# The Watermark

In my last post I began to display some astounding geometry encoded within the original Hebrew words of Genesis 1.1. These pixellated images are revealed when the 28 letters comprising the text (unchanged for well over 2000 years) are read as numbers, following the well-known and historically-attested numerical substitution scheme, introduced sometime between 200BC and 100BC, that the Hebrews used for everyday counting.

After sectioning off the final two words in Genesis 1.1 we found the number 703, which is the core triangle within triangle 2701. These have been dubbed the *Creation Triangle* and the *Lesser Creation Triangle*. [1] Here is the image again.

If we now section off the first two words, we create a symmetrical 2-3-2 pattern, trisecting 2701 into the following three numbers:

Words 1 and 2 -- **1116**

Words 3, 4 and 5 - **882**

Words 6 and 7 —- **703**

Now if we perform two simple calculations using all three numbers, we discover another ‘zip file’ ready to be opened:

1116 - 882 + 703 = **937**

703 + 882 - 1116 = **469**

Amazingly, these numbers define a Star of David! This is hexagram 937 and its internal hexagon of 469 units, and the star is formed when triangle 703, seen above, self-reflects. Again, we find the largest figure in its family that will fit inside the Creation Triangle. All this is shown shown below. [2]

Note that, as always, all the numbers defining these pixellated figures are already found within the text.

Figurate numbers were already part of mathematics in Biblical times. Could this have been the work of the original writer or even a later editor of Genesis 1.1? That’s a possibility, but there are at least six difficulties to consider:

First, there is the tremendous problem of creating a text that makes grammatical sense, yet is packed with encoded numbers. In a world without computers or electronic calculators, creating such a verse from scratch would surely be next to impossible.

Second, if a later editor made the textual changes, they would face the even more daunting task of working with what was already written. Letters would have to be inserted, moved around or deleted, while keeping words correctly spelled and the grammatical structure of the verse kept intact. Retrospectively inserting not just one but many figurate numbers into that verse really would be impossible.

Third, Genesis 1.1 is thought to have been written about 300 years before the Hebrews began to use letters as numbers. So the Hebrews would require to have learned alphabetic numeration long before all available evidence suggests they did.

For retrospective encoding, a fourth problem is that these are the most famous words ever written, at the very apex of the Torah, held within a scribal tradition obsessively concerned with accuracy and a religion holding that these words came directly from *YHVH*. If the lettering was altered in any way, it would quickly have been noticed and regarded as the greatest possible offence against God and man.

The fifth difficulty, both for initial and later insertion of numbers, relates to the beliefs held by the ancient Jews. The writer of Genesis 1.1 (and any possible subsequent editor) would have been a monotheist and would not wish to suggest God is a Trinity, clearly implied by the encoded triangular figures.

But there is another difficulty that is the most devastating of all for those who claim the Bible could not have been inspired by a higher power and which alone is enough to discount both possibilities: *there is mathematics encoded in Genesis 1.1 that was unknown to man at the time the verse was written*.

The Star of David shown earlier was certainly known, in this and other cultures. However, the self-reflection of a triangle to form a hexagram is step 1 of a mathematical process only discovered around the turn of the 20th Century. This process creates a mathematical object known as the Koch snowflake. [3]

Notice that the first step creates the hexagram.

Of course it’s only one step, not enough in itself to convince us. But the Koch Snowflake has a complimentary figure known as the Koch anti snowflake, which begins with the same triangle.

Starting with a triangle, the first step of this process creates a trefoil and if we begin with triangle 703 we create trefoil 505, a number also found within Genesis 1.1! We uncover it by subtracting the sum of the last three words from the sum of the first four words.

So contained within the Bible’s opening verse are two figures representing the first steps of two complimentary processes, one creating the Koch snowflake, the other the Koch anti snowflake.

These are famous examples of a new kind of mathematics known as *fractal geometry*, which was totally unknown 2500 years ago. The discovery and comprehension of fractals require a level of mathematical subtlety the ancients did not possess. For example, fractals have fractional dimension. The outline of the Koch Snowflake has a dimension of about 1.26 and this means it is not a one-dimensional line, like the outline of a circle or triangle, nor a two-dimensional plane, but *something in-between, *a line crinkly all the way down to infinity and therefore not really a line at all.

The idea of fractional dimension is startling and counterintuitive even today, but 2500 years ago Greek mathematicians were just getting to grips with the simpler Euclidean geometry we now learn at school.

There are an infinity of fractals. Why the Koch snowflake and anti snowflake? Around fifty years ago a discovery was made about fractals that caused a revolution in mathematics and science: *approximations of fractals are found everywhere in nature*. [4] Fractals are built into natural forms and patterns like people and trees, crystal growth, galaxy formation and the foldings of clouds and the ruggedness of a mountainside. The Koch snowflake and anti snowflake are particularly easy to see in many created forms.

The Koch process can be taken an infinite number of steps, each creating a unique snowflake. [5] These symbolise the infinite fractal variety of God’s Creation - which is the very subject of the Bible’s opening words! [6]

What I have shown here is the first part of an *authenticating watermark on the Bible*. Placed at the very apex of Scripture, the watermark deftly trumps all arguments against the Bible’s Divine origin by displaying encoded digital images. These display, for all to see, foreknowledge of fractal geometry in the account of how God Created our fractal universe.

Bill Downie 24/4/23

The next page is here.

Notes

The names are due to the late Vernon Jenkins, who laid the foundations for this work, finding much of the material in this and the previous two pages. The rest was found by other researchers, including myself. The interpretation is my own.

This was discovered by American researcher Richard McGough (Biblewheel).

Discovered by Helge von Koch.

Discovered by Benoit Mandelbrot.

The encoded fractals are always early-stage precursors of the true figures, although I call them all fractals for simplicity.

Fractal-like natural objects, like a fern or a tree, represent only a few steps towards the fractal they approximate. Pixellated images are ideal for their representation, standing between nature and the infinite perfection of mathematics.