Information Patterns – How Creating Works
Meaningful Information consists of items arranged in Patterns. The arranged items can be anything — atoms, molecules, digits, letters, acorns, checkers, species of plants, books of law, or pencil dots. Continuing Creation (which we abbreviate as C.C., and which we sometimes call “The Growing, Organizing, Direction of the Cosmos”) tends to create Patterns of increasing complexity, organization, and even beauty over time. This Continuing Creation of Complexity will happen as long as there is an open flow-through of energy, and a suitable environment of component parts. This Essay discusses the characteristics and evolution of Patterns and Information.
A common religious saying is “God moves in mysterious ways; His wonders to perform,” which is taken from a 19th century Christian hymn. There are several Bible verses that may seem to allude to this idea, including Romans 11:33: “O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!” (KJV) And also Isaiah 40:28: “…The Lord is the everlasting God, the Creator of the ends of the earth. He will not grow tired or weary, and his understanding no one can fathom.” 1
However, in the modern age of Science and Reason, we do know a great deal about how the inner Processes Continuing Creation work, although we certainly do not know it all. This Book has several Essays describing the Processes of Continuing Creation (C.C.) from the vantage points of different disciplines:
- Information Patterns – How Creating Works (what you are now reading)
- Mathematics and Continuing Creation
- Physics and Continuing Creation (still to be written)
- Complexity and Continuing Creation
- The Processes of Evolution & Their Meaning
Essays #1, 4, & 5 are easier to understand because they deal with CC at work in living things and in natural phenomena of nature like cyclones and whirlpools. Readers may elect to skip Essays 2 and 3 for now, and return top them later.
Patterns occur everywhere in Nature, including cracks, spots, stripes, tiles, bubbles, foam, waves and dunes, meanders, spirals, fractals, tessellations, Widmanstatten Patterns (a.k.a.Thomson Structures), spots, stripes, branches, webs, and symmetries. At the time of this writing, there is an excellent article in Wikipedia online called Patterns in Nature which explains how these natural patters arise and provides wonderful photographs of them. (https://en.wikipedia.org/wiki/Patterns_in_nature).
Note: A July 2023 Google search on July 3, 2023 on “Pattern formation books” yields fourteen titles, including Structure Formation in Astrophysics, Weak Chaos and Quasi-Regular Patterns, Pattern Recognition, Pattern Formation, Patterns that Explain the Universe, a Pattern Language, and Understanding Patterns.
This Essay looks at what the principles of Information and Pattern can tell us about the Growing, Organizing, Direction of Creation. Also in this Essau, we will present a few classic poetic descriptions of the Processes of Continuing Creation.
From Singularity to the Stars – A Review
However, we do need to start with a quick review of the cosmology and physics describing the origin of the universe.
The Universe began with an Initial Singularity – a point of immeasurably hot, dense energy, everywhere uniform and symmetrical, before time and before space.
- In a fraction of a micro-second, space and time were somehow created. (Many theories have been proposed.)
- Still in that micro-time frame, the Four Fundamental Forces successively “froze out” form the Grand Unified Force as the universe cooled. (Metaphorically, this freezing out can be thought of as a kind of crystallization.)
- Then there was a (quantum) disturbance, and the earliest matter came into existence – quarks and electrons.
- Then the quarks formed hydrogen nuclei, which attracted electrons to become hydrogen atoms.
- Then gravity collected the hydrogen in dense gas-bodies where the hydrogen was fused into helium and other heavier elements. At the same time, the fusion process ignited the gas-bodies, producing immense heat and light and turning them into stars.
- Using nuclear fusion, the stars sequentially fuse light elements (especially hydrogen) into all 91 of the heavier elements, including helium, carbon, oxygen, iron, calcium, gold, and uranium.
The Total Sum of All Energy and Matter Cannot be Created or Destroyed
Taking the Universe as a whole, the laws of physics tell us that the total energy cannot be created or destroyed. It can be transferred from one object to another (as when one billiard ball hits another), and it can change its form (as when the kinetic energy of falling water turns an electric turbine, generating electricity.) The energy that was created in the Big Bang is all that will ever be created.
Matter can certainly change form – Hydrogen (H) and Oxygen (O) can combine to make water = H2O. Matter can also change into energy, and vice versa. In a burning fire, for example, wood is converted to gases, ash, and energy in the form of heat.
Einstein’s formula, E=mc2, says that matter can change into energy and vice versa. (The “m” in this famous equation stands for “mass,” not “matter,” but laymen like us can use them interchangeably. The “c2” stands for the speed of light squared)
Many places within the universe experience an open energy flow. Earth is such a place. When our sun’s energy bathes the Earth, it builds structures such as evaporation, tornadoes, and every living thing. Each living organism takes in energy (food), grows, and often replicates itself. This is what we mean by Nature’s Continuing Creation.
But Information Can and Does Increase, and Decrease
Unlike the sum of energy and matter, what has increased in the Universe since the Big Bang is structure and information. This increase is the fundamental truth of the Continuing Creation: The Growing, Organizing, Direction of Creation.
Each time another of the Four Forces “froze out,” new information was created. Every time a new and heavier atom was forged by nuclear fusion inside the stars, new information was created.
Differentiation Creates Information
In other words, every time a new difference is struck, new information is created. Differentiation Creates Information.
Looking again at the 6 Steps of the Initial Creation listed above, we can see that the first three steps are steps of differentiation. They happen by the process (mysterious, at least to non-physicists), of “freezing out.”
- When the perfect unity of The Singularity was broken, information was created.
- With the creation of space-time, the universe suddenly possessed differences between left and right, then and now. That’s information.
- When the universe, initially filled with a uniform, undifferentiated quark-gluon plasma, cooled to become filled with separate quarks and gluons, information was created.
Differentiation in Religious Poetry
The process of Differentiation in Information Theory (“freezing out,” in the science of astrophysics) has been metaphorically captured in poetic passages from the world’s great religious texts. For example, we can see Differentiation anthropomorphically described in the first half (verses 1-6) of the Creation Story from the Bible’s Book of Genesis:
“In the beginning, God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, ‘Let there be light’: and there was light. And God saw the light, that it was good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day. And God said, ‘Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.’” (Genesis 1:1-6, King James Version)
In this marvelous poetry, Earth represents the universe, because the ancients had no knowledge of a universe beyond our own atmosphere. Saying that the Earth (universe) was “without form and void,” is poetically saying that the Initial Singularity was perfectly uniform and symmetrical, lacking all differentiation.
Before the four fundamental forces (which the poem calls the “light”) had frozen out, “darkness was upon the face of the deep.” Then, God “divides” (separates) light out from “dark,” which is a way of saying that the four forces (represented in the poetry by “light”) froze out and became distinct.
Differentiation continues on in the later story of Continuing Creation. We see it in the prevalent pattern of branching – when one branch of a tree into two, which later split into four, and so on. Differentiation also created by the process of natural selection, when somewhat different environments will best accommodate similar species with somewhat different characteristics – narrow-beaked finches on an island that has mostly small seeds, and heavy-beaked finches on another island with mostly nuts.
The purpose of each human life is to create and to build. This includes creating and building positive and constructive relationships with our loved ones, neighbors, and co-workers. Creating and building also include discovering, exploring, learning, preserving, and teaching. Each of us is here on Earth to sustainably contribute to the constructive processes of Continuing Creation.
The purpose of each human life is to create and to build. This includes creating and building positive and constructive relationships with our loved ones, neighbors, and co-workers. Creating and building also include discovering, exploring, learning, preserving, and teaching. Each of us is here on Earth to sustainably contribute to the constructive processes of Continuing Creation.
