Numbers and Mathematics in YEHOVAH God's Creation

The Bible clearly states that the earth is designed. When Job questioned YEHOVAH God he got the reply:

The hand of YEHOVAH God is evident to all, from flowers, to human love to the starry heavens:

Clearly, the Designer of all things must have great wisdom and understanding. Some describe YEHOVAH God as "the Master Engineer," and modern engineering sometimes copies what we observe in nature.

Engineering relies upon numbers and mathematics, and so it is not surprising to find amazing numbers and mathematics embedded in YEHOVAH’s creation (as well as in the Bible). We will examine a few of these, starting with some simple examples. In each case we see the hand of understanding and design, and often this appears to point to YEHOVAH God as the Designer.

In Gematria, the most holy name of God, referred to as the Tetragrammaton, embodies some very interesting Golden Ratio relationships.

Gematria is a system of assigning numerical value to a word or phrase. It is likely that the term derives from the order of the Greek alphabet, gamma being the third letter of the Greek alphabet (gamma + tria) or from Greek geometria, “geometry.” Although apparently derived from Greek, it is largely used in Jewish texts, most notably in those associated with the Kabbalah, a set of teachings meant to explain the relationship between an eternal and mysterious Creator and the mortal and finite universe (His creation).

The Tetragrammaton, meaning “[a word] having four letters,” refers to the name of the God of Israel as YHVH (Hebrew: י-ה-ו-ה) that appears 6,828 times the Hebrew Bible, the first of which is in Genesis 2:4, which says, “This is the account of the heavens and the earth when they were created. When the LORD [YHVH] God made the earth and the heavens....” The letters, properly read from right to left, are:

HEBREW	LETTER NAME	PHONETIC SOUND
י	Yud	“Y”
ה	Hey	“H”
ו	Vov	“V”
ה	Hey	“H”

These four letters are usually transliterated from Hebrew as IHVH in Latin, JHWH in German, French and Dutch, and JHVH/YHWH in English. This has been variously rendered as “Yahweh” or as “Jehovah,” based on the Latin form of the term, while the Hebrew text does not clearly indicate the omitted vowels. In English translations, it is often rendered as “the LORD,” following Jewish tradition which reads the word as “Adonai” (“LORD”) out of respect for the name of God and the interpretation of the commandment not to take the name of God in vain.

The gematria values of the four letters in the Tetragrammaton (Yud – Hey – Vov – Hey) are 10, 5, 6 and 5. This indicates the importance of the number 5 in this Holiest Name of YEHOVAH God. Yud has a gematria value of 10. Vov has a gematria value of 6, which creates various ratios within this name of YEHOVAH God:

HEBREW LETTERS	RATIO	DECIMAL
Yud / Vov =	10 / 6 =	1.666
Vov / Yud =	6 / 10 =	0.600
(Yud + Vov) / ( Hey + Hey) =	16 / 10 =	1.600
( Hey + Hey) / (Yud + Vov) =	10 / 16 =	0.625

As Phi and it’s reciprocal phi are 1.618 and 0.618, respectively, we see that this Holy Name of YEHOVAH God intrinsically represents a set of ratios that reflect the golden ratio, or the Divine proportion, that we see all throughout His creation.

The Hebrew word for “when they were created” is BeHebaram. This word can be divided to also say “With ‘Hey’ were they created”, which suggests the importance of the number five in the creation of mankind.

The Hebrew Bible says that The Holy One created man “in the image” of God. The Hebrew word “in the image” is made up of 4 letters -- Bet, Tsadi, Lamed, and Mem.

HEBREW LETTERS	VALUE
Bet	2
Tsadi	90
Lamed	30
Mem	40
Total	162

The number 8 is important in male circumcision. YEHOVAH God instructed Abraham to circumcise a male child when he is 8 days old (Genesis 17:12). Why day eight? Medical science has shown that on the eighth day the amount of blood clotting factor prothrombin present in the body is more than 100% above normal, and this is normally the only day in the male’s life when this is the case. Today, Prothrombin Complex Concentrate (PCC) is used to accelerate blood coagulation. So day eight is the optimal day for minimizing hemorrhaging during circumcision!

Dimensions of Noah’s Ark

Nevertheless, it turns out that this is sufficient to perform serious analysis of the Ark’s stability using modern ship design techniques. Since there are many definitions of the ancient cubit, ranging from 17.5 to 26 inches, which cubit applies here? Some believe it was the Egyptian Royal cubit of about 20.6 inches. This makes the Ark about 515 feet long, or 6180 inches. Several measurements of what appears to be an ancient boat found on the mountains of Turkey appear to confirm this length. It is intriguing that 6180 appears in the reciprocal of the "golden ratio" 1/Φ = 0.618034 (described later).

