For at least two and a half thousand years reason has been elevated above all other things. Reason has been elevated above instinct. Reason has been elevated above intuition. Reason has been elevated above God and religion. The single greatest factor in the decline of religion and religious authority has been its inability to deal with the consequences of permitting free rational debate.
What is reason? What is it about reason that gives it such power? Why has it effectively supplanted religion among the cultural elite?
To begin to understand what reason is, we have to go back two and a half thousand years, to the beginnings of philosophy in classical Greece. It was at this time that a community of people began to ask questions about the nature of reality, about human behaviour, about ethics and morality. A question generally implies a debate, and so, when one reads the dialogues of the philosopher Plato, one finds that these are structured as arguments or debates among a small group of people. A question is posed, such as that at the beginning of the dialogue Philebus:
Socrates: Philebus was saying that enjoyment and pleasure and delight, and the class of feelings akin to them, are a good to every living being, whereas I contend, that not these, but wisdom and intelligence and memory, and their kindred, right opinion and true reasoning, are better and more desirable than pleasure .
When one studies these debates, it is clear that the participants already accept that there are styles of argument which are more productive than others. Someone will make a statement, and the other participants will either agree with it, or someone will make a new statement that contradicts or modifies the original position. The discussion proceeds in this way, and more and more material relevant to the discussion is introduced, and reconciled with previous statements, until the participants arrive at a much expanded understanding of the subject under debate. If there are mutually contradictory positions that cannot be reconciled, and participants are being reasonable (that is, playing by the same rules) then this is a genuine impasse that all recognise.
It seems from these very early applications of rational discussion that reason is an agreement about how language is used. For example, if Socrates maintains that the cat is on the mat, and he is being truthful, then no reasonable person would maintain that the cat is not on the mat. If Socrates maintains, as a general property of cats, that all cats are on the mat, then we cannot reasonably deduce that there are any cats in any other place. The recognition that logic is a characteristic of the use of language was made by Platos student Aristotle, who went on to codify the first rules of logic.
A more formal and abstract application of rational argument can be found in mathematics. The most famous of the classical mathematicians was Euclid, who lived in Alexandria sometime around 300BC. It is impossible to under-rate the importance of Euclids Elements. It is said that next to the Bible, it has been the most translated, published and studied book in the Western world. It was still being used as a standard textbook up to this century. The arguments in Euclids Elements offered something miraculous: it was possible to state a proposition, and show beyond any possible doubt that it was true. For all time. For all people. One could argue about beauty and good and evil and God until the cows came home, and get nowhere, but with Euclid you could walk up to Truth and shake its hand. A mathematician could sit down after breakfast, follow the agreed (and largely self-evident) rules of argument, and be famous by lunch-time. He or she could present the proof, and the world would make obeisance. It was a miracle. It had to be divine.
And so it happened. The argument went like this. Everything we see in this world is transitory. Nothing lasts. Nothing is eternal. If, like Plato, we want to ask what is real and true, then we cannot find it in the world we live in. It must exist outside of the phenomenal world of the senses. Mathematical truth exists outside of the world of the senses, and it is both real and eternally true. So mathematical truth must come from another realm of being, what Plato and his followers called the realm of the Intelligible. Just as physical reality is perceived by the senses, so human beings must have another faculty for apprehending the realm of the Intelligible. The followers of Plato believed this came about because we are not unitary beings: we have a divine soul that not only remembers the divine realm from which it has fallen into a corporeal body, but is still capable of apprehending the Intelligible realm, in part through contemplation of mathematics and mathematical truths.
It was at this juncture that philosophy took on mystical flavour that was largely undiluted even as recently as two hundred years ago, and forms the backdrop to Christianity (via profuse borrowings from Aristotle and the Platonist philosopher Plotinus), and the backdrop to the development of modern science (via Copernicus, Galileo, Kepler and Newton, all of whom subscribed to the belief that the mathematics of the Intelligible realm was a key to unlock the mysteries of the physical universe).
