The section of the paper later. Briefly though

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.

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!

order now


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.


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.

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?


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.



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?


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.


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


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

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.


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

















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.



 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.


I'm Morris!

Would you like to get a custom essay? How about receiving a customized one?

Check it out