Concerning a Grain of Sand

Cosmology: Concerning a Grain of Sand

Drs. Enzmann & Funk

In the middle of nowhere they meet on a shining white beach of coral sands and pebbles, not quartz sands and granitic pebbles like the Scandinavian and New England sands the Mathematician eternally dreams of. This is Kwajalein, the easternmost island in an enormous atoll, an enchanting ring of islands around the world’s largest lagoon.

Kwajalein is a secretive military base. Rockets launched from California are detected, locked on by radars, tracked, and shot down by anti-missile missiles from the island. No one arrives or departs except by military orders, yet civilians and their families far outnumber those in the services. However, here there is a mindset. Additionally, there is an unusually well-educated and competent population. 

The Reverend, an unusually talented listener, instinctively knows how to both learn by listening, and at the same time give enough of himself to keep the talker interested, learning from and about the talker.

The Mathematician has an unusually gifted intellect. He gazes out over the water. Today it’s calm. Last night a three-day storm ended. 

He observes, commenting to the Reverend: “Three days of high seas, now it’s calmer. See the wedge-shaped piles of coarse material all along our sandy beach? Know what this is?” 

He holds out a coral pendant to the Reverend. There’s a hole bored through the thinner end. 

It’s a rhetorical question he himself answers: “It’s a sinker for a fishing net. Dates to somewhere between 1500 and 1700, before Spanish, German, or Japanese times. It’s hard work drilling this sort of coral. Try filing one of these kinds of shells! It’s tougher than filing metals.”

Most improbably, the Mathematician has survived decades of pre-World War II terror, assassinations, years of combat, then post-war terror genocide, mass executions, combat, murder, and various killer hunts. He and his are on the Missile Range by virtue of their unusual abilities. It’s a friendly island, so the Mathematician – an ever wary, cunning survivor with completely hidden capacity for creative violence – both probes and hopes to make an interesting, perhaps even a good acquaintance. The Mathematician is crushingly lonesome, his past is gone on the winds of war.

Reverend: Interesting. 

He examines the fishing-net sinker. Drilling a hole through that with coral tools would be difficult indeed. 

Mathematician: It was probably done with something like a fire bow, as the hole is cylindrical and oval rather than conical.

The Reverend really is interested. 

Reverend: Have you found any others?

Mathematician: Only one, many years ago.

To service, the Reverend is called. Extraordinarily sensibly did he organize his education. Rather than directly entering the ministry, he graduated from West Point and is now a combat veteran of nasty aspects of the Cold War and the Gulf War. He had thought it would help him better understand his calling; it would not just broaden, but really open his view of people and humanity. People he understands, selflessly giving of himself to them. 

Mathematician: Why do you suppose sand is carried up out of the deeps by waves? Can’t it be said that ‘everyone knows heavier things sink and are carried downward?’ I have taught; one of my favorite assignments was to write everything about something simple, say a needle, or just a grain of sand? No man explains anything; he can only describe. 

With this, the Mathematician is searching to see how deeply the Reverend studies religion and the world about him.

Mathematician: You know Reverend, the questions mathematicians, astronomers, and other scientists have, are identical with those addressed by theologians. Gauguin inscribed this on his painting from 1897: 

Detail: D’ou venons-nous: Que sommes-nous: Ou allons-nous? (‘from where

do we come: that we are: or will we?’)

The Mathematician speaks many languages. His beach-comber’s treasures include tiny shells and a smooth 4-inch coral pendant. 

Does the Reverend know the Mathematician is lonesome? Will the Reverend respond to such contention? Yes, he does. And so begins this joint study.

In their conversations, they will demonstrate that Faith is more fundamental than Logic, by reviewing the scope and limits of scientific logic. Free will, discussed for millennium, is logically addressed and reasonably demonstrated. Scholastics in quadrivium-logic still burdens much religious writing; they avoid this.

On the atoll, they often talked of the wonders of just plain sand. Both have taught and often, to demonstrate humankind’s limits, create such compositions as: Write down everything about a grain of sand. It’s both a compelling and fascinating thought, especially when walking on a beach. To write about a grain of sand would involve everything in the universe in a most interesting way. They start with a very fundamental question, one that has been asked for millennia. 

Reverend: Why is there anything?

Mathematician: That is forever unknowable by anyone or anything within and of the universe. Things are States; caused to begin, caused to change, caused then to end. What is a Cause? A Cause impels transition – genesis of states – their life cycles change. The Information-Existence and Time-Existence Theorems absolutely limit the extent of what’s knowable. In Scripture is written: 

“God thundereth marvelously with his voice; great things doeth he, which we cannot comprehend.” Job 37:5

Reverend: The God that can be explained is not God, as is stated in the Bible. 

