Irrational Encryptions

As explained in Gematria in a Nutshell, English gematria is a modern relative of Hebrew gematria and its Greek equivalent. Gematria is the discernment and study of what appears to be a kind of numerical cyphertext within at least some languages, whereby words and phrases related by meaning are also related through their numerical value. Through gematria, a second layer of meaning has been added to Scripture, including the English language NIV Bible (1984 version). Here, English and Hebrew gematria join forces to create a modern miracle in the encoding of three irrational numbers and one physical constant.

If the standard value of the Masoretic Genesis 1:1 (1) is divided by the ordinal value of the NIV Genesis 1:1 (2), a fair approximation of pi, the ratio of the circumference to the diameter of a circle, is obtained. The performance of similar calculations with the NIV Genesis 1:1 and other significant passages from within the NIV Bible, yields fair estimates of Phi (the Golden Section) and e (Euler's number). The three approximations sum to a number which differs from the true sum of pi, Phi and e by the phenomenally small margin of one part in five million.

I have also found an encoding of alpha, the electromagnetic fine structure constant, involving the NIV Genesis 1:2. This approximation is in error of the most recent estimate of alpha by only one part in five hundred thousand.

The Irrational Numbers

Pi, Phi and e are known as irrational numbers (3) and are probably the three most valuable absolutes in mathematics, supporting the entire edifice of science and technology. The numbers are introduced below.



The Biblically-Derived Numbers

The biblical passages from which the irrational numbers can be derived are given below, along with their numerical values. Note that these are some of the most theologically-significant verses in the whole of scripture.

1. Standard value Genesis 1:1 (Masoretic)

Masoretic Genesis 1:1 (a) = 2701 = G1:1 (Mas)

2. Ordinal value Genesis 1:1 (NIV)

In the beginning God created the heavens and the earth.

NIV Genesis 1:1 (o) = 430 = G1:1 (NIV)

3. Ordinal value John 1:1 (NIV)

In the beginning was the word, and the word was with God, and the word was God.

NIV John 1:1 (o) = 695 = J1:1 (NIV)

4. Summed ordinal values of the four versions of the Superscription (NIV)


S (Matt.) (o) = 343

S (Mark) (o) = 185

S (Luke) (o) = 269

S (John) (o) = 373

Sum of NIV Superscriptions (o) = 343 + 185 + 269 + 373 = 1170 = SI (NIV)

In a book of 31086 verses it would be relatively simple to find a few that gave these numbers. However, it should be immediately be obvious to any reader who is familiar with the Bible that these are very high-profile verses of great theological import and that there are thematic connections between them. The fact that these particular verses are involved is already suggestive of intelligent design. In the discussion section below I comment further on the apparent logic of the choices of verse and on other aspects of these encodings.

The Approximations Of Pi, Phi and e

Now we come to the calculations themselves, which are simple divisions of one of the derived numbers by another. A unifying feature of these encodings is the use of the NIV Genesis 1:1 as the denominator in every calculation, which I discuss later.

Note that in the calculation if pi a factor of 2 has been inserted into the formula to obtain the approximation. This is the only time such an adjustment is required. This always seemed to me to be a weakness in my argument that these numbers are encoded. However, in September 2009 it was brought to my attention that many mathematicians and scientists think that 2pi should replace pi as a fundamental constant. I also discuss this later.

1. The Approximation of Pi

2. The Approximation of Phi

3. The Approximation of Euler’s Number

All of the derived numbers are within +/- 0.11% of the correct values. In fact, they could easily substitute for these values in many calculations (4). However, it should be said that it is fairly easy to obtain this level of accuracy, even with small whole numbers. For instance, 22/7 is almost as close an approximation of pi as is obtained with the biblical numbers. Therefore it could reasonably be argued that these results are not spectacular enough to be convincing evidence of intelligent design.

Because two of the errors are underestimates and the third error is an overestimate, a cancelling effect will be evident when the values are added together. To measure this effect the approximations are summed and the result compared with the true sum of pi, Phi and e. This procedure is also implied by the use of Genesis 1:1 in all three calculations, suggesting the numbers are linked in some way. When the approximations are duly summed, something spectacular does command our attention...

4. The Approximation of The Combined Values Of pi, Phi and Euler’s number

The sum of the three approximations is in error of the true value by the fabulously small margin of 0.00002%, or one part in five million (5). This is about 4000 times smaller than the average magnitude of the individual errors, which is 0.078%. How much would the error be expected to cancel out? The simple arithmetic mean of the errors (which ignores the individual weighting effects of the three numbers) is 0.013%, about 6 times smaller than the average magnitude of the individual errors. Empirical work indicates that this is about the expected cancelling effect. However, the observed error is 700 times smaller than this - well beyond any expected reduction.

