Before modern science, humanity struggled with magnitude and seeming infinity of the universe by discussing the motion of the planets in terms of gods. These gods possesses worldly qualities and through the same lens, the motions of the heavens were anthropomorphized.
In our time however, it seems dissatisfying to resort to vague abstractions and analogies regarding the nature of the Universe. When faced with quantum electrodynamics, large hadron colliders and statistical mechanics, the mechanics of the Universe seem far more engrossing than the mysteries of existence.
In the context of writing on mathematics and thermodynamics, I have made some large suppositions and assumptions about the nature of the Universe and the place of certain types of very simple mathematics. My reasons for doing this are wrapped up in the argument itself; The elementary rules for the assembly of the Universe were, at the beginning of time, of elementary simplicity, and that through a process of expansion, cooling and evolving towards a greater complexity, we find ourselves in the present moment. I srgue that this transformation came about by a calculation that requires a computer exactly the size of the Universe to complete. Finally I agrue that the purpose or outcome of this Universal computation is equilibrium.
I then make some assertions regarding the Fibonacci sequence; that it is an elementarily simple, mathematical pattern that, due to its nature as being a method of approximating 2^n growth, is implemented on a Universal scale to calculate equilibrium. I will later argue that the logic underlying these sequences plays a direct role in thermodynamic outcomes and critical points in phase transition.
But my attempt to paint a concise semantic picture of the construction is a little far-fetched. Part of me is excited to find someone who is willing to invest the time to demonstrate I am wrong. Part of me fears failure in a way that has paralyzed my writing this site.
I was struck my Rohann's Post on my last blog entry where he discussed different perspectives on the universe (mathematical v. numerical). I am alos struck with the fear of falling into follies of confirmation bias.
I am convinced that this mathematics pervaded ancient spirituality and is the backbone of modern religions; that the study of the universe was so necessary and so amazingly important for survival, that the knowledge became entombed in religions.
This is a fine line to walk. I am not quite sure and I like that; I like that understanding God does not remove the mysteries of the Universe any more than does understanding physics.
I also hasten to remember that physics and science can only look back so far... What happened before time began? Why did creation happen? I think that these questions are the domain of spirituality and it is reassuring to know that people 5000 years ago asked much the same questions regarding our nature, though in a different way...
Nassim Haramein was the first to formulate a unified field theory based upon sacred geometry. Garret Lisi independently formulated a similar theory which showed a complete set of theoretical particles and their interactions with one another when rotated through various charge dimensions.
We see that there is growing convergence and awareness of some of the concepts of this site [notably the place of the golden ratio in the Quantum World].
In order to better understand the Geometry of the E8 Lie Supergoup and its 8-dimensional supersymmetry, I highly encourage you to peruse the following PDF, which is a concise overview of the history of the mathematics underlying this theory, taking us from the use of i (square root of -1) in the imaginary plane, to density and "packing" problems, ending finally with the 8-dimensional, E8 supersymmetry.
Many minds are pushing down the door of a Theory of Everything at the same time, right now, and the emergence of new theories has resulted in the death of some older ones. Notably String theory seems to be experiencing a noticable fall from popularity, and there are two significant reasons why.
First, from a purely scientific perspective, String Theory fails to actually make any testable predictions as to the state and nature of the Universe, and this failure relegates the theory, as a set of ideas, to never be anything more than theorhetical. Essentially, with no way to verify the results of String theory, in has become a lame duck.
The second, and often overlooked quality that String Theory is lacking is that of elegance. Elegance is not a concept of quantitative analysis, but rather a qualitative perspective on the neatness or a theory. In general, the more elegant something is, the less pain it causes a physicist or mathematician to describe.
So it was with great relief to some, when, over the past decade, new ideas began to emerge, intending to take the place of string theory by producing a more elegant concept that had testable results.
This set of new pictures of the nature of the Universe is rooted in one word: Simplicity.
Simplicity, in terms of thermodynamics, is about the high-energy origins of matter, the fundamental units of the Universe and their behaviors. In this sense, the key trigger for evolution has been Universal tendancy for complexity to emerge for simple systems.
The rules of thermodynamics tell us that when a system of reference loses energy to its environment, such that a change of state is provoked, the result of that state change will be more complex that the original participants. In this sense, water is the simpler phase, where ice would be the more complex; Atoms would be simpler, Molecules, more complex.
