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Ref. 0.5
In contrast to the approach described here, most scientists start with an assertion of reality. They claim - right at the beginning and without proof - that there exists an independent world prior to anybody studying it. Here, however, we recognise that the freedom to assert is logically prior to anything asserted with that freedom. Acknowledging this priority gives us a more relaxed approach to reality. This site also makes the reasonable claim that logic is more fundamental than reality.
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Ref. 1 This is similar to the way that computers treat the 'driver' of a piece of hardware installed within the machine as the hardware itself. The computer operating system cannot see hardware - only a software representation of it. Similarly, the logic of the world cannot see a hardware apple - only a logical representation of the apple.
Ref. 2 "How can'st thou be out of breath, when thou hast the breath to say to me that thou art out of breath???" - Juliet (Romeo and Juliet by Shakespeare)
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Ref. 3 This is similar to the way - in physics - that the state of a physical system can be represented by a vector in 'Hilbert space'.
Ref. 4 White holes - the time-reversed versions of black holes in our world - are rather like people insofar as they are the source of objects.
Ref. 5 (deleted 070928)
Ref. 6 Our son came home from highschool one day and told us that he had received good marks for a science assignment that he had handed in on the theme that astrology was bunk. He had proved his thesis by investigating the astrological claim that the position of a planet when a baby is born influences the child's personality. The mechanism for the planet's influence is supposed to be the planet's gravity extending down to Earth. Our son showed that the floor of the baby's delivery suite, if concrete, had a significantly greater gravitational effect on the baby than the planet Saturn. He concluded that astrologers should be more concerned about the construction of maternity annexes than about the position of the planets.
We congratulated him on a job well done, but then he made a surprising confession. He said that at first he had considered the planet Jupiter rather than Saturn, and had compared that planet's gravity with a wooden chair alongside the bed. But Jupiter is a huge planet and the calculations showed that it had more gravitational effect on the baby than the nearby wooden chair. So our son changed from Jupiter to Saturn and chose a concrete floor...
Ref. 7 John D. Barrow and Frank J. Tipler have written an excellent book on the anthropic principle called (somewhat illogically) The Anthropic Cosmological Principle (1986). The excellence of the book lies not so much in their treatment of the Anthropic Principle, but in their discussion of teleological principles and their review of the history of anthropic thinking.
Ref. 8 It is interesting to speculate that Schrodinger's variable Psi-conjugate represents belief. Currently there is no scientific consensus as to what Psi and Psi-conjugate represent, although a quantity related to Psi is given a probabilistic interpretation. In support of the belief interpretation of Psi-conjugate we may note: (a) both Psi and belief are associated with the reality that will exist as the result of observation; (b) both Psi and belief are free of determination by an underlying reality; and (c) both Psi and belief may be considered to have a 'vector' character allowing summation from the local to the global.
The idea is that Psi-conjugate represents the unconscious beliefs of people looking at the vast world of all logically possible things (or equivalently the 'multiverse' of all logically possible worlds) the latter represented by Psi. A measurement occurs when Psi-conjugate (conceptually a-ib) operates on Psi (a+ib) to form the real world represented by a^2+b^2.
Ref. 9 Although Penrose agrees that the temperature of the floor, and so on, might affect things, he is inclined not to give way to his critics. He is what might be called a 'dogmatic realist', and insists that reality be a given and not determined by those who stumble across it. Whatever a dogmatic realist sees in front of them is due to reality and has nothing to do with the seeing of it. Penrose is saying in effect: 'Given this experimental set-up, this is what we are forced to conclude'. He is right. We are indeed forced to conclude that. But he should acknowledge that what is 'given' depends on him. In the case of his thought experiment, he changes the givens between the two halves of the exercise!
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Ref. 10 Einstein used the velocity of light, about 300 million m/s, as a gauge to compare one observer with another. The velocity of light shall be one thing that all observers shall agree on, he said. He later said the same about the curvature of space-time. Velocity, mass, energy, simultaneity, and the flow-rate of time might depend on the observer, but the shape of space-time shall be absolute. Thus our world has four invariants: the speed of light, space-time, the physical laws, and now, object selfhood.
The invariance of space-time and the speed of light is given an interesting emphasis by Brian Greene in The Elegant Universe, 2000, p50. He points out that objects always travel though space-time at the speed of light, the motion being divided between space and time. A photon does not travel through time at all because it has used up its entire speed quota in travelling though space. At the other extreme, an object at rest in space travels through time only. (We need to keep in mind that time enters the equation with the opposite sign to the space dimensions.)
The fact that all objects always travel at the same speed suggests that object-speed is more fundamental than light-speed, light being the special case when the object in question is a photon. So it is intrinsic to an object that it travel at the same unvarying speed as every other object. It is interesting that our creation of an object gives it that space-time characteristic before anything else, i.e., before we give it the characteristics that distinguish the object from other objects.
