Scientific theology: a new theological hypothesis
Chapter 2: Language: our social playground
1. Language and communication2. Recursive conversation
3. Language is universal
4. Language, identity and symmetry
5. Sacred language: Sanscrit, Hebrew, Latin
6. Linguistics
7. Physical languages
8. Language and spirit
9. Continuity and discreteness
10. Insight and intelligence
11. Science and language
12. Mathematics
13. Infinity and set theory
14. Mathematics and imagination
15. Writing, time and memory
16. "The Word became flesh"
2.1 Language and communication
Our most common form of public communication is spoken language, named for the Latin word for tongue, lingua. Communication comes in many other forms however, all of which, like speech, are body language. All information in the world is carried by physical symbols. For us, as for everything, language is what makes the world go round. Every event is an act of communication in one of the countless languages of the universe. Language - Wikipedia, Spoken language - Wikipedia, Rolf Landauer: Information is a physical entity
We use to language encode and share our experiences of the world. A language serves as a model or frame of reference which connects all the people using it. It is a communication protocol, the shared set of tacit assumptions that underlies all communication. We can translate from one language to another because they all refer in some way to the same world of human experience. This is a symmetry of language, something common to them all. Communication protocol - Wikipedia, Polanyi: The Tacit Dimension
A group of people talking to one another forms a communication network. The basic element or atom of a network is an act of communication, which has three elements: make a connection; share some information; break the connection. We can see these elements clearly in a telephone call. In day to day communication these details may be invisible because conversations seem to be effortless and instantaneous. The plan here is to use our personal experience of language and networks to develop a coherent picture of the whole world. We can then examine this picture in the light of historical models of God to see whether it supports the proposition that the Universe is divine.
Language is the way we transform our experience the world in order to communicate with one another. I am part of the world, so I can express both my inner and my outer visions. I am watching a beautiful sunset, but the pain in my belly is distracting me. We know that our communications originate and terminate in our minds. Between the physical states of my brain, the muscles of my mouth and tongue and the receptors in my ears there is a long chain of complex unconscious transformations which encode and decode the things I say and hear. Language processing in the brain - Wikipedia
We are working through the assumption that the Universe is divine. We communicate through our bodies, and so we might expect the same of God: all our experience of the world and ourselves is divine revelation. Revelation is a motion and the study of bodies, that is physics, is principally a study of motion. We think of a motion as a transformation in which some things change and others stay the same. My car is more or less the same car in Adelaide as in Sydney, but on the way it undergoes a real transformation from one city to the other.
Can you think about something if there is not a word for it? Maybe. Can you talk about something if there is not a word for it? Yes, but it may take a long conversation to come to an agreement about what we are talking about. We might sum this book up as an attempt to produce a new theological understanding of the notion of creation.
Mind thrives on language. We think of language as any code that can be used to share information between independent entities ('sources'). As we develop from babies, we absorb and respond to the human language around us. Written representations of language, like this page, enable us to share knowledge through space and time.
What is happening when we communicate? The idea behind coding is to transform a body of information into different representations which are optimized for transport through different channels. We might optimize for speed, for security or to avoid error. If we are talking to one another, I convert images in my mind into into strings of sound. The strings of sound move through the air to your ears. They enter your mind and are transformed into images similar to those in my mind. And vice-versa. If we are writing to one another, we convert the contents of our minds into strings of written words. In other circumstances we might use a sign language. Whatever the code, we use language to correlate our minds. Each language is defined by the algorithms or processes used to encode and decode it.
One of the many apparent miracles of our development is the acquisition of language. We listen carefully for baby's first word, and enjoy the growing skills and interesting mistakes that our children make as they learn. de Boysson-Bardies: How Language Comes to Children
Language serves as a reference system, analogous to but much more complex than to the lines of latitude and longitude we draw on the Earth. We begin with a vocabulary, which matches spoken and written words to objects and events in the world, like 'horse' and 'fall'. We can then weave the words into larger structures to capture more complex meanings and events: I fell off my horse. We use long strings of text like novels to represents long strings of deep amd complex events, like the history of a family.
Back to top2.2 Recursive conversation
Simple messages like 'break one small brown hen's egg into a wine glass' convey clear images and unequivocally define a sequence of actions. We find sentences like this in recipe books. With a bit of experience in the kitchen, recipes are relatively easy to decode. Other message are more difficult. I read a novel. What does it mean? The critics pore over it and come up with different interpretations. In many cases, the beauty of artistic language lies in its ambiguity.
In more complex situations dialogue is necessary to get ideas across. A dialogue is a recursive process, each of us stimulating the other to a reply. It may be an unbounded ramble, or it may converge on the precise communication of one particular idea. I say 'mathematics is a language'. You say 'what do you mean by language?' I say '. . .'. Such dialogues may last a lifetime. Negotiations between families, corporations and nations may take even longer. The theological dialogue with God has been part of human history from the beginning.
A dialogue is relatively easy to establish if both sources speak the same language. If not, there are two options. One is to use an interpreter. An interpreter must know the language of both sources, and be able to transform one into the other and back again. The transformation takes place in the mind of the interpreter. The words of one source are first transformed to ideas in the interpreter's mind and then transformed again into the language of the second source.
Translation between natural languages is difficult because in many cases there are no exact equivalents. In simple practical matters, these difficulties may not cause much trouble, but in more complex matters of love and politics long dialogues may be required to settle on a common understanding.
The second option is for the sources to learn each other's language so that there is no need for an interpreter between them. This is a much more painstaking process, but we know that most of us are capable of fluency in two or more languages, particularly if we grow up in a multilingual community.