Let us now back up from all this profoundly accurate mysticism, and return to rationality, and ultimately, to language. Let us adopt the position that rationality is a structure imposed on the use of language. So the question what is rationality is in part subsumed within the question what is language?. In asking this question at the end of the second millenium we have an advantage over all predecessors. We live in an age when language, via computers, has taken on a new dominance. What began with argument and mathematics has given us a profound understanding of physical law, and in turn that has given us the technology to embody rationality in the form of computer programs. A computer program is encapsulated rationality. This in turn leads to a revolution in our comprehension of language.
This revolution can be stated succinctly. Everyday language is an encoding of the gross laws of physics as they appear to our physical senses. The way in which we structure the world into nameable objects, the relations between these objects, and the time-related processes in which they are involved, are influenced directly the gross physical properties of the world.
Rationality is not arbitrary at all. With some important caveats, it is universal. In order to begin to justify these assertions, it is necessary to look at language in more detail.
Much of the structure of language is spatial and temporal: in, out, behind, before, after, on, under, inside. Verbs not only provide relationships between subjects and objects; they also provide insight into when something happened. I am running conveys something different from I was running or I will run. Adjectives describe many objective attributes of things: big, small, light, heavy, rough, smooth, wet, dry. We understand that there is a degree of subjectivity, but there is an implicit frame of reference: the speaker. We understand that heavy for an average man is about 50 kilos, and less for the average woman. Rough makes me think of sand, or fabric; very rough makes me think of tree bark. I understand that when a French polisher says rough, it probably means not quite a mirror finish.
There is a great deal more to language than objective description. There are various social modes of inquiry - how are you, how do you feel, are you well, and so on. I can talk about subjective feelings, beliefs, opinions, but here I am on shaky ground. Much discussion centres around areas of subjectivity; people like to calibrate their feelings, beliefs and internal states with those of others. I cant be certain what a person means when they say they have a thumping headache, because there is no way to share the experience. I have to refer to the memory of my own thumping headaches, and my memory of how I felt at the time. We know that the subjective experience of pain is extremely variable if only because people behave in very different ways - for example, we have many records of life and conditions in the British army in the early nineteenth century that will seem completely incredible to the modern reader.
Language is capable of encompassing much of what we experience, but it functions most efficiently in the realm of shared physical reality. This is the region of consensus. If the cat is on the mat for me, it is one the mat for you. If the cat is in the box, it is not out of the box. If the bottle is empty, it is not full, and if it is full, it is not empty. We can see the structure of rational discussion and logic emerging in simple propositions about shared physical existence.
Real life has boundaries. Lines on maps have finite width, and sometimes we cannot tell which country a tree lies in. The steel ruler I use to measure your height expands in the heat. Already we are beginning to think about ideals: the ideal line with no width, the perfect circle, the frictionless plane, the inelastic string. Mathematics begins where real life leaves off, by providing us with ideal objects with perfectly defined ideal properties.
Take the idea of containment. A container is something like a box with a lid that can contain things. I can put something in the box. I can take something out. I can ask how many things are in the box. I can even put one box inside another box. Real boxes are messy - they have lids, things can be half in and half out, I cant put an elephant in a matchbox, and so on. The mathematician creates an ideal container called a set. A set is a pure abstraction of the idea of containment. I can put things in a set, and take things out. I can have a set composed of all even numbers, or a set of all people with green eyes. Much of mathematics can be formulated in terms of sets.
The point here is that ordinary language is rooted in our understanding of basic properties of the physical world. Mathematics takes the informal, imprecise language of everyday life and turns it into a formal language that applies to ideal objects with simple and totally defined properties. There are agreed methods of reasoning (the modus ponens) that allow mathematicians to get from A to Z - if A is known to be true, and there is a valid argument that gets us from A to Z (via B, C, D, .), then Z is also true. Do not be intimidated by the unfamiliar symbols in mathematics. Mathematics is a linguistic exercise, and its symbols are no more alien than the letters in the Cyrillic, Greek or Hebrew alphabets. However, mathematics may be a linguistic exercise, but there is a miracle hidden in it.
The miracle (and it really does seem to be miraculous, no matter how often it is contemplated) is this. Take a simple mathematical model, in the belief that in some way the behaviour of the real world is guided by simple underlying principles. Let the choice of model be inspired by a deep personal intuition. Apply the model to some aspect of the behaviour of the real world. Check the predictions with experiments. Reel back in astonishment. They fit.
