TheFabricOfReality
- Another one of my favorite authors. Not as good as Beginning of Infinity, but very interesting. Got a little wacky in places.
Thanks to a succession of extraordinary discoveries, we possess some extremely deep theories about the structure of reality. the book aims to develop a world view that takes these ideas seriously (for what they actually say) and incorporate them into a comprehensive view of reality. Our best theories are not only truer than common sense, they make far more sense than common sense does. We must take them seriously as EXPLANATIONS of the world. We can reach the greatest understanding by taking them together.
- Seems odd that this view point should be in anyway controversial, yet in practice it is. Each of these theories, when taken seriously, have very counter-intuitive implications All sorts of attempts have been made to avoid these implications (eg; ad hoc modifications or interpretations of the theories, or arbitrarily narrowing the domain of applicability) or using them only as a tool for prediction not as an explanation. This book is an investigation of what reality would look like if they were true.
- Facts cannot be understood just by being summarized, the can be understood only by being explained. Fortunately our best theories embody deep explanations in addition to accurate predictions. Explanation is the entire content of a theory. the most valuable part of the theory is that it explains a reality that we cannot directly perceive.
- Some philosophers – and even some scientist – disparage the role of explanation in science. However the overwhelming majority of theories are rejected b/c they are bad explanations not b/c they fail experimental tests. (eg: eating a kg of grass is a cure for the common cold)
- To say that prediction is the purpose of a scientific theory is to confuse the means with the ends. Passing experimental tests is only one of many things a theory has to do to achieve the real purpose of science, which is to explain the world.
- Explanation is a strange sort of food – a larger portion is not necessarily harder to swallow. It is hard to give a precise definition for explanation or understanding. They are more about the "why" than the "what"; about how things really are rather than how they appear to be.
- At present we know of nothing that is capable of understanding an explanation – or of wanting one in the first place – other than a human mind.
- We understand the fabric of reality only by understanding theories that explain it.
- Our theories are increasing in both depth and breadth. Breadth makes them harder to understand, depth make them easier to understand. One thesis of this book is that (slowly but surely) depth is winning.
- Higher level subjects are studied because under special circumstances the ridiculously complex behaviors of the vast number of particles involved resolves itself into a measure of simplicity and comprehensibility. This is called emergence: high-level simplicity emerges from low-level complexity.
- The structure of scientific explanation does not reflect the reductionist hierarchy. (B/c of emergence) There are explanations on every level of the hierarchy. If fact the very concept "high level" vs "low level" are misnomers. The laws of biology are high-level emergent consequences of the laws of physics, but logically, some of the laws of physics are then "emergent" consequences of the laws of biology.
What makes a theory more fundamental and less derivative is not closeness to the predictive base of physics, but its closeness to our deepest explanatory theories.
Our deepest theories are:
- Quantum Theory
- The Theory of Evolution
- Epistemology
- The Theory of Computation
Deep and diverse connections have been discovered between the basic principles of these theories. It has become impossible to reach our best understanding of any one of them without also understanding the other three. Taken together they form a coherent explanatory structure that is far reaching. Claim: Our scope of understanding begins to be fully universal. This "Theory of Everything" has a far wider scope than the "theory of everything" that elementary particle physicists are seeking. The fabric of reality does not consist only of reductionist ingredients such as space, time and subatomic particles, but also for example, life, thought, and computation.
- The basic experiments that demonstrate QM and the necessity of many worlds are austere and they require neither specialized scientific instruments or any great knowledge of math or physics. The essentially involve nothing but casting shadows. The patters of light and shadow that an ordinary light can cast are very strange. Explaining them requires not just a new physical law, but a new level of description and explanation that goes beyond what was previously regarded as being in the scope of science.
- Careful experiments show that light does not always travel in straight lines, sometimes it bends.
- How ductile is light ? How fine a thread can it be drawn into ? Gold can be drawn into threads one 10-7 m thick. It turns out that light is not as ductile as gold.
- The interfering entities behave exactly like photons … except that they cannot be seen. It appears that photons come it two sorts "tangible" and "shadow" photons. Tangible are the normal photons we can see. Shadow photons are invisible, detectable only indirectly through their interference effects on the tangible photons. What we infer is that each tangible photon has an accompanying retinue of shadow photons, and when a photon passes through one of the four slits, some of the shadow photons pass through the other three. Experiments imply that there must be at least a trillion (1012) shadow photons for each tangible one. The only thing in the universe that shadow photons can be observed to affect is the tangible photons that it accompanies. Shadow photons would go entirely unnoticed were it not for the phenomenon of interference. Reality is a much bigger thing that it seems, most of it is invisible. We, with our instruments, can only observe the tip of the iceberg.