Learning a second language in adulthood may be harder than learning it as a child, but our natural linguistic ability means that it is possible, particularly if there is no alternative. From my experience, exchange students in their high school years need about three months in a new linguistic environment to achieve a fluent working knowledge of the new language.
One of the most remarkable feats of translation is involved in the development of each new living organism. It is the translation from genotype to phenotype, that is the translation of the information coded in the organism's DNA into a new individual. In sexually reproducing organisms the translation mechanism, the tacit dimension that implements this process, is to be found in the maternal egg. Since the studies of inheritance by Mendel in the nineteenth century, we have learnt how the genetic information encoded in DNA is translated into proteins, and how the proteins serve both as structural and functional elements in the development of the new organism. History of genetics - Wikipedia
Back to top2.3 Language is universal
We may think that we are the only users of language on the planet, but here we take a wider view. Language is the means of coding and decoding information for transmission. One language is distinguished from another by the system of coding and decoding that it uses. Thus French speaking people use a different sequence of sounds to express a certain mental state than English speaking people. The coding used, that is the language spoken, by electrons is different again.
Language is not unique to us humans, nor is it confined to sound. Here we accept Landauer's proposition that all information is encoded physically. Any set of physical symbols can be used to represent information. The number of different ways physical phenomena can be arranged to represent information is practically infinite. We can see this in the enormous number of physical arrangements that have given us different molecules, species and modes of communication throughout the history of evolution.
We use physical symbols to carry information, but the sources of language are also physical. These sources have internal states, represented physically by neural synapses, particle states, positions of components, pressures, voltages and a wide spectrum of other physical conditions. We can imagine the messages shared between the individual grains in a heap of sand as a network, each grain asking for and receiving its place in the heap with respect to all the others.
Almost every cell in our bodies carries our genotype as a long series of chemical symbols ('bases') strung together to form DNA molecules. The DNA is organised into genes, each of which defines the structure of a particular protein or proteins. Each cell carries an elaborate mechanism to translate the messages in the genes into the proteins which form and operate the cell. As the cell passes through its life cycle, further molecular mechanisms which sense the environment of the cell determine which genes are to be decoded, depending on the conditions prevailing around the cell. DNA - Wikipedia
Back to top2.4 Language, identity and symmetry
Each individual of each species is defined by the genetic information received from its parents. We are all human because we all share human DNA and can reproduce with one another. Every other species has its own characteristic DNA which guarantees that the children are like the parents. But not exactly alike. There are usually variations. In the case of organisms like bacteria that reproduce by the parent individual dividing into two children, these variations arise through errors in copying the DNA. In organisms that reproduce sexually like ourselves the reproduction process mixes the DNA's of the parents to produce a child with a unique genotype, so that we are like our parents, but not identical to them.
We find a similar pattern of unity and differentiation in human languages. On the one hand I share a langage with a large class of people, English speakers. On the other hand, I speak my own unique version of English which is very important to my personal identity. My identity is layered. I am a living creature, I am an animal, I am a human, I am an English speaking human and finally I am me with all my personal quirks. Each of these layers is identified by the languages individuals use to communicate with one another in that layer. We call such individuals peers, and their layer a peer layer.
An important uses of human language is the establishment of law. In many jurisdictions, laws are the product of a parliament, a place where people speak (French parler) and after a certain amount of debate and voting, establish laws whose definitive form is promulgated as a text. In less democratic regimes, the laws may simply be dictated by the dictator. Tradition tells us that legal books of the Hebrew Bible were produced in this way, dictated by Yahweh to Moses. Torah - Wikipedia
An important feature of the rule of law is that it applies equally to everybody. It is rather like the genetic code of society. It reflects human symmetry. Of course we often find individuals and institutions which consider themselves above or beyond the law. They, like cancer, break away from the collective code. In modern times this status is often accorded to or taken by dictators and security forces whose task is to make the population follow the will of a government which is governing for itself, not for the society. Geoffrey Walker; The Rule of Law
We often extend the notion of human laws to laws of nature and divine law. For many, the laws laid down in the Bible are divine law and take precedence over laws devised by parliaments and dictators. Laws of nature take precedence over human laws as matters of fact. There is no point in making a law against gravity or the ebb and flow of the tides or people being attracted to one another. It will have no effect beyond bringing ridicule to the lawmaker.
The term 'law of nature' is currently falling out of favour, to be replaced by the notion of symmetry. A symmetry, like a law, is something that applies widely and stays the same in changing circumstances. A perfect sphere looks the same no matter how we rotate it. Ideally the rules of justice remain the same, no matter who we apply them to. Justice, we say, is blind to personalities. Every language remains the same (in principle) no matter who is speaking it. Neuenschwander: Emmy Noether's Wonderful Theorem
Symmetries are the basis of abstract knowledge. When it comes to symmetrical things, we can say that if you have seen one, you have seen them all. All hydrogen atoms are basically the same, so that chemists do not have to learn a whole lot of new facts about every hydrogen atom they encounter.
The symmetries we see in nature are reflection of the layered structure of the observable world. We may think of all hydrogen atoms as peers in the atomic hydrogen layer of the Universe. Every one of these atoms also exists in a particular place and time in some higher layer, perhaps in somebody's heart. The symmetry of hydrogen atoms is broken by the roles that they play in higher layers of the structure of the Universe.