The most famous example of this, although it did not take place in the rather naïve order described above, took place in the sixteenth and seventeenth centuries. Although the planets in the solar system had been observed for millennia, no one had produced an accurate model that accounted for their motions. Part of the reason for this was the long-held belief that the planets and sun moved around the Earth. Another part of the reason was the lack of sufficiently accurate observations. The second century Graeco-Roman astronomer Ptolemy had attempted a mathematical model based on circular orbits with epicycles, smaller circles that moved around the larger - this attempted to account for the fact that, seen from the Earth, the planets sometimes appear to move backwards along their orbits (moving retrograde). It did not work well by modern standards, but it was the right kind of idea, and it was not contradicted by the rough measurements available.
In the sixteenth century, the Danish astronomer Tycho Brahe (1546 - 1601) spent his life creating, with the crudest of instruments, a detailed catalogue of observations which he bequeathed to his pupil Johannes Kepler (1571 - 1630). It was Kepler, using the heliocentric ideas of Copernicus and the observations of Brahe who proposed the answer, and declared his three laws of planetary motion: that the orbits were elliptical with the sun at a focus, that a planet swept out equal distances in equal times, and the period of the orbit depended only on the distance from the sun.
It was Isaac Newton (1643 - 1727) however who performed the tour-de-force. Kepler had found an accurate rule that enabled one to predict the positions of planets. He had not found an explanation for why the orbits had that form. Given an arbitrary body set in motion about the sun, he could not predict in advance the path it would take, clearly a requirement for travelling about in a space ship, or for sending a satellite to Mars.
It was Newton who deduced the laws of motion and the law of gravitation, and who developed the mathematical tools necessary to solve general problems concerning gravitating bodies of any kind. His Philosophiae Naturalis Principia Mathematica, the Mathematical Principles of Natural Philosophy, has been dubbed the most important scientific text of all time. Not only did it solve specific problems, it provided genuine and deep insight into the structure and mechanism of the solar system, something that only a few hundred years earlier had been regarded as part of the divine realm. Newton took the first giant step in removing God from the creation. His was the first major act of disenchantment. He did it all in his head, and he told other people how it worked, not in general, but in detail, so that any person could understand and reproduce his method and calculations. He told other people how he did it by using marks on paper. By using language. We can still read his thoughts today, and reproduce his reasoning and calculations hundreds of years after his death.
This is the conclusive proof, if you are not already convinced, that mathematics is a language. A person makes marks on paper. Another person reads them. Given adequate intelligence and background, the second person can fully comprehend the substance and detail of what the first person is trying to convey (this is certainly true in most areas of mathematics).
We have now arrived at an important point. We began this essay by considering rationality as a convention in the use of language, and followed this convention into its formal use in mathematics. We have arrived at the magical discovery that there is a congruence between the formal use of language and the physical world we live in. There is nothing obvious about this. It took the human race hundreds of generations to arrive at this discovery. It is a discovery that owes as much to the rational mysticism of platonism and neoplatonism as any other human discipline. This congruence is an example of simulation.
The physicist David Deutsch has pointed out that our brains obey the laws of physics. There is no evidence that they do not, and a great deal of evidence, in the form of detailed models of cell function, that they do. But a human brain (such as Isaac Newtons brain) can compute the paths the planets will take in the sky. We have also been able to manufacture complex machines that will do the same thing, and they also obey the laws of physics. (It would be impossible to design and manufacture a computer without an exceedingly good knowledge of the laws of physics in the first place.)
This means that a part of reality (a brain, a computer) can simulate another part of reality (the solar system) in detail. Deutsch calls this property, and it is a property of the real world we live in, self-similarity. That is, parts of reality can simulate, to an arbitrary degree of precision, other parts of reality.
