Historical must also realize this fascination has transcended

   
Historical Perspective of Fibonacci, the Golden Ratio and Implications
in the Natural word extended and hypothesized to current works regarding the
Entanglement Theory.

    
The man to whom we owe such a wondrous start to this odyssey: Mr.

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Fibonacci hailed from Italy in the 12th century. Fortuitous 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 as child and it actually works although I was so young
I had no predisposed inhibitions about mathematics then. Today the device
frightens me.

    
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.

    
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). (3)

                  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.(3) (page 193) Berger.  Thanks to Canter, who reached out and
considered the counterintuitive, no mathematician today has a problem
encompassing the idea of multiple infinities. (Berger 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 reasonably 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 equal when, as the whole line is to the
greater segment, so is the greater to the lesser. Mathematicians first studied
what we now call the golden ratio because of its frequent appearance in nature
and DNA.” (4)

     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 then in
this also 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 (5)(6). 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 deoxyribonucleic
acid 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.” (5) 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 scientific society in Berlin, on 5
May 1927, entitled “Bestimmt Schrödinger’s
Wellenmechanik die Bewegung eines Systems vollständig oder nur im Sinne der Statistik?” (8)They spoke
of natural phenomena and nature’s 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. This was followed as a natural extension by
the 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. (9) 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. (6)

 

 

 

 

 

 

 

 

 

(1)Devlin, Keith. Finding Fibonacci,
The Forgotten Mathematical Genius Who Changed the World, 1st
edition, Princeton University Press, 2017

 

(2)Berger, 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

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

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

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

VitalBook file.

Unequal Decimals

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

(5),
(6) “A Man to Count On” Albert Einstein Archives, The Hebrew University of
Jerusalem, Israel Physical Review Bibcode 1935 PHRV…47…777
Edoi10.1103/PhysRev47.777ISBN978-16015179841

(7)
Berger, Edward B. The Heart of Mathematics: An Invitation to Effective
Thinking, 4th Edition. Wiley, 10/2012. VitalBook file

(8) The
Born-Einstein letters: correspondence between Albert Einstein and Max and
Hedwig Born from 1916-1955, with commentaries by Max Born. Macmillan. 1971.

p. 158., (Private letter from Einstein
to Max
Born, 3 March 1947:

 

(9) Hussey, John “Bang and Betwixt, Cosmos publishing, Jul 31, 2014,
p. 171