- Hence there is some sort of shadow barrier at the same location as the tangible barrier. It takes no great leap of imagination to conclude that the shadow barrier is made up of shadow atoms that we already know bust be present as counterparts of tangible atoms in the barrier.
- The behavior of objects that we observe can be explained only if there are unobserved objects, with very specific properties, present. Single particle interference unequivocally rules out the possibility that the tangible universe around us is all that exists.
- This talk of tangible and shadow atoms and photons is only compelling to those who seek explanations. This worldview is much more integrated, and makes more sense in so many ways, than any previous worldview, and certainly mare than the cynical pragmatism which too often nowadays serves as a surrogate for a worldview among scientists.
- Our primary objective is to understand reality.
- "The possible" cannot interact with the real: non-existent entities cannot deflect real ones from their paths.
- Every subatomic particle has counterparts in other universes and is interfered with only by those counterparts. It is not directly affected by any other particles in those universes. Therefore interference is observed only in special situations where the paths of a particle and its shadow counterparts separate and then re converge (eg: when the photon and its shadow photon hit the same part on the screen). The detection of interference between any two universes requires an interaction to take place between ALL the particles whose positions and other attributes are not identical in the two universes.
- "Observation destroys interference" is very misleading in three ways -) it suggest some form of psychokinetic effect of the conscious "observer" on basic physical phenomena, though there is no such effect -) the interference is not "destroyed" it is just (much!) harder harder to observe b/c doing so requires controlling the precise behavior of so many particles. -) it is not just "observation" but any effect of the photon on its surroundings that depends on which path the photon has taken that does this.
- We do not need deep theories to tell us that parallel universes exist – single particle interference tells us that. It turns out the QM naturally implies and refers to parallel universes (in the superposition of wave functions). IF our best theory of physics did not refer to parallel universes, it would merely mean that we needed a better theory, one that did, in order to explain what we see.
- The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation – the only one that is tenable – of a remarkable and counter-intuitive reality.
- I may feel subjectively that I am distinguished among the copies as THE "tangible" one, because I can directly perceive myself and not the others, but I must come to terms with the fact that all the others feel the same way about themselves.
- Summary: in interference experiments there can be places in a shadow-pattern that go dark when new openings are made in the barrier casting the shadow. This remains true when the experiment is performed on individual particles. A chain of reasoning based on this fact rules out the possibility that the universe we see around us constitutes the whole of reality. In fact the whole of physical reality, the multiverse, contains vast numbers of parallel universes.
- Not clear which is stranger the behaviors of the shadows itself, or the fact that contemplating them can force us to revise so radically our conception of the structure of reality.
- Observations of every smaller physical effects have been forcing ever greater changes in our world-view
- Solipsism (that only our mind exists) cannot be logically disproved. Since solipsism is an infinite number of related theories are logically consistent with perceiving any possible observational evidence, it follows that you can logically deduce nothing about realty from observational evidence alone. If scientific reason does not amount to logical deduction from evidence what does it amount to?
Theories that are more capable of giving more detailed explanation are automatically preferred.
- A problem (when the explanations of our best theories seem inadequate) is like an ecological niche, and a theory is like a gene or a species which is being tested for viability in that niche.
- Popper's theory that knowledge can grow only through conjecture and refutation (or criticism) "Evolutionary epistemology" and is an important unifying insight.
- In science and biological evolution, evolutionary success depends on the creation and survival of objective knowledge, which in biology is called adaptation.
- There are a large class of theories related to solipsism, differing on where they draw the boundary demarcating the part of reality which is comprehensible and that to which science is inapplicable.
- Against Solipsism: Joke/argument against solipsism: Professor who give a lecture in defense of solipsism. The students agree with every word of it. 'One so seldom has the opportunity to meet fellow solipsists'. What actually did the students agree with? If they adopt the professors opinion, they will not be solipsists, and if they become solipsists, they will have become convinced that the professor is mistaken. If we take solipsism seriously – if we assume that is is true and that all valid explanations must conform to it – it self-destructs. How does solipsism, taken seriously, really differ from the common-sense rival, realism? The difference is based on no more than a renaming scheme. The solipsists description of the world is in terms of interacting thoughts rather than interacting objects. But the thoughts are real and interact according to the same rules that the realist says govern the interaction of objects.
