Through the Bible with Jim Carmichael: Mathematics/ It’s a Quasicrystal World

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Our Mathematical Universe

MATHEMATICS and BUILDING BLOCKS
Universe: From the center of Harvard & Smithsonian…

MATTER AND ENERGY are the two basic components of the entire Universe.

An enormous challenge for scientists is that most of the matter in the Universe is invisible and the source of most of the energy is not understood.

How can we study the Universe if we can’t see most of it?

From the Independent Statistics and Analysis…U.S. Energy Information Administration

Scientists define energy as the ability to do work.

Modern civilization is possible because people have learned how to change energy from one form to another and then use it to do work.

People use energy to walk and bicycle, to move cars along roads and boats through water, to cook food on stoves, to make ice in freezers, to light our homes and offices, to manufacture products, and to send astronauts into space.

There are many forms of energy:

  • Heat
  • Light
  • Motion
  • Electrical
  • Chemical
  • Gravitational
  • These forms of energy can be grouped into two general types of energy for doing work:
  • Potential, or stored, energy
  • Kinetic, or working, energy

But what is it made of???

What is Energy Made Of? Waves? Particles?

We Have a New Theory

by Larry M. Silverberg, North Carolina State University

https://nationalinterest.org/blog/reboot/what-energy-made-waves-particles-we-have-new-theory-174160

THE FRAGMENT COULD BE A SINGLE POTENTIALLY UNIVERSAL BUILDING BLOCK from which to model reality MATHEMATICALLY –

and update the way people think about the BUILDING BLOCKS of the universe.

MATTER: Matter is what makes up the universe, but what makes up matter?

This question has long been tricky for those who think about it – especially for the physicists.

Reflecting recent trends in physics, Jeffrey Eischen and Larry M. Silverberg have described an updated way to think about matter.

they propose that matter is not made of particles or waves, as was long thought, but – more fundamentally – that…

MATTER IS MADE OF FRAGMENTS OF ENERGY.

History Lesson:

The ancient Greeks conceived of five BUILDING BLOCKS of matter – from bottom to top:

  1. earth,
  2. water,
  3. air,
  4. fire and
  5. aether.

Aether

The matter that filled the heavens

and explained the rotation of the stars, as observed from the Earth vantage point. These were the first most basic elements from which one could build up a world. Their conceptions of the physical elements did not change dramatically for nearly 2,000 years.

  1. Then, about 300 years ago, Sir Isaac Newton introduced the idea that all matter exists at points called particles.
  2. One hundred fifty years after that, James Clerk Maxwell introduced the electromagnetic wave – the underlying and often invisible form of magnetism, electricity and light.

The particle served as the BUILDING BLOCK for mechanics and the wave for electromagnetism
– and the public settled on the particle and the wave as THE TWO BUILDING blocks of matter.
Together, the particles and waves became THE BUILDING BLOCKS of all kinds of matter.

This was a vast improvement over the ancient Greeks’ five elements, but was still flawed.

In a famous series of experiments, known as the double-slit experiments, light sometimes acts like a particle and at other times acts like a wave.
And while the theories and math of waves and particles allow scientists to make incredibly accurate predictions about the universe, the rules break down at the largest and tiniest scales.

Einstein proposed a remedy in his theory of general relativity.

Using the mathematical tools available to him at the time, Einstein was able to better explain certain physical phenomena and also resolve a longstanding paradox relating to inertia and gravity.
But instead of improving on particles or waves, he eliminated them as he proposed the warping of space and time.

Using newer mathematical tools, Larry M. Silverberg and his  colleagues have demonstrated a new theory that may accurately describe the universe.
Instead of basing the theory on the warping of space and time,
They considered that there could be A BUILDING BLOCK that is more fundamental than the particle and the wave.
Scientists understand that particles and waves are existential opposites: A particle is a source of matter that exists at a single point, and waves exist everywhere except at the points that create them.

Silverberg and his  colleagues thought it made logical sense for there to be an underlying connection between them.

Flow and Fragments of Energy Their theory

begins with a new fundamental idea – that energy always “flows” through regions of space and time.