There have been a number of naval studies based on the Ark’s biblical dimensions. One 1993 study using a cubit of 20.4 inches (510 feet long) concluded that the biblical dimensions were optimal for stability, strength and comfort, and that the Ark could handle 30m waves. A 1977 study assumed the common cubit of 18 inches, making the Ark some 450 long, 75 feet wide and 45 feet high. This study concluded that "the Ark was extremely stable" when four major stability features were examined, even in 210 knot winds. So, in major design aspects, Noah’s Ark was as good as modern shipping!

Footprint of Solomon’s Temple

Consider the footprint of Solomon’s temple in Jerusalem.

The biblical accounts about Solomon's Temple give a few of its dimensions, but not enough for a precise reconstruction of the layout. The oldest surviving information about the detailed layout of the entire Jerusalem Temple precinct is relatively late. It was transmitted in Mishnah Middot 2.1 from the end of the second century of our era and may therefore appear, at first sight, to refer to the then recently destroyed Herodian Temple. Leen Ritmeyer, an archaeologist, states that those Rabbis are more likely to have described the original plan of King Solomon's First Temple.

Solomon had used a 2:1 table (20 x 40 cubits) in the Hekal, or Sanctuary, which extended as far as the Holy of Holies, which was itself a cube of 20 cubits on each side. The Temple was thus divided into 1/3 and 2/3rds. The porch was 12 cubits by 20 cubits, which when divided by each other yield 1.6, a close approximation of phi or the Golden Ratio. The Sanctuary was itself a double cube, being 20 cubits wide by forty cubits long, this floor plan yielding the square root of 5, itself used in calculating the Golden Ratio.

A double cube floor plan, where the diagonals intersect in exactly the center of the veil between them (as in the Temple between the Holy of Holies and Holy Place) marks the center point of a compass distance that can hit every corner of the double cube. This complete circle when drawn, can then be intersected by the adjoining side extension from the double cube. This making the classic and exact phi length from side to circle along the veil adjoining side. A cube as formed by the Holy of Holies is also made use of in art and proportional geometry to construct the human head.

The impressive edifice built by Solomon housed the mysterious Ark of the Covenant. Exodus 25:10 gives the dimensions of this artifact: “Have them make a chest of acacia wood -- two and a half cubits long, a cubit and a half wide, and a cubit and a half high.”

A cubit is the measure of the forearm below the elbow. The ratio of 2.5 to 1.5 is 1.666…, which is as close to phi (1.618 …) as you can come with such simple numbers, and is certainly not visibly different to the eye. The Ark of the Covenant also approximates the Golden Section, or Divine Proportion.

Geometry of Sun, Moon and Earth

Scientists say "it is a happy accident of nature," "it is a striking coincidence," "sheer chance" or "a fluke of celestial mechanics." They are referring to the amazing geometry associated with the Sun, Moon and Earth. During a total eclipse the Moon casts its umbra (shadow) upon Earth’s surface so that the Sun is totally obscured, as depicted in Fig.1. The Earth, Moon, Sun geometry is such that only the beautiful corona of the Sun is left (conveniently permitting astronomers to analyze the Sun’s atmosphere). Since the Sun’s diameter is about 400 times that of the Moon, the eclipse can only happen if the distances of Sun and Moon from Earth (the geometry) are just right. It turns out that this is the case and both Sun and Moon subtend virtually that same angle Θ such that they look virtually the same size in the sky. Amazing!

Let’s do the math. Taking some average measurements, (space.com), the Moon’s diameter DM is about 2,159 miles, the Sun’s diameter DS is about 864,938 miles, the Moon’s average distance EM is about 238,855 miles (elliptical orbit) and the Sun’s distance ES is one astronomical unit (AU) or about 92,956,000 miles. So considering the angle subtended by the Moon, Θ = 2 × arctan (0.0045195) = 0.52° and the angle subtended by the Sun is Θ = 2 × arctan (0.0046524) = 0.53°. Chance, or YEHOVAH God’s amazing design?

In Genesis 1 we read that YEHOVAH God created (designed) the moon and the earth:

So, as with Solomon's Temple, we might expect His signature in the dimensions of these objects. If the moon is put directly on top of the earth, the combination of the mean radii of the earth and moon forms the height of a triangle with the mean radius of the earth as the base. Mean radius of the earth = 6371 km; Mean radius of the moon = 1737.1 km; 6371 + 1737.1 = 8108.1 (height of the triangle) 6371 (base of the triangle) ?(?6371?^2+?8108.1?^2 ) = 10311.69 (Hypotenuse of triangle) 10311.69/6371 = 1.61853... ? ?

Although there are many models describing the solar system's attributes, such as orbit times, distance between consecutive planets/satellites and period of rotation in terms of the golden ratio; it is remarkable that (like the pyramid of Giza) the moon and the earth on top of each other form a near approximation to the golden triangle.