In reality, every symmetry is broken. We may know about horses in general, but every horse is unique. We are all equal before the law, but every case that comes before the courts is made unique by the detailed circumstances in which the law must be applied. In the same way, the English language is a symmetry shared by all English speakers. This symmetry is is recorded in written dictionaries and grammars, but it is also broken by every speaker, whose words are specified by all the circumstances in which they are spoken, including the personalities of the speaker and the listener.
In the previous chapter I recorded my experience with Bernard Lonergan's metaphysics. He argued that the symmetries in the Universe pointed to meaningless data, empirical residue. This, he claims, means that the Universe is not divine. He overlooks the fact that every symmetry is broken. Every event has a specific meaning and intelligibility determined by its local position in space, time and all the other dimensions of reality. The Universe as we experience it is intelligible to the limits imposed by consistency, and so fittingly called divine.
Back to top2.5 Sacred language: Sanskrit, Hebrew, Latin
Natural languages are very fluid. Even though all English speakers speak English, the English that each speaks is unique to the individual. One effect of the invention of writing has been to standardise the spelling and pronunciation of languages and this in turn led to a closer specification of meaning. Some language, particularly the foundation texts of the ancient religions, has acquired sacred status. Through long use and familiarity the language is seen to reflect the eternity and omnipotence of heaven and is no longer open to the normal dynamics of linguistic evolution and interpretation.
The meaning of language becomes very important in matters of law and science, particularly theology. So we find that the Roman Catholic Church prepares all its most important and binding documents in ecclesiastical Latin, which is itself derived from the ancient Latin of the emperors and classical Latin authors. Sanskrit has played a similar role in the religious and literary traditions of India. Sanskrit - Wikipedia
One advantage for the Church of this approach is that Latin is a 'dead language': it no longer has an active community of speakers who are continually modifying it, as has happened during the evolution of Latin into Italian, French, Spanish and other Romance languages. Latin has a certain formal eternity which serves well in a Church which thinks that it has got the gift of ultimate truth, and whose 'deposit of faith', written mainly in Latin and Greek, is fixed for all time. Romance languages - Wikipedia
The Latin expressions of Catholic dogma thus become 'sacred language' with meaning defined by the magisterium of the institutional Church rather than the users of the language. Sacred language - Wikipedia
The Hebrew Bible was written in ancient Hebrew which slowly went out of use in the early centuries of the Common Era. This Hebrew formed the foundation for the recovery of Hebrew as a living language following the establishment of Israel.
One motivation for the use of sacred languages for prayers, liturgy and general theological and religious communication is the belief that the ancient God will be more likely to hear our prayers if they are addressed in familiar formal and ancient terms. From the point of view of this site, none of this has much to do with God but more to do with pleasing the faithful, particularly those who find security in familiar terminology. The Episcopal Church
Back to top2.6 Linguistics
Linguistics is the study of all aspects of language, from the genetic relationships between natural and artificial languages to the anatomy of the organs of speech and hearing and the neurophysiological processes of encoding and decoding meaning. Linguistics - Wikipedia
It is generally conceded that one of the founders of linguistics was ancient Sanskrit grammarian Panini. We know next to nothing about Panini himself but his work, which defined classical Sanskrit, has come down to us through the Ashtadhyayi. Panini developed a formal, almost mathematical approach to the grammar of Sanscrit which predated nineteenth century grammatical developments by more than two thousand years. Joseph writes of Panini:
[Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. . . . On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. . . . An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was . . . partly an outcome of linguistic developments in India. Pāṇini - Wikipedia, George Joseph: The Crest of the Peacock: Non-European Roots of Mathematics
One of the most important developments in linguistics is the art of writing, that is of representing spoken sounds by written symbols. Sanskrit has no native script, but is traditionally represented with Brahmic scripts. Panini may have composed his work orally. Only later was is committed to writing. Brahmic scripts - Wikipedia
Much of modern linguistics has to do with recovering lost or almost lost languages, and with developing software techniques for the automatic translation from one language to another. A further line of development is programming machines to develop some 'understanding' of language in order to mine large volumes of data for marketing purposes and to detect conversations which may have some relevance to national security. Dan Froomkin: The Computers are Listening2.7 Physical languages
All the languages of life are realized in atomic and molecular processes, and all these processes are rooted in the fundamental languages of physics. Physical languages are sometimes called forces, since, like human languages, they enable individuals to move or change one another.
Physicists have identified four forces: strong, weak, electromagnetism and gravitation. The sum of their communication is the life of the Universe at every scale from the majestic whole to events so small that they are measured by the quantum of action. The first three of these languages are studied by quantum field theory which is built on quantum mechanics and relativity, as we shall see. Despite many efforts to develop a quantum theory of gravitation, it remains the exception. We explore this situation further in chapter 6. Strong interaction - Wikipedia, Weak interaction - Wikipedia, Electromagnetism - Wikipedia, Gravitation - Wikipedia
Each of these forces is associated with sets of fundamental particles. There particles form a dynamic alphabet for the Universe. The encode the processes and messages exchanged in the quantum network that forms the foundation of the universe. We try to decode them to understand how the Universe works. The best known are probably the photon, electron, proton and neutron, from which atoms are constructed. Protons and neutrons are constructed from even simpler particles, quarks and gluons. High energy accelerator experiments have identified many other particles which are summarized in the Particle Adventure. CPEP: Particle Adventure
The languages of elementary particles are far from trivial. Centuries of physics have still to yield a full understanding. Practical physical calculations, which try to imitate the way the fundamental particles communicate with one another, are enormously complex. Each of us is an enormous society of trillions of trillions of trillions of these elementary particles, and our physical integrity depends absolutely on the complex networks of communication between them.
