A Different View of God
Having written somewhat extensively about our need to re-examine, re-define, and reconsider God, I have suggested that we should move beyond our anthropomorphic representations and human characterizations of the Creator. God, I contend, is beyond our grasp. Our conception of God must expand and deepen if we are to become closer to God – even if God is by their very nature incomprehensible. Let us not be naïve: we are simply too ignorant and shallow to give God their due. But that does not excuse us from trying our best.
The approach I have suggested in pursuing awareness of God is through God’s creation – “Creation”. Specifically, our best chance of knowing anything about God is by knowing and grasping the reality of our existence within the reality of the Universe. Because physics (and its cosmological, astronomical, and quantum fields) has revealed deep and broad order within the physical Universe and clear underlying “intelligence” behind its processes, we rightfully presume that physics also reveals much about the Creator.
Here, we will attempt another perspective using a similar approach – only now we will work from mathematics instead of physics (as if they are different). In the same manner that I contend a need to clear one’s mind of pre-misconceptions regarding God, I insist that you work hard to rid yourself of similar detractive ideas and attitudes regarding mathematics. Mathematics is one of God’s greatest gifts, it is probably the closest language we could share with God, and it is the most fundamental proof for the existence of a Creator. And although mathematics encompasses arithmetic and algebra and calculus and the like, it is much MUCH more. In order to utilize mathematics to get closer to God we should begin by re-examining, re-defining, and reconsidering mathematics.
The single most unexpected and astonishing quality of the Universe is the existence of mathematics. Yes, I just said that mathematics is even bigger and better than sex. It is even bigger and better than us. It represents a level of ordered complexity which far transcends our own (and we are hands down the most ordered and complex objects that we know of). For thousands of years we have systematically pursued an understanding of mathematics and every time we seem to be getting close to some finite representation of mathematics we find another deeper level. Know we understand that we have just reached the point where we have some idea of how much we don’t know about mathematics. But, before you run away screaming, let me assure you that we are going to keep it simple here.
Let us begin by re-defining mathematics. To do that we should know something surprising about reality, something we generally overlook. Science has revealed the true underlying nature of Creation as information. Every physical thing is made up of energy (including matter as “E=MC2”) and energy is all about information. At the most basic level – the quantum level – we find that all energy is built from quantum particles and that those particles are complex packets of information. Every particle in the Universe interacts with other particles through a complex array of forces, fields, and “laws” – all of which are informational. And, all that information comes in one standard format – mathematics. That is why every object in the Universe will eventually be represented within a mathematical expression.
Mathematics is the Creator’s way of creation. “Wow!” Did you just say “Wow”? If not, please keep reading and re-reading the above until you do. Good…
Eugene Wigner, Nobel Laureate for physics, wrote about “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” referring to the uncanny ability of mathematics to describe and predict phenomena in the physical world. He wrote:
"The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve".
Paul Dirac was clearly correct – “God is a mathematician”. How else do we explain the apparently omnipotent powers of mathematics to describe the world we live in.
It is not that we create mathematics, but that we discover the mathematics that underlies the design of the Universe. More than “poetry of logical ideas” (Albert Einstein), mathematics reveals the “thoughts of God” (Euclid) and the manner in which mathematics has been written into the nature of Creation reveals much about the nature of the Creator. So let us take another look at what mathematics actually are.
One of the best indications of our limited understanding of mathematics is our inability to properly define it. Viewed as a concrete science, mathematics deals with numbers, quantities, shapes, and relations. If it was nothing more, it would still amaze us with coherence and complexity. Viewed as an abstract science, mathematics is the study of all possible patterns and the study of the properties and interactions of any object. Viewed as a language, mathematics is a high-order language with specialized symbols, explicit syntactical rules, and broad descriptive power. Viewed as a philosophical system, mathematics is an inductive activity which consists of the sequenced execution of specific mental constructions (logic) which are necessary and effective. Mathematics is that mental construct which “draws necessary conclusions”.