I feel that the source which I got this from is reliable, but the author does tend to slightly over exaggerate some claims. For example, the golden triangle is only approximated when assuming the earth and the moon are perfectly spherical, which is not the case. Even though using an average radius to rectify this fact may give us very close values, it is beneficial to bear in mind that if we take the radius at different points on the earth then this can shift outputs immensely.

It is likely that this may be a coincidence, seeing as it has not aroused much interest within the scientific community, nor has it received much attention. However, I do feel that this is an interesting finding; independent verified readings for the radii were taken from a reliable source, cross referenced and mathematical calculations were then performed. Even with no bias and the utilization of independent figures -- the calculations still yield a close approximation to the golden triangle.

The "Just Right" Universe

Instead of a randomly evolving universe, wherever we look the physical, chemical and biological conditions appear to be "fine-tuned for life”. Some see this as the hand of a Designer and evidence of a Transcendent Intelligence. Others attempt to explain the fine tuning using the Anthropic Principle:

Put simply, the Anthropic Principle says there can be no observations without observers and so our observations must satisfy the conditions necessary for our existence. But this alone does not eliminate the concept of a “Designer”.

Examples That Appear “Just Right” for Life

(a) the distance of earth from the sun and moon and the relative sizes of the sun and moon give perfect eclipses

(b) the earth’s axial tilt of nominally 23.5 degrees gives moderate seasons and prevents temperature extremes anywhere on the planet

(c) the earth’s atmospheric oxygen is regulated (e.g. by methane) at about 21% for the dominant life forms today

(d) the earth’s magnetic field helps to keep the planet’s fragile atmosphere from being blown into space by the force of the solar wind. It also provides shielding from cancer causing cosmic radiation and aids navigation for man, birds, sea creatures

(e) even tiny changes in most of the physical constants (such as proton mass, gravitational force, and velocity of light) tend to make life as we know it impossible

Fine Tuned Physical Constants

Scientists point out that if one tweaks many of the dimensionless physical constants, then none of the cosmos we see would exist. For example, according to Einstein’s E=mc2, even small changes in the velocity of light will lead to huge changes in energy or mass. This implies, for example, that stars would produce the wrong elements for life.

If the proton mass increased by just 0.2% the proton would become unstable and decay. Since the hydrogen nucleus comprises just a single proton, then all hydrogen atoms would be destroyed, implying the destruction of water molecules etc. In fact, no more chemicals (or even elements) of any kind.

Gravitational force goes as the reciprocal of distance squared. The factor 2 here appears finely tuned and any variation from 2 would lead to decay of planetary orbits. And after studying the fine-tuning of the nuclear ground state energies of helium, beryllium, carbon, and oxygen, mathematician and astronomer Fred Hoyle concluded that:

We now turn to what might be termed "golden" mathematical ratios, sequences and spirals readily found in nature. It is often claimed that these can be seen for example in DNA molecules, human facial beauty, sea shells, insect populations, plants and galaxies. The "golden ratio" (designated Φ or "Phi") is an irrational mathematical constant, approximately 1.618, and this can be used to form the "golden rectangle" and from that we can develop the "golden spiral." When it comes to number sequences, the "Fibonacci sequence" (see later) is often found in nature, and this too can be extended to form a Fibonacci spiral. Moreover, the golden ratio can be found in the Fibonacci sequence.

Many claim that these mathematical laws appear to be beneficial (giving a sense of harmony and balance) and so man often tries to adopt them in his work, from art to music to building design. It is also claimed that, whilst we do not find such mathematics to be universal law, there is nevertheless a fascinatingly prevalent tendency to such laws in nature.

Reality Check:
Hoax, Superstition, Product of Evolution, or YEHOVAH God’s Design?

First, it is important to ask some general questions about the claims of "golden mathematics". Some claim they are pure conjecture and a numerical hoax:

It is claimed here that whilst there are indeed some Fibonacci spirals and golden ratios in nature, this doesn’t make them extraordinarily prevalent. Not all plants show the Fibonacci numbers and there are many other mathematical patterns in nature. Whilst some galaxies can be found that approximate to the golden spiral, most don’t. It is argued that people have a tendency to ascribe meaning or significance to things which really mean nothing! Clearly, any counter to such claims must show how golden mathematics points to a "Designer."

Many see the golden ratio and related mathematics as simply a remarkable result of evolution. For example, they claim plants have evolved the optimal arrangement of leaves on the stem as they grow, and the arrangement is often described by a Fibonacci series. More generally, it is claimed that the winning design in evolution allows an organism to survive longer than other designs and that the design with a golden ratio simply helped the host organism to survive better. It is readily admitted that the golden ratio has a real contribution to the "evolved" world:

That said, for these evolutionary claims to be true, evolutionary theory itself has to be verified. But to date, there is little tangible scientific support for evolution.