Information Requires a Difference
The first creation of information is the creation of difference:
We’ve seen that differentiation creates Information. In fact, information requires a difference to exist. There is no information without Difference. If the entire universe is an endless field of black in all directions, forever, there is no information. If some of that black field is changed to white, there is a “First Difference.” Similarly, if the endless field is all white, that “white” would present no information no meaning. Only when some of that white field is changed to black, there is a “First Difference.” In the binary computer language of zeroes and ones, if we have 0’s in all directions, there is no information. But if somewhere there is a least one “1,” then there is one bit of information.
Foreground and Background
Once some white is present in an endless black field, we often say that “white” is the foreground,” and black is the background. Or the designations could be reversed.
In order for the white and the black to create information, there must be a boundary between them.
For there to be a difference, there must be a boundary – a line demarking black from white.
In biology, a Boundary is one of the three key requirements of life. Even the most primitive bacteria has these three things:
- A boundary separating the living cell from its environment,
- A metabolism for powering the cell, and
- A map (e.g., DNA) for the cells’ reproduction.
Frame of Reference
We can also say that “black” (background) is the frame of reference for the “white” foreground.
Here’s a short poem by J.X. Mason which captures what we have said so far:
THERE IS NO black without white,
No white without black,
No foreground without background,
No object without a frame,
No yin without yang,
No truth without falsehood,
No left without right,
No up without down,
No “0” without a “1”,
No form (peiron, in ancient Greek) without formlessness (apeiron)
Clearly, a solid gray field would contain zero information. But what about a “gray” field that is composed of billions of tiny black and white specks? While it is true that such a dotted field would require a huge amount of information to describe the location of each and every dot, to a distant human observer, the dotted gray field provides zero information – it is just gray. In this Essay, however, we are talking about the definition of “information” as useful information (structure, organization, pattern).
Combination Creates Still More Information
Let’s leave poetry and return to our informational and scientific description of Creation. And let’s look at how Creation is continued, and greatly expanded, after Differentiation.
After Differentiation (the initial “freezing-out”), Continuing Creation continued to create the universe by a different process — the Process of Combination. From this point on in the history of the universe, all new information has been created by combining already existing things into new and different things.
Atoms combine to make chemical elements; chemical elements combine to make compounds.
Combining happens at the hands of one of the Four Fundament Forces. These forces bring things together and hold them together.
First, the subatomic particles of quarks, gluons, W-Z’s, and electrons are joined together by the Strong Nuclear Force to form atoms of hydrogen and some helium.
Gravity is the force that assembles the great hydrogen gas clouds so tightly that they ignite into stars.
Then, in the nuclear furnaces of stars, Continuing Creation uses the Nuclear Forces to fuse hydrogen atoms together to successively forge 91 additional natural elements that are heavier than hydrogen — including oxygen, carbon, calcium, iron, gold, and uranium.
In our everyday world, the electromagnetic force holds atoms of hydrogen and oxygen together to make molecules of water; and joins sodium and chlorine together to make table salt.
The mysterious and creative thing about Combining is that the result is often so very different from the things that make it up. For example, the element Carbon has very different properties from the hydrogen atoms that were forged together to create it. Gold, also composed of fused hydrogen atoms, is very different from Carbon. All these created differences mean that information has been created.
The Positions of the Combined Things Creates Still More Information
But even more information can be created by the mere positioning of the atoms in a single element. The element Carbon is a prime example. Pure Carbon naturally occurs as amorphous carbon (coal, soot, etc.), graphite, or diamond, depending on how the individual carbon atoms are positioned and linked. These various forms are called allotropes of carbon. A new man-made allotrope is the carbon nanotube.
In graphite (the main ingredient of pencil “lead”), the carbon atoms are joined in flat layers one-atom thick. These layers easily slide apart under light pressure and leave a mark when a pencil is moved across a piece of paper. In a diamond, the carbon atoms are joined together on all sides (in a face-centered cubic crystal) by enormous pressure and temperatures inside the Earth, making the Diamond the hardest natural element on Earth.
Physicists like to say that the perfect unity of the Initial Singularity had “complete symmetry.”
Physicist Michio Kaku has said, “Whenever you see a beautiful snowflake, a beautiful crystal, or even the symmetry of stars in the universe, that’s a piece, or remnant, of the original symmetry at the beginning of time.” (Michio Kaku, on the program The Big Bang Machine, NOVA, January 2015)
Sunflowers, daisies and most other flowers have left-right and top-bottom symmetries of their blossoms. Most mammals have left-right symmetry of their bodies and faces. When we look at Penrose tiles and other complex patterns, we recognize that symmetry can be side-to-side, top-to-bottom, back-to-front; and that symmetries can be as complex an overlapping as the rhythms of Latin or African music.
Combining Atoms to Make Compounds Adds Vast New Information
Moving up to the next-higher level of physical creation, elements often combine, chemically, to make compounds. Most of these compounds are very different from their component elements, vastly increasing the amount of Information in our world.
For example, hydrogen and oxygen are atmospheric gases on the surface of the Earth on a typical summer’s day. But when they combine to make the compound water, it is not a gas, but a free-flowing liquid. Here are three more examples:
- When hydrogen, oxygen, carbon, and nitrogen are combined, they can make amino acids – which in turn make the proteins used in human bodies.
- When wheels are combined with axles, they can make stable frames for moving carts, trains, and automobiles.
- When the letters of that English alphabet are combined, they can make words, and the words can combine to make sentences.
“The time has come,” the Walrus said,
To talk of many things:
Of shoes–and ships–and sealing-wax–
Of cabbages–and kings–
And why the sea is boiling hot–
And whether pigs have wings.”
– Lewis Carroll, Through the Looking Glass
In our day-to-day lives, we all know that the color Green is as fundamental to our senses and minds as both Yellow and Blue. However, we learn in elementary school that Green is actually made by combining Yellow and Blue. A bit of science tells us why: Yellow paint reflects most light at long wavelengths and absorbs light at short wavelengths. Blue paint does the opposite: it reflects most light at short wavelengths and absorbs light at long wavelengths. Because blue paint and yellow paint both reflect middle wavelengths, when blue and yellow paint are mixed together, the mixture appears as green.
Organizing Permits Emergence of Dynamic Systems, Including Living Systems
Organizing consists of positioning and connecting in some logical or meaningful manner. Consider the elements oxygen, carbon, hydrogen, nitrogen, calcium, phosphorus, potassium, sulfur, sodium, chlorine, and magnesium. A jar full of these eleven elements would contain a lot of information. For starters, there are 11 different things in the jar. Their differing properties add still more information – e.g., some are solids, and some are gases.
After 13.7 billion years, the Miracle of Creating achieved by the Processes of Continuing Creation has organized these same 11 elements (along with tiny amounts of about another dozen “trace elements”) into the astounding informational complexity that is the human body.
Combination and Organization in Religious Poetry
Now, let’s again pick up the poetry of Genesis creation story. After verses 1-6 of the Genesis passage talk mostly about God Differentiating, verses 7-10 talk about God Combining, when the latter passages say that God “made” and God “gathered:”
“And God made the firmament and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. And God called the firmament Heaven. And the evening and the morning were the second day. And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so. And God called the dry land Earth; and the gathering together of the waters called the Seas: and God saw that it was good. (Genesis 1: 7-10)
Finally, in Genesis verses 11-12, God continues the Process of Creation-through-Combination by using the Earth as God’s agent in creating (“bringing forth”) grasses, herbs, and trees. Those plants also become organizing agents of God, because they have the ability to create subsequent generations of themselves:
“And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good.” (Genesis 1:11-12)
Taken together, the entire Genesis Creation story, verses 1 through 12, is an apt poetic statement of the Processes of Continuing Creation as we know them today – Differentiation, Combination, Organization, Complexity, Reproduction, and Evolution.