Think of energy as made up of lines that fill up a region of space and time, flowing into and out of that region, never beginning, never ending and never crossing one another.Working from the idea of a universe of flowing energy lines, they looked for A SINGLE BUILDING BLOCK for the flowing energy. If they could find and define such a thing, they hoped they could use it to accurately make predictions about the universe at the largest and tiniest scales.

There were MANY BUILDING BLOCKS to choose from MATHEMATICALLY, but they sought one that had the features of both the particle and wave – concentrated like the particle but also spread out over space and time like the wave.
The answer was a BUILDING BLOCK that looks like a concentration of energy – kind of like a star – having energy that is highest at the center and that gets smaller farther away from the center.

Much to their surprise, they discovered that there were only a limited number of ways to describe a concentration of energy that flows. Of those, they found just one that works in accordance with our MATHEMATICAL definition of flow.
They named it a fragment of energy. For the MATH and physics enthusiasts, it is defined as A = -⍺/r where ⍺ is intensity and r is the distance function.Using the fragment of energy as a building block of matter, they then constructed the math necessary to solve physics problems. The final step was to test it out.

  1. Back to Einstein, Adding Universality

More than 100 ago, Einstein had turned to two legendary problems in physics to validate general relativity: the ever-so-slight yearly shift – or precession – in Mercury’s orbit, and the tiny bending of light as it passes the Sun. These problems were at the two extremes of the size spectrum.
Neither wave nor particle theories of matter could solve them, but general relativity did. The theory of general relativity warped space and time in such way as to cause the trajectory of Mercury to shift and light to bend in precisely the amounts seen in astronomical observations.

If their new theory was to have a chance at replacing the particle and the wave with the presumably more fundamental fragment, they would have to be able to solve these problems with their theory, too. For the precession-of-Mercury problem, they modeled the Sun as an enormous stationary fragment of energy and Mercury as a smaller but still enormous slow-moving fragment of energy.

For the bending-of-light problem, the Sun was modeled the same way, but the photon was modeled as a minuscule fragment of energy moving at the speed of light.

In both problems, they calculated the trajectories of the moving fragments and got the same answers as those predicted by the theory of general relativity. They were stunned.
Their initial work demonstrated how a new building block is capable of accurately modeling bodies from the enormous to the minuscule.
Where particles and waves break down, the fragment of energy BUILDING BLOCK held strong.

THE FRAGMENT COULD BE A SINGLE POTENTIALLY UNIVERSAL BUILDING BLOCK FROM WHICH TO MODEL REALITY MATHEMATICALLY –and update the way people think about

THE BUILDING BLOCKS OF THE UNIVERSE.

The Conversation

First let’s look at the cosmos being a closed system…

The difference between a closed and open universe is a bit like the difference between a stretched flat sheet and an inflated balloon, Melchiorri told Live Science. In either case, the whole thing is expanding. When the sheet expands, every point moves away from every other point in a straight line. When the balloon is inflated, every point on its surface gets farther away from every other point, but the balloon’s curvature makes the geometry of that movement more complicated.

“This means, for example, that if you have two photons and they travel in parallel in a closed universe, they will [eventually] meet,” Melchiorri said.

In an open, flat universe, the photons, left undisturbed, would travel along their parallel courses without ever interacting. A system is isolated when there is no energy exchange with the surroundings. For example the contents of a vacuum flask are isolated. In practice there is an error in the isolation parameter, i.e. delta(energy) that is why after some time the contents will be found to be in room temperature.

Experiments are designed so as to work within the errors. The universe is by definition of the word isolated, because it contains everything by definition, and thus there can be no exchange of energy with anything. If there could be, it would be counted within the universe.

Now models may be found where “universe” is defined with some error in this energy exchange. Even speculated as many isolated ones, but there would be no way of knowing since no energy would be exchanged. In fact science is starting to become convinced the Cosmos is a closed system, but there are many hold-outs… this points out the confusion in modern science… they all see the same evidence, and come to different conclusions… so lets see if science agrees with scripture.