- Explanations are not judged by how they were derived, but only by their ability, relative to rival explanations, to solve the problems they address.
- Even purely mathematical arguments derive their reliability from the physical and philosophical theories that underpin them.
- If something can kick back, it exists. Kick is when the object affects us in ways that require independent explanations.
- The claim was made above about the 'inescapable' conclusion that something must be coming throughout the second pair of slits to prevent light from reaching the screen from the first. It is not logically inescapable, for if we were not looking for explanations we could just say that the photons we see behave AS IF something passing throughout other slits had deflected them, but that in fact there is nothing there. Similarly, we could have said that our foot rebounded AS IF there was a rock there, but that in fact there was nothing there. (The Inquisition did say that the planets were seen to move as if they and the Earth were in orbit around the Sun, but in that in fact they moved round the fixed Earth). But if the object of the exercise is to explain the motion of planets, or our foot, or photons, we must adopt the rule that if something behaves as if it existed – by kicking back – then one regards that as evidence that it does exist. Shadow photons kick back by interfering with the photons that we see, therefore shadow photons must exist.
We do not feel the presence of our counterparts in other universes. Nor did the Inquisition feel the Earth moving beneath their feet. And yet, it moves!
- We should regard as real those complex entities which, if we did not regard them as real, would complicate our explanations. Its not how hard something kickbacks that makes its existence compelling. What matters is its role in the explanations that the theory provides.
- Physicists trying to avoid the many-worlds conclusion try to explain QM as "No shadow photons exist and what carries the effect of the distant slits on the photon we see is – nothing. Some sort of action at a distance simply makes photons change course when a distant slit is opened" But this action at a distance is not simple, the photon is affected by distant objects exactly AS IF something were passing through the distant gaps and bouncing off distant mirrors etc to intercept the photon at the right time and place. Doing the calculation would require the same computational effort of working out the history of a large number of shadow photons. A story that is in in effect about shadow photons necessarily appears in any explanation of the observed effects. The irreducible complexity of the story makes it philosophically untenable to deny that the shadow objects exist.
- Bohms theory also requires the same computations as the what the shadow photons do.
- Logically, reality need not be science-friendly in the sense that evidence for explanations can be found. Reality contains not only evidence, but the means (such as our minds, and our artifacts) of understanding it.
- To the extent that theories are true - that is, they resemble in appropriate respects the concrete or abstract things they refer to - they give reality a new sort of self-similarity, the self-similarity we call knowledge. Some parts resemble other parts. It may be concrete: eg: physical images in a planetarium resembling the night sky, or abstract: when theories are printed in books.
- Science and other forms of knowledge are made possible by a special self-similarity property of the physical world. It was not physicists that first recognized and studied this property; it was mathematicians and computer scientists. They called it the theory of computation.
- The theory of computation has been studied almost entirely in the abstract, as a topic in mathematics. This is to miss the point of it. Computers are physical objects and computation is a physical process; what computers can and cannot do is determined by the laws of physics, not by pure mathematics.
- A universal computer is usually defined as an abstract machine that can mimic the computations of any other abstract machine in a certain well-defined class. The fact that universal computers are possible and can actually be built, is part of the self-similarity of physical reality that makes the world comprehensible. Stated another way, the fact that virtual reality is possible and that the multiverse has this property, makes science possible.
- What constraints, if any, do the laws of physics impose on the repertoires of virtual-reality generators? The laws of physics impose no limit on the range of accuracy of image generators.
- One cannot certify that a virtual reality rendering is accurate, but experience can sometimes show that a rendering is inaccurate. This mirrors the case of theory and experiment in science. If the environment is physically possible, rendering it is the equivalent to finding rules for predicting the outcome of all possible experiments that can be performed in that environment.
- If we assume that any virtual reality generator that can in principle be built, can at least be built twice, then it follows that every virtual reality generator running a program is rendering SOME physically possible environment. It may be rendering others things as well, including physically impossible environments, but there is always some possible environment that it is rendering.
- Imagination is a straightforward form of virtual reality. Our "direct" experience of the world throughout our senses is virtual reality too, rendered to us by our unconscious minds from sensory data and complex inborn and acquired theories (ie: programs) about how to interpret them.