In particle physics, the idea of a phase change that takes a system from a simpler, higher-energy state, to a more complex, lower-energy state is called symmetry-breaking.
Symmetry, in this sense is defined in Wikipedia as:
Symmetry breaking in physics describes a phenomenon where (infinitesimally) small fluctuations acting on a system crossing a critical point decide a system's fate, by determining which branch of a bifurcation is taken. For an outside observer unaware of the fluctuations (the "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a disorderly state into one of two more-ordered, less probable states. Since disorder is more symmetric in the sense that small variations to it don't change its overall appearance, the symmetry gets "broken".
Symmetry breaking is supposed to play a major role in pattern formation.
Enter Garrett Lisi and his talk on e8 theory:
In this lecture, Lisi describes a new group of theories that attempt to construct a unified field theory by contemplating the origins of all matter and energy to be from a symmetric object (in n dimensions) that, as is loses thermodynamic potential, sees aspects of its symmetries broken. The resulting distortions of these now no longer symmetric objects results not only in the building blocks of matter, but the interaction-particles that carry charge and force.
So let's think quickly about what is actually going on at the CERN Large Hadryon Collider: We are taking high energy particles, and colliding them together, creating higher energy particles. Here, our thermodynamic principles are reversed: the participants in change are lower energy and thus more complex than the higher-energy particles produced. In turn, these particles are possess a higher symmetry. We are probing the origins of a once super-symmetric universe!
This from wikipedia, http://en.wikipedia.org/wiki/An_Exceptionally_Simple_Theory_of_Everything
Consider a wavy, two-dimensional surface, with many different spheres glued to the surface—one sphere at each surface point, and each sphere attached by one point. This geometric construction is a fiber bundle, with the spheres as the "fibers," and the wavy surface as the "base." A sphere can be rotated in three different ways: around the x-axis, the y-axis, or around the z-axis. Each of these rotations corresponds to a symmetry of the sphere. The fiber bundle connection is a field describing how spheres at nearby surface points are related, in terms of these three different rotations. The geometry of the fiber bundle is described by the curvature of this connection. In the corresponding quantum field theory, there is a particle associated with each of these three symmetries, and these particles can interact according to the geometry of a sphere.
In Lisi's model, the base is a four-dimensional surface—our spacetime—and the fiber is the E8 Lie group, a complicated 248 dimensional shape, which some mathematicians consider to be the most beautiful shape in mathematics.[8] In this theory, each of the 248 symmetries of E8 corresponds to a different elementary particle, which can interact according to the geometry of E8. As Lisi describes it: "The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known fields and dynamics through pure geometry."[1]
The complicated geometry of the E8 Lie group is described graphically using group representation theory. Using this mathematical description, each symmetry of a group—and so each kind of elementary particle—can be associated with a point in a diagram. The coordinates of these points are the quantum numbers—the charges—of elementary particles, which are conserved in interactions. Such a diagram sits in a flat, Euclidean space of some dimension, forming a polytope, such as the 421 polytope in eight-dimensional space.
In order to form a theory of everything, Lisi's model must eventually predict the exact number of fundamental particles, all of their properties, masses, forces between them, the nature of spacetime, and the cosmological constant. Much of this work is still in the conceptual stage—in particular, quantization and predictions of particle masses have not been done. And Lisi himself acknowledges it as a work-in-progress: "The theory is very young, and still in development."[9]
Stay tuned and I will discuss how this symmerty breaking is the mechanism by which order increases in the Universe. In fact, the Theory of Order, in time, will be expanded to include some ideas on how the logic of Gibonacci sequences can determine the relationship between energy of concurrent states; this "Logic of Order" is creates the thermodynamic behavior from which Gibonacci spirals emerge.
Where did you first learn about/start researching your theory?
I have been blessed to work professionally with friends who are mind-bogglingly brilliant. One such person, Robb Gray was a friend before a colleague. I always envied Robb; when I met him I was 16, and Robb was more cool, cultured and brillinat than I can describe. He is perhaps the best software developer I have ever touched and, to this day, I still have people telling me the same.
I remember travelling from the suburbs one night to visit Robb in the city. We ate pizza and watched a crazy Chinese movie about a guy who sees this spiral everywhere and, for some unknown reason, this drives him crazy and he cuts his ears off, as they too depict the Fibonacci spirals. I had heard of this concept before, but in math class, perhaps once before.