To give an example, in the University of Oxford there is the worlds most realistic simulation of a human heart, composed of millions of simulated nerve and muscle cells, which in turn are composed a dozens of simulated ion channels in a simulated cell membrane. The simulation is now so accurate it can be used to study heart disease and the effects of drugs. Simulations are now used routinely in many areas of industry because it is less costly and just as accurate to simulate a system. Deutsch comments:
Thus reality contains not only evidence, but also the means (such as our minds and our artifacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical. In those symbols - in our planetariums, books, films and computer memories, and in our brains - there are images of physical reality at large, images not just of the appearance of objects, but of the structure of reality. There are laws and explanations, reductive and emergent. There are descriptions and explanations of the Big Bang and of sub-nuclear particles and processes; there are mathematical abstractions; fiction; art; morality; shadow photons; parallel universes. To the extent that these symbols, images and theories are true - that is, they resemble in appropriate respects the concrete or abstract things they refer to - their existence gives reality a new form of self-similarity, the self-similarity we call knowledge.
Deutschs point here is profound. Once we abandon the Cartesian duality of mind and external reality, and treat our brains and computers as physical devices operating according to physical laws, then the ability of one physical system to simulate another comes as a surprise. It isnt in any way obvious that this should be so. It is possible (Deutsch gives an example of a chess board world) to think of worlds that operate by laws which are not capable of supporting this self-similarity.
Deutsch also points out that this property is essential for life as we know it, in that living organisms embody knowledge of their environment in order to maintain their internal coherence. A universe without the self-similarity property would not be capable of supporting living organisms of any kind, far less human beings.
Deutschs arguments are not obscure. They derive from a long-standing question that dates from the origins of computer science: what kinds of computation can a computer carry out.
The notion of a computation or an algorithm is not well defined, and in the 1930s there were a number of proposals. That is, a number of mathematicians attempted to formalise their intuitive notions of computation, based on the kinds of paper-and-pencil computations that people had been doing for centuries. These quite different proposals were subsequently proved to be equivalent - that is, if you could compute something by one method, you could compute it by any other. Although there was no way to prove that this was the limit to computation, the limit was embodied in something called The Church-Turing Hypothesis, after the mathematicians Alonzo Church and Alan Turing. Without going into the details, one can liken this model of computation as equivalent to what you can do with a large piece of paper, a pencil, and a rubber. You can use silicon and electrons instead, and it will go a lot faster, but it cant compute anything that the paper and pencil cant.
We know that computers can be used to simulate physical systems. The question is, given the constraint on computation imposed by the Church-Turing Hypothesis, is there any limit to the kinds of physical system that can be simulated? This is a completely legitimate and well-posed question. Is there anything we know of in the laws of physics which cannot be simulated, even in principle.
The Nobel prize winning physicist Richard Feynman was interested in this question. He realised a Church-Turing computer could not simulate a quantum mechanical system. This is important because the laws of physics are quantum mechanical. At the level of everyday life we do not observe many of these effects, and we have approximations (classical physics) which work at this level, but classical physics is just an approximation, a convenient rule of thumb that simplifies calculations involving objects on the scale of human beings. A Church-Turing computer can simulate behaviour at this human scale, but not behaviour on the tiny quantum mechanical scale. Imagine what it would be like if we could use computer simulation to simulate the behaviour of any system composed of objects larger than a billiard ball, but nothing smaller. What a bizarre situation! Certain types of system would be essentially unknowable in principle. We would live in a universe with a cosmic censor inking out parts of reality, and we'd never really be sure where the precise boundary between the knowable and the unknowable was.
This is not the kind of question that had ever been asked in the past. There had always been some kind of naive assumption of "Seek and ye shall find", even if it meant, like John Dee, we had to implore God for the answers. The idea of a structural Cloud of Unknowing built into the fabric of reality had never occured to anyone. The fact that we had already been able to perform basic mathematical calculations about quantum mechanical systems such as the hydrogen atom suggested that the situation was not as bad as it might be (that is, our brains can simulate the hydrogen atom in detail), and Feynman was able to propose a simple computer-like system that did simulate other quantum mechanical systems.