The earth free-floats in space (Job 26:7 affected only by gravity. While other sources declared the earth sat on the back of an elephant or turtle or was held up by Atlas, the Bible alone states what we now know to be true – “He hangs the earth on nothing.”

The First Law of Thermodynamics established (Genesis 2:1-2. The First Law states that the total quantity of energy and matter in the universe is a constant. One form of energy or matter may be converted into another, but the total quantity always remains the same. Therefore the creation is finished, exactly as God said way back in Genesis.

The Second Law of Thermodynamics (Entropy) explained (Psalm 102:25-26). This law states that everything in the universe is running down, deteriorating, constantly becoming less and less orderly. Entropy (disorder) entered when mankind rebelled against God – resulting in the curse (Genesis 3:17; Romans 8:20-22). Historically most people believed the universe was unchangeable. Yet modern science verifies that the universe is “grow(ing) old like a garment” (Hebrews 1:11). Evolution directly contradicts this law.

  1. Environmental devastation of the planet foreseen (Revelation 11:18). Though evolution imagines that things should be getting better, the Bible foresaw what is really occurring today: pollution, destruction and corrupt dominion.
  2. The universe had a beginning (Genesis 1:1; Hebrews 1:10-12). Starting with the studies of Albert Einstein in the early 1900s and continuing today, science has confirmed the biblical view that the universe had a beginning. When the Bible was written most people believed the universe was eternal. Science has proven them wrong, but the Bible correct.
  3. Scripture assumes a revolving (spherical) earth (Luke 17:34-36). Jesus said that at His return some would be asleep at night while others would be working at daytime activities in the field. This is a clear indication of a revolving earth, with day and night occurring simultaneously.
  4. The sun goes in a circuit (Psalm 19:6). Some scientists scoffed at this verse thinking that it taught geocentricity – the theory that the sun revolves around the earth. They insisted the sun was stationary. However, we now know that the sun is traveling through space at approximately 600,000 miles per hour. It is literally moving through space in a huge circuit – just as the Bible stated 3,000 years ago!
  5. God created “lights” in the heavens “for signs and seasons, and for days and years” (Genesis 1:14-16). We now know that a year is the time required for the earth to travel once around the sun. The seasons are caused by the changing position of the earth in relation to the sun. The moon’s phases follow one another in clock-like precision – constituting the lunar calendar Evolution teaches that the cosmos evolved by random chance, yet the Bible agrees with the observable evidence
  6. The Bible speaks of “heaven and the highest heavens” (Deuteronomy 10:14). Long before the Hubble Space Telescope, Scripture spoke of the “heaven of heavens” and the “third heaven” (1 Kings 8:27; 2 Corinthians 12:2). We now know that the heavens consist of our immediate atmosphere and the vast reaches of outer space – as well as God’s wonderful abode.
  7. The universe is expanding (Job 9:8; Isaiah 42:5; Jeremiah 51:15; Zechariah 12:1). Repeatedly God declares that He stretches out the heavens. During the early 20th century, most scientists (including Einstein) believed the universe was static. Others believed it should have collapsed due to gravity. Then in 1929, astronomer Edwin Hubble showed that distant galaxies were receding from the earth, and the further away they were, the faster they were moving. This discovery revolutionized the field of astronomy. Einstein admitted his mistake, and today most astronomers agree with what the Creator told us millennia ago – the universe is expanding!
  8. The Pleiades and Orion star clusters described (Job 38:31). The Pleiades star cluster is gravitationally bound, while the Orion star cluster is loose and disintegrating because the gravity of the cluster is not enough to bind the group together. 4,000 years ago God asked Job, “Can you bind the cluster of the Pleiades, or loose the belt of Orion?” Yet, it is only recently that we realized that the Pleiades is gravitationally bound, but Orion’s stars are flying apart.
  9. So…it had a beginning, there is limited energy which does not change, the cosmos is running down, deteriorating, the Sun moves in a circuit through the universe, which means it moves in a closed circuit,  and that is a pattern for the earth moves around the Sun, and the moon revolves around the Earth… and that pattern is followed throughout the cosmos…

Now, you attempted to visualize nothing, and you were unable to do it… there has to be a point of reference…

An example:

 

When Howard Hughes made the movie “Hell’s Angels” he had the airplanes flying in a clear sky but couldn’t find a way to demonstrate the speed of the planes until he realized there was no reference point… He had to wait for a cloudy day in order to shoot the scene so the speed of the planes would be apparent when compared to the stationary clouds behind the plains.