If we think of a force as that which makes something move, it is easy to understand language as force. 'Will you please make me a cup of tea' is the force that moves a willing listener into the tea making routine. Even if the listener is unwilling, the mere reception of the words has modified the contents of their mind and they will remember being asked, even if they do not want to do the work..
We assume in this book that all information is physically embodied. This is certainly true of our spoken and written language. We know that the transmission and reception of speech, music and all other sounds depends upon physical vibrations in the air. This is possible because air is an elastic medium. Until recently, most written words were embodied in ink on paper. Now we are able to use electrons and electromagnetic radiation to transmit written messages but it is hard to imagine paper and ink disappearing entirely. Nevertheless electrons and photons are just as physical as paper and ink.
The language of physics supports the language of chemistry, which in turn is used to build the languages of life like genomic, the language of genes. Genomic encodes the detailed molecular structure of every creature. Like sentences in human language, genomes are divided into words called genes. Each gene has a certain basic meaning which is nuanced by the context in which the gene is decoded. The dialogue between creature and environment that shapes genomic sentences is evolution by natural selection.
I imagine this work as the genome of a very simple virus. A virus, unlike a cell, cannot read its own genes. Instead it must inject its genome into a cell so that the cell reads its genes and produces new viruses. The replication of viruses usually leads to the death of the cell, so that the viruses are released to invade other cells. I hope the the viral analogy breaks down at this point, and my message goes viral not by the death of my readers, but because they like my story and and pass it on. The genes here are by analogy pages. My pages are laid out in a narrative order, but, as in any book they may be read in any order and visited any number of times. Virus - Wikipedia
Hopefully, through this process, you may be able to build in your mind a version of the structure that exists in my mind. Like the instructions in a cookery book, this communication has a practical purpose. That purpose is to show, by looking at the world in a particular way, that it is possible to realize our dreams of heaven on earth.
These dreams are themselves fuelled by language. Through the Bible the Christian God is believed to have revealed themself once for all time to all mankind. It could be difficult to overestimate the influence that the Bible has had on human life. In particular, we have the notion that life on Earth is not meant to be easy. It is a trial, designed to separate sheep from goats. The sheep are destined for an eternal life of bliss. The goats for an equally eternal life of pain.
Is this true? Maybe not. A new linguistic picture may drive a new dream: to manage our lives on Earth so that they are heavenly. The Christian paradigm would say that this is not possible, because we are inherently evil. The physical paradigm says that as far as we can see, our Universe is as perfect as can be and divine. We can make our lives quite good given the necessary knowledge, cooperation and acceptance of reality. Human welfare suffers enormously from those who prefer their own fantasies to the realities revealed by science. Evolution, however, is on the side of science. To paraphrase an old line, those who live by error die by error.
On the other hand, the possibilities of truth are enormous. First we dreamt about flight, then we flew. Later we wanted to travel to the moon, and we did. Do we want to live in peace and harmony with ourselves and our planet? If your answer is yes, it may help to read on.
Back to top2.8 Language and spirit
The words of the Gods begin their career in the minds of inspired individuals. They are then transmitted by speech, written on paper, carved in stone and embodied in temples. The ancients, however, and many of their modern followers, thought that information could also be stored and transmitted spiritually or immaterially. This idea is very important for the traditional Christian understanding of God.
On the one hand God is considered to be purely spiritual and absolutely simple, with no 'marks' within it to encode information. On the other hand, God is felt to be omniscient, knowing every detail of our immensely complex Universe, past, present and future. How this information is represented in God cannot be explained. It is one of the leaps of faith needed to deal with the mysteries of ancient theology.
Our hypothesis is that the Universe is divine and that the physical symbols we use to transmit information are fixed points in the divine dynamics. This enables us to reconcile the absolute simplicity of God with the complexity of the Universe. God's simplicity is reflected in its seamless dynamics. The complexity of the Universe is reflected in the fixed points of the dynamics These points are not outside God, they are simply points in the divine dynamics that do not move. Here, following Landauer's contention that all information is physical, we see the fixed points in the universal dynamics as messages, revelations of the divinity.
Thomas asks if there is knowledge in God, and replies:
. . . it is clear that the immateriality of a thing is the reason why it is cognitive; and according to the mode of immateriality is the mode of knowledge. . . . Since therefore God is in the highest degree of immateriality as stated above (I, 7, 1), it follows that He occupies the highest place in knowledge. Aquinas, Summa I, 14, 1: Is there knowledge in God?, Christopher Shields: The Active Mind of De Anima III 5
This answer depends on Aristotle's theory of matter and form and the axiom that matter 'contracts' form. As forms become more immaterial, they approach a certain infinity, and so are better able to know. God, the most imaterial, has supreme knowledge.
Here, instead, we take guidance from the technology of memory. A computer memory is a device with a large number of physical locations which can be set into one of two states, usually designated by the binary digits 0 and 1. The size of the memory is measured by the number of such locations, each of which has an address. Today computer memories may have trillions of such locations. A human brain may have hundreds of trillions of synapses, the biological analogue of a memory location. Each synapse may have many different states, rather than just two, which accounts for the enormous power of our minds.
When we come to look at matter from a quantum mechanical point of view, we see that even a particle as small as a hydrogen atom may have an infinity of states. This suggests that matter as we now understand it places a very weak constraint on knowledge. We will see below that there is no limit on the number of fixed points in the whole Universe. If we assume that knowledge and spirituality increase with the number of memory locations, we may see that identifying God and the Universe places no limit on divine knowledge.