In 1985 I was given a paper by a colleague who had just returned from a visit to the University of Oxford. The paper was written by someone called David Deutsch, and in it he proposed that as computers were physical devices (just as pencil and paper is physical), then the types of computation possible would ultimately be limited by the kinds of physical devices we can build. He then went on to show, using the known laws of quantum mechanics, the theoretical existence of a Universal Quantum Computer, a computer based on quantum mechanics that could simulate any quantum mechanical system. The old Church-Turing Hypothesis had been formulated by mathematicians who had intuitively adopted models of computation based on everyday life (paper-and-pencil). The real world does not work that way.
Deutschs paper had an immense impact on me. Nearly fifteen years later it has had an immense impact on physics and computer science. People are building quantum computers. Deutsch has been awarded the Dirac Prize in recognition of the importance of his work. The theoretical framework for quantum computing is being laid down. We are as far from a useable quantum computer today as Alan Turing was from a Pentium PC, but the impact is far more than carrying out computations. This work is transforming our view of physics. In trying to explore the properties of complex quantum mechanical systems from the point of view of representing, computing and transmitting information, many new insights are being made. Some of these (for example, insights and experiments into a quantum mechanical phenomenon called entanglement or non-locality) will almost certainly lead to breakthroughs in our understanding of reality.
It should be clear now that the phenomenon that Deutsch calls self-similarity isnt a vague metaphysical principle. It is derived directly from what we know about the theoretical ability of a physical system (the universal quantum computer) to simulate any other physical system. This has been formulated by the physicist and mathematician Roger Penrose as The Turing Principle. In this form it is a statement as physically significant as Newtons Laws of Motion, or the Laws of Thermodynamics, or Einsteins Equivalence Principle. The Turing Principle is:
There exists an abstract universal computer whose repertoire includes any computation that any physically possible object can perform.
In his book The Fabric of Reality, Deutsch proposes a number of variants, the strongest of which is:
It is possible to build a virtual reality generator whose repertoire includes every physical possible environment.
That is, we can build a system, a mechanism, out of physical matter available to us which can perfectly simulate any part of reality. It can simulate reality to the extent that (given an arbitrary clever programmer) if we were to interact with it, we would not know that it was a machine.
This is the idea of simulation/self-similarity in a form where it is a principle of physics. The laws of the physical universe appear to be constituted such that a physical system can simulate any other physical system on any scale to any degree of precision. This principle is a necessary condition for the existence of living organisms as we understand them - a living organism is a limited simulator of reality. How does a bird fly if it does not embody deep and extensive knowledge about air and gravity?
It now becomes apparent why the universe is comprehensible: it is comprehensible because has the property that it is possible to create physical devices that can simulate reality. The human brain is such a physical device.
The idea of self-similarity has a long history in European thought. During the Renaissance, when many (now considered) occult and hermetic ideas were current at the highest levels of intellectual debate, this idea was expressed in the form of the concepts of the macrocosm and the microcosm. The microcosm, or human being, was believed to be a simulacrum of the creation, and this provided a mechanism whereby the powers of the macrocosm (the stars and planets) could act on human beings. Conversely, a human being could exploit the congruence to influence the macrocosm, and some magical or theurgic systems exploited this idea that a human being could affect the supernal realms of the divine.
Figure 1: The Macrocosm and Microcosm (from a title page by Robert Fludd)
The idea of self similarity was almost certainly suggested by the Bible, which states
And God created man in His image, in the image of God he created him; male and female he created them.
The idea was further elaborated in Jewish Kabbalah in many differing forms, too complex to detail here, in which a human being was seen as a complete functioning simulacrum or embodiment of the divine powers that provided the dynamic basis for the visible creation. Another variant on the idea can be found in the legendary (but nevertheless highly influential) Emerald Tablet of Hermes Trimegistus, which again implies that the lower world is in some sense congruent with the upper world.
Another idea of great antiquity is that of the world as a text in the most literal sense. Jewish mystics believed that the whole of creation was detailed in the Torah (the first five books of the Bible), and hence all the hidden mysteries of the creation were to be found there. The Kabbalist would study the Torah in the expectation that with divine guidance, operational mysteries such as secret names would be revealed. These names could then be used in practical and mystical workings. It was this belief in the operational potency of names (subroutines, procedures, URLs) concealed in the text of the Torah that gave rise to the title Baal Shem, or Master of the Holy Name.