So Robb actually became obsessed with the idea before I did. He performs under the stagename "Friend of Phi"... and for that I am eternally grateful, because he set me off on an adventure of a lifetime...
Traditionally, Fibonacci is introduced in "Finite" math, permutations and combinations. and in its original form: counting the number of bunnines in successive generations of birth...
Gibonacci is not taught in school. I have shown my work to graduate-level math students and not one has seen this prior.
Nonetheless, Fibonacci is commonly taught in computer science, because it is the simplest of all nontrivial, recursive functions, a point I will address in great detail shortly. Ironically, it is this idea of Fibonacci being the simplest of all available recursive functions that makes it so ubiquitous throuout the universe.
For what it is worth, writing this site and beginning this journey is part of a lifelong adventure and an intellectual pursuit that is rivaled by none. I am going to make this blog more visible this coming monday, posting on twitter with some regularity, facebook, et cetera.
I am truly blessed to have this opportunity to impart this discourse, and if you are reading this, you can do me no greater honour.
Fibonacci and Gibonacci as mathematical concepts are really only the beginning of a far greater pursuit that discusses the place of Gibonacci in thermodynamics and information theory and further probes its links to theology. It is the purpose of this site to build the cornerstone for the simple logic of a theory of everything.
Nonetheless, while I was doing research on Gibonacci Sequences, I, very much accidentally, discovered a new way of describing Gibonacci Numbers; a new, nonrecursive function that produces Gibonacci Numbers using Binomial notation. I feel that it is sufficently interesting to warrant contemplation, however it is not directly related to the theory in any way but rather a little bonus that the universe tossed my way for having taken the time to look.
So, what happens next? We start with everything, I suppose.
I am making a concerted effort to understand entropy.
From the sedond law of thermodynamics, we see that "In a closed system, entropy always rises."
From wikipedia, entropy:
From a macroscopic perspective, in classical thermodynamics the entropy is interpreted as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. The state function has the important property that, when multiplied by a reference temperature, it can be understood as a measure of the amount of energy in a physical system that cannot be used to do thermodynamic work; i.e., work mediated by thermal energy[citation needed]. More precisely, in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat (TR is the temperature of the system's external surroundings). Otherwise the process will not go forward. In classical thermodynamics, the entropy of a system is defined only if it is in thermodynamic equilibrium.
so, in this sense, entropy is not a measure of disorder of a system, but rather a measure of the loss in disorder of a system, a quantity of thermodynamic potential, used, actualized. Entropy is then an unrecoverable quantity of energy, used to do work and lost to, I think, the expansion of space-time.
Finally, while in a closed system, system entropy always increases, there is astounding and ultimately common evidence to suggest that the Universe is an open system and as such, the entropy of the universe is decreasing; space is expanding, time is progressing and the potential is becoming the actual...
ScienceDaily (Jan. 7, 2010) — Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture.
The research team is publishing these findings in the Jan. 8, 2010 issue of the journal Science.
On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.
When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain -- or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."
By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture." Radu Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system -- a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material," he explains.
The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology. Prof. Tennant remarks on the perfect harmony found in quantum uncertainty instead of disorder. "Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state."
The researchers achieved these results by using a special probe -- neutron scattering. It allows physicists to see the actual atomic scale vibrations of a system. Dr. Elisa Wheeler, who has worked at both Oxford University and Berlin on the project, explains "using neutron scattering gives us unrivalled insight into how different the quantum world can be from the every day."
However, "the conflicting difficulties of a highly complex neutron experiment integrated with low temperature equipment and precision high field apparatus make this a very challenging undertaking indeed." In order to achieve success "in such challenging experiments under extreme conditions" the HZB in Berlin has brought together world leaders in this field. By combining the special expertise in Berlin whilst taking advantage of the pulsed neutrons at ISIS, near Oxford, permitted a perfect combination of measurements to be made
The Second Law of Thermodynamics is stated as follows in wikipedia:
The entropy of an isolated system consisting of two regions of space, isolated from one another, each in thermodynamic equilibrium in itself, but not in equilibrium with each other, will, when the isolation that separates the two regions is broken, so that the two regions become able to exchange matter or energy, tend to increase over time, approaching a maximum value when the jointly communicating system reaches thermodynamic equilibrium.