Fixed point theory provides a bridge between 'matter' and 'spirit'. The fixed points in the Universe are no longer outside the dynamics. They are simply points of the dynamics that do not move. This enables us to understand that spirits are at once dynamically simple and nevertheless have fixed markers that can represent information. Spirit and matter are identical.
We can observe this structure in our own minds. What we call mind is a manifestation of the information processing power of our central nervous systems. We are conscious of much of the input of our senses, but it is clear that we are aware of only an infinitesimal fraction of what is going on within ourselves. Our hearts pump, our lungs breathe, our digestive systems digest. All this process is the invisible and mysterious source of our speech. As I sit here writing sentences form themselves in my consciousness out of my apparently empty subconscious mind.
The foundation of all these processes lies at the microscopic scale. Each of us (and every living thing) is an enormous network of molecular nanomachines. We are conscious of none of this. Nor are we conscious of most of the processing that goes on in our minds. We converse with one another, performing the enormously complex tasks of encoding and decoding our language with very little conscious awareness. More complex or unfamiliar inputs take longer to decode, however. The whole human species has spent tens of thousands of years trying to understand the revelation of God, for instance, and we still have a long way to go.
Back to top2.9 Continuity and discreteness
Speech, like music, is a modulated flow of sound. We call them flows because while the speaker is speaking or the musician is playing, the sound seems continuous. We say the flow is modulated because instead of being on one simple note like like siren, the flow contains a sequence of distinct sounds. In music we call these notes. In linguistics they are called phonemes. It is this modulation (usually assisted by other body language like expressions and gestures) that carries the information in speech and music. Phoneme - Wikipedia
One of the most important events in the history of human communication was the invention of writing. Numerous ways have been devised to encode both music speech in a permanent written form. If it were not for writing, we would know very little about the lives, activities and thoughts of people separated from us in space and time. Writing may itself be continuous ('running writing') but its important feature is that the sounds of speech and music are represented by discrete symbols, like the letters and words you are reading here. Learning to read and write are important skills in the modern world. A basic measure of education in a community is the level of literacy.
Literacy, particularly in societies with low levels of literacy, gives individuals great power over others and consequent wealth. Gods, monarchs and parliaments usually promulgate their commands in writing. One may ask why something must be done, and the powers that be may answer: it is written, that's why. Writing is a static and enduring form of communication, and people are inclined to have very high regard for theological and legislative texts. In the Exodus, Yahweh is said to have engraved the ten commandments on tablets of stone. The Code of Hammurabi is a famous ancient legal text, also carved in stone. Code of Hammurabi - Wikipedia
Writing is also the foundation of science, providing a permanent record which enables many people to share their observations through space and time. This sharing contributes to the cumulative development of the deeper insights into the working of the world. The insight implicit in this communication is that the recording and communication of information requires strings of discrete symbols.
This insight stands in contrast to the ancient belief that the world is continuous. It is easy to see that the world is made of a huge number of discrete objects, like people, chairs and trees. Despite this, the apparent continuity of motion is enough to convince many of us that the world is continuous, not discrete.
The invention of writing not only enables us to communicate through space and time, writing itself provides us with a very informative model of the world. We begin with the observation that languages are encoded in discrete symbols: phonemes for spoken language, letters for written language, musical notations for music, plans and diagrams for architects and engineers and so on. In all these media, symbols may run together, but they carry information by virtue of their individual character.
We can also see that large texts are made from small texts. Letters are assembled into words, words into sentences, sentences into paragraphs, paragraphs into books, and ultimately into the whole corpus of written and spoken language. Further, since we invented microscopes (which include particle accelerators), we can see that all big things are made out of smaller and smaller particles, until we come to the fundamental particles, which are believed to have no spatial size even though they last through time. In our dynamic world, the most important fundamental particle is the atom or quantum of action. Every event, at every scale, is an assembly of quanta of action.
Quantization was discovered, by the physicist Max Planck at the end of the nineteenth century. Planck found it necessary to assume that action is quantized in order to explain communication between matter and radiation. From our point of view, the quantum of action is so exceedingly small that we do not notice it, but it is there. When the receptors in our eyes receive a single photon of light one quantum of action is executed. Planck constant - Wikipedia
Ultimately, it seems, the appearance of continuity in the world is an illusion arising from the huge numbers fast and tiny steps that make up any process in the world. The world is very much like a cinema. In the cinema we are shown a sequence of still pictures, each differing slightly from its predecessor, but projected so quickly we perceive their sequence as a continuous flow. This is called the phi phenomenon. Our visual system does not resolve the discrete images, it blends them into a flow. Phi phenomenon - Wikipedia
The mathematical theory of communication, which we will examine in chapter 5, explains why communication depends upon discrete symbols: discreteness is necessary to reduce the probability of error.
Back to top2.10 Insight and intelligence
We study coding in a formal way in the context of computation and communication. From a psychological point of view, insight and intelligence are analogous to encoding and decoding.
When we are discussing familiar subjects in our natural language, the coding and decoding are effectively instantaneous. On the other hand, a bystander who does not know our language will not be able to understand what we are saying. From the bystander's point of view, the conversation is hidden or encrypted. Encryption - Wikipedia
The science and art of cryptography aims to make messages unintelligible when people wish to have a secret conversation. This requires that they use a private language, known only to themselves. Since languages are defined by the algorithms used to encode and decode messages, secret communications require encodings that are unique to the authorised recipients. Since the encoding and decoding us usually done with computers, this requires that the encoding and decoding algorithms be computable and that the 'keys' which instantiate the algorithms be unique to the users. Cryptography - Wikipedia
Cryptography is concerned with deliberately hiding and revealing messages, but there is an enormous amount of meaningful information in the world which is not deliberately encrypted, but is nevertheless hard to understand, ranging from crossword puzzles to the causes and cures of disease. Here we are particularly interested in the puzzles which confront scientists trying to understand nature. Our current scientific understanding is a cumulative effort that has been under war for the lifetime of our species.