Meaning Requires a Frame of Reference
We said a few paragraphs back that Differentiation was the first creator of Information, and that Combination increased differences and added Information. But we must realize that if there is only difference, there is limited information and no meaning.
Meaning is something that emerges from the presence of a Frame of Reference; and deep meaning emerges from having an Observer with multiple and interrelated frames of reference. A frame of reference is more than a background to some object (foreground). Because as we humans think of it, a frame of reference also has some commonality with the object foreground.
Information is limited unless there is some common aspect between the two things that are different; unless there is a frame of reference, or a context. Deeper information – meaning – requires a frame of reference or a context.
If you find a sheet showing irregular lines of X’s and O’s on a piece of paper, there is not much information there. But if you are a soldier in the “framework” (“context”) of a battlefield, and you find the paper in the “context” of a deceased enemy officer’s pocket, you would likely conclude that this is a map, perhaps showing the placement of troops, and you would rush it to your intelligence officers for evaluation.
For humans, the games of checkers and chess add considerable context and meaning to the simple pattern of a checkerboard.
For hundreds of years, ancient Egyptian hieroglyphics remained meaningless to archaeologists and linguists, because they had no frame of reference with which to read them. The Rosetta Stone, discovered in 1799, displayed an official decree of King Ptolemy V carved in 3 different languages – hieroglyphics, Demotic, and Ancient Greek. This stone was the key – the frame of reference — that unlocked the meanings of hieroglyphic writing.
Changing the Frame of Reference Can Change the Meaning
If we change the Frame of Reference, we often change the meaning. In ancient times, when people had an Earth-centered frame of reference, the sun was believed to move across the sky from east to west during the course of every day. Once it became known that the sun was the center of our solar system, we understood that it’s really the Earth spinning once each day on its north-south axis that makes the sun appear to move across our sky.
Consider a white field with many, many black dots all over it. To a person with a close-up frame of reference, the dots are many and distinct. To a person with a very distant frame of reference, the field appears gray.
In the last 100 years, discoveries in both mathematics and physics have shown that meaning, and even information itself, can greatly depend on frame of reference. Here’s a list of three such discoveries, which we will take up more fully in our later Essays:
- Einstein showed that everything is in motion, and that the motion of one object is relative to the motion of other objects.
- Mathematician Kurt Goedel showed that no one system of mathematics or logic can express all the truths present in reality. For example, in the Euclidian geometry of a flat plane, two parallel lines never meet. But in Non-Euclidean geometry of a spherical surface, they do!
- Modern physics says that forces can be interpreted as or waves or particle-like bundles of energy, depending on what the observer is looking for. This concept is called the wave-particle duality.” It has led to the larger and lately popular concept of model-dependent reality – the belief that we can only know reality through models, with each model presenting a different and partial aspect of the complete truth.
Meaning Requires an Observer
Next, we realize there must be something or someone that holds and uses the frame of reference! Generically, this someone or something is called the “Observer.”
Can an oscilloscope be an Observer? How about a big, powerful supercomputer — can that be an “Observer”? Yes, they both can, although a simple observer like an oscilloscope, likely having only one or two frames of reference, (e.g., wave amplitude and frequency), can only garner limited kinds of meaning.
Like an oscilloscope, a newborn baby’s brain is limited. It comes equipped only with the machinery to separate notes according to their pitch, and objects according to their color. But an adult Human mind holds many different frames of reference or contexts. Each frame provides a different perspective, a view that’s from outside the system (or at least partially outside the system). Meaning emerges as the mind interrelates those different perspectives. The more contexts a human mind has, the more meaning it can experience. Contexts are gained by learning, which includes both “book learning” and “experience.”
For example, for most humans, the checkerboard fits into several frames of reference. It is part of the game of checkers, part of the game of chess, and part of millions of vinyl-tiled kitchen floors.
But through the game of checkers and chess, the checkerboard also fits into wider and deeper frames of reference, including warfare and game theory.
The checkerboard is part of a still larger frame of reference – the science of Artificial Intelligence, because building a super-computer that can successfully play chess against a human World Chess Master was long a milepost goal of this science, achieved in 1997.
The consciousness of a mind is itself a special kind of difference. Consciousness occurs when the observer is aware that he, she or it is different from everything around it, i.e., different than everything its senses perceive.
Interestingly, the concepts of Frame of Reference and Having an Observer are also behind Einstein’s Theory of Relativity. Einstein began by recognizing that speed is relative to the observer. So, if I am on a horse riding at 10 miles per hour, and a train passes me going 30 miles an hour relative to the ground, the train is moving at 20 miles per hour relative to me. What we forget is that the Earth is also moving at a very fast speed relative to the Sun; and the Sun is moving fast relative to some other distant star, and so on. Einstein went on to prove that when something travels at very, very high speeds, time itself slows down… as perceived by an outside observer who is going slower.
Does Reality Exist Without Perception?
Another question about information and meaning is posed by the old conundrum: “If a tree falls in the forest and no one (no observer) is there to hear it, does it still make a sound?” In other words, does noise even exist without hearing? More generally, is there any objective reality? Or is reality purely subjective – merely a matter of an observer’s perceptions?
This question has been debated since philosophy and science began – thousands of years ago. If may be unanswerable, because there is no observer who stands outside the entire universe – outside the entire Process of Continuing Creation.
However, the practice of Continuing Creation holds that a falling tree does make the air and ground vibrate, and this vibration can be sensed as sound. Moreover, an oscilloscope does contain a Frame of Reference and is an Observer; but a human mind is a more fulsome Observer, because a human mind holds multiple frames of reference, and most of them are interrelated. Similarly, a trained and experienced human mind is a still more fulsome Observer than a naive human mind.
Participants in Continuing Natural Creation do recognize that Object and Frame are mutually dependent; that Reality is entwined with the Observer. It verifies our spiritual tenet that each of us is an active and involved agent in C.C. — also called the Growing, Organizing, Direction of the Cosmos. But we also know that when two theories say different things, it very often means that the theories need to be reconciled. A new, third framework often emerges that encompasses the first and the second ones.
Although the debate between objective reality and subjective reality can never be formally resolved, the Book of Continuing Creation chooses to hold that there is an objective reality. Because when reality appears to be subjective, it usually means:
- that our senses and brains (together with all our scientific apparatus) may not be able to perceive that reality; or
- may not be able to perceive the reality fully; or
- may perceive it in two or more seemingly conflicted ways, ways that need reconciling.
We will discuss this more in a later Essays, when we look at Physics.
Consider a white field covered with many, many distinct small black dots. Such a field would contain a great deal of information, because it would take pages and pages of words to describe to every black dot – each one’s position, exact size and exact shape.
However, almost none of that information would be useful or interesting, i.e., meaningful, to most Observers. In fact, a very distant Observer would not even distinguish the different black dots – to him the whole field would appear as gray.
Even if the observer were very close to the field, the “sameness” of the pattern would provide no “real” information.
On the other hand, If the black and white parts of our endless field have been placed according to a rule or set of rules, the field has a pattern. An example of a simple pattern is, once again, the checkerboard. One rule for creating a checkerboard would be:
“Place equal-sized squares of black and while on an empty, endless flat plane, such that:
- Each side of every black square touches only a side of a white square, and
- Each side of every white square touches only a side of a black square, and
- The black and white squares fill up the entire plane, with no spaces between any of the squares.
