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Fundamental constants in the Bible
1. Fundamental constants in the Bible
2. Constant
Different fields of study have different definitions of "
constant".
In mathematics, a constant is something that never changes.
π (pi) ≈ 3.1415...
e (exponential constant) ≈ 2.71828...
In physics, a constant is something that is assumed not to change.
speed of light c, Planks constant h, etc. (actual values depend on the units used)
In programming, a constant is a name given to a literal value.
const HourlyRate = 12.34;
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The two fundamental mathematical constants π (pi) and e are related by Euler's formula.
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3. Mathematical constant pi
The Greek symbol
π, pronounced "
pie", is used to refer the ratio of the diameter
d of a circle to its circumference
c.
c = π * d = π d
The radius
r of a circle is half the diameter
d, so the following holds.
c = π * d = π*2*r = 2 π * r = 2 π r
Numbers such as
π are transcendental and, like irrational numbers, have no exact representation and can only be approximated.
4. Exponential constant
e(0.0) = e0.0 = 1.0000...
e(1.0) = e1.0 = 2.7182...
e(2.0) = e2.0 = 7.3890...
...
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The exponential constant e, Euler's number, discovered by Jacob Bernoulli in 1683, is defined such that the slope (first derivative) of the function e(x) is e(x) (i.e., as a fixed-point). The value of e = e(1.0) = e1.0 is approximately 2.718281828459.
Numbers such as e are transcendental and, like irrational numbers, have no exact representation and can only be approximated.
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5. Euler's identity
The value of the constants
π, sometimes written as "
pi", and
e are two of the
fundamental constants in mathematics. These constants appear often in formulas in physics, engineering, etc., and are related by
Euler's identity.
Both
π and
e are transcendental numbers that are defined by in infinite series of diminishing term values (see below for an example of each).
The term
i is the
imaginary number as the square root of
-1.
The use of
imaginary numbers allow these mathematical relationships to be applied to physical phenomena such as electricity and magnetism.
6. Notation
At times, either mathematical notation or computer notation or both will be used. In computer notation, the asterisk "
*" will be used for multiplication and the caret "
^" will be used for exponentiation.
Math notation: 7 x2
Computer notation: 7 * x^2
Mixed notation: 7 * x2 or 7 x^2
7. Equidistant letter codes
An
ELS (Equidistant Letter Sequence) is a sequence of letters that are a fixed distance apart and appear to have some meaning. These are sometimes called a "
Bible code" or "
Torah code".
Finding such codes is a part of a field called
gematria.
With the advent of computer analysis, it appears that such codes can be found for almost anything desired, especially in a language such as Hebrew that does not have vowels.
Some have tried to save the idea by using statistical clustering techniques. Personal opinion: Any idea that is difficult to analyze and then explain is not the best idea to use in an argument.
What is being described here is
not an
ELS.
8. Hebrew and Greek gematria
The English word
"gematria" is from the ancient Greek word
"γεωμετρία" ≈ "geometry".
Greek dropped some Hebrew/Phonecian letters (except for numbers) as unneeded or duplicate sounds.
The Hebrew and Greek languages had numerical values for most of their letters. These values are well established. Analyzing and conjecturing about the resulting values of words, phrases, and sentences is a field called
gematria.
9. Evaluating formulas on a sentence/phrase
For a sentence or phrase, the following formula can be computed after assigning each letter the traditional numerical value associated with that letter.
Obviously, since only additions, multiplications, and divisions are done, the result of evaluating this formula using integer values for letters and words can only result in rational numbers, not irrational or transcendental numbers.
Rational number examples: 0, 1, 2, ..., 1/2, 2/3, 3/4, 4/5, etc.
Irrational number examples: √2, √3, √5, etc. (square root of prime numbers)
Transcendental number examples: π, e, etc.
Note that this equation is dependent on the letters in each word but
not on the word order in the sequence of words.
This independence on word order is similar to that of Bayesian topic modeling that uses a bag of words approach.
10. Example
As a simple English example, consider the phrase
A BAD CAB with
3 words and
7 letters.
The number values for each letter are as follows:
A=1,
B=2,
C=3, and
D=4. The following values are thus matched up with each letter.
| Word |
letter
values |
letter
sum |
letter
product |
| A |
A=1 |
1 |
1 |
| BAD |
B=2 A=1 D=4 |
BAD:(2+1+4)=7 |
BAD(2*1*4)=8 |
| CAB |
C=3 A=1 B=2 |
CAB:(3+1+2)=6 |
CAB:(3*1*2)=6 |
The ratio for
A BAD CAB with
3 words and
7 letters would be determined as follows.
| product of letters/words |
*number of |
over/under |
| A:(1=1)*BAD:(2*1*4=8)*CAB:(3*1*2=6) = 1*8*6 = 48 |
*letters:7 |
48*7=336 |
| A:(1=1)*BAD:(2+1+4=7)*CAB:(3+1+2=6) = 1*7*6 = 42 |
*words:3 |
42*3=126 |
The final value is then
336/126≈
2.66666...