The mathematical theory of communication shows us how to transmit symbols without error. Once we know how to transmit symbols without error, we can turn to the question of meaning. We learn our first languages effortlessly, and for this reason do not remember much about how we learnt them. Later, when we try to learn new languages, whether natural or technical, we become more conscious of the coding and decoding processes that enable us to communicate.
A key feature of language is the correspondence between sounds, words, things and actions. In any given language, these correspondences are so familiar and have such a long history that we feel that they are natural. When we come to compare different languages, however, it becomes clear that many of these correspondences are not so much natural as arbitrary. Anything can be called anything. We take this to the extreme when we use arbitrary numbers like serial numbers to represent people, appliances and vehicles.
Single words can get us only so far, so there is more to language than just words. The form and order of words is also significant. Natural speakers of a language can easily tell if the words are being used properly, so that phrases and sentences make sense. Learners, on the other hand, must learn such rules of syntax and grammar as there are to help form meaningful sentences. Usually these rules do not cover everything, and there are all sorts of irregular and colloquial constructions which must be learnt one by one. These, and the way the words are pronounced, often differentiate native speakers from learners.
The construction of sentences begins to reveal the true power of language. There may only be a few thousand words in a language, but there are many more ways of modifying these words and stringing them together, so that there is a huge number of possible sentences. Nowak et al: The evolution of syntactic communication
Even a language with only ten words can make about 4 million different ten word strings, although only a fraction of these will make sense. Full blown natural languages can make an effectively infinite number of sentences, and then the sentences themselves can be combined into conversations and lifetimes of communication, to give us an unbounded collection of meaningful expressions.
The essence of language is mapping or meaning, the establishment of correspondences between different things, like a cup and the word cup. A dictionary establishes correspondences between single words and their meanings. We cannot reasonably expect to be able make a dictionary of all possible sentences, although we do construct limited phrasebooks to enable travellers in a foreign land to find food and lodging.
Longer strings of words, like books, establish correspondences between themselves and chunks of the drama of human life, or the anatomy of the body, or the behaviour of the chemical elements. A big library may contain ten million books, and the advent of electronic storage and transmission of words mean that we all have access to billions of documents of all sizes, each of which represents, in one way or another, a tiny slice of life, like the words you are reading now.
All this is to say that human languages are exceedingly complex. One thing we have noticed about ourselves is that our brains are also very large and complex. The reason for this may be the processing power we need to encode and decode the language which we use for everyday communication. The complexity of our languages is dictated by the complexity of the physical and psychological environments in which we live. This complexity also makes natural languages hard to study.
We have distinguished between sources and messages, with the tacit assumption that individual messages are much simpler than their sources. So the things I say every day are infinitesimally small compared to my total being. But we have also noted that large messages can be constructed of small components. From this point of view, I am myself a message, a large and complex symbol passing from one generation to the next. Continuing this line of thought the planet Earth is itself a message within the Universe.
This analogy is possible, because, as we shall see, communication networks are scale invariant. No matter how large they are they are made of smaller networks, and the same principles hold at all networks, large and small. This is an example of symmetry. We have noted that symmetry is the foundation of knowledge. Symmetry with respect to size and complexity is what made it possible for William Blake to see the world in a grain of sand. William Blake: Auguries of Innocence
Back to top2.11 Science and language
Survival depends on knowledge. Simple organisms like bacteria and plants are probably born with all the knowledge they will ever need. Their responses to their environment are relatively automatic, rather like we imagine self driving cars to be, responding in a pre-programmed manner to environmental changes. More complex organisms are born with programmable minds, able to learn from their parents and through experience. Homo sapiens has managed to populate the whole world through learning to deal with almost every possible environment. We have extended our powers of knowledge with the technologies of social organization, hunting, gathering, agriculture, building and all the other arts we have learnt to enhance our lives.