In more practical terms, I have defined the second law of thermodynamics with the two corresponding ideas:
1) In a closed systems, entropy will increase. Conversely, in open systems, entropy will tend to increase.
2 ) If energy is inputted into a system and a state change occurs, the result of the change will be simpler/less ordered than the original participants. Conversely, if energy dissipates from a system and state-change occurs, the result is more complex/more ordered than the original components.
But I recently met a man, if but briefly, named Johannes. He raised some doubt as to the converse nature of my understanding; he conceded that in a closed system entropy always increases but did not agree that in an open system entropy will tend to decrease.
So I posed an online correspondent, Vince Ciricola (http://thermohistory.org/) in the following form:
Can I ask for your help re:2nd law/thermodynamics? Argument: In a closed system, entropy always increases. ... Life requires decreasing entropy. It it rhen fair to conclude that the universe is NOT a closed system? That the rule is reversed? ... rather, by reversed, the universe is an open system and entropy is always decreasing?
His response was delightful:
Entropy's original definition related to heat & energy unavailable to produce work. Later the notion of disorder was incorporated. Some think increasing order on a macro scale violates the 2nd law. But thermodynamically (re heat degradation) there is no confusion. To produce order on a macro level, high quality energy has to be used (degraded) &becomes low quality; which translates to increased entropy. Heat can not be transformed 100% to work. The rejected heat 'quality' is irreversibly degraded. Re entropy: http://tinypaste.com/146ba
To begin to understand entropy on its most basic level, the excerpt below will be helpful. Work can not be produced nor can order be achieved from chaos without the expenditure of (for the sake of this explanation)(thermal) energy
The following is excerpted from: http://pespmc1.vub.ac.be/ENTRTHER.html
The first law of thermodynamics says that the total quantity of energy in the universe remains constant. This is the principle of the conservation of energy. The second law of thermodynamics states that the quality of this energy is degraded irreversibly. This is the principle of the degradation of energy.
About 1850 the studies of Lord Kelvin, Carnot, and Clausius of the exchanges of energy in thermal machines revealed that there is a hierarchy among the various forms of energy and an imbalance in their transformations. This hierarchy and this imbalance are the basis of the formulation of the second principle.
In fact physical, chemical, and electrical energy can be completely changed into heat. But the reverse (heat into physical energy, for example) cannot be fully accomplished without outside help or without an inevitable loss of energy in the form of irretrievable heat. This does not mean that the energy is destroyed; it means that it becomes unavailable for producing work. The irreversible increase of this nondisposable energy in the universe is measured by the abstract dimension that Clausius in 1865 called entropy (from the Greek entrope, change).
I found this video on twitter, posted by Vince Ciricola. It offers a succinct explanation of Time Dialation under special relativity. Time dialation will prove to be a key feature in forthcoming sections of the theory of order, asthe relative mechanics of space-time relate greatly to the total motion of a system. The motion is in turn a measure of comotion, and in the future, I will contend a relationship between the energy used universally for motion and the emmision of a potential space-time into an actual space-time.
I have been trying to use social media networks to market my "product". My "product", in this case is a series of ideas that I have put together, called the theory of order, regarding the Golden Ratio and the Fibonacciu Sequences; why they appear everywhere in nature. I make some bold conclusions and there are many statements that I make which are uncommon interpretations of physical laws.
It is my desire to captivate enough interest that the general public writes and contributes. In effect, this user input is the monetization of an idea: To have people read, absorb, contribute to and change your theories is an amazing priviledge.
So I have been scouring Twitter to see if I can find people out there who have an interest in physics, thermodynamics, number theory, creation, evolution and/or spirituality. As the first in a long line of bold assertions, I will now suggest that all of the aforementioned fields of human interest are indeed related.
So I want to welcome you to this adventure in multidisiplinarism. Please leave your comments and questions. It is your interest and attention that fuels my pursuits.
Today I have been musing on a few thoughts regarding the nature of space-time and its relationship to change. I feel that the propensity for thermodynamic systems to seek and maintain equilibrium is the key force driving creation and evolution. Le Chatelier's principle is at the centre of thermodynamics and is a chemical expression of a greater and more fundamental tendancy towards universal equilibrium.
In chemistry, Le Chatelier's Principle, also called the Le Chatelier-Braun principle, can be used to predict the effect of a change in conditions on a chemical equilibrium. The principle is named after Henry Louis Le Chatelier and Karl Ferdinand Braun who discovered it independently. It can be summarized as:
If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or partial pressure, then the equilibrium shifts to counteract the imposed change.
