by Allen Williams
We have often
heard from evolutionists that those holding the view that life is a product of Intelligent Design are
‘Creobots’ or ‘ID’iots, as if there was nothing more than one’s emotions or a
less evolved intellect in order to consider the possibility of design rather
than natural selection.
Evolutionist, Richard Dawkins claims, that the ‘God delusion’ is behind the
notion of design and purpose to mankind and its surroundings. Is this true? The
field of mathematics is a highly structured and orderly application of human
reason and logic, which did not evolve but was developed through incisive
thought and mathematical tests.
of mathematics developed through observation and the desire to quantify what
was observed. It’s definitions, identities, and axioms define an absolute
truth, which is unerring and undeviating, and is the basis that establishes the
theorems of application. The foundation of Mathematics rests on logic and is a "deductive study of numbers,
geometry and various abstract constructs". - Columbia
Encyclopedia, 1991. So, how is the mental reasoning that allows truth to be
discovered in the world of numbers, suddenly flawed when it comes to
discovering the truth of an Intelligent
evolutionist claims that "Real life is not binary, it uses real
numbers (I’m not saying that binary numbers aren’t real, but that real life can
use rational and irrational numbers). At the core, proofs in biology are not
different from proofs in mathematics. "
then if real life can use irrational numbers to represent physical phenomena
then it can equally utilize binary numbers, i.e. ‘0, 1’ to describe the state
of certain life conditions. After all, what is life or death but a binary
function? You’re either alive or dead, there isn’t any in-between. Now
according to this evolutionist’s statement, if numbers in life forms can be
shown to be real and part of a family, then that would constitute evidence for
the existence of an Intelligent
Designer as it would for the existence and validity of a
where equations of the form xn
+yn = zn, have been shown to
be irreducible and modular, therefore part of a family of elliptic curves. So,
is there any biological evidence of some common mathematical relationship in
living plants and animals? If not, then this would tend to support evolution’s
notion of randomness in creating life but if so, then design is inferred.
mathematician by the name of Leonardo
Fibonacci or more properly,
Leonardo da Pisa brought the modern decimal numbering system to
Europe in 1200 AD. His travels as a merchant throughout Algeria, Syria, Greece,
etc., brought him into contact with the Arabian number or 10 based number
system. He is best known for a simple mathematical series introduced in his
publication, Liber Abaci, named
as Fibonacci numbers in his honor.
The series begins with zero and each successive number is the sum
of the last two, i.e. 0 + 1 = 1 and 1 + 1 = 2, etc. 0, 1, 1, 2, 3 , 5 , 8, 13,
21, 34, 55 and so on defines the series.
attribute of the series is that dividing a number by the preceding smaller one
yields a ratio called the ‘golden mean’ or ‘divine number’, as it is called.
It’s the ratio of the current number in the Fibonacci series, i.e. x(n+1)
divided by the previous number x(n), i.e. 55/34 = 1.6176. This number series
can be visualized as a group of boxes or rectangles as shown in Figure 1.
Figure 1 – Fibonacci Blocks
consider the line segment, 'ac'
If we postulate
that there exists an optimum ratio, i.e. height to width, which may be
represented by the line segment above. We can pick an arbitrary point along the
line to represent this optimum, called 'b', then: ab/bc = bc/ac
An optimum ratio is an ideal length relationship between line segments. Such a
relationship might be expected to be more than simply an interesting
intellectual exercise. The line segment ratio in our example is the length of
bc to ab. Now if we set ab = 1 and let x represent the segment bc, we have:
1/x = x/(1+x)
(1 + x) = x2. This can be put into
standard quadratic form as:
x2 – x –1 = 0 with a root of 1 +
Sqrt(5)/2 = 1.618, or the golden ratio. The equation may also be expressed in
terns of its coefficients:
x2 - (b/a)x – 1 = 0 where a = 1 and b= x.
The term (b/a)
approaches a finite limit for the series as the Fibonacci ratio approaches
LIM [(b/a)] -> µ = 1.618. This relationship is also found
to exist in angle groups as well as lines.
