The man to whom we owe such a wondrous

start to this odyssey: Mr. Fibonacci hailed from Italy in the 12 century. Fortutitious

for us too was the inference that his father was a traveler and thus Fibonacci

was able to learn about the Hindu Arabic numbers. (1)he traveled much himself

later and learned more and more and resultant of this he wrote the Liber Abaci

a book about using the abacus. I owned one a child and it actually works.

Due to this work and mathematics of

that style coming to Europe he was patronized by leaders and paid for his

research and government work. His early work made the use of 0-9 a standard and

introduced place holding additionally.

The Fibonacci sequence, however was

postulated in this work and took a look at how many rabbits can be reproduced

via a population in hypothetical terms at first. This postulation was as the

generations went on in the rabbit population was seen and bore out a sequence.

The mathematics will be discussed in the mathematics section of the paper later.

Briefly though it’s a sequence with

number succeeding as a sum of the previous two. In the Fibonacci sequence of

numbers, each number is the sum of the previous two numbers. At this point

though he did not really get into the PHI aspect of the numbers. This is

implied when extrapolated as two amounts are in the golden ratio if their ratio

is the same as the ratio of their sum of the larger of the two numbers.

Many of our world’s best-known math

folks; inclusive of Euclid and Pythagoras and leading all the way to my

previous accolade for Leonardo Fibonacci; have for eons now been taking a look

and spending great effort on this ration. Of course, we must also realize this

fascination has transcended virtually all aspects of the human expression and

fields of study.

(mine)Historically as expressed in

sequence: Phidias used it in the Parthenon. Plato writes of geometric figures

having the ratio. Euclid as described prior. Fibonacci and his sequence when

extrapolated into the ratio show the ration. Piccioli calls the proportion

divine. Maestlin shows its inverse properties. Kepler combines this ratio with

the Pythagorean theorem to the Kepler triangle. How nice he names it after

himself. IN the natural realm Bonnet shows us in the spirals of plants the

sequence exists from Fibonacci. Lucas calls it by its name. Barr PHI. Bonnets proposal is further extrapolated to

the helix pattern, celestial orbits, atomic particulate orbits. With that as a

possibility of enhances transference of information though some divine or

innate science nature of natural word; I began looking at the DNA helix as an

extension of and inherently patterned via the golden ratio as are celestial l

rotations, and tiny atomic orbits too. This caused be to postulate there may be

a link between this and the manner by which a new field of quantum mechanics

may be coming into fruition via the entanglement theory or as I called it the

comingling theory, so I could better understand it. This class has open a whole

new way of seeing the natural world though mathematics and has caused me to see

there may be a link between the building pyramidaical ideas of the past to

connect with the vanguard ideas of the future.

With that as my basis I began looking

at the pattern in nature not just as a given but I began wo ponder the reason

so many supposedly naturally occurring patterns and structures in nature held

the influence of this Fibonacci extended golden ration resultant. I was

especially intrigued by the notion that the DNA helix and celestial bodies

orbits inferred this measurement. My explorations of the research became

extremely tangential in nature and began to border on the metaphysical in

addition to the mainstream science as we know it today.

This led to further questions that I

began to self-produce through long introspection and reflection. Does this

exploration require a choice between spirituality and science? Or for that

matter between metaphysics and science? Having read the subliminally suggestive

sayings delicately sprinkled strategically within our text book; such as to be

no afraid to speculate about things unknown, etc. I began to look at the

historical scientific record regarding the philosophy about randomness in

science, mathematics, and theoretical physics. I wondered if the axiomatic saying

that we ought to just take a proven theory at its face value or not. And if we

don’t do so; are we bound to end up in the asylum for being shunned by our

peers as Canter was? Should we look at the experiment and the ensuing theory as

to the improbability of looking at such a condition as the seeming innate

Golden Ratio as a casual evolution. As a harmonious pre-established order.

If this is not necessarily the case

and it does or does not infer a divine design, then could it hold a more

mysterious implication for us? After all, there was a time when something as

elementary as electricity was still unknown, when radio waves were not heard

but still existed, when a cell phone did not exist!

For me the possibility of a mathematical

implication quantifiable for this pattern in nature seems both wondrous and

troubling in that I am placed contestably off balance not fully understanding

the causal basis for such a property. I myself am not inclined to give up

determinism in the world of atoms. Although I easily could see a scientific

explanation or a divine design too and either of the above also. But that is a

philosophical question for which physical arguments alone are not decisive.

With that in mind; I took a close look at the arguments of Cantor and infinity.

He didn’t get in trouble for his ideas the was just so discouraged from lack of

support that he became disillusioned and depressed. I shan’t not do that here.

One-to-one correspondence should be elementary today as it is. Or should it be necessarily?

Gödel; in turn proved that we could not disprove the Continuum Hypothesis. Then

we found out that Cohen showed us we could not prove it either?! (Burger P.

184).

To further indicate that there are

more hidden variables and distinct gaps in the ability of our simian brains to

comprehend new and uncanny though as we have been either hard wired to not

allow for contradictions or we just are not yet versed in the basic principles

to leap forward. Perhaps some of us folks who take Mathematics 135 have not yet

been tainted in such as way and cautionary; we are just to naive to really understand

some things just can’t be. Further complicating this are excerpted form our

text such as: It turns out that the set of points of line S has the same

cardinality as the set of points of line B. (page 193) Berger.

Thanks

to Cantor, who reached out and considered the counterintuitive, no

mathematician today has a problem encompassing the idea of multiple infinities.

Bergen Chapter 3.1 Text

Could there be more to infinity in that DNA

and or atomic particles can provide more than physical communication with the

determination of the next offspring and do atomic particles harbor a hidden

manner in which hey can communicate uninhibited by space and time. And If so

can DNA connect us with our past ancestors and future descendants in more than

just a sequence of information as they’re essentially made up of atomic

particles too?

