2 - THREE FUNDAMENTAL CONSTANTS
To make this page largely self-contained the following appendices are provided:
Appendix 1 - Reading Hebrew and Greek words as numbers
Appendix 2 - Some observations on squares and square roots
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)
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
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:
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.
Let us briefly recap:
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:
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Vernon Jenkins MSc
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.