- We realists take the view that reality is out there: objective physical and independent of that we believe about it. But we never experience this reality directly. All our experience is VR. And every last scrap of our knowledge – including our knowledge of the non-physical worlds of logic, math and philosophy – is encoded in the form of programs for the rendering of those worlds on our brains own VR generator.
- The relationship between "ordinary" reality and virtual reality is part of the deep unexpected structure of the world which this book is about.
- We know from QM that all relevant variables are quantized and thus that the set of possible programs that simulate reality is discrete. (Each program specifies a particular set of values for physical variables) There are infinitely many possible programs, but each can only contain a finite number of symbols, because symbols are made of matter is recognizable configurations. (JA: Then are there really an infinite number of possible programs ???)
- The feasibility of a universal virtual-reality generator depends on the existence of a universal computer - a single machine that can calculate anything that can be calculated.
- Universality was first studied by mathematicians, they were trying to make precise the intuitive notion of computing (or "calculating" or "proving") but they failed to realize that mathematical calculation is a physical process. It is therefore impossible to to determine by mathematical reasoning alone what can or cannot be calculated mathematically. That depends entirely on the laws of physics.
Connection of Math and Physics
- Turing came up with the Universal calculator or Universal Turing machine which he conjecture could calculate anything that could be calculated. eg: everything computable by mathematics.
- Quantum computers will be able to perform computations which no (human) mathematician will ever, even in principle, be able to perform.
- If a question is non-computable, it does not mean that it has no answer or is in any sense ill-defined or ambiguous. It has an answer, it is just that there is physically no way of obtaining the answer.
- Claim: The Turing principle: It is possible to build a virtual reality generator whose repertoire includes every physically possible environment. This is the strongest form of the Turing principle. It says that not only can various parts of reality resemble one another, but that one constructable object can perform the task of describing (mimicking) any other part of the multiverse. This is what makes reality comprehensible.
- The laws of physics are to be comprehensible they must be capable of being embodied in another physical object – the knower. It is also necessary that physical processes capable of creating such knowledge be physically possible. Such processes are called science. The laws of physics seem to meet this criteria. B.c the Turing principle seems to be true, the laws of physics can be said to mandate their own comprehensibility.
- Define something as physically possible as something that actually occurs somewhere in the multiverse.
- There is no logical necessary connection between truth and explanatory power. So then what justifies relying on theories that are our best explanations as guides to practical decision-making ? This is the modern form of the "problem of induction".
- An "inductivist" is someone who thinks that the invalidity of the inductive justification is a problem for the foundations of science. eg: there a gap that must be filled, if not by induction then by something else. How to justify any conclusion about the future from past evidence.
- Claim justification (which is always tentative) comes from the explanations provided by the relevant scientific theories. Only argument every justifies anything.
- Theories postulating anomalies without explaining them are less likely than their rivals to make true predictions. Theories are postulated to solve problem, therefore any postulate which solves no problem is to be rejected. A good explanation qualified by such a postulate becomes a bad explanation.
- It is an interesting FACT that the physical universe admits processes that create knowledge about itself. We should try to explain this fact in the same way as we explain other facts, through explanatory theories. I think that the Turing principle is the appropriate theory in this case. It says that it is possible to build a virtual-reality generator whose repertoire includes every physically possible environment. If the Turing principle is a law of physics (we I have argued that it is), then we should be surprised that we can form accurate theories about reality, b/c that is just VR in action.
- An argument doesn't begin with "axioms" or end with "conclusions". It starts in the middle with a version that is incomplete, has gaps ambiguities and irrelevancies. It is not the same species as a deduction, or the non-existent induction. It is not based on anything or justified by anything. It doesn't have to be, its purpose is to solve problems and to show that a given problem is solved by explanation.
- Claim: life is fundamental. Something is fundamental if a deep understanding of the world depend on understanding that phenomena.
- Not all fundamental phenomena have large effects. Some do, like gravity, some dont, like quantum interference. However QM interferes is indeed fundamental b/c we need to understand it to understand a basic property of the world: the parallel universes.
- Life is both fundamental and has large physical effects
- To quantify adaptation we need to consider both the replicator in question and also a range of possible (but not actually realized) variants. For highly adapted replicators we need consider only fairly small variations, b/c with most large variations they would no longer be replicators. So we are contemplating replacing replicators by broadly similar objects.
- The degree of adaptation of a replicator depends not only on what that one replicator does in its actual environment, but also on what a vast number of other possible alternatives WOULD DO in a vast number of possible environments. This is strikingly similar to accuracy of VR rendering which depends on what the user COULD DO in addition to what they actually do.