IT

could then be reasonable referred to as not only the golden ration but as the

golden egg. Geometry uses it to figure

out relationships in figures and lines ratios. Euclid’s golden ration was

expressed as thusly: A straight line is said to have been

when, as the whole line is to the greater

segment, so is the greater to the lesser. (6)

mathematicians first studied what we now call

the golden ratio because of its frequent appearance in nature and DNA.

With

those issues at stake I then stumbled upon the impetus for my leap into the

later discussed quantum physics realm. To wit; the text stated this: First, we

notice that we will not change the cardinality of the line segment S if we bend

it a little bit. We would be changing its shape, but not its cardinality

(Burger 193). IF that is the case then if I

look at Fibonacci and the golden ratio being everywhere and fundamentally

independently embraces by so many fields of study and by natural design and

functionality what else in this might be a hidden variable?

This

in mathematically applied and extrapolated physics the theories regarding

hidden variables were touted and proposed by some that said something that

exists within the set parameters of the theory do not necessarily account for

all the dynamics of the existence nor for quantum mechanics for that matter.

This even according to Albert Einstein for that matter. He even said that is

not always the case can that there may be far more to the mechanics of this

view then we can imagine as yet. Rosen, Einstein,

and Podolsk postulated the other things may come into play here. These hidden variables or “elements of

reality” (hidden variables) would be prudently mingled with the overall

theory to make sense of this entanglement theory. I found this theory to be a

natural world extension to the Fibonacci sequence as found in nature. This in

the most expansive realm of space and as minute as the deoxyribonucleic acid

might be useful to the theories so we can better understand quantum mechanics

and entanglement and action at a distance even (2)(3). Within this further

dance of the Fibonacci sequence and the following golden ratio as seen in

nature I stumbled upon the possibility of a correlation between the

transference of beauty in nature and DNA information for living organisms into

a study of its possible explanation for and a divine intervention or design or

natural explanation for Later, suggested that of certain types are impossible,

or that they evolve non-locally.

Einstein, being the humanist and realist that he began looking into and

spread the idea that there might be a paradox called the EPR that his theory

was not an end all nor that it was necessarily complete. The remarked that,

“God does not play dice.” (1) The theory of quantum entanglement that discusses

that possibility in that separated particles can briefly share common

properties and respond to certain types of measurement as if they were a single

particle. In this observed experiment and hypothesis, a seen and observed

measuring of one particle in a place can change how likely the results of a

measuring of another one elsewhere. If both then are observed in different

location to have similar stimulation then, then local hidden variables can

reasonably be ruled out.

Quantum

mechanics is very much a natural tangent worthy of exploration of this way of

searching for the possible explanation of why this ratio is so prevalent. An inner voice tells me that this could be a

profound endeavor, but if it proves fruitless at least it may open another door

or further understanding. Axiomatically and historically this lens leads me to

the comment by Einstein that God does not play dice. Others told him not to

tell God what to do; most humorously.

Shortly after making his famous “God does not play dice”

comment, Einstein attempted to formulate a deterministic counterproposal to

quantum mechanics, presenting a paper at a meeting of the

in Berlin, on 5

May 1927, title “Bestimmt Schrödinger’s Wellenmechanik die Bewegung eines Systems vollständig oder nur im Sinne der

Statistik?” They spoke of natural phenomena and natures occurrences such

as the golden ratio. However, as the paper was being prepared for publication

in the academy’s journal, Einstein decided to withdraw it, possibly because he

discovered that, contrary to his intention, it implied chaos of systems, which

he regarded as absurd. Even he had trouble with outlandish contradictions of

conventionality.

Bell Theorem 1964, which exclude some classes of hidden

variable theories were first discussed by Albert Einstein further that:

· No

physical theory of local hidden variables all of the predictions of quantum

mechanics. shortly thereafter published a seminal paper defining and discussing

the notion of “étranglement”.

· Einstein

later famously derided entanglement as “spukhafte Fernwirkung” or

“spooky action at a distance”

· In

1935, Einstein returned to the question of quantum mechanics. He considered how

a measurement on one of two entangled particles would affect the other. He

noted, along with his collaborators, that by performing different measurements

on the distant particle, either of position or momentum, different properties

of the entangled partner could be discovered without disturbing it in any way.

then used a hypothesis of local realism that the other particle had these

properties already determined. The principle he proposed is that if it is

possible to determine what the answer to a position or momentum measurement

would be, without in any way disturbing the particle, then the particle

actually has values of position or momentum.0

This

principle distilled the essence of Einstein’s objection to quantum mechanics.

As a physical principle, it was shown to be incorrect when the Aspect

experiment 1982 confirmed Bells’ Theorem had been promulgated in 1964.

(3)

“A

man to count on”Albert Einstein ArchivesThe Hebrew University of Jerusalem, IsraelPhysical ReviewBibcode1935PhRv…47..777Edoi10.1103/PhysRev.47.777ISBN978-0615179841

Burger,

Edward B. The Heart of Mathematics: An Invitation to Effective Thinking, 4th

Edition. Wiley, 10/2012. VitalBook file.

PAGE 199 A LOOK BACK REF TO

NATURAL SHAPES IMPORTANT

Burger,

Edward B. The Heart of Mathematics: An Invitation to Effective Thinking, 4th

Edition. Wiley, 10/2012. VitalBook file.

Burger, Edward B. The Heart of Mathematics: An

Invitation to Effective Thinking, 4th

Edition. Wiley, 10/2012. VitalBook file.

Edward B. The Heart of Mathematics: An Invitation to Effective Thinking, 4th Edition. Wiley, 10/2012. VitalBook file.