The golden ratio is also known as the "divine proportion," implying that it is real (not superstition and a hoax), it is designed (not a random result of evolution) and it is used by YEHOVAH God in His creation. Such a claim can only be verified by taking examples of golden mathematics in nature (YEHOVAH’s creation) and relating them back to truth, i.e. to YEHOVAH God, the source of truth. Does what we observe point to YEHOVAH? Let’s see.

The Golden Ratio and Number Sequences

The golden ratio Φ is a geometric proportion that has been known for millennia (Euclid wrote about it around 300 BC). It is an irrational number in that it cannot be written as a simple fraction, and so the decimal part goes on forever without repeating! Moreover, it is the most irrational number, and it is claimed that this property has real significance in YEHOVAH God’s creation.

The best way of defining Φ is to segment a line as in Fig.3. From this, a quadratic solution gives Φ= 0.5[1+√(5)] = 1.6180339… Note the perfect self-replicating property of Φ: if we fold b over a it will divide it in the golden ratio. If we then take the smaller part and fold it again it will again divide the line in the same proportion. This can be done ad infinitum without variance. A "golden rectangle" is a rectangle with ratio length/width = Φ.

It is important to realize that there is a mathematical relationship between Φ and numbers in the Fibonacci sequence (each number can be derived from Φ):

Here, each number is the sum of the two numbers before it, and the sequence of the ratio of successive Fibonacci numbers Fn+1/Fn converges to Φ. For example, 89/55 = 1.618181 and 2584/1597 = 1.6180338. In fact, starting with any two positive numbers, the corresponding sequence of the ratio of successive numbers formed by adding the last two numbers always converges to Φ.

We now ask: "Is there a clear link between Φ and Fibonacci numbers to YEHOVAH God’s creation?" Consider the following.

The Golden Spiral is a pattern that can be found in nature, art, engineering, and even human construction. It has several names: Golden Ratio, Golden mean, the divine proportion, and Phi (similar to Pi, in the respect that the digits theoretically go on forever). Phi is the infinite number of 1.618 used to represent this so-called Golden Spiral. Is your head spinning yet? Let�s take a look at this visually:

You start with the main rectangle, which is drawn to that Phi number, in ratio form: 1:1.618. If you draw a line inside the rectangle to form a perfect square, the remaining rectangle will have the same ratio as the main rectangle. You can keep doing this over and over forever! Look at the spiral shape found within the drawing. See how the line starts at the bottom left corner, and the spiral forms by following the opposite corner of each square as it goes clockwise?

How does the Fibonacci Sequence fit into this? An Italian mathematician, named Leonardo Fibonacci, discovered this idea of finding the Golden Spiral within the design of our universe. Think of it as the recipe for how to make that Golden Spiral! As we have already seen, his �recipe� is a simple pattern of numbers made by adding the previous two together to get the next number in the sequence, which looks like: 0,1,1,2,3,5,8,13, 2, 34, 55, etc. The math looks like this: 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8 and so on.

Why is it important? Lots of geometric shapes found in nature and art are related to the Golden Spiral and Fibonacci Sequence, from sunflowers to hurricanes to galaxies to the Mona Lisa painting! For example, sunflower seeds are arranged in a Fibonacci Sequence, keeping the seeds uniformly distributed no matter how large the seed head may be, which helps harness the sun more efficiently! While this series of numbers from this simple brain teaser may seem silly, the Golden Spiral and the Fibonacci Sequence have been rediscovered in an astonishing variety of forms, from computer science to engineering new buildings, the stock market, and even Picasso�s art!

In Music

Music is a fundamental element of YEHOVAH’s creation. It was present at the dawn of creation (Job 38:7) and man’s musical instruments are used in praise to YEHOVAH God:

Musical instruments can embed Fibonacci numbers. Consider the piano keyboard. We find 5 black keys and 8 white keys making up an octave of 13 keys. And 2 black keys plus 3 black keys making up 5 black keys within the octave. These are simple progressions through the Fibonacci sequence! Fibonacci and Φ relationships are often found in the timing of musical compositions e.g. the climax of songs is often found at roughly 61.8% of the song. Fibonacci and Φ are also used in the design of violins. So did YEHOVAH God embed Φ in music?

In the Earth and Earth-Moon System

Consider a golden rectangle of sides a and b placed inside the Earth, as in Fig.4. By definition, tan(Θ) = b/a = 0.6180340, or Θ = 31.72°. So point X on the earth’s surface would be at latitude 31.72°. Now, the latitude of the Messiah’s birthplace, Bethlehem, is about 31.68°. So does Φ point to YEHOVAH's chosen redeemer?

Let’s redraw Fig.2 as in Fig.5 with triangle side b linking the centers of earth and moon. Using the same moon-earth sizes assumed in Fig.2 and scaling the sides of the triangle to give a = 1, we find c = 1.618590 i.e. very close to Φ (using other moon-earth dimensions gives c = 1.618454).