So with that thought in mind. There had to be something eternal, something that existed for there to be nothing…. I’m going to use a very simple way of illustrating this…

We can visualize a box without anything in it…. Nothing.. But if there is no box, how can we visualize it being empty? What is empty?…..

Let me take this a bit further.

Let’s say we have some boards. And we have some nails. So all we have is boards and nails. Unless, we insert those nails Into the boards in such a way that it forms a box. Now we have two choices. We can build a open end box or we can build an enclosed box. So let’s say we built an open box. That means it has an opening at the top. Where it has a lid  so we can put some stuff in it. Now. A closed system or a closed box means that it is enclosed. There’s no way to put anything into it. So if a man decided to build a closed box, considering he is of normal intelligence and mentally sound. He would build that box with himself on the outside. He would not even consider building the box with himself on the inside.

However, speaking of the cosmos, God does have access to the inside of the box, and can move between the dimensions which are inside the box and outside the box.

Let’s apply that to the cosmos.

God created the Cosmos first, and he is on the outside, and the cosmos is the box. However, later he created a thing called the Earth and put it inside. And then later he created some more stuff and put that inside the box as well.

Now that’s a very weak example. so let’s put it a different way, because it can only be explained through MATHEMATICS.

You could do this by using brackets [ ]. You have the brackets but nothing inside the brackets until you started adding MATHEMATICAL FORMULAS.

This is how you can visualize nothing… nothing between the brackets.

Example: []=empty box… [2 + 2] now you have something inside the brackets, or in the case of the box…something is now in the box, placed there after the box existed…

Why do I use MATH as the example as the only correct way to demonstrate the nothingness?

Emergence Theory

General Overview in Layperson Terms

Emergence theory is a unified first-principles quantum gravity unification theory currently in development by a Los Angeles-based team of scientists.

Emergence theory weaves together quantum mechanics, general and special relativity, the standard model and other mainstream physics theories into a complete, fundamental picture of a discretized, self-actualizing universe.

This scientific research team in Los Angeles, Quantum Gravity Research, (consists of a group of MATHEMATICIANS and physicists working together), states that all things are made up of  MATHEMATICAL data,  called a 3D quasicrystal which they believe is the fundamental substructure of all reality, a tetrahedron, which is a three-dimensional equilateral triangle,  The size of each edge on this shape is the smallest unit of length in existence, the smallest that can exist. it’s called the Planck Length, it’s 10 to the 35 times smaller than a meter… enough of that, in short it could never be seen by the human eye…

And in the end they say the foundation of all this is a conscience mind… but deny God, when that is exactly what they describe.

(JIM’S INPUT: self-actualizing universe… this is their mistake, because they refuse to accept a creator as the answer, so it must have been self-creating)

And, as I say this I want to let you know on this webpage there are several videos from these people and others to help clarify.

At the root of emergence theory’s formalism is a concept quickly taking hold in the theoretical physics community––THAT ALL OF REALITY IS MADE OF INFORMATION.

What is information?

Information is meaning conveyed by symbols. Languages and codes are groups of such symbols that convey meaning. The various possible arrangements of these symbols are governed by rules. And, The language user (the one using the language) makes free-will choices regarding how to arrange the symbols, in order to produce meaning, according to these rules.

Fundamentally, then, the existence of information must therefore imply a “chooser,” or some form of consciousness, in order for it to be actualized.

(JIMS INPUT:  GOD!!!!!!!!— this is just common sense)

They identified two classes of symbols.