This ancient idea of "the world as text" is no longer implausible; it is guaranteed by the Turing Principle. Consider the idea that we can decide to build a successively larger and larger computer to simulate more and more of reality. Perhaps we need an interlinked network of such megacomputers. This detail hardly matters - we can consider a network of computers to be one extremely large computer.
This computer is going to need a program. This program will embody all the laws of physics (we already know how to embody many of these laws), and so it will describe how every subatomic particle in the universe simulation will behave. The Turing Principle guarantees that we can write such a program. The important point is that the program does not have to grow in proportion to the size or complexity of the system under simulation.
To give an example, suppose I want to simulate how two million particles interact via gravity. The program that simulates two or three particles is just as complicated as the program that simulates two million, and we know we can simulate two or three. The larger the number of particles, the more physical resources such as memory I will need in my computer, and the longer the computation will take, but the program does not become more complicated.
As we simulate more and more of the universe, we will reach a point where the program does not become more complex. We can then print it out onto paper and deposit it in a library. This program contains everything you need to know to carry out a perfect simulation of reality. Of course, it needs a computer to run on, so it would be useful for the program to contain a complete simulation of the computer it was designed for. If this sounds improbable, consider that many computer games written in the early 1980s were written for computers that no longer exist, so enthusiasts have written simulators for most of these early computers, and run these games on current PCs, which provide perfect simulations of early Atari and Sinclair computers.
So there we have it: the world as a text. The idea is not in the least far fetched. The Turing Principle guarantees that such a text can be created. A computer program is a purely rational exercise, akin to writing a proof in mathematics (when I worked as a computer science lecturer in the University of London, first-year students were taught to prove their programs correct by using standard mathematical proof techniques).
I am now in a position to propose an answer to the question posed by the title of this essay: why is it reasonable to be rational?
Rationality is a specialised use of language that mirrors properties of physical reality. In the form of mathematics, rationality leads to the ability to carry out simulations of physical systems, and this ability to simulate reality led directly to the scientific and technological revolution of the last three centuries.
An even more specialised form of mathematical language is the computer program, and this leads in turn to even more sophisticated simulations of reality. These simulations are now used routinely to design aeroplanes, to crash-test virtual cars, to evaluate the effects of virtual drugs, to design new medicines. The most sophisticated physical simulator we know of is the human brain: it can fly aeroplanes to the edge of space at several times the speed of sound, drive cars at hundreds of miles an hour, compute the trajectory of a tennis or cricket ball flying at over a hundred miles an hour, perform the most incredible gymnastics and acrobatics, juggle several balls, balance the most incredible assortment of junk, climb vertical surfaces, and spot a member of the opposite sex in the most improbable circumstances. We can echo the sentiment of Hermes Trimegistus that A great miracle, Asclepius, is man.
It is reasonable to be rational because the laws of physics make simulation possible. Living beings exploit this fact in order to exist. There would be no living beings if such simulation was not possible. Knowledge, whether genetic or acquired, whether dispositional or propositional, is the basis for survival in a hostile and changing environment. A paramecium or amoeba is as miraculous on a small scale as a human being, in their ability to transform simple substances into complex proteins and enzymes, their ability to reproduce and so pass on the knowledge of how to use the raw stuff of the world to maintain coherency. Life is no less a miracle and no less a wonder just because it is rationally comprehensible. Its miracle is based in something just as mysterious as a divine craftsman: the miracle of self-similarity, the congruence of part to whole, an extraordinary closure of the idea that we are made in the image of God.
Rationality is a way of using language such that language can be used to simulate complex physical systems. The rational use of language provides us with access to the deep structures underlying physical reality, such as the Hilbert Space model of quantum mechanics. We can use language to create programs for universal simulators. The Neoplatonic idea that reason has the power to grasp the forms or archetypes underpinning reality, an intuition based on an inspired guess about the significance of reason and mathematics, is validated.
There is more.