Let’s extend the concept of a divine proportion to the rest of the solar system. Since YEHOVAH God created the planets we might expect His signature to be in their orbits for example. Consider nine planets, from Mercury to Pluto. Pluto has been reclassified as a "dwarf planet," but is, nevertheless, still there! The same goes for Ceres (the largest object in the asteroid belt between Mars and Jupiter) which is also classified as a dwarf planet. So in all we could consider ten "planets" in our solar system. Each planet has an eccentric (non-circular) orbit, so we work with mean orbital distances from the sun, and normalize this distance for Mercury (set it to 1). In this case, it has been shown, that the average of the mean orbital distances of each successive planet in relation to the one before it is 1.61874, very close to Φ.

Clearly, calculations like this are subject to further scientific discoveries, as in the dwarf planet Eris, but the close agreement with Φ is interesting, suggesting YEHOVAH God’s signature on the solar system. This concept is supported when we consider the period in days of each planet’s revolution around the sun. When these periods are compared with that of Pluto, the ratios in round numbers come close to Fibonacci numbers. And since there is a close relationship between Fibonacci numbers and Φ, and between Φ and YEHOVAH God, some argue that YEHOVAH’s signature can be seen in the Solar System.

It should be no surprise that the Golden Ratio�s organizing role in nature also extends to human beings. Golden proportions, Fibonacci numbers, and the Golden spiral all reveal themselves in the bodies of human beings. The Golden Ratio makes some surprising appearances in the area of cardiology.

With respect to the measurement of the heart, based on research, the ideal ratio between the overall vertical measure of the heart and the left ventricle transverse is thought to be f. Studies of cardiac patients conducted in China and Sweden have found that patients with heart failure are very unlikely to have measurements whose ratio is close to f. This leads to the conclusion that the Golden Ratio can be used to detect subtle deviations from the norm, which should really be thought of as deviations from stability, earlier in the disease process to help improve outcomes for patients.

A 2019 paper reporting research on blood pressure and mortality finds that ratios of systolic to diastolic blood pressure values that deviate from the Golden Ratio are associated with greater �allcause mortality.� The research, which was conducted in the United States, includes a total of 31,622 participants, 2,820 of whom died during the course of the study. Through an analysis of the patients who died, the researchers reached the following conclusion:

The research team suggests that rather than using absolute parameters for each blood pressure value (that frequently change due to conflicting research) to assess risk, it might be more helpful to calculate ratios of systolic to diastolic blood pressure to look for deviations from the most stable value, f. L�ttge explains that �fluctuating asymmetry is a widely used measure of developmental instability� and describes a stability continuum ranging from perfect symmetry to death (12, p. 102).

Again, considering cardiology, even the Golden angle makes an appearance in the anatomy of the heart: The �angles between the outflow tract axis and inflow tract axis and angle between pulmonary trunk and ascending aorta approximate the golden angle.�

An interesting example of the Golden spiral in the human body appears in the inner ear. As can be seen in Figure 9.3, the cochlea replicates the spiral of the Nautilus. The cochlea is a complex organ whose function is to translate sound vibrations into nerve impulses that get sent to the brain. Depending on the frequency and intensity, different parts of the cochlea move in different ways. Research shows that the spiral shape of the cochlea makes it possible for humans to hear low frequency sounds.

Let’s turn from anatomy to the molecular. YEHOVAH God has made both and we might expect His signature on the very coding of life -- our DNA.

Deoxyribonucleic acid (DNA) plays a crucial role in all living organisms because it is the key molecule responsible for storage and self-replication of genetic information. DNA can form a wide range of double helical structures and the most common form is B-DNA (Crick and Watson), Fig.6. The "pitch" (one full 360 ° rotation of the helix) is just 34 angstroms, whilst the diameter of the B-DNA helix is variously given as approximately 20. So the geometry of the most common DNA molecule might be seen to reflect the divine proportion: 34/21 = 1.6190.

X-ray crystallography has been used to examine the structure of the DNA molecule. A detailed geometric analysis (axial view) reveals five sets of concentric double pentagons. Each double pentagon can be seen as a pair of pentagons offset from each other by 36°, creating a decagon. A decagon pattern is clearly seen in the axial view of ideal B-DNA, Fig.7.

So axial analysis of DNA reveals 10 concentric pentagons. Others have constructed a helix (as in Fig.6) from 10 regular pentagons orientated about a decagon.

Why is the pentagon so important to DNA? Consider the double pentagon (decagon) in Fig.8. If the base of the pentagon is 1, then the span (diagonal) of the pentagon is Φ. And we know that Φ has the unique self-replication property. Some claim that DNA uses this fundamental self-replication property:

The DNA double helix molecule accomplishes (self-replication) feats by means of the very same self-replicating attributes of the very geometry upon which it is built.