This result is not very interesting but it does show the method. Obviously, the numerator (top,
336 in the above example) will grow much more quickly than the denominator (bottom,
126 in the above example).
11. Exponential notation
The result
2.66666 can be expressed in exponential notation as follows.
2.66666E0000
which means the following.
2.66666 * 100
= 2.66666 * 1
= 2.66666
If the result were
26.6666 then the exponential notation would be as follows.
26.6666
= 2.6666 * 101
= 2.6666E0001
To see the pattern more easily, here are some additional examples.
2.66666 = 2.66666E0000 = 2.6666 * 100
26.6666 = 2.66666E0001 = 2.6666 * 101
266.666 = 2.66666E0002 = 2.6666 * 102
2666.66 = 2.66666E0003 = 2.6666 * 103
26666.6 = 2.66666E0004 = 2.6666 * 104
266666. = 2.66666E0005 = 2.6666 * 105
In
all cases, the significant digits are
266666. It is only the power of
10 that is changing.
12. Challenge
Here is a challenge: Come up with meaningful sentences or phrases whose significant digits are approximations to the transcendental numbers
π and/or
e.
For
6 significant digits, the goal is as follows.
314159 for π from the (approximate) value of 3.1415926535898...
271828 for e from the approximate value of 2.718281828459...
Two sentences that meet this criteria, using the long-established numerical values for letters in the languages used, are now presented along with the spreadsheet models that can be used to perform and thus verify the calculations.
13. Original text
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Genesis 1:1
Hebrew Old Testament
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John 1:1
Greek New Testament
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The images are from e-Sword,
http://www.e-sword.net. (as of 2008-04-20)
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Use the formula to analyze Genesis 1:1 (Hebrew gematria) and John 1:1 (Greek gematria).
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14. Current research
In 2023, the results were updated using Bible text from crosswire.org.
In addition to verifying the results, all other verses in the
HOT (Hebrew Old Testament) and
GNT (Greek New Testament) were checked. These verses were the only verses close to the desired result. Some other fundamental constants and common ratios but no significant results were found.
This research is not yet in a form to publish here.
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Details are left as a future topic.
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15. Genesis 1:1
Genesis 1:1 In the beginning God created the heaven and the earth. [kjv]
בראשית ברא אלהים את השמים ואת הארץ׃ [he]
This formula using this verse in the original Hebrew computes to the following.
3.14155450783110E+0017
For comparison, the value of
π (pi) is approximately the following.
3.14159265358979E+0000
The significant digits (ignoring the exponent) are within
4 parts in
100,000, or
-0.0038%.
16. Genesis 1:1
KJV: In the beginning God created the heaven and the earth.
Hebrew: בראשית ברא אלהים את השמים ואת הארץ׃
Greek: εν αρχη εποιησεν ο θεος τον ουρανον και την γην
17. John 1:1
John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God. [kjv]
εν αρχη ην ο λογος και ο λογος ην προς τον θεον και θεος ην ο λογος [gnt]
This formula using this verse in the original Greek computes to the following.
2.71831281219642E+0040
For comparison, the actual value of
e is approximately
2.71828182845905E+0000
The significant digits (ignoring the exponent) are within
3 parts in
100,000, or
-0.0031%.
18. John 1:1
KJV: In the beginning was the Word, and the Word was with God, and the Word was God.
Greek: εν αρχη ην ο λογος και ο λογος ην προς τον θεον και θεος ην ο λογος
19. Results verification
Here are some results. No other verses are close.
Genesis 1:1 and
π:
31415926... actual significant digits (of π)
31415545... approximation from Genesis 1:1 (000004 parts under)
John 1:1 and
e: (discovered in 1683)
27182818... actual significant digits (of e)
27183128... approximation from John 1:1 (000003 parts over)
Combined
π+
e:
58598745... actual sum (π+e)
58598673... approximation sum (000000.7 parts under using above scale)
Are these results significant or are they just a chance happening? That is left for you to decide.
20. Over and under factors
The over and under values consist of integers that can be factored. The result is a rational number. Here are the prime factorizations of each.