We may understand science as the work of decoding the communications we receive from the natural world which, of course, includes ourselves. The foundation of science is patient observation. One of the first and most important sciences was the study of the heavens, both for navigation and for trying to foretell the future. It took tens of thousands of years of careful study to arrive at our current understanding of the solar system. By long and careful study of chimpanzees, Jane Goodall was able to understand much about the personalities of individual chimpanzees and their interactions with one another and their environment. Jane Goodall - Wikipedia
At the other end of the scale of complexity, physicists, by subjecting fundamental particles to various forces and observing their reactions, have devised a comprehensive theory, called the Standard Model, which explains much of the behaviour of these particles. The standard model is the deepest foundation for much modern technology. Standard model - Wikipedia
When we come to study the world in detail, we often find that natural languages have no words for most of the things we see. So science is a prolific coiner of specialised words, names for the millions of chemical and living species we find, verbs to describe some of the amazing operations these things can do. Catalogue of Life, International Union of Pure and Applied Chemistry
Because scientific language is largely artificial and its terminology is closely mapped to the events that it observes, it had a universal flavour which makes it relatively easy to cross the boundaries between the natural human languages of the world. One of the foundations of this universality is the close relationship between science and mathematics. Mathematics - Wikipedia
Back to top2.12 Mathematics
It has long been recognized that mathematics is a very important language for describing our world. Plato is said to have inscribed over the door of his academy the words 'Let no one ignorant of mathematics enter here'. Nearly 2000 years later, Galileo laid a foundation for modern science with his manifesto:
Philosophy is written in this great book of the Universe which is continually open before our eyes but we cannot read it without having first learnt the language and the characters in which it is written. Wikiquote: Galileo Galilei
Galileo's mathematics was more or less confined to arithmetic and geometry. Since his time, mathematics has expanded greatly. Isaac Newton began a revolution in both mathematics and cosmology when he published his Principia, which documented the force guiding the motions of the planets, making it possible to predict these motions quite precisely. Later his work was updated by Einstein's general theory of relativity, which is itself a mathematical tour de force. Isaac Newton - Wikipedia, General relativity - Wikipedia
The expansion of mathematic began when it began to reflect upon itself. This started when mathematicians began to examine the foundations of the calculus which Newton used to model the heavens. Physics is the study of motion, and we measure the velocity of a motion as a function of time, kilometres per hour, for instance. Another feature of motion that we can measure is acceleration, the rate of change of velocity as a function of time. Since velocity is a function of time, acceleration is a function of a function of time. Calculus - Wikipedia
Calculus brings us face to face with both the infinite and the infinitesimal. But does it make any sense to talk about the ratio of infinitesimal quantities? The historical route to understanding has been notion of a limit. We start off with something large and obvious like the ratio of two finite numbers, and then we examine the trend as the numbers become smaller. On the assumption that this trend will continue no matter how small we make the numbers, we arrive at the notion of limit. The limiting process depends on symmetry, a property that does not change with the size of the numbers to which it applies. This symmetry we might call continuity. Continuity is where nothing happens.
When something does happen we can record it with a measurement. Geometry means earth-measurement, and we imagine its distant origins in the location and measurement of plots of land in an otherwise almost featureless landscape like the floodplain of the river Nile. One measures the length of a line in by counting some unit of length, maybe the queen's foot. Given a certain starting point this system assigns a number to every distance. This is the idea behind coordinate geometry, known since antiquity but formalized by Rene Descartes in the seventeenth century. Cartesian coordinate system - Wikipedia
Clearly there are lot of points in a line which do not correspond to whole numbers of feet or any other unit. It has also been known since antiquity that there are also many points that do not correspond to any fractional or rational number. The real numbers were invented to provide a number for every point in the real line, including those lying between the fractions. Real number - Wikipedia
By numbering the points in a line, we construct a dictionary of points. This changes their character from anonymous points to named symbols. These points become a vocabulary for mathematics, analogous to the vocabulary of a natural language, but infinitely more numerous. This change ultimately led to Georg Cantor's invention of set theory and the development of a foundation for mathematics, now known as formalism, which embraces all possible symbolism, extending from arithmetic and geometry to natural language.
Back to top2.13 Infinity and set theory
Real numbers, were invented to correspond to the points that could not be named with fractional numbers. George Cantor asked: 'how many real numbers are there? More technically 'what is the cardinal of the continuum?'. Cardinality of the continuum - Wikipedia
To find out, Cantor invented and applied set theory. A set, he wrote, is a collection into a whole of discrete objects of our intuition or our thought. The number of such objects in a set is called the cardinal number of the set, and the order in which these objects are arranged is the ordinal number of the set. Set theory - Wikipedia
The central concept in Cantor's theory is the notion of order. Order was already known as an important concept in the decimal representation of numbers. As we move from right to left, the power of each digit is multiplied by 10. This enables to represent large numbers that would be impossible if we used systems that gave the number symbols equal value in any position, like Roman numerals. Positional notation - Wikipedia
Here we may understand Cantor's insight in terms of permutation. The key to Cantor's system is that the cardinal of the set of permutations of a given set is greater than the cardinal of the set. So, he said, let us imagine the set of all the natural numbers. There is no largest natural number, so the cardinal of this set cannot be a natural number, but rather the first number greater than all the natural numbers, which Cantor called "aleph zero", ℵ0, 'the first transfinite number'. ℵ is the first letter of the Hebrew alphabet. Natural number - Wikipedia, Permutation - Wikipedia
Now let us consider all the different ordinal numbers that can be made out of the natural numbers. This number is ℵ0!, where ! is the factorial symbol: n! = n × (n−1) × . . . . 1. This is a very big number, and we can write ℵ0!= ℵ1, where ℵ1 is the second transfinite number.
A key notion in set theory is one-to-one correspondence. Each new permutation establishes a new set of correspondences between the elements of original unpermuted set and the new permuted set. This set of correspondences is called a mapping. Each permutation of the natural numbers is a new mapping of the natural numbers onto themselves.
Mappings are the mathematical way of representing the physics of a dynamic system. All the points of a revolving wheel are continually mapping onto new points of the wheel as it goes round, except for one point in the center. A mapping establishes a dictionary: this corresponds to that. We have noticed in the vast variety of natural languages that almost any sound can be associated with almost any idea. Words, even though they may have very long histories, are essentially arbitrary. Any mapping between words and things would make sense. This idea is called general covariance. It is an important foundation of physics. General covariance - Wikipedia
Mathematics has a number of scientifically valued features. First, it is a universal symbolic language, so nothing is lost in translation. Second, in the numbers, it has an infinite vocabulary, a set of symbols large enough to correspond to every event in the Universe. Third, the only limit on mathematical relationships between symbols, called functions, is consistency.
These features make mathematics an ideal language for talking about God, since the only limit on the power of God is also consistency. Aquinas, Summa I, 25, 3: Is God omnipotent?