Rules like this (which are also called algorithms in computer science) are also mathematical descriptions of patterns. We talk more about this in our Essay, Mathematics and Continuing Creation.
Patterns can be quite elaborate, and their rules can be complex. For example, the English language has patterns for letters, words, and sentences; also rules of grammar; and conventions-of-use for clear expression. Plus, spoken English has rules for pronunciation.
If we use “zero’s” instead of a white field, and “one’s” instead of black dots, we can create information by the way we arrange the “0’s and 1’s” in patterns. Certain pattern of zeros and ones can represent letters of the alphabet; other patterns can represent photographic pixels. We can then use those higher-level patterns to represent, and transmit, virtually all human information.
In mathematics, Geometry establishes rules for drawing patterns composed of points, lines, angles, and curves. Using geometric shapes like circles, squares, pentagons and the like, patterns can be created that are far more complex and “interesting” than the simple checkerboard.
Patterns that Repeat in Nature and Science
The geometric patterns we just mentioned are often found in nature and science. Why is this so? For a number of many reasons:
- If you take a string of any given length, you can enclose more area by forming it into a circle than you can by forming it into any other shape – triangle, square, octagon, rectangle, or whatever. This makes the circle an efficient enclosure used by living organisms.
- The grid or “stacked boxes” pattern is everywhere. The cells of all living things are assembled in this pattern, because it provides the optimum way for each cell to be at once individual (with its own enclosing walls) and yet in communication with cooperative neighboring cells.
- The branching pattern and the network pattern are also ubiquitous (tree branches, roads, blood vessels), because they preserve some connection while exploring and covering more distance and space. This greater coverage permits access to light, air, water, and transportation (cars, trucks, blood cells).
- As shown on the Home Page of our ContinuingCreation.org website, the Spiral Pattern is present in everything from galaxies to snail shells. Why? Probably because this pattern can be generated by adding together a simple series of numbers.
- Fractals, where a pattern is repeated over and over on different scales, as seen on a head of broccoli.
Science and mathematics can also explain how Nature produces many other patterns, such as the following:
- Chains and ladders, like the strands of DNA found in every living thing.
- Weaves, such as spiders’ webs and birds’ nests.
- Concentric rings, like the growth rings in tree trunks.
- Hexagons, such as the cells in bees’ honeycombs.
- Spots and Stripes on animals – leopards, tigers, zebras.
- Waves, Bubbles, and foam in liquids.
- Tesselations (tiling patterns) on things like dried mud, fish scales, and pineapples.
- Widmanstatten Patterns seen in the cross sections of meteorites
We will talk more about the amazing but still simple mathematics behind such patterns in our Essay, Mathematics and Continuing Creation.
Mathematicians have studied tiled patterns and have developed formal descriptions of their various characteristics, including the presence or absence of “aperiodicity, reflection symmetry, self-similarity, and translational symmetry.” In the 1970’s, Roger Penrose investigated a set of elaborate tiling patterns which have been named for him. Penrose Tiles are aperiodic patterns, meaning that it is impossible to mark exactly where the pattern starts to repeat itself. An illustration is the so-called French Pattern. You can see the French Pattern and other Penrose Patterns by searching online for “Penrose Tiling.” Considering the Penrose Tiling below, any attempt to tile the plane with regular pentagons necessarily leaves gaps, but Johannes Kepler showed, in his 1619 work Harmonices Mundi, that these gaps can be filled using pentagrams (star polygons), decagons and related shape 2
A Penrose Tiling based on pentagons, pentagrams and related shapes.
Even more elaborate are the patterns called “quasi-crystals” – metal-based crystals discovered in the 1980’s whose patterns, like those of Penrose Tiles, are ordered but do not regularly repeat. Quasi-crystals are also a blend of liquid and solid states of matter. In the 1980’s, the mathematical description of aperiodic Penrose Tiles was used to describe newly created, man-made quasicrystals composed of an aluminum and manganese alloy. Subsequently, many other quasicrystals have been man-made.
Then, in 2009, a naturally-occurring quasi-crystal – a mineral dubbed icosahedra — was found in eastern Russia. 3 In geometry, an icosahedron is a polyhedron with 20 faces. There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
Co-Creators in C.C. say – Penrose Tiles and quasicrystals illustrate a true inner Process of C.C. Creating is a dance between light and dark, Yang and Yin; a dance that creates ever-increasing meaning. The Path of Creation depends on both difference and similarity. Even Yang and Yin are opposites, each one requires the other. The Yin-Yang symbol, showing pulses of Yang chasing Yin around and around; while at the same time new yang emerges as a spot in the center of the pulse of Yin, and new Yang emerges as a spot in the center of the wave of Yin — is a timeless pictorial expression of Continuing Creation.
Patterns can be self-referencing or self-similar – meaning that they repeat themselves on several scales within the same natural structure. The Branching Pattern that leads off this Chapter is a good example. Main branches split off from the trunk; and this format is repeated as small branches split off from the main branches; and repeated again as twigs branch off from the little branches. Of course, the repetition is not exact, but it is distinct and clearly recognizable.
Similarly, the indentations-and-projections pattern of a continental coastline is generally repeated on every scale of the coastline’s distance. So, the indentations and projections pattern of a rocky ten-mile-long coast, is repeated (generally; not exactly) within a mere 50 yards of that coast.
Note that self-referencing patterns in nature, like the two mentioned above, are often irregular: We generally know that one to four main branches will sprout out between 4 and 8 feet up on the trunk of a certain species of tree, but we cannot say exactly how many or exactly where they will appear.
Even the growth of crystals is influenced by random events in the “neighborhood” surrounding them. In a geode of amethyst crystals, neighboring crystals will have different sizes and stick out at different angles. (me)
In addition, irregular patterns exist in natural and human creation which can be described by statistics. A normal statistical distribution is a good example. We know that a graphical plot of the intelligence of individual humans will generate a “bell-curve,” i.e. a “normal distribution,” centered on an IQ level of 100. But we cannot say exactly where the individual data points will fall. The pattern is statistical, not absolute.
Mathematics is itself information. Like English or Arabic, it is a language used to describe patterns of reality, and the rules that govern how some parts of reality change, through time, in response to changes in other parts.
The Fibonacci Sequence of numbers (named after the twelfth-century Italian mathematician who “discovered” it) is the sequence of integers where each successive number, (after two initial number “1s”), is the sum of the two numbers to its left. So, 1+2=3, and then 2+3=5, and then 3+5=8, and so on. This rule gives us the Fibonacci Numbers, which are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, … and so on.
Mysteriously (or at least very interestingly), there are patterns in nature that are based on the Fibonacci sequence of numbers! Examples include the spiral patterns of snail shells, pinecones, the flowering of an artichoke, and others.
The Fibonacci numbers are also closely related to the Golden Mean principle used in art composition. If you take any 2 consecutive Fibonacci numbers – say 89 and 144, and divide the larger by the smaller, i.e., 144 by 89, you always get a result approaching 1.618. This proportion — 1.618 to 1 – has for centuries been known as the Golden Ratio or the Golden Mean because buildings and paintings constructed using this proportion are considered to be most pleasing to the human observers.
Patterns with the Greatest Meaning.
If we think about these more elaborate patterns – Penrose Tiling, Branching, Self-referencing, the English language, Fibonacci patterns – we can see what makes a pattern important, deep, unusual, or ground-breaking: meaning advances when new differences and new similarities are discovered that were not seen before.