English: A BAD CAB
over: 23
under: 31
result: 2.6666666667
Greek: John 1:1
over: 259 39 548 79 131
under: 111 171 293 312 671 711 3733 7191
result: 27183128121964234165317352899020962398208.0000000000
Hebrew: Genesis 1:1
over: 240 36 526
under: 71 112 291 372 431 791 831 4011
result: 314155450783110080.0000000000
21. Pie spreadsheet models
Here are spreadsheet models for each text analyzed.
English: "A BAD CAB"
Greek: John 1:1
Hebrew: Genesis 1:1
22. English: A BAD CAB
select text Here is how to verify the calculations using a spreadsheet.
Select and copy the above text into the clipboard.
Paste the copied text into a new spreadsheet into cell A1.
Adjust the formatting and cell widths as desired.
23. Greek: John 1
select text Here is how to verify the calculations using a spreadsheet.
Select and copy the above text into the clipboard.
Paste the copied text into a new spreadsheet into cell A1.
Adjust the formatting and cell widths as desired.
24. Hebrew: Genesis 1
select text Here is how to verify the calculations using a spreadsheet.
Select and copy the above text into the clipboard.
Paste the copied text into a new spreadsheet into cell A1.
Adjust the formatting and cell widths as desired.
The purpose of this page is to get you thinking critically about the subject matter and then decide what you should do about it.
25. Iota subscript
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Words: ιωτα=1
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ᾳ = α + ͅ = ᾳ = ᾳ
ῃ = η + ͅ = ῃ = ῃ
ῳ = ω + ͅ = ῳ = ῳ
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At one time in ancient Greek, the letter "
ι" as English
"iota", when following the Greek letters "
α" (alpha), "
η" (eta), and "
ω" (omega), had a distinguishable sound.
Eventually, the sound difference disappeared but the iota was still written. Once learned, academics (scribes)
never give up the complexity.
Sometimes this
iota subscript analogy is used by pastors but this iota subscript did
not exist in
GNT or
LXX (Septuagint) times.
26. Iota subscript
One potentially confusing part of the analysis is that the Greek has a double letter eta with iota subscript "ῇ" that acts as if it were a separate iota "ι" or "jot" with an eta "η". This double letter appears in the second word "αρχῇ" meaning "beginning". We get the word "archaic" from this Greek word.
27. Iota subscript
Matthew 5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled. [kjv]
αμην γαρ λεγω υμιν εως αν παρελθη ο ουρανος και η γη ιωτα εν η μια κεραια ου μη παρελθη απο του νομου εως αν παντα γενηται [gnt]
Greek: John 1:1 (with iota)
over: 259 39 548 79 131
under: 111 171 293 312 671 711 3733 7191
result: 27183128121964234165317352899020962398208.0000000000
Greek: John 1:1 (without iota)
over: 256 310 547 79
under: 111 293 312 671 711 3733 7091
result: 2703640352349749056076162169243198029824.0000000000
The two values are within
1% of each other. This reference to "
iota" by Jesus may have deeper meaning than one might otherwise expect.
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Details are left as a future topic.
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28. Matthew 5:18
KJV: For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
Greek: αμην γαρ λεγω υμιν εως αν παρελθη ο ουρανος και η γη ιωτα εν η μια κεραια ου μη παρελθη απο του νομου εως αν παντα γενηται
29. History
2008: After hearing about the results described on this page, I decided to check the claims out in detail. After confirming the claims, I wanted to make it easy for anyone to verify (or refute) the formula by visual inspection and then copy-paste the formulas into a spreadsheet for verification of the calculations.
2023: This series of pages was originally started in April 2008. The pages were updated in 2012 and eventually became disconnected from the web system until December 2020 when they were updated (but not published) to use the new formatter system and new web system approach (ASP to PHP) with new research using multiple corpus collections using the entire corpus rather than just the two verses (one Hebrew and one Greek). They were eventually updated with more comprehensive analysis.
The following is some extra material not needed above.
30. First and the last
One interesting part of this verse is the Hebrew untranslated word "את". Since "א" (aleph) is the first Hebrew letter and "ת" (taw) is the last Hebrew letter, this is similar to the Greek "α" (alpha) and "ω" (omega). In Greek Jesus said he is the alpha and the omega, the first and the last. In Hebrew, the word for God (and Jesus in prophecy) is often associated with the untranslated word consisting of the two letters aleph and taw.
31. Digamma
The digamma "Ϝ" can be written as "Ϛ", called "stigma", which was developed during the Middle Ages and can easily be confused with the ending "sigma" character "ς".
The digamma "Ϝ" is named because it looks like two gammas "Γ" offset somewhat. The Greek digamma "Ϝ" ("v" or "f" sound) is related to the English "F" through Latin which is why the two characters appear similar.
32. End of page