To these definitions, I would add a theological meaning: mathematics is a creative language used by God to provide coherence, structure, and depth to the information which underlies the Universe. Mathematics is truly divine…
I would also propose that there is another worthwhile view of mathematics – that it also functions as a “programming language” in a manner akin to computer/programming languages. Mathematics includes instruction sets, commands, functions, operands, specifications, declarations, symbols, components of syntax (form) and semantics (meaning), specifications, algorithms, relations, constructs, expressions, and abstractions (for defining, manipulating, or controlling the flow of execution). When viewed as such mathematics requires a processor which executes the language. We might view the Universe generally as an information processor and we might see our own meaning as including mathematical “computations”. (To be dealt with more thoroughly elsewhere).
Fundamentally, mathematics is about structure, order, and relations. The most compelling unifying thread of all of mathematics is its ability to describe relationships between things that vary over time (e.g. “algebra”). As al-Khwarizmi (the “discoverer” of algebra) realized, the key relation in the Universe is equality and the "reunion of broken parts") is the broadest essence of mathematics (together with number theory, geometry, and analysis). By studying the symbols and the rules for manipulating the symbols of the Universe we discover properties of operations and the structures these operations which we term “physics”. Mathematics is the descriptor of physical reality.
When we re-conceptualize the Universe as the Creation of a mathematician, we immediately see the significance of “information”. Knowing that information is symbolic representation of truth and that mathematics is the language of that truth, we can only conclude that mathematics is essential to our understanding of God – the Creator of Truth.
Hopefully, you have now jumped ahead of me. If not, here is where I’m headed… We may define God as the ultimate cause of Creation and the essence of Creation as Truth. The Universe is an operational platform (let’s not say “computer”) which processes information using the language of mathematics. Thus, objects are created which have equivalent representations in symbols and methods are employed which operate as functions and “logic”. The physical reality which we experience is comprised entirely of objects, forces, and laws – all of which are essentially information in a mathematical system.
The Universe began as a “singularity” – a unity of truth (information which allows the accurate prediction and control of the totality). The unity (with perfect symmetry) was broken as the primary act of causation yielding an asymmetrical (“broken parts”) universe. Our search for a “theory of everything” (or “ToE”) is a mathematical pursuit to represent the original unity of creation. While interesting, the original unity means far less to us than the mathematical progression which has followed. (While it is nice to have a “starting point”, we may follow a progression from any point in its continuum). We must also note that the ToE hardy encompasses “everything” since it only represents primordial physical forces without addressing dimensions, laws, and other non-physical aspects of reality. It also presumes a substrate upon which the forces may operate.
While our mathematics are “primitive”, we can begin to understand the potential. Thus far, wherever we look in the physical universe we find a mathematical representation which parallels the reality we observe. We also find that there is a mathematical reality which transcends the physical universe and its potential is largely unexplored. Perhaps most significant in the unexplored potentiality of mathematics is what it states logically about the Creator and Creation.
Our view of God as a mathematician reveals the truth and beauty of the Divine (as per Russell, above). In a Universe founded upon indeterminism, chaos, and entropy, there emerges predictability, order, and progress (“evolution”) – all based upon mathematics. As we transition from beings focused primarily upon materials to societies based essentially upon information, we may find hope and direction from Creation which began with information and which seeks a clear outcome of better information (truth).
In mathematics the final realization of truth is a “proof”. Soon we may realize that the final proof of theology is the truth of mathematics.
 Yes, God is a plurality.
 From “The Cosmic Code : Quantum Physics As The Language Of Nature” by Heinz R. Pagels, Simon & Schuster (1982) – one of my favorite books.
 “The laws of nature are but the mathematical thoughts of God.”
 “First-order languages” define the use of a vocabulary to form complex, sentence-like entities by assigning each term an object that it represents and then assigning each sentence a truth value whereby all logical and non-logical constants are denoted (within that language). High-order languages determine a domain of discourse (within a specific range of quantifiers).
 Algebra literally (as Arabic الجابر) means the "reunion of broken parts".
 The ToE is one step beyond the theoretical “grand unified theory” where the primordial forces of electro- magnetism and the nucleus are not yet distinct in the grand unification epoch of the early universe. When gravity is unified with the other fundamental forces, we’ll have a ToE.
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