The three separate calculations can be reduced to a single pair of numbers:

When I tried to find a more accurate approximation of the sum by dividing whole numbers, another startling fact emerged: no two whole numbers below 8000 give a more accurate estimation of the combined value of pi, Phi and e than this pairing. This is another piece of evidence that strongly suggests the biblically derived numbers were deliberately encoded. But why combine these three mathematical absolutes? The answer is apparently in their sum, which has obviously been chosen for this encoding because of its first four digits, which serve as a kind of calling card.


The Calling Card

The first four digits of the combined approximation we just calculated are as follows:


If we calculate the ordinal values of the two words 'Jesus' and 'Christ', we obtain 'Jesus' = 74 and 'Christ' = 77 . Placing the two numbers side by side, instead of summing them as we would normally do, we obtain these same four digits.



1. We find apparent encodings of the three most important numbers in mathematics.
2. The numbers are encoded in such a way as to suggest that they are somehow linked.
3. When these numbers are summed, the individual errors, already small, almost completely cancel out.
4. This leaves a number, the first two pairs of digits of which are the ordinal values of 'Jesus' and 'Christ'.

I think the digits 7477 reveal to us the identity of the Author of this encoding, an Author who has signed His work elsewhere.


Could mere chance explain this phenomenon? The text of the bible is a large data set from which to derive numbers, and pseudo-encodings could easily be found from selected portions of texts. However, I think that there are very significant mitigating factors against a chance hypothesis.

1. The individual approximations of pi, Phi and e are fairly accurate: all fall within the range +/- 0.11% - and are of similar magnitude.

2. The individual errors almost completely cancel each other out, to leave an extremely precise value for the combined irrational numbers. The huge difference in magnitude between the errors in the weighted and unweighted averages is enormously unlikely to have happened by chance, although further work is needed to quantify this statement.

3. Pi, Phi and e are not obscure numbers. They are the three most famous numbers in mathematics, pi and e in particular supporting the entire edifice of science and technology. The importance of Phi in art and architecture has been recognised for millenia.

4. The Bible is no ordinary book: it is the most influential written document in existence. Furthermore, the NIV Bible is the most popular modern English translation of the Christian Bible (now outselling even the KJV) and the Masoretic Text is the standard text of the Hebrew Bible.

5. Of the Bible's sixty-six books, five of the most theologically significant for Christians happen to be involved: Genesis, the first book in the Bible, and the four gospels.

6.The verses themselves could scarcely have greater theological import, especially in connection with the status of Jesus Christ and His last days on earth:
a) Genesis 1:1 (pi, Phi and e), a sweeping statement of our origins, is the most important single sentence in the bible.
b) John 1:1 (Phi) introduces the Word, present with God in the beginning, and identified with Jesus Christ.
c) The four versions of the Superscription are within verses that are integral to the drama of The Crucifixion, which, along with The Resurrection, was the fulfillment of Christ's Incarnation.

7. The verses are also found in extremely prominant locations:
a) The most important number of all, the denominator for each calculation, is derived from the Bible’s very first verse.
b) The numerator for pi is derived from the standard Hebrew version of this same verse.
c) The numerator for Phi is derived from the first verse of John.
d) The numerator for e is derived from the sum of ordinal values of the four Superscriptions, which are so important that they are always written in capital letters.

8. Three of the portions of text are complete verses, rather than parts of verses. The other four portions are different versions of the same statement within four verses: the Superscription. As such they have huge import to Christians.

9. There is a high degree of relatedness between John 1:1 and Genesis 1:1. They mirror each other in subject matter (the beginning of Creation) and placing (the first verse of each prologue).

10. The four versions of the Superscription are also highly related and are found in the four gospels, no less. Moreover, they are thematically related to the event that the New Bible Code itself exists primarily to interpret: the terrorist attacks of September the 11th, 2001. As this website shows, 9/11 was the first of two events that were manifestations of the Second Coming and was a staged drama, representing the Crucifixion of Jesus Christ. Therefore, as the principal marker event for the ‘end times’, it is thematically fitting that the Superscriptions should take part in these encodings.

11. The NIV Genesis 1:1 provides the number for the denominator in every division, and so a common thread links each calculation. In the derivation of pi, Genesis 1:1 provides the numerator (Masoretic) and the denominator (NIV). It is singularly appropriate that pi, perhaps the brightest jewel in the crown of mathematics, should be woven like a sequin into these historic versions of the bible's first verse.