Behold, God is great, and we know him not, neither can the number of his years be searched out.” – Job: 36:26

“Touching the Almighty, we cannot find him out: He is excellent in power, and in judgment, and in plenty of justice: he will not afflict.” – Job: 37:23

One could also ask ‘how do we know anything?’

Mathematician: Indeed, how does anything know anything – from amoeba, through squids, cats, dogs to humans? It’s seen in the most fundamental structure of language, yet Faith is more fundamental than language. 

Mathematician: We agree; I will detail my reasons when we discuss faith and logic. Let’s talk a little about a grain of sand and bring our discussions down to Earth. There was a genesis of elements which comprise a grain of sand; with hammers of light upon the anvil of inertial space are worked the silicate garments of God.

Your cosmology has a void between æther and QMs. Was nothingness created by God? My model includes æther, QMs, and void. I’m aware that æther and QM’s must-have structures. Perhaps sometime something about these structures will be knowable, however, there will be a substructure. Ultimate reality is unknowable. As was said in Rome, “from nothingness there can come nothing.”

Reverend: Why does the universe cohere? What force holds some objects together and keeps some others apart? Paul teaches in Colossians 1:15-17 that Jesus is “the image of the invisible God, the firstborn over all creation. For by him all things were created; things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities: all things were created by him and for him. He is before all things, and in him, all things hold together.”

Likewise, the Psalmist wrote, “I choose the appointed time; it is I who judge uprightly. When the earth and all its people quake, it is I who hold its pillars firm.” Psalms 75:2-3. 

If the Lord were to let loose his grip on the world, all would collapse in chaos.

Mathematician: Note that this chaos is not the void between stars and island universes called galaxies. The sort of nothingness we speak of is that envisioned by the Greek who asked: What would happen if I stuck my hand in nothingness? By nothingness, I mean absolute void, not space of the inertial continuum in which virtual particles appear and disappear, not space which cloaks an electron with a virtual field such that its electrostatic potential is never and can never be fully expressed.

Reverend: Are the duration and extents of all things’ transmissions limited?

Mathematician: As rigorously proven in the Information and Time existence axioms, durations and physical extents of all things are limited. No thing within and of the substance of the knowable universe can either endure infinitely or have infinite physical extent.

Reverend: You have commented on consistency transcending any knowable causes; causes as defined by St. Thomas and applied to transitions between state spaces. This to me demonstrates a transcendental power that can carry information across infinite space and through an infinity of time. 

Mathematician: Yes, this is true. We have considered the following unknowables: Consistency, ultimate coherence, and infinite-extent.

Reverend: Monotheism? For me, it’s an article of faith.

Mathematician: In physics, we demonstrate a single force, it’s simpler.

Reverend: An ultimate single force like monotheism appears from Scripture in verses such as, “all things were made by him, and without him was not anything made that was made. In him was life, and the life was the light of men.”- John 1:3-4.

“For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even His eternal power and Godhead; so that they are without excuse:” – Romans: 1:20.

“But to us, there is but one God, the Father, of whom are all things, and we in him; and one Lord Jesus Christ, by whom are all things, and we by him.” – 1 Cor: 8:6.

“For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him.” – Col: 1:16

There are many, many more. 

Mathematician: Best I can offer is a reasonable mathematical model of all forces being varied perceptions of a single force. Yet, it’s only a model. In addition, I can offer an experimentally demonstratable finding that a perfect consistency underlies all events, and why such consistency can never ultimately be described by men or any combination of men and their machines, either now or in any future. Wonderfully consistent are the characteristics of elements: O, Si, Na, Ca, K, with perhaps a dash of Fe and other traces giving it color, which together comprise a grain of sand. 

Reverend: How would you, a mathematician, talk in a methodical way about the world, the universe, about us, and ourselves?

Mathematician: I claim nothing original here. These most fundamental of all questions and the ways to address them are millennium – likely tens of millennium old. I’ll proceed based on the excellent capitulation of St. Thomas Aquinas to arrange questions by which to methodically describe the world, universe about us, and ourselves.

Reverend: What, who, where, when, how, and why? Is that what you will say?

Mathematician: Sure, and the archaics: what-to, what-from, what-with, and what-for prepositionals. It’s valid to imagine that with the very inception of speech, perhaps among Homo Erectus of ca. 450,000 years ago who built huts, made crayons, carved statuettes, and likely built boats – and certainly among Homo Sapiens well before France’s Chauvet Cavern was painted, reasoned just as we do. So here, based on St. Thomas are questions: What’s a Cause? What’s a Thing? What’s Energy? Does anything endure forever? 