So does DNA carry the signature of YEHOVAH God via the self-replicating property of the "divine proportion," Φ? And if not, who designed-in the coded genetic information in the DNA nucleotides?

Let’s stay with small things. In order to study nanoscale quantum effects, researchers focused on the magnetic material cobalt niobate. The golden ratio has quite recently been observed in the quantum world of solid state matter. Researchers in Helmholtz-Zentrum-Berlin, Germany, in tandem with researchers from Oxford and Bristol University, UK, have made an extraordinary observation of phi in the nanoscale world of solid state matter. This recent, scientifically verified discovery is quite unprecedented as it demonstrates the underlying symmetries that can be found within systems of complexity; moreover what is even more exceptional is that phi is easily detected in the process.

The golden ratio has only been observed due to the revolution in sub atomic detection, which is owed to the increase in human understanding. (SciTechStory, 2010) (PhysOrg, 2010) The research was concerning the oscillation properties of a chain of cobalt niobate atoms. Cobalt Niobate is a mixture of the element Cobalt which is magnetic; Niobium, which is a transition metal and Oxygen. A significant property of this material is the fact that when its atoms are liked up into a chain, cooled down to near absolute zero (0 kelvin or -273.15 degrees), a phenomena known as ferromagnetism occurs. Ferromagnetism is another term for saying the atoms magnetize and de-magnetize like an iron bar, or a thin atom-wide bar in this case.

Since the atoms have a quantum property known as spin, internal angular momentum, this means that they interact with a magnetic field. The researchers realized that when they applied a magnetic field at right angles to this "spin" it introduced a lot of uncertainty; the whole system collapsed into a new state called "quantum critical" where the line of atoms acted like a "guitar string". The main researcher behind the paper explains:

This result, from an experiment conducted in January 2010, was the first of its kind to report the discovery of phi in the quantum behavior of atoms. This is an extremely significant scientific experiment to report such an overt observation of the golden ratio. It displays the relationship between a mathematically simple ratio and an area mainly describable by advanced mathematics; it also displays the association between large and small things alike. For example phi is observed in the living organisms alongside the planets in our solar system. It speaks volumes that such a well-known ratio can be seen in diverse situations regardless of size and still be applicable.

A quasicrystal is a crystal which has a structure which is ordered but not periodic; this means that it follows a certain pattern that does not seem to repeat itself. (Sample, 2011) This is referred to as five-fold symmetry as a pattern cannot be translated in any way to fit the original. Quasicrystals were discovered in 1982 by Daniel Shechtman when a compound of aluminum was observed at nano-scale level using diffraction techniques; the compound seemed to have a different atomic structure than the currently prevalent crystal theory predicted (Shechtman, 2011). When this discovery was announced it caused uproar in the scientific community. However, after much opposition and skepticism Shechtman was awarded the Nobel Prize for Chemistry in 2011.

The relationship this has with the golden ratio is, once again, implicit. Quasicrystals can only be modeled as a set of Penrose tiles, since these tilings are the only mathematical entities to display five-fold, ordered and aperiodic symmetry. Penrose tiling contains an array of shapes related to the pentagon; the most commonly known one is the rhombi tiling (Figure B). (Poliakoff, 2011) The pattern this makes has no translational symmetry but has rotational symmetry of order 5; hence the name fivefold symmetry. Penrose tiling has a very close relationship to the golden ratio (Dunlap, 1998, pg. 111 -- 121). When a simple way of modeling a complicated crystal structure in matter is intricately connected with the golden ratio; it begs the question whether it is a mere consequence of Penrose tiling or something even more significant in the makeup of nature. The Master Designer, maybe?

An interesting aspect of this discovery is that fivefold symmetry was realized in early Islamic architecture, very similar to the Penrose set of tiles; the tiling used to tile the walls of a palace was analogous to the structure of the quasicrystal. The significance of this is that it illustrates the link between art/architecture and science, in some part, due to phi (Hamish Johnston, 2007).

My sources for this are mainly web based; since this was a relatively new discovery it has garnered most of its attention on the internet. Although the majority of my sources are web based I am fully confident that they are reliable as experts in their fields are recorded lecturing about the given topics. One video source features the person who did the research: Daniel Shechtman whereas the other video resource is provided by the University of Nottingham's chemistry department. The two web based articles are quoted from a site run by the Institute of Physics and the Guardian newspaper. Whereas my paper-based source is from Richard A. Dunlap who is a university physics professor at Dalhousie University (Canada) and has had numerous books published.

So Φ is found even at the quantum level! Is this coincidence, or YEHOVAH God’s design?