One class contains those symbols that subjectively represent something other than the symbols themselves. For example, the shape of two intersecting diagonal lines (“X”) can represent the MATHEMATICAL concept of multiplication, it can represent an English letter, or it can represent a kiss. The shapes known as the letters “D-O-G” can represent a certain animal that we all know and love, but they can also represent anything else if we decide that they do, such as a mistake “He really dogged that one.”

The second and arguably more fundamental class of symbols are those symbols that represent themselves with ultra-low subjectivity. An example is the shape of a square representing the shape of a square. Such a geometric language using geometric symbols could express geometric meaning.

Reality is experimentally observed to be geometric at all scales, from the Planck level to the largest structures. Their group hypothesizes that an entirely geometric language or code, using geometric symbolism, is the fundamental way in which meaning, in the form of our physical reality, is expressed by……..well, we’ll get to that.

A central feature of reality behaving geometrically is that all fundamental particles and forces in nature, including gravity, can transform into one another, through a process called gauge symmetry transformation, in a manner that corresponds precisely to the vertices of the 8-dimensional polytope of a crystal called the E8 lattice. However, we do not appear to live in an 8-dimensional universe. Experimental evidence indicates that we live in a universe comprised of only three spatial dimensions.

What kind of geometric language or code, then, would express a geometric, 3-dimensional reality that is deeply linked to the 8-dimensional, E8 lattice?

They believe the answer is in the language AND MATHEMATICS of quasicrystals. A quasicrystal is an aperiodic, but not random, pattern.

A quasicrystal in any given dimension is created by projecting a crystal – a periodic pattern – from a higher dimension to a lower one.

For example, imagine projecting a 3-dimensional checkerboard – or cubic lattice made of equally spaced and sized cubes – onto a 2-dimensional plane at a certain angle. This 3D cubic lattice is a periodic pattern that may stretch out infinitely in all directions. The 2D, projected object is not a periodic pattern. Rather, it is distorted due to the angle of projection, and instead of containing only one shape that repeats infinitely like the 3D crystal does, it contains a finite number of different shapes (called proto-tiles) that are oriented relative to one another in specific ways, governed by a set of MATHEMATICAL/GEOMETRICAL rules, to fill the 2D plane in all directions.

I would suggest you watch the videos associated with this subject in order to understand it better

By analyzing the 2D projection it is possible, with the CORRECT MATHEMATICAL AND TRIGONOMETRIC toolkit, to actually recover the “mother” object in 3D (the cubic lattice crystal in this example.)

A famous example of a 2D quasicrystal is the Penrose tiling conceived by Roger Penrose in the 1970’s, in which a 2D quasicrystal is created by projecting a 5-dimensional cubic lattice to a 2D plane.

https://youtu.be/th3YMEamzmw / https://youtu.be/orMtwOz6Db0

Emergence theory focuses on projecting the 8-dimensional E8 crystal to 4D and 3D. When the fundamental 8D cell of the E8 lattice (a shape with 240 vertices known as the “Gosset polytope”) is projected to 4D, two identical, 4D shapes of different sizes are created. The ratio of their sizes is the golden ratio. Each of these shapes are constructed of 600 3-dimensional tetrahedra rotated from one another by a golden-ratio based angle. They refer to this 4D shape as the “600-Cell.” The 600-Cells interact in specific ways (they intersect in 7 golden-ratio related ways and “kiss” in one particular way) to form a 4D quasicrystal. By taking 3D subspaces of this 4D quasicrystal and rotating them from one another at a certain angle, we form a 3D quasicrystal that has one type of proto-tile: a 3D tetrahedron.

On a TV or computer screen the smallest, indivisible unit is a 2D pixel. In our 3D quasicrystalline reality, the tetrahedron is the smallest, indivisible unit. A 3D pixel of reality, if you will. Each tetrahedron is the smallest possible 3D shape that can exist in this reality: the length of each of its edges is the Planck length (the shortest possible length known in physics – over 10^35 times smaller than a meter) These 3D pixels combine with one another according to specific, geometric rules, TO POPULATE ALL OF SPACE.