Ref. 11 It's like an animal species evolving eyes so that they can see things and avoid dangerous objects. Then the economists of that species come along and decide that sight is bad. 'Only adherence to the principle that brought us here - the Principle of Blind Bumping - will keep us strong and fit for the future,' they solemnly intone. 'You must keep your eyes shut!'
Ref. 12 Many of the world's social problems can be blamed on the error of seeing the world in terms of winners. This is particularly the case with economic theory, which has no prescription for losers other than for them to join the winners. If they can't join the winners, they should go out of existence or become invisible. This prescription applies even if the economic competition is between two races of people. One of the races is expected to become invisible if it does not become the dominant economic player. Unfortunately, the losing race of people might not like to become invisible. They might object to going out of existence. Certainly the Palestinians did not take it lying down.
I believe that 'winners prejudice' is the principle mechanism for the recent troubles in the Middle East. After the formation of Israel, the two peoples had an uneasy cooperation until one got richer and the other got poorer. One of them won the economic contest. As is customary for winners, particularly for winners who play by the rules, the dominant Israeli side expected to take over the whole country as their prize. They were following orthodox economic theory in not caring what happened to the Palestinian losers, who were supposed to take their loss with good grace and go away.
Democracy has a similar problem to economics. With democracy, the winner of the electoral competition is theoretically permitted to exterminate the loser, or at the very least, to consign the loser to invisibility. Any brake that might act to prevent the winner from doing this can only be applied from outside the democratic system. For instance, the thing preventing the winning political party from exterminating the opposition might be a written constitution, the threat of international sanctions, or moral considerations. Whatever the brake is, it must lie outside the democratic system. And that is the only place it can lie in the case of economic theory too. Unfortunately, in economics we are increasingly moving towards having no brakes at all i.e., of letting economic losers die literally. Certainly, we are letting losing countries become invisible.
We would do well to keep in mind this requirement for 'outside action' whenever we are tempted to think that economic theory or democracy can solve the world's problems.
Ref. 13 A conversation between Lisa and her father:
'Dad, why do I exist?'
Homer winced. He was not good on the birds and bees.
'Well, Lisa, darling, the fact that you exist and can ask that question puts constraints on how the world must have been a million years ago. Now, if the world was like that way back, it was inevitable that it would turn into the world of today, isn't it. So that's why you exist.'
'That's an explanation?'
'It's called the Anthropic Principle.'
Ref. 14 Probably all energy is relative. Gravitational potential energy and kinetic energy certainly are relative. Gravitational energy depends on the reference height that you choose, and kinetic energy depends on the platform from which you choose to judge the velocity. Electromagnetic energy is similar to gravitational energy. It is possible that rest-mass energy (Einstein's E = mc2) is relative too, perhaps depending on how we choose to break an object down into 'parts'. (Which is not the same as breaking it down into 'its' parts.)
Ref. 15 ...cannot see any further reduction. The process depends on us. It is similar to how 'coarse graining' in phase space depends on our view as to what states of a system are macroscopically indistinguishable. (Roger Penrose, The Road to Reality, p691) (Coarse graining would appear to be a dodgy notion in physics, making the second law of thermodynamics equally suspect.)
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Ref. 16 How to manufacture Tool A:
Step 1: Assemble ingredients P, Q, R and S
Step 2: Using tool A, join P to Q and R to S
Step 3: Join PQ to RS
Result: Now we have Tool A
Step 4: Make the reference to tool A in Step 2 implicit rather than explicit
Ref. 17 Many scientists define the world (the Universe) as 'everything', meaning there can be nothing outside it by definition. (For instance, Lee Smolin's first substantive chapter in his book Three Roads to Quantum Gravity is titled 'There is nothing outside the Universe'.) These scientists are relying on an outside platform without acknowledging it. To define something, you need to be outside the thing you are defining. In any case, I do not think the scientists do view the Universe as everything. If they really did have that unconscious belief, they would not be able to conceive the Universe as an existent thing. They would be as much puzzled by the suggestion of a 'Universe' as by the suggestion of a 'God'.
Ref. 18 This identicality actually means that there is just one quark and one electron, at least as far as they themselves see things. If we see a large number of quarks and electrons in the world, it's probably due to us.
Ref. 19 This suggests a possible explanation for sexual reproduction. In current biology, sexual reproduction is understood to increase variation and so speed-up evolution; and that's why it exists. But a radioactive environment increases variation too. Except in that case, the increased variation leads to destruction rather than speeded-up evolution. We say sexual reproduction is good because it 'just happens' to provide 'just right' variation. This is a rather unprincipled answer.