I must also add this: We can never explain anything, we can only describe. To emphasize that we describe rather than explain, I have selected a topic sometimes given to uppity students: Write a composition about something simple. In it, explain everything about a grain of sand. To this end we will do our best to describe – making believe we are trying to explain a grain of sand. Our description will include all of mankind’s sciences and in the last chapter, an illustrative example of a grain of sand will demonstrate why we fail; why mankind only describes and never explains.

Reverend: Let there be light, and then how – now from light to a grain of sand? Can we describe all that exists? Is description simpler with God or without God?

Mathematician: Currently the best available description of everything is the Expanded Theory of Morphological Orders (Published in the Rhodes Fairbridge Encyclopedia of Geomorphology, Reinhold, NY, 1968) It encompasses everything in the observable universe. It subdivides all things into orders which transform one-into-another. The transformations are the causes written about by St. Thomas Aquinas.

Mathematician: Why is sand sand? Sand grains are neither small pebbles nor large particles of silt. The use of human, animal, and other figures in the Magdalenian culture’s writing identifies and locates states and shows transformations between states. It’s a very fundamental way of writing. Some decades ago, in the N.Y. Academy of Sciences series on Planetology and Space Mission Planning, I had Dr. Hicks work out the stellar sequence showing stars from Bok globules through O,B,A,F,G,K,M (A mnemonic for the order of star temperatures), etc., as Markovian states (A Markov model is a stochastic model used to model randomly changing systems) with transformations represented as Lyapunov Servo Loops.

People, plants, creatures, and things (states) begin, do things, and end (transitions). St. Thomas’ causes are verbal descriptions of transitions. All things inanimate and animate – states describe existences with life cycles: conception, birth, youth, maturity, old age, death, dissolution, transfiguration. Order Theory describes all things with nouns. 

Reverend: Does that description point to any conclusions? 

Mathematician: Conclusions? Perhaps not. But it compels us to search for ways to describe. To date, the best way seems to begin with taxonomy, continue with detailing the smaller structures which comprise the whole, going further by discovering the processes – the causes of St. Thomas – transforming the larger thing we observe and continuing on down through its smaller and even smaller components. That description, The Expanded Theory of Morphological Order, and earlier descriptions have led to method rather than conclusion. 

Reverend: Method?

Mathematician: Algebras in their many forms do note that riddles cast shadows of algebra to come before them; that algebra has indeed led to some conclusions, and I can’t resist adding that much of alleged advanced algebra is less credible than most riddles. 

You should first ask: What is time? 

Reverend: Very well, what is time?

Mathematician: Time is only knowable as a sequence of events, as measurements made with repetitive sequences of events by clocking or by timing a single clocked event. An increment of time can be clocked. An accurate memory is needed for clocking. Clocking requires a record; a clocked event only requires the measurement of an interval without relating it to the continuous passage of time.

Yet ultimately the nature of time is a mystery. We can ask about time and is there: no beginning no ending, a beginning and ending, a beginning but no ending, or no beginning but an end? Information Existence Theorem and Time Existence Theorem as formulated by Enzmann and Enzmann state there are beginnings and ends. 

Reverend: “In the beginning was the Word…” It seems Scriptures indicate a beginning and St. Thomas states there is no such thing as infinite regression – so here he says there is an end? All relate to time – you say clocking requires an accurate memory. I must ask here, what is memory? 

Mathematician: Memory – information – is stored-abstraction. The evolution of information is molecular coordination, autocatalysis (Catalysis of a reaction by one of its products. Catalysis: the acceleration of a chemical reaction by a catalyst) cascaded reactions, cascaded reactions with alternate paths, sensors, sensor-effector loops (A sensor, also a receptor, is a component of a feedback system that monitors a physiological value. An effector is the component in a feedback system that causes a change to reverse the situation and return the value to the normal range) One might here mention intelligence. 

The evolution of intelligence is a molecular response, abstracted control of reactions with alternate paths, awareness, and cognizance – which is a real-time function. Mathematics is a metric language. Words and intelligence are parametric (Relating to or expressed in terms of a parameter or parameters; big, bigger, biggest, etc.) Explicit vs implicit. 