- The most important factor determining a genes niche is usually that the genes replication depends on the presence of other genes. An organism is not a replicator, it is part of th environment of replicators.
- Life is a form of virtual reality generation. Living processes and VR renderings are the same sorts of process. they involve the physical embodying of general theories about an environment.
- It is a piece of knowledge rather than a physical object that is or is not adapted to a certain niche. Life is based on replicators, but life is really about knowledge. An entity is adapted to its environment if it embodies knowledge that causes the niche to keep that knowledge in existence. Life is about the physical embodiment of knowledge. The Turing principle (a law of physics) is also about knowledge. IT says that it is possible to embody the laws of physics, as they apply to every physically possible environment, in programs for a VR generator. Genes are such programs. Life is a means (presumably a necessary means) by which the effects referred to in the Turing principle have been implemented in nature.
- Astrologers used to believe that cosmic events influence human affairs; science believed for centuries that neither influences the other; now we see that human affairs influence cosmic events.
- In the universe as we see it, life has affected nothing of significance, but we only see the past, and a small part of it at that. This is just a small part of physical reality.
- All of the oxygen in our atmosphere – 1e16 tons was created by plants ans was therefore a side effect of the replication of genes: molecules. Life achieves its effects not by being larger, more massive or more energetic than other physical processes, but by being more knowledgeable.
We need to take the multiverse view of QM to see that there is a difference between knowledge-bearing and non-knowledge-bearing objects, that depends neither on the objects environment nor on the effects on the remote future, bot only on the objects' immediate physical conditions. A single cosmic-ray strike on a single DNA molecule will in general cause a large range of different mutations to appear in different universes. The multiversal perspective reveals additional physical structure in an organisms DNA. The sequences of base pairs that are in genes will tend to be replicated across universes, those same sequences in junk DNA which are not in genes will vary greatly between nearby universes. If we are being too parochial (and looking only in our universe) we may be lead to the false conclusion that knowledge-bearing entities can be physically identical to non-knowledge-bearing entities, which casts doubts on the fundamental status/significance of knowledge. However knowledge-bearing structures are physically distinct which looking across the multiverse. Knowledge is like a crystal in the multiverse.
The better adapted genes will have the same structure over a wider range of universes – they will have bigger crystals.
- Let us look around the universe. What will catch our eye will be the most striking structures: galaxies and clusters of galaxies. But those objects have no discernible structure across the multiverse. Nothing extends far into other universes without its detailed structure changing unrecognizably. Except, that is in those few places where there is embodied knowledge. Such places would standout in the multiverse as the location of the processes of life and thought. These have generated the most distinctive structures in the multiverse.
- Scientific progress since Galileo has seemed to refute the ancient idea that life is a fundamental phenomena in nature. Modern biology seems to have confirmed this. However life is associated with a fundamental principle of physics – the Turing principle – since it was the means by which VR was first realized in nature. Life is also significant on the largest scales of both time and space. And the largest-scale regular structure ACROSS universes exists where knowledge-bearing matter, such as brains or DNA gene segments, have evolved.f
- The direct connection between the theory of evolution and quantum theory is a striking and unexpected connection between the four strands of the fabric of reality.
- (When we are considering what a particular object may look like in other universes we must not look so far afield in the multiverse that it is impossible to identify a counterpart.)
- All present-day computers are different implementations of the same CLASSICAL idea, the universal Turing machine. A quantum computer is a machine that uses unique QM effects, interference, to perform wholly new types of calculation that would be impossible, even in principle, on any Turning machine. It is therefore a new way of harnessing nature.
- QC will be the first technology that will allow us to perform useful tasks in collaboration with the parallel universes. A QC essentially the components of a complex task across the vast number of parallel universes and the brings the results together in the end.
- Feynman considered the computer simulation of QM objects: he showed that predicting the behaviors of QM systems (ie: rendering the QM environments in VR) is in general an intractable task.
- Chaos occur only in classical physics (JA: Check this against quantum chaos…) The flapping of a butterflies wings does not in reality cause hurricanes, b/c the classical phenomena of chaos depends on perfect determinism which does not hold in any single universe. Quantum systems are unpredictable because they behave differently in different universes and so appear random in most universes.