2.14. Mathematics and imagination
Cantor's theory mimics the human imagination. We begin with individual ideas or images, and then begin to arrange them in different ways. Mathematically, this is a permutation. Cantor knew that permutation is a very powerful way to generate new structure.
According to the Catholic Church, the Christian revelation was given to us once for all. There is to be no further dialogue with God until the end of the world. The Church has taken it upon itself to represent its silent and invisible God to the world. It calls itself the "vicar of Christ". On the other hand, if the world is divine, we can talk to it as much as we like. Every moment of our lives is guided by our divine environment. Even our bodies are parts of our divine environment, sustaining our consciousness of ourselves.
An authority may utter one sentence and expect everyone to obey, no questions asked, but normal conversation is very different. We have already noticed that it is recursive. I say "we should put it there". You say, "No, it will be in the way when we bring in the thingy". I say ". . . " and so we go on, for years perhaps, until we arrive at a mutually satisfactory resolution.
Our scientific and technological dialogue with the Universe follows a similar pattern, if at a larger and slower scale. Every creature has a spectrum of responses to its environment, sufficient to enable it to survive, given a bit of good luck and no disasters. From a tradesperons point of view, we might call this a spanning set of tools. I go to a job and assess the problem. Do I have the tools to fix it, or am I missing something? If something is missing I am incomplete and at a dead end until I go and get the missing tool to execute the necessary process.
In conversation, however, we can make the tools as we go along, working our way around difficulties by trying to focus on exactly what we are talking about.
With an adequate set of tools, I can modify the environment to fix the problem. In this book we suppose that there is a universal set of tools, defined mathematically by computable functions. We will return to this when we introduce the transfinite network, our proposed model of God.
One of the beauties of language is that we can use it to talk about itself. This has led us to realize that languages like mathematics have boundaries, they are incomplete. This incompleteness makes room for imagination. Unlike a self driving vehicle, we are not limited to a fixed set of algorithms. We can try all sorts of different arrangements in the hope that we will find a good one.
This imaginative assortment is the source not only of the literature of fiction, but of scientific hypotheses. The diference between fiction and science lies not in imagination, but in the observation and testing.
2.15 Writing, time and memory
We communicate across time by writing, that is by encoding our ideas in some form more permanent than the aerial sound waves that join us in conversation. We can carry on conversations in writing for instance, but usually they are much slower because of the time spent encoding, recording, transmitting and decoding messages. Writing - Wikipedia
Writing gives us a key to the thought of people who lived in the past. The earliest records we have are sculptures, paintings, tools and structures from ancient times that are studied by prehistorians. We may see these things as representations of thought rather than representations of speech. About five thousand years ago, people began to represent the sounds of speech with symbols like hieroglyphs and many other scripts that emerged in this period as the idea of writing spread.
Written texts are effectively outside time. Of course the medium in which they are written is physical and exists in time. It is subject to wear and decay, but the formal content can last forever if it is copied into a new medium whenever the old medium fails.
Living creatures face a similar problem. As we age, our bodies are subject to wear and tear and eventually fail. We can reproduce ourselves, however, passing clean copies of our DNA into our offspring so that our species continues generation after generation. Life is written in genes that have carried it across billions of years of time.
This essay relies on about five thousand years of written history to paint a picture of the the evolution of theology. Archaeology and oral history can take us even deeper into the past. Reid, Nunn & Sharpe (2014): Indigenous Australian stories and sea-level change
2.16 "The Word became flesh"
Speech and and writing are just two of the media we use to represent our ideas. All the arts from painting to opera serve a similar purpose, representing ideas, often in dramatic form, to make them accessible and emotionally meaningful. In day to day life we are bombarded with advertising, the product of a billion dollar industry devoted to getting us to think and do what the advertisers want, mostly to spend money on their products, but also to elect them, to obey the law, to help people less well off than ourselves. This art of business often works against enlightened behaviour
The writers of the New Testament performed a dramatic masterpiece of representation when they made the mysterious and rather grumpy God of the Hebrew Bible human in brilliant and charismatic Jesus of Nazareth. The story built around Jesus has captivated billions of people over thousands of years. The Word of God became the Son of God, to reveal God and God's plan for the world and to die a painfully to give satisfaction to God their Father for the crime of the the first humans. This human sacrifice improved the Father's attitude to the human race so that they are going to repair all the damage they did to us as punishment for the original sin. The payoff will not come until the end of the world, however. Hebrew Bible - Wikipedia
The New Testament is a brilliant work of art which has won a place in the world beside all the other dramatic texts that form the foundations of world religions. We can suspect that there are similar works of equivalent power that failed to win the acclaim given to Christianity. The world is a very uncertain place, so success is very hard to plan. Nevertheless a comparison of all the major religions suggests that a charismatic person, with a gift for politics is an excellent starting point. New Testament - Wikipedia
Adding to Jesus' influence was the story of their birth and upbringing, the miracles attributes to them, their excellent knowledge of the Hebrew Bible, particularly their identification of their Father as the God of the Hebrew Bible and the many old prophecies which seem to fit Jesus.The theology proposed here depends far less on an individual personalty and hopefully has the tone of scientific work, the collective work of the people referenced within it. Like Jesus, such people combine genius with charisma and give concrete substance to ideas which are often very abstract and difficult to understand: significant ideas made flesh.
We evolved blindly into the light created by forces we still hardly understand. The world is reasonable and reliable, however, and we have become aware in the last few centuries that we can engineer a good life if enough people will abandon the old ways and accept that the world created us and is perfect for us if we learn to know and live with it.
(revised 6 July 2021)