Parametrics are parts of language; compare with a standard and parametrics become metrics, and soon mathematics evolves. All description is linguistic: verbal description is parametric, mathematical description is linguistic-metric. Note that mathematics is a part of language, but language is neither part of mathematics nor can it be reduced to mathematics. All verbal descriptions can be expressed as Western Union Ladder Diagrams (Specialized schematics commonly used to document industrial control logic systems) and these as binary Karnaugh Maps (A method of simplifying Boolean algebra expressions). This is not a reduction of language to mathematics; it is a translation of phonetic symbols into binary symbols. 

Reverend: What is good? Why be good, what’s piety? Why be pious? Why be evil? Why do we have a conscience? 

Mathematician: Piety is best discussed in conjunction with ethics. Let’s consider in this order: evil, good, then conscience. 

Reverend: What, to a mathematician, is evil?

Mathematician: Define evil, or sin, as that which by its existence or non-existence, action and/or lack of action, extent and/or lack of extent, location and/or non-location, time-of and/or duration of and/or lack of this, directly and/or indirectly harms itself. Here self must be taken in the broadest sense, where it’s recognized that no entity is, or can be, complete by itself. Note that this includes parthenogenic life forms that couple with complete efficiency to the inanimate environment.

Reverend: What is good? Why be good? Scripture says all humans are born in God’s image, corrupted by Original Sin. “For all have sinned and come short of the glory of God.” -Romans 3:23. As a mathematician, do you believe all persons are born good?

Mathematician: Deeply fundamental to the subject are the Golden Mean, music and astatization, foul smells tastes and toxins, morning sickness, prismatic color, neoteny (the retention of juvenile features in the adult), and beauty contests, toys, and monsters. Then there is the matter of inner grace, deconstruction and confounding of the senses, and currently manifesting diseases not heard of since the early Middle Ages. Rather than answering that question, which you must admit is dogma, may I, without indicating my view in any way whatsoever, ask questions and consider your answers?

Reverend: Do you intend to answer my question by asking a series of questions?

Mathematician: No, I don’t. I’ll express no opinion whatsoever – positive, negative, agnostic, and so on. It’s a technique used by some of the world’s best industrial consultants.

Reverend: A way of answering the question I just asked you?

Mathematician: To consider the precepts upon which the question is based as honestly as possible, perhaps arriving at an answer. I both state and repeat Original Sin – the essence of being born good or not – is an article of both deeply-held faith and concurrently the dogma of many, but not all, varieties of Christianity. I don’t believe it’s a component of any other religion. Again, I’m taking no position whatsoever, giving no indication here or elsewhere as to my personal views, so please don’t construct any by either suggesting ‘he protests too loudly’, or ‘he’s basically positive’

In this joint effort of ours, I will listen to but make no effort to analyze any dogmas. It’s beyond any mathematics I can know. I can say we are born imperfect. This we can deduce through logic. Were we not born imperfect, or mortal, into this world we would be immortal. Imperfection leads to errors – small ones, big ones – and as often as not, evil. This is the nature of Original Sin.

The Mathematician and the Reverend have many lengthy and deep conversations. They discuss the nature of creation, sin, eternity, free will, and evil. 

The Mathematician later writes in his Archive:

William of Ockham states that God, by executive fiat, created moral principles. St. Thomas Aquinas says moral principles that occur naturally are instilled in us by God. We discover these by rational analysis and our God-given mental ability for moral reasoning and prayer. Atheists hold that moral principles exist in a universe in which all causes, states, and effects have natural causes available for observation (which is cardination or taxonomy), and then, therewith, available for measurement (or ordination in which they are fully described.) I lack sufficient intelligence to be an atheist. 

To this should be added Gödel’s Proof (Something can be either complete or consistent, but not both.), that all description, taxonometric to mathematical ordination, is subject to error, for no measurement can be made with infinite precision. Even the best mathematicians can include ambiguity and singularity in their descriptions. 

Consider the gravitational formula in which:

1) there is at least one ambiguity

2) where direction is omitted

3) there are six singularities (impossibilities)

4) neither masses can be zero or infinity

5) distance cannot be zero or infinity 

Consider the major implication that gravity is an attraction. It would be far wiser to call it impulsion, knowledgeably leaving ambiguous what we don’t know. In addition to ambiguity and six impossibilities, the gravitational formula contains an enormously significant implication that a spherical mass acts upon another sphere as though each was concentrated at a point. 

In conclusion: singularities (impossibilities), ambiguity (direction), implication (it’s attraction! But is it?), mathematical approximation (it acts as though at a point), and clash of descriptors has tortured the so-called higher mathematics of astrophysicists and cosmogonists. Cosmologists have been touting one-after-another so-called theory of everything for the last several centuries. We lack sufficient intelligence to be atheists.

For more Cosmology see ENDEAVOR.