On a 2D screen, the pixels never move. They simply have different brightness and color values, and an illusion of meaning (in the form of a picture) is created by their combined values. Similarly, the tetrahedra in the 3D quasicrystal never move either. Instead, they act as a binary language: in any given moment, each tetrahedron can be chosen by the code operator to be either “on” or “off.” If it is “on,” it can be in one of two states: “rotated left” or “rotated right.”

Imagine a single, frozen moment in time throughout the entire universe.

Let’s call this moment “moment 1” for the purposes of illustration. In moment 1, the 3D quasicrystal filling the entire universe is in “state 1” and in this state, some tetrahedra are on, some are off, some are rotated left and some are rotated right. Now imagine the next frozen moment in time, “moment 2.” In moment 2, the quasicrystal is in “state 2.” In this new state, many of the tetrahedra are in different states from their states in moment 1.

Now imagine a hundred of these moments. Now imagine an animation of all of these frozen moments. If you think of a movie, the moving-image is composed of single, frozen frames that are filmed and projected at a certain speed (24 frames per second in most modern movies). In our model, one second contains 10^44 frozen frames. Over many of these frames patterns emerge on the 3D quasicrystal. These patterns become more and more meaningful and sophisticated with time. Gradually patterns resembling and acting as particles form on the quasicrystal. In fact, one of the most groundbreaking predictions emergence theory will make is about a specific, pixelated substructure of electrons––particles currently thought of, without proof, as dimensionless. With time, these particles take on more and more complex forms, and eventually the reality we all know and love emerges.

Emergence theory views spacetime in a way that builds on Einstein’s spacetime model, in which the future and past exist simultaneously in one geometric object. They view this object as a system in which all frames of spacetime interact with all other frames all the time. In other words, there is a constant, dynamic, causality loop relationship between all moments in time, in which the past influences the future and the future influences the past.

WE VIEW CONSCIOUSNESS AS BOTH EMERGENT AND FUNDAMENTAL.

In its fundamental form, CONSCIOUSNESS EXISTS INSIDE EVERY TETRAHEDRON/PIXEL IN THE 3D QUASICRYSTAL IN THE FORM OF SOMETHING WE CALL VIEWING VECTORS.

Think of viewing vectors as micro-scale observers in THE TRADITIONAL QUANTUM MECHANICAL SENSE.These observers actualize reality by making ultra-fast, Planck scale choices about the binary states of the pixels (on, off, left, right) at every moment in time. This fundamental,  primitive, YET HIGHLY SOPHISTICATED FORM OF CONSCIOUSNESS STEERS THE PATTERNS on the quasicrystalline point-space toward more and more meaning. Eventually consciousness expands into higher degrees of order such as nature and life as we know it. From there life and consciousness keep expanding, growing exponentially, into all corners of the universe.

Imagine humankind one day populating trillions of galaxies, its instantaneous communicative channels and high levels of consciousness growing over time into a massive, universal-scale neural network––a collective consciousness of sorts. This collective consciousness conceives the fundamental, “primitive” consciousness that powers the quasicrystal from which it emerges.

  1. A creates B.
  2. B creates C.
  3. And C creates A.

There are no known laws in physics that place an upper limit on what percentage of the universe can exponentially self-organize into freewill systems such as us humans. Indeed, PHYSICS ALLOWS THE POSSIBILITY THAT ALL THE ENERGY OF THE UNIVERSE CAN BE CONVERTED INTO A SINGLE, CONSCIOUS SYSTEM THAT ITSELF IS A NETWORK OF CONSCIOUS SYSTEMS. Given enough time, what can happen will eventually happen. By this axiom, universal emergent consciousness has emerged via self-organization somewhere ahead of us in 4D spacetime. And because it is possible, it is inevitable. In fact, according to the evidence of retro-causality time loops, that inevitable future is co-creating us right now just as we are co-creating it.
(pre>(can you see where their heading? Evolution!… they just can’t accept God as the answer…it’s beyond them)

These extensive scientific statements each in their own way point to a conscience mind that created all things, yet they refuse to name that power… GOD!!!

What does Scripture say about this?