12. Very good approximations of pi and e have already been found within Genesis 1:1 (pi again) and John 1:1 (e), as originally penned, by Vernon Jenkins and coworkers. These results support the new findings, and are in turn upheld by them. Encodings have also been found within the same texts of the other two numbers discussed in this page: Phi and alpha. Therefore all four numbers are encoded in the original scriptures, three are encoded within the NIV, with one number, pi, encoded between them.

13. One of the numbers, pi, is encoded as its double, 2pi. The extra factor of 2 and the fact that two versions are involved in this encoding is consistent with the fact that the code exists to announce the events that were manifestations of the Second Coming. But this is making the best of what could be viewed as a slight imperfection in the code. It may be that such a compromise was necessary but it would be more elegant and satisfying if pi itself had been encoded. However, I was recently (9/09) pointed to compelling evidence from mathematics and physics that 2pi, the ratio of the cirmcumference to the radius of a circle, is more fundamental than pi. So the encoding of 2pi may be a deliberate reference to this possibility, something which was certainly unknown to me when I found the encoding in 2004. 2pi is 6.2831853 ... The first four digits of this number are 6283, a numerical anagram of 2368, standard value of Ihsous Christos. 

Addendum: Another intriguing link between Jesus Christ and pi is found in the standard values of the accepted spellings of the Greek and Hebrew versions of the Lord's name. These are as follows:

Ihsous Christos (Gr., s) = 2368

Yehoshua HaMashiach (Heb., s) = 754

Dividing the larger number by the smaller gives another reasonable approximation of pi:

2368/754 = 3.14058355 . . .

This is in error of the true value by 0.032%, or 1 part in 3000.

14. Further evidence of a link between Jesus Christ and the encoded numbers is found in the gematria of the name 'Jesus Christ' itself. The first four digits of the combined value of pi, Phi and e are 7477, which embodies the ordinal values of 'Jesus' and 'Christ' and the numerico-geometric properties of which link it to the reduced values of names for our Lord.

Taking all these points together, is it likely that such highly specific portions of text would just happen to give the numerators and denominators of fractions that are good approximations of the fundamental mathematical constants? For the reasons given above, I would suggest that chance is not a tenable explanation for this phenomenon and that these numbers have been deliberately woven into the biblical verses.

The Fine Structure Constant

Alpha, the electromagnetic fine structure constant, is a physical constant, the coupling constant for the interaction of photons with electrons (7). Put more simply, alpha quantifies the strength of the interaction between light and matter. It is important to be aware of the nature of alpha, because its encoding in the NIV involves two numbers, one related to light, the other to matter.

The most recent calculated value for alpha is shown below.

1. The Biblically Derived Numbers

a) The ordinal value of 'light'.

Light (o) = 56

b) The ordinal value of Genesis 1:2 (NIV). This describes the earth (matter) in a state of darkness (without light).

Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.

NIV Genesis 1:2 (o) = 1279 = G1:2 (NIV)

2. The Approximation of alpha

The error here is just under 1 part in 500000, a fabulously small deviation from the most recent estimate of alpha. The added factor of 6 may seem arbitrary, but 6 is related to the number 1279 in a geometric setting that is central to the New Bible Code (see below).

3. The Geometric Connection With Six

In The Creation SnowflakeI show how gematria associated with Jesus Christ is related to a fractal snowflake created by a process mimicking the growth of real snowflakes. The fifth generation of the snowflake requires snowflake 3517 to be surrounded by an outer ring, comprising six snowflakes of 1279 units. This outer ring,which is the denominator in the calculation of alpha, is shown below.


Snowflake Ring of 7674 (6 x 1279) Units


Bill Downie 31/5/04

Latest update 26/4/16


1. Masoretic text. This is the text used for the Biblia Hebraica Stuttgartensia (the Hebrew Bible), and is regarded as the authoritative version.

2. Holy Bible: New International Version (2001). This particular piece of the New Bible Code is also found in the New King James Version, the English Standard Version and the Revised Standard Version, which have the same wordings.

3. Irrational numbers are those numbers that can never be precisely calculated by the division of one whole number by another. Pi and e are also transcendental numbers.

4. If the derived value of pi were used to calculate the volume of water needed to fill a circular pond 3 metres in diameter and 0.5 metres deep, the calculated addition would be just 1 litre short of the required volume of 3534 litres.

5. If an error of -0.00002% were made in the calculation of the earth's circumference, the answer would be a mere 8 metres short of the true value.

6. Possibly related is the fact that the number 7477 is the 946th member of the prime number sequence. 946 is a rare trifigurate number: 11th in the series of hexagonal pyramidal numbers, 22nd in the series of hexagonal numbers and 43rd in the series of triangular numbers. Lord (r) = 22, Jesus (r) = 11, Jesus Christ (r) = 43.

7. Alpha is a measured physical constant, as opposed to pi, Phi and e, which are mathematical absolutes.