- Whichever path you set a single photon on inside the apparatus it will emerge randomly. Only when interference occurs between the two paths is the outcome predictable. It follows that what is present in the apparatus just before the end of the interference experiment cannot be a single photon on a single path. There must be something else present, preventing it from bouncing downwards. We can construct further experiments to show that the "something else" has all the properties of a photon that travels along the other path and interferes with the photon we see, but with nothing else in our universe.
- Computing this classically, since there are only two kinds of universe in this experiment, the calculation will take only twice as long as it would if the particle obeyed classical physics. But Suppose that there are 1000 holes in the barrier, we must now calculate the mutual interference of 1000 parallel-universe version of the photon. The computational complexity shows there is a lot more happening in the QM environment that meets the eye. This complexity is the core reason why it does not make sense to deny the existence of the rest of the multiverse. The number of different histories we have to calculate increases exponentially with the number of interacting particles.
- It would appear that no practical VR rendering is possible for environments that show the effect of QM interference. However you can turn this around as say that the if it requires so much computation to work out what will happen in an interference experiment, then the very act of setting up such an experiment and measuring the outcome is tantamount to preforming the complex computation. There are computational tasks that are "intractable" if we attempt to perform them using an existing computer, but which would be tractable if we were to use QM objects as special-purpose computers. (Note that this requires that QM objects not be subject to chaos) Feynman conjecture, correctly it turned out, that all the QM properties of any target environment could be simulated by an array of qubits, a "universal quantum simulator". Deutsch proved there is also a universal quantum computer which could perform any computation that any other quantum computer could perform.
- The fact that the repertoire of the universal quantum computer contains environments whose rendering is classically intractable implies that new classes of purely mathematical computation must have become tractable too.
- Prime factoring a 250 digit number would take over a millions years on a network of a million computers. When a quantum factorization engine is factorizing a 250 digit number the number of interfering universes will be of the order 1e500, which is why Shors algorithm makes factorization tractable. A few thousand operations, IN EACH UNIVERSE, being performed in parallel contributes to the answer through interference.
- Challenge to those who still cling to the single-universe world-view: Explain how Shor's algorithm works. Do not merely predict that it will, provide an explanation. When Shors algorithm has factorized a number using 1e500 times the computational resources that can be seen to be present, where was the number factorized ? There are only 1e80 atoms in the universe. If the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Then who did it? How, and where was the computation performed?
- Unpredictability caused by chaos is in general swamped by the indeterminacy caused by identical universes becoming different.
- Our knowledge of mathematical truth depends on, and is no more reliable than, our knowledge of the physical world.
Connection of Math and Physics
- In the traditional view the crucial difference between a proof and experiment is that a proof makes no reference to the physical world and that when we have proved something we know with ABSOLUTE CERTAINTY that it is true. The idea that mathematical knowledge and scientific knowledge come from different sources, and that the "special" source of mathematics confers absolute certainty, to this day this accepted by virtually all mathematicians.
- The study of logic itself revealed that the scope of logical deduction as a means for discovering truth is severely limited. By around 1900 there was a crises in mathematics, namely there was no foundations. Russell proved set theory inconsistent.
- Intuitonism is the expression, in mathematics, of solipsism. In both cases there is a an over-reaction to the thought that we cannot be sure of what we know about the wider world. In both cases, the proposed solution is to retreat into an inner world which we can supposedly know directly and therefore (?) can be sure of truly knowing. In both cases the solution involves either denying the existence – or at least renouncing the explanation – of what lies outside. And in both cases this renunciation makes it impossible to explain much of what lies inside the favored domain.
- The fatal flaw in intuitonism is revealed not when it is attacked, but taken seriously on its own terms as an explanation of its own.
- Godel proved first that any set of rules of inference that is capable of correctly validating even the proofs of ordinary arithmetic could never validate a proof of its own consistency. Second, Godel proved that if a set of rules of inference in some branch of mathematics IS consistent (whether provably so or not), then within that branch of mathematics there must exist valid methods of proof that those rules fail to designate as valid. This is called Godel incompleteness theorem.
- Thanks go Godel, we know that there will never be a fixed method of determining whether a mathematical proposition is true, any more than there is a fixed way of determining whether a scientific theory is true. Nor will there ever be a fixed way of generating new mathematical knowledge. Progress in math therefore will always depend on the exercise of creativity. It will always be possible and necessary, for mathematicians to invent new types of proof. They will validate them by new arguments and new modes of explanation depending on their ever improving understanding of the abstract entities involved. Godel's own theories were a case in point: to prove them, he had to invent a new method of proof. Godel's proofs are as compelling as any in mathematics, but only if one first understands the explanation that accompanies them.