Hebrews 11:3 By faith [that is, with an inherent trust and enduring confidence in the power, wisdom and goodness of God] we understand that the worlds (universe, ages) were framed and created [formed, put in order, and equipped for their intended purpose] by the word of God, so that what is seen was not made out of things which are visible.

Let’s step a little deeper into mathematics…. Mankind did not create mathematics, we discovered it…

Does God’s word relate to mathematics in anyway?

Yes… deeply…

In 2014 the MIT physicist Max Tegmark a believer in evolution, not creation argues in “OUR MATHEMATICAL UNIVERSE” THAT MATHEMATICS IS THE FUNDAMENTAL WORLD REALITY THAT DRIVES THE UNIVERSE. It could be said that MATHEMATICS IS OPERATING IN A GOD-LIKE FASHION.

However, Tegmark and others believe this perfectly MATHEMATICALLY ORDERED UNIVERSE came from chaos billions of years ago, and not from an intricate planning Creator.

At first, it looked random. Astronomers saw giant galaxy clusters, each containing a thousand or more galaxies. And there were also much smaller groups of galaxies, , groups of galaxies, and galaxies hanging out by themselves. Taken together, the observations made it appear as if there were no overarching pattern to the cosmos. And astronomers were fine with that. They had long assumed an idea called the cosmological principle — that is, that the universe is mostly homogeneous (roughly the same from place to place) and isotropic (roughly the same no matter which direction you look). A bunch of random galaxies and clusters fit right into that principle.

But in the late 1970s, galaxy surveys became sophisticated enough to reveal the beginnings of a pattern in the arrangement of galaxies. Besides the clusters, there were also long, thin filaments of galaxies. There were broad walls. And then there were the voids — vast expanses of nothing. Astronomers called it the cosmic web. This pattern would violate the cosmological principle, because it would mean that large regions of the universe did not look like other large regions of the universe.

One proposal came from MATHEMATICIAN BENOIT MANDELBROT, the father of fractals.

Fractals are frustratingly hard to define, but they can be simple enough to intuit: They are patterns that repeat no matter how far in or out you zoom. Mandelbrot didn’t invent the concept of fractals — MATHEMATICIANS had been studying self-similar patterns for ages — but he coined the word “fractal” and ushered in our modern study of the concept. Let me state again… that no human invented MATHEMATICS… they discovered them… they were there all along, just unseen by human eyes.

Fractals are everywhere.

    1. If you zoom in on the point of a snowflake, you see miniature snowflakes.
    2. If you zoom in on the branches of a tree, you see miniature branches.
    3. If you zoom in on a coastline, you see miniature coastlines.

Fractals surround us in nature, and THE MATHEMATICS OF FRACTALS have enabled us to understand a vast variety of self-similar STRUCTURES IN THE UNIVERSE.If fractals are everywhere, Mandelbrot guessed, then perhaps the entire universe is a fractal. Maybe what we saw as the pattern in the arrangement of galaxies was the beginning steps of the greatest fractal possible. Maybe if we built sophisticated enough surveys, we would find nesting structures — cosmic webs inside cosmic webs, filling up the entire universe to infinity.

In MATHEMATICS, THE FIBONACCI NUMBERS, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian MATHEMATICIAN LEONARDO OF PISA, later known as Fibonacci, who introduced the sequence to WESTERN EUROPEAN MATHEMATICS in his 1202 book Liber Abaci.

Fibonacci numbers appear unexpectedly often in MATHEMATICS, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly.Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone’s bracts.

Fibonacci NUMBERS are also strongly related to the golden ratio: Binet’s formula expresses the nth Fibonacci NUMBER in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci NUMBERS tends to the golden ratio as n increases. FIBONACCI NUMBERS are also closely related to LUCAS NUMBERS, which obey the same recurrence relation and with the FIBONACCI NUMBERS form a complementary pair of Lucas sequences.

Why the Golden Ratio?

The golden ratio–also called the golden mean, the golden section, or the ”Divine Proportion”–holds special significance to artists, MATHEMATICIANS, and other scientists. As you may well know, it is directly related to FIBONACCI NUMBERS as well as Phi, which plays a role in determining a golden rectangle and a Fibonacci spiral.