The Turing Principle states that complete simulation of any physical system is possible. With sufficient resources, it would be possible to simulate the universe. From the point of view of a self-conscious organism simulating the universe, the ancient mystical goal of the union of microcosm and macrocosm would be achieved. To simulate the universe I would simulate you, perfectly, and I would simulate myself, perfectly. I would have perfect knowledge (within the limits of physical law) of all that is. Deutsch equates this point with the Omega Point the physicist Frank Tipler, who owes a debt to the Christian philosopher and theologian Teilhard de Chardin. Western mysticism still exists against a dualistic backdrop of body and spirit, and the belief that the subject of mysticism is spirit, where true knowledge can be found. The creation is disenchanted, a dead thing, mechanical. The human body is a dead thing, mechanical, a conscious corpse, as one of the books of the Corpus Hermeticum puts it. This is a relic of beliefs that can be found in the writings of Plato, and are probably much older.
Deutsch presents us with a monist view of a world in which there is no Platonic Intelligible, no metaphysical dual of the real world, no hidden realm of secret knowledge to be wrested from angels by the power of secret names. His is a purely rational world, but it is no longer a disenchanted world, a world of clacking billiard balls and clicking gears. It is a world of infinite quantum parallelism, of non-locality, of entanglement, of multiple unseen dimensions, of black holes and space-time singularities. In a non-local, entangled world, there are no billiard balls. There is no matter. We have mathematics (the axiomatic Hilbert Space formulation of quantum mechanics) that provides superb simulations of this world, but the mathematical entities do not seem to correspond to any simple physical intuition. The idea that there are things with properties turns out to be unsustainable. Where there are properties, they dont seem to exist anywhere in particular. It is a world a thousand times more mysterious and magical than anything to be found in the most extravagant works of mysticism.
But, the diehard dualist will protest, It is still rational, it is still mechanical.
There are arguments about that too. Roger Penrose has made the case, using rational argument of course, that human mathematical reasoning exceeds what is possible using reasoning automata. The sophistication of his argument excites admiration, and whether he is correct or not is to some extent, irrelevant.
It is irrelevant because whether we are automata or not, creativity is still creativity. Beauty is still beauty. Kindness and compassion are still kindness and compassion. Everything we know, in our genes, in our books, in our cultures, in our heads, keeps us alive on a lump of rock flying through an endless vacuum, keeps us one step ahead of the scythe. Set against the backdrop of geological time, it is a wild and desperate explosion of protoplasm that has reached the critical point of any simulation, the ability to include limited simulations of itself. We are self-conscious.
In the unimaginably vast and mysterious universe where we live we will find our angels and our devils, sages who are the living embodiment of wisdom, works of mysterious knowledge, and perhaps, the text that is the text of the world. We will find every imaginable form of life. All this is suggested by the Turing Principle, because it states that the universe is self-similar. This principle was arrived at, not through abstruse metaphysical arguments, but through a conceptually simple application of known laws of physics to the process of computation. The answer to the question: can one quantum mechanical system perfectly simulate another quantum mechanical system, is yes. This is an extraordinary and unexpected result of straightforward mathematical reasoning. As a conceptual breakthrough, it is as profound as Newtons Laws of Motion. The ability of one part of the universe to simulate another is, in the most abstract sense, the phenomenon we call life. Life is as basic and universal a principle as gravitation. It can and will exist everywhere, in every possible embodiment.
Perhaps even in every imaginable embodiment, because imagination is a physical process that is self-similar to a thing imagined. That is, what is imagined can be simulated. A cave picture (a physical object) of a buffalo is self-similar to a buffalo (a physical object). Computer animations are self-similar to entities in the human imagination that is how planes are designed these days, and questions about the physical behaviour of a complex flying object are now easier to answer with a computer simulation than with a wind tunnel. What we do today with silicon, we will do tomorrow with DNA. Every human artefact on this planet is a simulation of an imagined object and began its life in the human mind. There is little that is impossible. The Turing Principle restores enchantment to the universe, because it suggests that the phenomena of life and creativity are in physical fact something that human beings have always believed to be true: a well of unfathomable possibility, an endless unfolding of wonder and mystery.