This remarkable property is by no means restricted to the series developed by Leonardo Fibonacci but occurs
in limitless mathematical sequences. For example take the polar coordinate
axes, 0, Pi/6, Pi/4, Pi/3, Pi/2, 2Pi/3, 3Pi/4, 5Pi/6, Pi, 7Pi/6, 5Pi/4, and so
on. A Fibonacci series can be created from the polar axes themselves by adding
together the last two numbers to get the next one in the sequence, which are:
0.79, 0.79, 1.84, 2.63, 4.47, 7.10, 11.57, 18.67, 30.24, 48.91, 79.15, and so
on. A plot of the sequence is shown in Figure 2.
This length to width relationship produces what is referred to as the ‘golden
rectangle.’ It occurs time and again throughout nature, in the human body, as
well as the animal and plant world. Note its similarity to both the Fibonacci
spiral and the seashell of Figures 5 & 6 respectively.
Greek sculptor and many others in Greece and Egypt used this relationship in
creating their works of art and architecture.
Furthermore the ratio and the golden spiral are ubiquitous throughout
creation", so says Frederick A. Willson in "Ubiquity of the Divine" (Golden)
Ratio and Fibonacci Numbers Throughout the Heavens and Earth." See also: http://plus.maths.org/issue3/fibonacci
Figure 3 shows the plot of progressive (b/a) calculations of
the polar axes as determined from the polar series of Figure 2. Note that this
series limit is the predicted 1.618, the same ratio as our line segment, 'a-c'
"The Golden Mean or Phi occurs frequently in nature and it may be that
humans are genetically programmed to recognize the ratio as being pleasing.
Studies of top fashion models revealed that their faces have an abundance of
the 1.618 ratio." – Frederick A. Willson in "Ubiquity of the Divine."
See: Fibonacci Numbers in nature
exhibits this same divine number or golden mean. The double helix structure of
DNA shown in Figure 4, measures 34 angstroms long by 21 angstroms wide for each
full cycle. So, 34/21 = 1.619. The length between major and minor grooves, the
blue and yellow line), exhibits this same 1.618 ideal ratio.
Human DNA: http://goldennumber.net/dna.htm
Figure 4. – Human DNA
(Photo: Double Helix)
Francis Crick, the discoverer of the double helix structure
of DNA has calculated the probability that such a complicated molecular string
could have formed on its own as essentially zero.
The biological code written into the human cell
would fill 1,600 pages.
There is as much information in the cell as is contained in 600 encyclopedias.
Cell mechanics are also extremely complex: "Life
at the molecular level is composed of tiny machines
…There are more machines inside the human
body than all the combined factories of the world… There are 2 trillion
chemical processes that take place in the human cell
Michael Behe, ‘Darwin's Black
shown that mankind is all ONE blood (Acts
17:26) requiring no more than a 0.012% variation in DNA to
account for all the outward physical characteristics, including skin color.
It seems a
stretch to the logical mind that evolution
not only produces life by random acts of chance but has also
produced it in an optimal
aspect ratio of length to width, i.e. 1.618: 1. In one case,
natural selection's chance combinations purportedly create life through
confusion, while on the other hand, we have evidence of Intelligent Design as noted
in I Corinthians 14:33,
which states that "For God
is not the author of confusion.."
Intelligent Design’s ‘Anthropic Principle’ suggests that there are
a series of optimum constants necessary to support life, one of which is the spiral
galaxy. There are three basic galactic forms, elliptical, irregular and spiral.
However, only spiral galaxies have a near round orbit capable of supporting
Figure 5 – Spiral Galaxy
(Photo: Ursa Major)
The golden mean in spiral galaxies: http://www.wisdomportal.com/Geometry/SpiralPage.html
exhibit the Fibonacci series in petals, leaves, sections and seeds: http://goldennumber.net/plants.htm
Fibonacci numbers are also found in living organisms including the cochlea of
the human ear: http://www.world-mysteries.com/sci_17.htm
Figure 6 -
(Photo: Nautilus Construct)
Using the blocks of Figure 1, we may construct an idealized
spiral by drawing a series of lines through the diagonals of each of the
Fibonacci squares and then connecting them with a series of smooth curves or
chords as shown in Figure 5.
The resulting figure looks remarkably like the Nautilus seashell of Figure 7.
Figure 7: Nautilus Shell (Photo: http://www.sacredarch.com/sacred_geo_exer_shell.htm
Matter, Chance and Time are the
trinity of evolution. And so, unique mathematical relationships conflict with
material science’s assertion that there are no absolute truths. The fact that a
unique aspect ratio is so pervasive through out nature is strong evidence of
intentional design rather than chance combinations in matter as evolutionist’s