The Path of Continuing Creation says — Deep meaning happens when there are differences within similarities, and similarities within differences. Creativity – creation itself — consists in finding deep similarities and connections between things that are (or were) considered different and disconnected.
Most inventions happen when an inventor combines existing technologies in new ways. To create the electric light, Edison connected an electric current with an enclosed glass bulb, a fine wire filament, and an absence of oxygen. The invention would not have been possible without the prior inventions of electric generation, current transmission, blown glass, and the ability to remove oxygen from the glass bulb. 4
Similarly, the idea for using punch cards to load data into the first computers was adopted from the decades-earlier use of punch cards to control weaving looms. It just took the mind of an inventor to make the connection and do the adaptation.
Evolution connected the forearm bones of small dinosaurs and the early feathers that had evolved to cool their blood, to create (over hundreds of thousands of years), wings that achieved flight through Earth’s air.
What Makes a Pattern Beautiful?
Beauty happens when there is pattern. But what kinds of patterns? Patterns with these features:
- Uniformity, Repetition, Symmetry – A beautiful face is uniform and symmetrical.
- Proportion, Balance – Perfect symmetry (like the perfect grid on the side of a modern glass office building), can be boring. Shapes that are proportionate – as on our photo of the Parthenon’s use of the Golden Ratio at the beginning of this Essay, can be more pleasing.
- Variety, Novelty, Surprise – Japanese flower arrangements (ikebana) are never symmetrical, never perfect. An adventurous branch or blossom always ventures out from the others, seeking the new.
- Naturalness, Imperfection — To be natural, a shape must be imperfect – as we saw when we discussed ideal circles versus real circles. Japanese potters and flower artists always introduce deliberate imperfections into their art, to connect it to Nature.
Ikebana – Japanese Flower Arrangement
More Poetry from the Bible — “In the Beginning Was the Word”
Earlier, we saw that the Bible’s Genesis creation story poetically anticipated the Creation story of modern physics. God’s “separating” light from dark in Genesis is the “freezing out” of the four Fundamental Forces in physics. Then, God’s “gathering” and “making” in Genesis are like the physics of combining (fusing) hydrogen to make the more complex elements.
Let’s pause here to consider another poetic story of Creation, one that talks about the Creation is terms of Information and Pattern. This creation story opens the New Testament’s Gospel of John:
“In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things came into being through Him, and without Him nothing came into being that has come into being. In Him was life, and the life was the light of men.” (John 1:1-4, New International Version).
For most Christians, “Word” in this passage from John simply means “Jesus.” But The Gospel of John was written in Greek, and “Word” is really an English translation of the Greek word Logos. And as we explained in our Essays on Christianity, Logos clearly does NOT mean Jesus.
Logos really means information, pattern, or meaning – the subjects of this Essay.
Classics scholar Dr. Matthew Carter explains: “There are a number of meanings for Logos, and some were emphasized more than others in different periods of Greek history. For example, Logos can mean ‘logic,’ ‘the wisdom,’ or ‘the knowledge.’ For the Stoic philosophers of ancient Greece, Logos meant the divine animating principle pervading the Universe.”
In the 18th century, Logos was identified with the idea of God’s “natural law,” which would include the scientific laws of gravity, electricity, biology and so on, to the extent that such laws were then known.
So, we Practitioners of Continuing Creation might re-write the Gospel of John’s creation story like this: “In the beginning was the Information-pattern-meaning (logos) and they were with Continuing Natural Creation, and the Information-Pattern-Meaning were Continuing Natural Creation. The Information-pattern-meaning was present in the very beginning. All things were made through the Information-Pattern-Meaning (Logos), and without them nothing was made. In the Logos was life, and that life was the light of all mankind.” John 1:1-4 (Book of Continuing Creation version.)
Human Perceptions Can Be Wrong
There are limits to our five senses (see, feel, taste, touch, smell, and hear), and limits to our “common sense.”
The truth sometimes lies outside our own five senses. For example, we cannot see the color infra-red. Or perhaps we should say that there is an infra-red wavelength of light, but its wavelength is too long for human eyes to perceive it, and therefore it has no “color” for humans.
Similarly, we humans cannot use sound to echo-locate objects… but bats and whales can. We humans have a sense of smell, but a dog’s is 10,000 to 100,000 times more acute. (Peter Tyson, Inquiry Column, Nova, posted 14-04-12)
Similarly, the truth can lie outside out of human’s “common sense.” Reality is different from what first meets our eyes. For example:
- For millennia, humans perceived that the sun rises in the east and sets in the west – the sun crosses the sky. But Galileo proved to the world that the sun only seems to rise in the east and set in west. In reality, the apparent movement is caused by the Earth’s axial rotation in front of the sun. The real truth (sun-centered) can turn out to be different from what we first experience (earth-centered). Depends on frame of reference, or point of view.
- Cholera is not really caused by “miasma” in the night air, as people had thought for hundreds of years, but by microbes in the water. (Steven Johnson).
However, we note that our example about the sun’s motion, is really a question of the Frame of Reference being used. An Earth-centered frame of reference works just fine for people who had (and still have) no concerns about astronomy, astrophysics, or space travel. But once humans did have those larger concerns, a larger, more encompassing – and therefore truer –frame of reference was required.
Science Can Go Beyond Perception by Our Senses
Science (along with logic and mathematics) provides a way our understanding can extend beyond our senses and perceptions, providing a better – more fulsome — frame of reference.
The Mobius Ring
A deceptively simple “parlor trick” called the Mobius Ring also shows that our ordinary perception can be wrong.
Take a strip of paper and make a circular ring from it by taping the two ends of the strip together. Such a ring can fit over your finger, (or if you made a really big one, over your whole hand). Based on our everyday experience and on our logic, all paper rings have two sides.
But, take another paper strip, but before taping the two ends together, turn one of them over. This is now a Mobius Ring (named after the German mathematician A.F. Mobius, who discovered it in 1858). The Mobius Ring has only one side… and also only one edge. We still perceive two sides to this paper ring, but if we use a “scientific instrument” – a pencil – and trace a line all the way around, we come back to the starting point! The drawn line has traversed what appear to be both sides… because the end point of our penciled line joins our starting point. In fact, the “two apparent sides” are actually one and the same side. When we twisted the paper strip before pasting, we turned a two-sided ring into a one-sided ring.
In addition, cutting a Möbius strip along its center line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips, and this new longer strip is not a Mobius strip.
If we search online for “Mobius Strip,” we can see that the branch of mathematics called Topology has categories and equations that further “explain” how and why a ring can have just one side. Also, we can see online that if we glue two mobius strips together in the right way, we get a three-dimensional vessel called a Klein Bottle. A Klein bottle has no inside or outside – which you can verify by drawing a pencil line over its surface. Even though the Klein Bottle has no inside, it can hold water; but not as effectively as a regular bottle. Here is how the ring and the Bottle are described in the formal language of Topology:
“Like the Möbius strip, the Klein bottle is a two-dimensional manifold which is not orientable. Unlike the Möbius strip, the Klein bottle is a closed manifold, meaning it is a compact manifold without boundary. While the Möbius strip can be embedded in three-dimensional Euclidean space, the Klein bottle cannot. However, the Klein bottle can be embedded in 4-dimensional space.” (See the Wikipedia article, Klein Bottle)
A nice thing about the Mobius example is that it shows us how we can sometimes use just logic to extend our senses. We don’t always need an oscilloscope or a Geiger counter. A simple pencil can get us non-scientists where we need to go.
Even science can be incomplete.