- On the basis of present day science, we must conclude that Plato had it backwards, We can perceive perfect circles in physical reality (ie: virtual reality) but we shall never perceive them in the domain of Forms. When we imagine circles we are doing a VR rendering within our own brains.
- Any physical experiment can be regarded as a computation, and any computation is a physical experiment. Proof is a physical process. A proof is a type of computation. "Proving" a proposition means performing a computation which establishes that the proposition was true. Neither the theorems of mathematics, nor the process of mathematical proof, nor the experience of mathematical intuition, confers any certainty. Nothing does. Proof theory is not a branch of mathematics – it is a science. Proofs are not abstract. There is not such thing as abstractly proving something, just as there is no such thing as abstractly calculating or computing something. Proof theory is about how to ensure that those physical processes that are the computations of proofs correctly mimic the abstract entities they are intended to mimic.
Connection of Math and Physics
- In the classical case, converting between a proof process and proof objects (the list of the steps in the calculation) is always a tractable task. With a Quantum computer there is no way to keep a record of everything that happened during the proof process. So creating an old-fashioned proof object would be infeasible. There are vastly more steps in the proof than there are atoms in the known universe.
- Turing hoped that his universal computer was so simple and transparent that it would not depend on any assumptions about physics that could conceivably be falsified, and that it could therefore become the the basis of an abstract theory of computation that was independent of the underlying physics. "He thought that he understood paper" - Feynman. But we was mistaken. Real, QM paper is wildly different from the abstract stuff that the Turing machine uses. The Turing machine is entirely classical, and does not allow for the possibility that the paper might have different symbols written on it in different universes, and that those might interfere with one another. Turings intuition, b/c it included false assumptions from classical physics, caused him to abstract away some of the computational properties of his hypothetical machine, the very properties he intended to keep.
Connection of Math and Physics
- Mathematics is the study of absolutely necessary truths. The truths are absolutely certain, but that does not mean that our knowledge of those necessary truths is itself certain, nor does it mean that the methods of mathematics confer necessary truth on their conclusions. Necessary truth is the subject matter, not the reward. The objective of mathematics is not and cannot be mathematical certainty. It is and must be mathematical explanation.
Connection of Math and Physics
- Why does mathematics work as well as it does? Why does it lead to conclusions, though not certain, can be accepted and applied unproblematically for millennia ? Ultimately the reason is that SOME knowledge of the physical world is also that reliable and uncontroversial. And when we understand the world well, we also understand which physical objects have properties in common with which abstract ones.
- Mathematical entities are part of the fabric of reality b/c they are complex and autonomous. They exist objectively and have properties that are independent of the laws of physics. However it is physics that allows us to gain knowledge of this realm, and it imposes stringent constraints. Whereas everything in physical reality is comprehensible, the comprehensible mathematical truths are precisely the infinitesimal minority which happen to correspond exactly to some physical truth. That is they are truths that can be rendered in VR. We have no choice but to assume that the incomprehensible mathematical entities are real too, b/c they appear inextricably in our explanations of the comprehensible ones.
Connection of Math and Physics
- The common sense theory of time is inherently nonsensical, not just factually inaccurate. We do not experience time flowing or passing. What we experience are differences between our present perceptions and our present memories of past perceptions. We interpret those differences, correctly, as evidence that the universe changes with time. We also interpret them, incorrectly, as evidence that our consciousness or, or the present, or something moves through time. The idea of the flow of time really presupposes the existence of a second sort of time, outside the common-sense sequence-of-moments time. Our theories of physics are, unlike common sense, coherent and they first achieved this by dropping the idea of the flow of time.
- In spacetime physics the future is not open. It is there with definite fixed contents, just like the past and present. Spacetime is incompatible with the existence of cause and effect. C-and-E always involves statements about what have happened, if other things being equal, something else had been different. In spacetime exactly one thing happens in reality and everything else is fantasy.
- physical reality is not a space time, it is a much bigger and more diverse entity, the multiverse. To first order the multiverse is like a very large number of co-existing and slightly interacting spacetimes. They are present in definite proportions, so it is meaningful to say that certain types of events are "rare" or "common" in the multiverse and that some events follow others "in most cases". Most logically possible universes are not present at all (eg: there are no universes where the charge on an electron is different) The multiverse can thus be used to define cause and effect.
