Though Fibonacci Numbers are certainly a wonder in and of themselves, I feel that Euler's Identity goes much further into the nature of reality itself to reveal 'the fingerprint of God;
"A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.”
Michael Denton - We Are Stardust - Fine Tuning Of The Elements - Fred Hoyle Atheist to Theist - video
What could make a scientist who was such a staunch atheist, as Hoyle was before his discoveries, make such a statement? The reason he made such a statement is because Hoyle was expertly trained in the exacting standards of mathematics. He knew numbers cannot lie when correctly used and interpreted. What he found was a staggering numerical balance to the many independent universal constants needed to synthesize carbon in stars. These independent constants were of such a high degree of precision as to leave no room for blind chance whatsoever. Thus, with no wiggle room for the blind chance of materialism, Fred Hoyle had to admit the evidence he found was compelling to the proposition of intelligent design by a infinitely powerful, and transcendent, Creator. Let's look at some of these exacting mathematical standards, and finely tuned universal constants, to see the precision of 'intelligent design' he saw for the math and for the foundational building
blocks of the transcendent universal 'information' constants for this universe.
Finely Tuned Big Bang, Elvis In The Multiverse, and the Schroedinger Equation - Granville Sewell - video
To solidify Dr. Sewell's observation that transcendent 'math' is found to be foundational to reality, I note just one little equation:
0 = 1 + e ^(i*pi) — Euler
Believe it or not, the five most important numbers in mathematics are tied together, through the complex domain in Euler's number, And that points, ever so subtly but strongly, to a world of reality beyond the immediately physical. Many people resist the implications, but there the compass needle points to a transcendent reality that governs our 3D 'physical' reality.
God by the Numbers - Connecting the constants
Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e*pi*i. This number is equal to -1, so when the formula is written e*pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e*pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician."
(of note; Euler's Number (equation) is more properly called Euler's Identity in math circles.)
Moreover Euler’s Identity, rather than just being the most enigmatic equation in math, finds striking correlation to how our 3D reality is actually structured,,,
The following picture, Bible verse, and video are very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere which 'coincidentally' corresponds to the circle of pi within Euler's identity:
Picture of CMBR
While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,
The Known Universe by AMNH – video - (please note the 'centrality' of the Earth in the universe in the video)
The flatness of the ‘entire’ universe, which 'coincidentally' corresponds to the diameter of pi in Euler’s identity, is found on this following site; (of note this flatness of the universe is an extremely finely tuned condition for the universe that could have, in reality, been a multitude of different values than 'flat'):
Did the Universe Hyperinflate? – Hugh Ross – April 2010
Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,,
This following video shows that the universe also has a primary characteristic of expanding/growing equally in all places,, which 'coincidentally' strongly corresponds to e in Euler's identity. e is the constant used in all sorts of equations of math for finding what the true rates of growth and decay are for any given problem trying to find as such:
Every 3D Place Is Center In This Universe – 4D space/time – video
Towards the end of the following video, Michael Denton speaks of the square root of negative 1 being necessary to understand the foundational quantum behavior of this universe. The square root of -1 is 'coincidentally' found in Euler's identity:
Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video
I find it extremely strange that the enigmatic Euler's identity would find such striking correlation to reality. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In e we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space-time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was first proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in the preceding video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's identity, to the foundational characteristics of how this universe is constructed and operates, points overwhelmingly to a transcendent Intelligence, with a capital I, which created this universe! It should also be noted that these universal constants, pi,e, and square root -1, were at first thought by many to be completely transcendent of any material basis, to find that these transcendent constants of Euler's identity in fact 'govern' material reality, in such a foundational way, should be enough to send shivers down any mathematicians spine. Further discussion can be found here relating Euler's identity to General Relativity and Quantum Mechanics:
Here is a very well done video, showing the stringent 'mathematical proofs' of Euler's Identity:
Euler's identity - video
The mystery doesn't stop there, this following video shows how pi and e are found in Genesis 1:1 and John 1:1
Euler's Identity - God Created Mathematics - video
This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1:
The Underlying Mathematical Foundation Of The Universe -Walter Bradley - video
The Five Foundational Equations of the Universe and Brief Descriptions of Each:
Also of interest is that Einstein's General Relativity Equation uses the constant of pi in its construct, whereas the square root of negative one is essential for Schrödinger's Quantum Mechanic Equation. Yet those two equations are notorious for there difficulty to be reconciled with each other into a 'theory of Everything'. Yet, pi and the square root of negative one readily reconcile with 'e', the constant for growth, in Euler's Identity. As well it seems that what man has failed to achieve for a 'unification into a theory of everything' was achieved by Christ:
The End Of Christianity - Finding a Good God in an Evil World - Pg.31
William Dembski PhD. Mathematics
Excerpt: "In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity."
Moreover there actually is physical evidence that lends strong support to the position that the 'Zero/Infinity conflict', we find between General Relativity and Quantum Mechanics, was successfully dealt with by Christ:
The Center Of The Universe Is Life - General Relativity, Quantum Mechanics, Entropy and The Shroud Of Turin - video
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? — Albert Einstein
“… if nature is really structured with a mathematical language and mathematics invented by man can manage to understand it, this demonstrates something extraordinary. The objective structure of the universe and the intellectual structure of the human being coincide.” – Pope Benedict XVI
"The reason that mathematics is so effective in capturing, expressing, and modeling what we call empirical reality is that there is a ontological correspondence between the two - I would go so far as to say that they are the same thing."
Richard Sternberg - Pg. 8 How My Views On Evolution Evolved
But Is it Evolution? - February 2011
Excerpt: The chambered nautilus is a “living fossil,” that uses “jet propulsion,” New Scientist said, with origins way back in the Cambrian. Has its fitness improved over all that time? “Its movement is ungainly and slow, but it has survived virtually unchanged for at least 450 million years, so it must be doing something right,” reporter Michael Marshall remarked.
"Fingerprints of God" Steven Curtis Chapman
Intelligent Design - The Anthropic Hypothesis