Sometime, an entire system of reason, science, and/or mathematics – called a paradigm or a model – systemically changes to accommodate new discoveries that didn’t seem to fit into the old system. These are called paradigms shifts. Here are two famous examples:
- Newtonian Physics, vs. Einstein’s Theory of Relativity: Newton’s classical laws of motion treat time as universal, with a constant rate of passage. This works just fine at the relatively slow speeds we experience on Earth. But Einstein’s Theory of Relativity showed that at super-high speeds, the clocks on the super-speeding object will run slower when compared to a stationary observer’s clock. If it were possible to travel in a spaceship at, say, 99.5% of the speed of light, a hypothetical observer looking in would see the clock moving about 10 times slower than normal and the astronaut inside moving in slow-motion, as though through molasses. This effect does not come from workings of the clocks, but from the fact that space and time are actually woven together in one thing called spacetime. Moreover, what we humans experience as the force of gravity is actually due to the curvature of spacetime, caused by very massive objects like suns and planets.
- In mathematics, the geometry we study in high school is Euclidean geometry. It is geometry of flat planes and three-dimensional objects that we deal with in everyday life. One of its assumptions (postulates) is that two parallel lines never meet. It is called a postulate because it cannot be proven. So, if we instead postulate that two parallel lines do meet – which they in fact do on the of an ellipse or a hyperbolic saddle-surface – two new Non-Euclidean Geometries have been created. These Non-Euclidean geometries have proved invaluable for calculations in global navigation and astrophysics. For example, the shortest flying distance between Florida and the Philippine Islands is not a straight line, it’s a curve — a “great circle route” path across Alaska.
Can Any Scientific Theory or Mathematical System Capture all of Reality?
We’ve seen, for example, that Euclidean Geometry does not capture all truths about geometric relationships, and we’ve seen that Newtonian physics leaves out things that the Theory of Relativity includes. As we’ll see in the Essay, Physics and Continuing Creation, Quantum Theory includes even more.
So, it may be that no scientific theory or mathematical system can capture all the truth about our universe; it may well be true that no model is big enough. This is about the same as saying that C.C., the Growing, Organizing, Direction of the Cosmos, cannot be fully described; that Continuing Creation is ultimately unknowable. That has surely been the position of Judaism, Christianity, and Islam.
Why would we humans not be able to fully describe Continuing Creation? Perhaps it is because we humans are part of C.C. It is impossible for us to stand outside the systems of C.C., and therefore we cannot “see” all of C.C., i.e., the Growing, Organizing, Direction of the Cosmos. Being inside the Cosmos’ frame of reference, we can never achieve the objectivity of standing outside that frame of reference.
Why would this be so? Many thinkers (philosophers, mathematicians, and scientists) say it is because when an Observer stands in the frame of reference, her observations must be, to some degree, self-referencing. And self-reference leads to paradox and meaninglessness — because there are (always) truths that lie outside the system.
The Liar’s Paradox
A simple verbal conundrum called the “Liar’s Paradox” provides a good example of self-referencing. Here are two versions of the Liar’s Paradox:
- “I am Lying.”
- “This sentence is false.”
If the speaker is indeed lying, then he is telling the truth about being a liar. But if he is telling the truth when he says, “I am lying,” then he’s lying when he says he is a liar. And we go around and around, getting nowhere.
Or take the statement, “This sentence is false.” If “this sentence is false” is true, then the sentence is false, but then if “this sentence is false” is false, then the sentence is true, and so on.
Since each statement refers to something only inside its own two-statement system, truth and falsity are non-determinable. The system is paradoxical and meaningless.
The Liar’s Paradox tells us many things, and one of them is that there will be contradictions within this Book of Continuing Creation, just as there are contradictions in the Bible or the Koran; and the philosophies of Plato, Kant, and every other philosopher who ever wrote.
There is always a truth that lies outside the system. For every air-tight argument, there is an “escape hatch.” In some real situations outside the framework of a flat plane, two parallel lines can meet.
This is why scientific explanations – even if immensely formal, logical and supported by evidence — are still called scientific theories – as in the Theory of Gravity.
In our Essay, Mathematics and Continuing Creation, we will look at Kurt Goedel’s Incompleteness Theorems, which prove that for every coherent and consistent system of mathematics, there are true relationships which cannot be proven by that system.
In other words, there is no logical system, no logical argument, that can capture the whole truth about any subject. Thus, the common saying, there is always “The exception that proves the rule.” This saying means that the presence of an exception establishes (“proves”) that a general rule exists. Unless there is an exception to the rule, the rule (or system) is likely some kind of bogus sleight-of-hand, and not connected to reality at all. To use another common saying, such a bogus rule or system would be “too good to be true.”
One common logical system is to rank things or place them in a hierarchy.
Suppose we rank humans. Perhaps we want to rank them by their power.
But what is an individual’s power and how do we measure it? Rank by size may not be the same as rank by weight. And neither rank weight nor size is rank by power. Rank by power is also not same as rank by IQ score, and rank by IQ-score is not same as rank by wisdom.
Consider the common schoolyard decision-making game, Rock-Paper-Scissors. It seems hierarchical, but it is really circular – Rock breaks Scissors, and Scissors cuts Paper, but Paper covers Rock. There is no “highest” rank, no “highest” power. If you wish to be “one level up,’ then wish it again, and then once more, you find yourself to be where you started.
Rock-Paper-Scissors is an example of what Douglas Hofstadter, in his book, Goedel, Escher, Bach, calls a strange loop, because it crosses a hierarchical boundary that turns out to be relative, or “tangled.” Rock-Paper-Scissor shows that the truth of rank, the truth of power, is relative… and circular. It depends on the situation, on the frame of reference. (See also, wiki article on “strange loop.”)
Thus, in European feudal society of 1100 CE, only the Lord and his knights could carry swords and ride war horses. They held all the military power. But the farmers held the power of sustenance, because they grew all the food. The merchants held the power over commerce – only they could access and import iron for the swords, spices for the food. The clergy held power over writing and spirituality. By 1100, there was also a considerable body of common law, administered by lawyers, which held the lord’s military power in check. In real life, all hierarchies of rank are “tangled.” In real life, who holds the upper hand depends on the specific circumstances – on the frame of reference – which can change day to day.
“Model-Dependent Reality” is Wrong
Unfortunately, here in the year 2023, many people have taken the concepts related to Frame of Reference too far. They are saying that there is no objective reality; that reality itself changes depending on how the Observer is looking at it. This new and mistaken doctrine is called Model-Dependent Realism. Here is how Wikipedia describes it:
“Model-dependent realism is a view of scientific inquiry that focuses on the role of models of phenomena. It claims reality should be interpreted based upon these models, and where several models overlap in describing a particular subject, multiple, equally valid, realities exist. It claims that it is meaningless to talk about the “true reality” of a model as we can never be absolutely certain of anything. The only meaningful thing is the usefulness of the model. The term “model-dependent realism” was coined by Stephen Hawking and Leonard Mlodinow in their 2010 book, The Grand Design.”
Popular culture has picked up on this and in now using it to justify a number of incorrect assertions, including these:
- Every individual has her or her own truth.
- Every religion is equal; there are not significant differences between them.
- Pseudo-science (crystal power, vortex power, personal auras) are as valid as scientific facts.
The Book of Continuing Creation rejects all this nonsense. Reality is not dependent on Models; rather Models are dependent on Reality. We hold that Reality is true and objective. If observed reality varies in different experiments and/or different theories, it is the experimenter and his/her theories that vary, not the reality.
We also firmly assert the following responses to the three bullet points just above:
- Every individual has her (or his) own genetics and own life experience; but not her own truth. In fact, no individual has the truth. (But every individual in a free society has the right to peacefully express her own opinion about what the truth is.)