In Plants

The golden ratio crops up indirectly in plant life via the Fibonacci sequence. The relationship between the Fibonacci sequence and the golden ratio is very strong. A Fibonacci sequence has, as noted previously, the main characteristic of a term in the sequence being defined as a sum of the preceding two terms. The first ten terms are: 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55., the relationship of phi with this sequence is that the ratio between two consecutive terms converges to 1.61803. (the golden mean) as the series continues.

5/3=1.666... => 8/5=1.6 13/8=1.625 => 21/13=1.61538 34/21=1.619.. and so on.

The Bible states that YEHOVAH God created herbs and trees (Genesis 1.11) and so we can expect to see YEHOVAH’s signature here too. A link between Φ and plants comes from the "golden angle," Fig.9. As in Fig.3, we make the ratio of two (arc) lengths a and b such that a/b = Φ. In this case, the golden angle Θ = 360/(1+Φ) = 137.5° approximately.

The golden angle plays a fascinating role in the arrangement of leaves on some plant stems or in the arrangement of petals on certain flowers. A common arrangement is for leaves to emerge at different nodes and at different angles on the stem, forming a spiral pattern (leaves 1,2,3…10 in Fig.10 form a spiral). A key feature is the fraction of a circle rotated between successive leaves, called the divergence angle when measured in degrees. In beech and hazel this is 1/3, in oak and apricot 2/5, in popular and pear 3/8, and in willow and almond 5/13. Some 250,000 plant species use such regular fraction phyllotaxis. It is interesting to note that the numerator and denominator of these regular fractions are numbers from the Fibonacci sequence discussed above!

Consider beech and hazel. Here we move by 1/3 of a circle each time such that leaves emerge at angles of 120°. Ignoring lateral growth (a decreasing spiral), the third leaf will then align vertically with the first leaf, shading the first leaf from capturing sun and rain. Similar vertical alignment will happen if we move 1/4 or 2/3 round the circle for each new leaf, and there will be unused spaces in the circle. Even for 5/13 there will be gaps in the circle (try it).

The problem is that we are moving by increments of a rational number (a fraction of two integers). In order to fill gaps in the circle we should progress with the help of an irrational number, and the most irrational number is Φ. So let’s progress in intervals of 1/Φ = 0.618034 of a circle, corresponding to a divergence angle of 360/Φ or about 222.5°. Equivalently, two successive leaves will subtend an angle of about 137.5°. It is claimed that this angle gives optimal packing density of the leaf buds, and optimal exposure to light and falling rain. For flowers or petals it gives the best possible exposure to insects to attract them for pollination.

Fig.11: Sunflower Golden Spirals

The spirals formed by a plant which uses the golden angle can exhibit another mathematical property. Consider the sunflower head in Fig.11. In the head of a common sunflower, Helianthus annuus, the fruits are packed very tightly. Each fruit is produced in the center of the floral head and then must migrate outward as new fruits are created. Once the first fruit moves from the center, the second fruit automatically develops in a direction that is approximately 137.5 degrees from the path of the first fruit. This movement continues and each new fruit is positioned at an angle of �137.5 degrees from the very last fruit maximizing the number of fruits that can be produced by a single floral head.

That this happens at all is incredibly amazing but biologists and physicists also study how it happens. Since a sunflower does not have a computer inside of it, complex biochemical and biomechanical processes are responsible for making sure that the fruits get dispersed in such a highly accurate arrangement. Once the fruits are in their positions, an equiangular spiral pattern becomes apparent. In a sunflower, there are 21 clockwise spirals and 34 counter-clockwise spirals that appear to emerge from the center. Noticing that 21 and 34 are both Fibonacci numbers, another connection to the Golden Ratio is revealed! 21 and 34 are in fact adjacent Fibonacci numbers.

This same pattern also occurs in daisies, but it is much easier to see in sunflowers. Many other organisms also have similar arrangements with spiral patterns occurring in frequencies of adjacent Fibonacci numbers. Two well-known examples are the composite fruit structure of pineapples which have eight clockwise and 13 counterclockwise spirals, and the arrangement of the bracts on pinecones, which have five clockwise and eight counterclockwise spirals. They are easiest to see in the pinecone.

We could go on. For example, the number of petals in a flower often follow the Fibonacci sequence e.g., the lily has 3 petals, buttercups 5 petals, chicory 21 petals and daisy 34 petals. Of course, not all plants follow Fibonacci numbers and the golden angle, but it is widely recognized that there is a "fascinatingly prevalent tendency" to do so! The Fibonacci sequence also shows up in the numbers of petals on flowers such as lilies, asters, and cosmos, in reproductive dynamics, in the number of seeds in fruits like apples and bananas, and in the optimal growth patterns of trees which maximizes the ability of a tree to grow more leaves. Despite much analysis, the "golden ratio" in plants remains intriguing.