This principle has a variety of names, depending upon the discipline using it. See for example Lenz's law and homeostasis. It is common to take Le Chatelier's principle to be a more general observation, roughly stated:
Any change in status quo prompts an opposing reaction in the responding system.
In chemistry, the principle is used to manipulate the outcomes of reversible reactions, often to increase the yield of reactions. In pharmacology, the binding of ligands to the receptor may shift the equilibrium according to Le Chatelier's principle thereby explaining the diverse phenomena of receptor activation and desensitization.[1] In economics, the principle has been generalized to help explain the price equilibrium of efficient economic systems. In simultaneous equilibrium systems, phenomena could occur, which are in apparent contradiction to Le Chatelier's principle; these can be resolved by the theory of Response reactions.
Chemistry
Concentration
Changing the concentration of an ingredient will shift the equilibrium to the side that would reduce that change in concentration. The chemical system will attempt to partially oppose the change affected to the original state of equilibrium. In turn, the rate of reaction, extent and yield of products will be altered corresponding to the impact on the system.
Suppose we were to increase the concentration of CO in the system. Using Le Chatelier's principle we can predict that the amount of methanol will increase, decreasing the total change in CO. If we are to add a species to the overall reaction, the reaction will favor the side opposing the addition of the species. Likewise, the subtraction of a species would cause the reaction to fill the “gap” and favor the side where the species was reduced. This observation is supported by the collision theory. As the concentration of CO is increased, the frequency of successful collisions of that reactant would increase also, allowing for an increase in forward reaction, and generation of the product. Even if a desired product is not thermodynamically favored, the end product can be obtained if it is continuously removed from the solution.
Temperature
The effect of changing the temperature in the equilibrium can be made clear by incorporating heat as either a reactant or product. When the reaction is exothermic (ΔH is negative, puts energy out), we include heat as a product, and when the reaction is endothermic (ΔH is positive, takes energy in), we include it as a reactant. Hence, we can tell whether increasing or decreasing the temperature would favour the forward or reverse reaction by applying the same principle as with concentration changes.
For example, the reaction of nitrogen gas with hydrogen gas. This is a reversible reaction, in which the two gases react to form ammonia:
This is an exothermic reaction when producing ammonia. If we were to lower the temperature, the equilibrium would shift to produce more heat. Since making ammonia is exothermic, this would favour the production of more ammonia. In practice, in the Haber process the temperature is set at a compromise value, so ammonia is made quickly, even though less would be present at equilibrium.
Changes in pressure are attributable to changes in volume. The equilibrium concentrations of the products and reactants do not directly depend on the pressure subjected to the system. However, a change in pressure due to a change in volume of the system will shift the equilibrium.
Once again, let us refer to the reaction of nitrogen gas with hydrogen gas to form ammonia:
N2 + 3 H2⇌ 2 NH3 ΔH = −92kJ mol-1
4 volumes ⇌ 2 volumes
Note the number of moles of gas on the left hand side, and the number of moles of gas on the right hand side. When the volume of the system is changed, the partial pressures of the gases change. Because there are more moles of gas on the reactant side, this change is more significant in the denominator of the equilibrium constant expression, causing a shift in equilibrium.
Thus, an increase in pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas.[2] A decrease in pressure due to increasing volume causes the reaction to shift to the side with more moles of gas. There is no effect on a reaction where the number of moles of gas is the same on each side of the chemical equation.
.Effect of adding an inert gas
An inert gas (or noble gas) such as helium is one that does not react with other elements or compounds. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift.[3] This is because the addition of a non-reactive gas does not change the partial pressures of the other gases in the container. While it is true that the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant; rather, it is a change in partial pressures that will cause a shift in the equilibrium. If, however, the volume is allowed to increase in the process, the partial pressures of all gases would be decreased resulting in a shift towards the side with the greater number of moles of gas.
Applications in Economics
In economics, a similar concept also named after Le Chatelier was introduced by US economist Paul Samuelson in 1947. There the generalized Le Chatelier principle is for a maximum condition of economic equilibrium: where all unknowns of a function are independently variable, auxiliary constraints — "just-binding" in leaving initial equilibrium unchanged — reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run.[4]
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