- Religions are not equal. They are not even that similar. This Book of Continuing Creation has Essays which explain in detail how they are different. Of all the religions (or spiritual paths,) we hold that the Path of Continuing Creation is the best; as this Book works to explain. Yet, each person has the right to follow his or her own religion, so long as this practice does not infringe on the rights of other individuals.
- Pseudo-sciences, such as Creationism and Crystal Power, are bunk. Double-blind scientific experiments do not support them, the historical record does not support them, and they do not produce workable, useful inventions such as electricity and vaccines as does real The Book of C.C. strives to be consistent with real science.
- The denial of objective truth may just be the most threatening single problem facing human civilization. It leads to the denial of Global Warming, the continuation of fundamentalism and warfare between religions, the rise of totalitarian regimes such as the world now sees in North Korea, and attendant political propaganda, and brainwashing, in concentration camps.
Furthermore, there are two additional facts which contradict the bogus idea of model-dependent realism:
- First, science and mathematics proceed in a succession of paradigms, with each successive paradigm accounting for and encompassing the previous one.
- Second, each new branch of mathematics, each new interpretation of physics, is an additional Creation of the Growing, Organizing, Direction of the Cosmos. If the Processes of C.C. were fully known and fully-described, Discovery and Creating might halt. Since we Weavers participate in and celebrate Continuing Creating, we welcome mathematical and scientific diversity.
Let’s take a closer look at each of these two points:
New Paradigms Usually Encompass Old Paradigms
The term Paradigm Shift was coined by Thomas Kuhn in his 1962 book, The Structure of Scientific Revolutions. (Frankly, we think that the old appellation “Scientific Revolution” was plenty good enough.)
Scientific paradigms “shift” when a large, coherent scientific theory gives way to a new and larger, coherent scientific theory.
Below is a partial list of Paradigm Shifts from the physical and social sciences. In almost every case, the new paradigm accounts for the experimental results and scientific laws of the old paradigm, and also goes beyond to cover new facts and new experimental facts as well.
Examples of Paradigm Shifts in Science
The most famous paradigm shift happened when Copernicus showed in 1543 that our solar system is sun-centered, not Earth-centered. Copernicus’ system could predict the positions of the planets in the sky, but they did so with mathematical equations that were much simpler (more “elegant”) than the calculations that had been used before. Here are a number of other historical paradigm shifts:
- When Non-Euclidean geometries were developed.
- When Evolution replaced the direct creation of species by God.
- When the Sun, not Earth, was understood to be the center of our solar system.
- When Lavoisier’s theory of chemical reactions and combustion replaced of “phlogiston theory.”
- When it became understood that germs cause disease, not “miasma.”
- When Einstein’s Theory of Relativity replaced (and encompassed) Newtonian Physics
- When Keynesian Economics replaced and encompassed Economics based on Say’s Law.
- When Monetarist Economics replaced and encompassed Keynesian Economics.
- When Behavioral Economics replaced and encompassed Monetarist Economics
- When Quantum Physics replaced Classical Physics at sub-atomic scale.
- The discovery of Plate Tectonics as the explanation for large-scale geologic changes.
- The rise of computer science, programs, algorithms, databases.
- The “Gaia Paradigm,” which sees the Earth as a single living biosphere.
- When “laryngeal” consonants were postulated in the Proto-Indo-European language (PIE). This theory was confirmed by the discovery of the Hittite language in the early 20th century and has paved the way for the internal reconstruction of the syntax and grammatical rules of PIE.
The Practice of Continuing Creation agrees with Thomas Kuhn, “who vehemently denied the false belief that paradigm shifts make a case for “relativism” — the view that all kinds of belief systems are equal. We agree with Kuhn that when a scientific paradigm is replaced by a new one, (albeit through a complex social process), the new one is always better, not just different.” (The Structure of Scientific Revolutions, 3rd ed., p. 199)
The Practice of C.C. says — Succeeding theories of physics encompass all the old experimental findings, and go on to answer new questions, creating new more universal truths, explain more experimental results, and lead to more new technologies. In other words, we have a succession of nested frames of reference, each one larger and including all the others that came before it. This is the position of the Book of C.C. In fact, Our Practice of explains, includes, and enlarges all the Old Religions that have gone before it.
New Mathematical and Scientific Systems are New Products of Continuing Creation
When existing science or mathematics is discovered to be incomplete or inconsistent, it leads to the discovery of new science and mathematics. This is a good thing: it is like adding complementary new rooms onto an existing house.
Newtonian physics works just fine here on Earth. On Earth, we never move fast enough for Time to slow down by any perceptible amount. But in the super-speeds of space, we need the Theory of Relativity to correctly reflect reality.
In the last 50 years, when physicists uncovered the links that prove electricity, magnetism, and the weak nuclear force are all part of one encompassing “electro-weak” force, their search was directed by a disciplined focus on finding mathematical symmetry between those three “sub-forces.”
As we write this, three of the four Fundamental Forces (the strong nuclear force, the weak nuclear force, and the electro-magnetic force) have all be unified in one successor theory. But the fourth force – gravity – has yet to be unified. We expect to achieve that, and we expect that it will reveal things about the nature of reality and the origin of the universe.
“In the history of science, we have discovered a sequence of better and better theories or models, from Plato to the classical theory of Newton to modern quantum theories. It is natural to ask: Will this sequence eventually reach an end point, an ultimate theory of the universe, that will include all forces and predict every observation we can make, or will we continue forever finding better theories, but never one that cannot be improved upon? We do not yet have a definitive answer to this question.” (Stephen Hawking & Leonard Mlodinow, The Grand Design, p.8)
So far in human history, each new discovery, each new paradigm, has revealed new questions to ask and new “mysteries” to solve. Will this always be true? Perhaps. For now, we still have or find things that appear unreconcilable… but so what? – the old anthropomorphic God was always mysterious. Why should the Growing, Organizing, Direction of the Universe be any different? Perhaps successive mysteries are an inherent and eternal part of the Universe.
Educated Hindus know this. None of the Hindu gods and goddesses is Brahman — the transcendent and immanent ultimate reality. The hundreds of Hindu gods and goddesses are all just faces or aspects of Brahman.
The Taoists also know this. The Tao Te Ch’ing says, “The Tao that can be told is not the eternal Tao; The name that can be named is not the eternal name.”
The Creation Story of the Tao Te Ch’ing
In this section we present a third poetic Creation Story from a major religion — the Creation Story from the ancient Chinese religion of Taoism.
The poetic verses below are from the Tao Te Ch’ing, the principal text of Taoism. This text is attributed to Master Lao-Tzu, who wrote it in China as early as 550 BCE – long before any “Physics” had been formulated. The “Tao” means the Path, the Way, or the Process of the universe. “Te Ch’ing” means “and its power.” So, the whole title is “The Way and Its Power.” Of all the ancient conceptions of the Creative Force of the Universe, the poetry of Taoism’s Tao Te Ch’ing is perhaps the closest to a correct description of the Processes of Continuing Creation.
In the beginning was the Tao.
All things issue from it;
All things return to it.
The Tao can’t be perceived.
Smaller than an electron,
It contains uncountable worlds.
The Tao is like a well:
Used but never used up.
It is like the eternal void:
Filled with infinite possibilities.
It is hidden but always present.
I don’t know who gave birth to it.
It is older than God.
Every being in the universe
Is an expression of the Tao.
— (Tao Te Ch’ing, Chapters 52, 23, 4, and 51. Translated by Stephen Mitchell.)