The Golden Ratio in the Bible

In Exodus 25:10 YEHOVAH God instructs Moses to make the Ark of the Covenant 2.5 cubits long and 1.5 cubits wide. The ratio of these two dimensions, 5/3, is a rational approximation to Φ. There are better approximations e.g. 21/13 = 1.615, but clearly, 5/3 simplifies construction and visually there is little to choose between 5/3 and Φ!

The Messiah was crucified in a place called "Golgotha" or "the place of a skull," a well-known spot and thoroughfare outside the city gate and on the Mount of Olives (Matthew 27:33; Mark 15:22; John 19:17). Golgotha represents in Greek letters the Aramaic word Gulgaltha, which is the Hebrew Gulgoleth. Consider its gematria, with reference to Strong’s Concordance:

Golgotha does not appear in the corresponding passage of Luke. So in Luke 23:33 (NKJV) the translators use the term "Calvary," the name being taken from the Latin Vulgate translation "Calvaria" of the Greek word "kranion" or "skull." Consider its gematria:

So the two terms (Golgotha and Calvary) both refer to the place of "the skull." Suppose we ratio the two Greek gematria, giving 301/186 = 1.61828, which is curiously close to Φ = 1.6180339. Coincidence, or holy spirit inspiration? Note that some modern Bible translations omit "Calvary," and some even appear to modify inspired scriptures, particularly those relating to the Messiah. Better to stay with a widely trusted translation like the NKJV!

YEHOVAH God -- the Master Engineer

Oswald Chambers once remarked: “God is the Great Engineer”. Engineers design things to solve problems and make life easier. Consider just two examples in nature:

Sonar in Mammals

Consider the technique of Echolocation. This is an acoustic process used to locate and identify a target by sending sound pulses and receiving the echoes reflected back from the target. Today echo ranging (Sonar) is used for detecting submarines, and the principle is extended, using microwaves, to Radar.

But nature used echolocation first! Echolocation is used by several mammals including dolphins, whales, and bats. Whales use echolocation for navigation and to locate food, whilst Dolphins emit clicks with their nasal tissue and use the echoes to find their way around and to hunt. Echolocation in bats has attracted a large number of scientific researches due to their extraordinary abilities to fly in complete darkness and to capture their prey.

The Spider's Web

The building of a web is an engineering feat for the orb (aka circular) web spider. It starts by floating a line on the wind to another surface, which is then secured. The spider then drops another line from the center, making a “Y”. The rest of the scaffolding follows with many radii of non-sticky silk being constructed before a final spiral of sticky capture silk.

The resulting orb-web is a natural, lightweight, elegant structure with an extreme strength-to-weight ratio that is rarely observed among other structures, either natural or man-made. The “two-dimensional vibrating system” has been mathematically modeled. Numerical simulations show that identification of the prey’s position (in the web) is rather good, even when the observation is taken on the discrete set of points corresponding to the eight legs of the spider.

Much is made of the “strength” of the spider’s silk in that it outperforms the synthetic fiber, Kevlar, in “fracture toughness”. Unlike Kevlar or steel, spider silk is highly elastic, allowing the silk to absorb the impact of an insect hitting and struggling in the web.

Is sonar in mammals, or the amazing math and technology of the spider’s web the result of a very long evolutionary process (which is certainly not scientifically proved)? Or is it part of YEHOVAH God’s intricate design to help creatures find food?

YEHOVAH God’s Amazing Design: Summary

We have examined some numbers and mathematical concepts which appear to suggest a Designer, namely YEHOVAH God. The simple dimensions of the Ark are surprisingly close to modern ship design, and the footprint of Solomon’s Temple appears to relate to YEHOVAH God, as do the relative sizes of earth and moon. Astronomical distances and sizes also appear to be just right for the perfect solar eclipse -- but surely not "a fluke of celestial mechanics," as some maintain.

Then there’s the fascinating "golden ratio" Φ = 1.6180339… which appears to relate to YEHOVAH God. For example, it might even point to the orbits of the planets. At the other end of the scale, many see Φ in the double helix molecule of our DNA, and in the leaf arrangements of many growing plants. Plants also demonstrate the mathematically related Fibonacci sequence, as does music. Φ is even found at the quantum level in atoms.

Of course, taking measurements in an analogue and fallen world will always generate uncertainty in such calculations, and there are always exceptions. But is the mathematics too close to the ideal to ignore, too close for chance? The diversity of examples where numbers seem "almost right," and where Φ and Fibonacci are found is surely intriguing. And especially so when they appear to point in one direction -- to YEHOVAH God, the Designer! Remember, the Bible says that all things were done by YEHOVAH's holy spirit:

Hope of Israel Ministries -- Preparing the Way for the Return of YEHOVAH God and His Messiah to This Earth!

Hope of Israel Ministries
P.O. Box 853
Azusa, CA 91702, U.S.A.
www.hope-of-israel.org

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