One of the finest documents of the Renaissance is Giovanni Pico della Mirandolas Oration on the Dignity of Man. It still has the power to move:
God the Father, Supreme Architect of the Universe, built this home, this universe we see all around us, a venerable temple of his godhead, through the sublime laws of his ineffable Mind. The expanse above the heavens he decorated with Intelligences, the spheres of heaven with living, eternal souls. The scabrous and dirty lower worlds he filled with animals of every kind. However, when the work was finished, the Great Artisan desired that there be some creature to think on the plan of his great work, and love its infinite beauty, and stand in awe at its immenseness. Therefore, when all was finished, as Moses and Timaeus tell us, He began to think about the creation of man. But he had no Archetype from which to fashion some new child, nor could he find in his vast treasure-houses anything which He might give to His new son, nor did the universe contain a single place from which the whole of creation might be surveyed. All was perfected, all created things stood in their proper place, the highest things in the highest places, the midmost things in the midmost places, and the lowest things in the lowest places. But God the Father would not fail, exhausted and defeated, in this last creative act. God's wisdom would not falter for lack of counsel in this need. God's love would not permit that he whose duty it was to praise God's creation should be forced to condemn himself as a creation of God.
Finally, the Great Artisan mandated that this creature who would receive nothing proper to himself shall have joint possession of whatever nature had been given to any other creature. He made man a creature of indeterminate and indifferent nature, and, placing him in the middle of the world, said to him "Adam, we give you no fixed place to live, no form that is peculiar to you, nor any function that is yours alone. According to your desires and judgement, you will have and possess whatever place to live, whatever form, and whatever functions you yourself choose. All other things have a limited and fixed nature prescribed and bounded by Our laws. You, with no limit or no bound, may choose for yourself the limits and bounds of your nature. We have placed you at the world's centre so that you may survey everything else in the world. We have made you neither of heavenly nor of earthly stuff, neither mortal nor immortal, so that with free choice and dignity, you may fashion yourself into whatever form you choose. To you is granted the power of degrading yourself into the lower forms of life, the beasts, and to you is granted the power, contained in your intellect and judgement, to be reborn into the higher forms, the divine."
Imagine! The great generosity of God! The happiness of man!
Freedom is about unconstrained choice. We are self-simulating simulators, and within the limits of physical law we can be (simulate) anything we want. Picos Oration was never more valid than now.
And the answer to the question: why is it reasonable to be rational? Rationality is how human beings become self-similar to the universe.
David Deutsch, The Fabric of Reality
[In a lifetime of reading, this is the most important book I have read. His style is terse, incisive, and lucid, and he tears into his subject matter like a terrier after rabbits. This isnt a low-brow popularisation of speculative physics. This is the work of a genius who takes as much pleasure in exploring the arguments of the Inquisition vs. Galileo as he does in demolishing solipsism and explaining the two-slit diffraction experiment better than anyone else.]
Feynman, Leighton, Sands, The Feynman Lectures on Physics Vol III, Addison Wesley 1965
[This was my first quantum mechanics textbook. Possessed of a vast physical intuition, Feynman exposes the conceptual simplicity and beauty of QM by starting where most expositions leave off, with the Hilbert Space formulation of QM. On the basis that Any fool can make something complicated, this is a masterpiece of exposition.]
The New Physics, ed. Paul Davies, Cambridge University Press 1989
[This is a series of monographs by leading contemporary physicists. Pitched at a similar level to articles in Scientific American, it is an overview of progress in the last two decades. One paper in particular caught my attention, because it presents in a concise, axiomatic form, the Hilbert Space theory of quantum mechanics. This theory is probably the greatest intellectual achievement of the 20th. Century, not because it is hard, abstruse, and unimaginably complex, but because it is extremely simple, and can be presented in a few pages. Unfortunately, very few physicists have bothered to do this. However, Abner Shimony has, in Conceptual Foundations of Quantum Mechanics]
The Structure and Interpretation of Quantum Mechanics, R.I.G. Hughes, Harvard University Press, 1989.
[This book isnt a light read, and requires an understanding of Hilbert Spaces (multi-dimensional vector spaces with a complex field) along with the normal mathematical notation. It explores not only what QM is, but what it means.]
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