These passages from the Tao could be about a singularity as described in physics – a point of hot, dense energy. Or they could be about a mathematical truth that underlies the universe. Or they could be about the genesis of information which has been the subject of this Essay. Most likely, the Taoist poetry is simultaneously all those things. That’s why the Tao “can’t be perceived,” and is “hidden but always present.”
In a perfectly symmetrical universe, there would be no differentiation and therefore no creation – no chemicals, no mountains, no living things. But the probabilistic aspect of laws of quantum mechanics also show that that symmetry is inherently unstable. The slightest flaw, the smallest perturbation, and the symmetry is broken, leading to the cascade of creation.
Earlier, we talked about the dance between Yang and Yin in Taoism’s most famous symbol. This is the dance between Sameness and Differentiation; creation and destruction; black and white; object and foreground; zeros and ones; fact and frame of reference; between unchanging perfection and evolving creativity.
In this well-known symbol, the Feminine principle (Yin) and the Masculine principle (Yang) pursue each other endlessly in an eternal circle of creation. And within each half there is a small dot of the other’s color, saying that each principle contains the germ of the other. So, we have both difference and sameness, moving together is the dance of creation.
Hinduism’s Dance of Shiva
Our fourth and last poetic expression of Creation is Hinduism’s Dance of The Lord Shiva.
In Hinduism, the four-armed representation of Brahman known as Lord Shiva performs a cosmic dance called the Ananda Tandava, meaning the Dance of Bliss, which symbolizes the cosmic cycles of creation and destruction, as well as the daily rhythm of birth and death. The dance is a pictorial allegory of the five principal manifestations of eternal energy — creation, destruction, preservation, salvation, and illusion.” (Nataraj: The Dancing Shiva, By Subhamoy Das. http://bouthinduism.com.)
Modern physicist Fritjof Capra in his article, The Dance of Shiva: The Hindu View of Matter in the Light of Modern Physics,” and later in The Tao of Physics, writes that “every subatomic particle not only performs an energy dance, but also is an energy dance; a pulsating process of creation and destruction…As in Hindu mythology, it is a continual dance of creation and destruction involving the whole cosmos; the basis of all existence and of all natural phenomena.” (Also from Nataraj: The Dancing Shiva, By Subhamoy Das. http://bouthinduism.com.)
Here’s an excerpt from a beautiful poem about Shiva’s Dance, written by Ruth Peel:
“The source of all movement,
Gives rhythm to the universe.
He dances in evil places,
In sacred, He creates and preserves,
Destroys and releases.
We are part of this dance
This eternal rhythm,
And woe to us if,
Blinded by illusions,
We detach ourselves
From the dancing cosmos,
This universal harmony…”
(Nataraj: The Dancing Shiva, By Subhamoy Das. http://bouthinduism.com)
Can there be Creation without Destruction?
It is often said that nothing can be created unless an existing thing is destroyed – “You can’t make an omelet without breaking eggs.” It is true, for example, that a tree cannot grow without nutrients from the soil, and those nutrients mostly come from plants that lived and died before.
But we also know that the sum of matter and energy in the universe can never be created or destroyed. What dies and what is born is not the matter (e.g., the carbon and other elements), but their information content – the complexities and symmetries of the patterns in which they are arranged. The carbon compounds in a handful of dirt are re-assembled in higher patterns to make a leaf on a tree.
In the physical world of matter – of things — there can be no change without destruction. This is true even for rocks; even for geography. A plain must be destroyed in order for a canyon to be formed. A tree must die in order for new plants and insects to grow from its nutrients.
Only in the world of information can new thing be created without destroying the old. Algebra can be created without the destruction of Geometry. On the other hand, the Sun-centered picture of the solar system has maybe not destroyed the old earth-centered picture, but it has surely replaced it.
The False Path of “Non-Duality”
We’ve seen that it has become fashionable to assert the “relativity of truth,” which the Practice of Continuing Creation rejects.
As the Book of Continuing Creation is being written today in 2015-2023, it has also become fashionable for educated people to pursue so-called “non-duality” through the practices of meditation and discussion. Hindu yogis, Buddhist monks, Christian hermits, and Islamic Sufis can devote their lives to achieving “non-duality” – to finding Nirvana, to being with God, to a making peaceful union with “The Eternal One.”
The Practice of Continuing Creation rejects the goal of union with Nirvana, because such a union calls for the cessation of all personal creating, the end of all achievement. (Even the end of all family relationships in certain “holy orders.”). It is negative, pessimistic, and too much like death itself. However, we embrace periodic meditation as a way to calm the mind, discover hidden connections within Nature’s Continuing Creation, and renew our energy. We hold that all things are at once connected and separate.
Instead, Hindus should observe that Lord Shiva is a whirlwind of activity – destroying the old and creating the new at every turn of his dance. All four of Shiva’s arms are required for this ceaseless creative effort.
Taoism’s Yin and Yang symbol is also a symbol of creative activity – not of passive contemplation.
Of course, the Practice of C.C. certainly uses meditation as a practice of rest and re-charging. Daily meditation for half an hour or an hour can renew our minds and our spirits, greatly increase the richness of our relationships, and provide positive direction in our active, constructive lives. See our Chapter, Living a Fulfilled Life.
We’ve now looked at four different poetic metaphors that express key aspects of Physics and Cosmology. Many are tempted to ask themselves: “If the poetry says pretty much the same thing as the physics, why spend so much time and energy learning higher math, building particle accelerators, and conducting expensive experiments? Because the poetry does not light up dark rooms like electricity does, nor search inside the human body for cancer cells like MRI machines do, nor perform eye surgery like lasers do.
Some might counter with the argument: We’d be better off without all the fancy technology: people would be happier living closer to the Earth, and the Earth would be less threatened by pollution, species extinction, and global warming. Well, most of us appreciate the longer life spans given to us by modern nutrition and modern medicine, which are double the length they were in ancient times. And as for saving the Earth – we don’t need to abandon technology; all we need to do is stop having so many children.
Followers of the desert religions have “faith” that their miracle stories are true, despite all common sense and in the face of all reason and scientific evidence.
Followers on the Way of Continuing Creation do not have blind faith. But we do have confidence in the eventual triumph of reason, knowledge. We do not believe Jesus amazingly rose from the grave; we rather understand that Electromagnetic Force Fields amazingly produces energy that makes our light bulbs shine. We do not think love alone will further Humanity; we think that love and reason and creativity will further humanity…. and heal the Earth.
Additional Reading: Wikipedia articles: “Pattern” and “Patterns in Nature.” Books: Rebecca Hoyle, Pattern Formation: An Introduction to Methods; Philip Ball, The Self-Made Tapestry: Pattern Formation in Nature; Michael Cross and Henry Greenside, Pattern Formation and Dynamics in Nonequilibrium Systems; Daniel Walgraef, Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science. Many other books on Pattern Formation are listed on Amazon.
Essay edited on 8/31/23
- Romans 11:33. Isaiah 40:28
- Roger Penrose, “The role of aesthetics in pure and applied mathematical research”. Bulletin of the Institute of Mathematics and Its Applications. 10: 266ff. See also, Branko Grünbaum & G.C. Shephard, 1987, Tilings and Patterns, 1987, W.H. Freeman, section 2.5, ISBN 978-0-7167-1193-3.
- L. Bindi, P.J. Steinhardt, N. Yao, and P.J. Lu, “Natural Quasicrystals,” Science, 2009, 324 (5932): 1306–9. Bibcode:2009Sci…324.1306B.
- Steven Johnson, Where Good Ideas Come From, 2010, Riverhead Books, p.41.