Coneglan, Craig Paardekooper, Iain Strachan and Bevan
Williams.
email: vernon.jenkins@virgin.net
http://www.otherbiblecode.com