Many Worlds PhilosophyOfPhysics
- Other times are just special cases of other universes. It is tempting to suppose that the moment of which we are aware is the only real one, or is at least a little more real that the others. But that is just solipsism. All moments are physically real. The whole of the multiverse is physically real. Nothing else is.
- If there were no VR programs that rendered time travel, then the Turing principle would imply that time travel was physically impossible (everything that is physically possible can be rendered).
- Einsteins equations admit the existence of pathways into the past. Until recently, the accepted practice has been to systematically ignore these. This was because physicists were under the impression that time travel would "lead to paradoxes" and that such solutions must therefore be "unphysical". At present we know of nothing in the laws of physics that rules out past-directed time travel.
- Visitors from the future cannot know our future any more than we can, for they did not come from there. But they can tell us about the future of their universe, whose past was identical to ours.
- Knowledge creation and biological evolution are physically significant processes. They create trans-universe structure by making different universes become alike. Possession of a time machine would allow us access to knowledge form an entirely different source, the creativity of minds in other universes. A time machine is effectively a computational resource that allows certain types of computation to performed with enormously greater efficiency than they could on any individual computer. It achieves this by effectively sharing work among copies of itself in different universes.
- Without time machines, the knowledge created in one set of snap shots reaches few others, namely those stacked in the future.
- Time travel is not paradoxical. If one travels into they past one retains once normal freedom of action, but in general ends up in the past of a different universe.
- All four basic strands have the unusual status of being simultaneously accepted and rejected, relied upon and disbelieved, by most people working in those fields.
- Kuhns theory explains the succession from one paradigm to another in sociological or psychological terms, rather than as having primarily to do with the objective merit of rival explanations. This is a fatal flaw that forces Kuhn to deny that there has been objective improvement in successive scientific explanations, or that such improvement is even possible. The growth of objective knowledge cannot be explained in Kuhns theory
- The Copenhagen interpretation was motivated to avoid the conclusion that reality is multi-valued,and for that reason alone it is incompatible with any genuine explanation of quantum phenomena. Generations of physicists have found it sufficient to regard interference as a "black box", where Quantum theory is used to predict the outcome, but they neither know nor care how the output comes about as a result of the input. There are two branches of physics where this attitude is impossible b/c the internal working of QM is the subject matter: Quantum computation and quantum cosmology.
- The idea AI is possible in principle is not taken for granted by the field, however the opponents dont seem to understand that they are contradicting a fundamental principle (The Turing principle) of a fundamental discipline.
- Very few philosophers agree with Poppers claim that there is no longer a "problem of induction". Both Poppers and Everett's heretical innovation was the claim that the methodology has been valid all along.
- Although Darwin made no use of any specific law of Newtons, his discovery would he been inconceivable without the world-view underlying those laws. No one could have explained what life is under Kepler's conception of a "law of physics" they would have been looking for a law that mandates elephants in the same way that Kepler's lays mandate ellipses. This is the sense in which the problem of "What is consciousness?" is expected to depend on quantum theory. It will not invoke a specific QM process, but it will depend crucially on the QM (multiversal) world picture. We dont know what consciousness is, but it is intimately related to growth and representation of knowledge within the brain. We therefore need to understand knowledge as a physical process. Such an explanation has been elusive in the classical theory of computation. But, as explained above, in quantum theory there is a good basis for one: complexity that extends across large numbers of universes.
- On the face of it, the price of understanding interference is to create or exacerbate many philosophical problems. But we see that the very opposite is the case. The fruitfulness of the multiversal theory in contributing to the solution of long-standing philosophical problems is so great that it would be worth adopting even if there were no physical evidence for it at all.
- Individually all four theories have explanatory gaps that can make them seem narrow, inhuman and pessimistic. But when taken together as a unified explanation of the fabric of reality, this property is reversed. Instead of denying free will, placing human values in a context where they appear trivial and insignificant, it is a fundamentally optimistic world-view that places human minds at the center of the physical universe, and explanation and understanding at the center of human purposes.
- There is a historical tendency for physics to swallow up subjects that previous seemed unrelated to it.
- The Turning principle (Church-Turing conjecture) is on par with conservation principles or thermodynamics. All other theories conform to it.
- The predictions of the theory of evolution follow logically from the laws of physics, but the explanations in the theory of evolution are not believed to follow from physics at all. A non-hierarchical explanatory structure allows for the possibility of explanatory emergence.