A principled answer is suggested by the plain-of-tiles analogy described here. A biological body is indeed unique, and truly cannot be picked out of the plain of tiles. It therefore cannot exist simply by being seen. But if we create it by some special action, it will then exist as the result of that action. Thus we do something to make this thing exist, something different from just seeing it. The essence of sexual reproduction is that the new life that results is not something that occurs deterministically, but is the result of somebody doing something i.e., the result of non-deterministic creating action. It's that free will action that creates the unique object that is now seen to exist.
We can look at this from another angle. In the simulation of evolution on a computer that I have been talking about, the appearance of an evolved animal on the screen was linked to the random disintegration of an atom at an earlier time. The atom's disintegration was required to exist to make sense of the process. So not only was the outcome of the random event at the start required to have a certain value according to the evolved animal on the screen, the random event itself was required to exist. (The event needn't have been a disintegrating atom - it could have been a monkey hitting the keyboard, or something else seen as random.)
When we transfer from a computer simulation of evolution to the real world around us, the unique products of evolution also require the existence of a 'random' past event to start the deterministic chain leading to their unique existence. Sexual reproduction provides such a random event. The randomness lies in the 'crossing over' of alleles that occurs in the reproductive process.
(In the case of genetically identical twins, the random event could be the developmental environment in the uterus, which is also understood to be random. No two individuals have exactly the same developmental environment.)
Whatever way we might choose to see things, the process leading to the birth of the individual must not be allowed to be deterministic, because then the resulting individual would not be unique.
In the case of vegetative propagation - an asexual process - there is only one individual 'body', and yet it is unique and we see it. This is contrary to what we would expect from the above argument. So why do we see asexual reproduction? Perhaps it is because we divide the individual body in question into identically-specified parts and it is our dividing action that we see. For instance, we might see a plant popping up all over the lawn - 'suckering', as they call it. Each of the suckers is theoretically the same plant, but it's because we see them in different places that we treat them as different plants. So again, we are seeing our free will in action - in this case, our unconscious decision to see them as different plants.
The reason that artificial life is impossible is that there isn't a random event at the beginning of the deterministic chain leading to the artificial life's appearance. If scientists assemble items A, B and C to create life, the origin of the life will be seen to lie in the assembly of A, B and C; i.e., it will be deterministic. Indeed, that is the point of the exercise. It is to allow anyone to make the required assembly. But if the individual created by the assembly is to be unique, which it will have to be if it is 'living', its origin must have an undetermined start. The bald assembly of some components will not do the trick.
In any case, no physicist would make the mistake of assuming that an assembly of components would be sufficient to do the job on its own. At the very least, a physicist would also want to specify the velocities of the components as they enter the assembly. Otherwise, the instant after assembly the various components might move in totally the wrong direction. More generally, an object seen to exist is different from an object seen to exist but which we have made. The latter is different in that it has been made. It enters the logic of the world differently.
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Ref. 20 The Blind Watchmaker p367, 384
Ref. 21 It is not strictly correct to say that the number was set at an earlier time. In fact it was set when we determined its value to be 11. Until we did that, the number 11 did not take part in the world's logic, i.e. was not real. We only imagined that it might be real before then.
This is similar to the way that we imagine that random particles have reality before we examine them. For instance, scientists might describe the nitrous oxide molecules in a flask as 'random', but then let their imaginations take over and imagine that at any particular moment a particular volume-element contains a real molecule moving a certain real way. But that cannot be right. It would mean that the molecules were not random after all. The scientists cannot have it both ways. Either the molecules are random or they are not. If they are random, they have no specific reality in their motions.
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Ref. 22 Quantum mechanics provides a different view from Einstein's, making gravity the exchange of particles called gravitons. But few physicists would say that Einstein was wrong on that account. Indeed, quantum physicists are still looking for a guiding principle - similar to Einstein's equivalence between gravitational and inertial mass - to validate the graviton picture.
Ref. 23 Lisa asks Homer a question:
'Dad, why doesn't the wind blow straight from the H to the L?'
'What do you mean, Lisa?'
'You told me that a High on the weathermap is where there is too much air, and a Low is where there isn't so much. Why doesn't the wind blow straight from the High to the Low? It seems to go at right angles.'
Homer winced. Lisa was right. Darn stupid weather map! Why does it have Highs and Lows anyway?
'Well, Lisa, darling - if the wind blew directly from the H to the L, there wouldn't be an H and an L for us to see, would there?'
'What do you mean?'
'If the air went straight from the H to the L, the amount of air in both places would soon be the same, and there wouldn't be an H or an L for us to ask questions about.'
'So there is a force deflecting the wind from blowing straight?'
'No, no, no! There's no need to invent a mystical force. It's a simple matter of existence. If H's and L's are going to exist, then the air can't move straight. (And if they're not going to exist, you're not going to ask questions about them, are you?) The brute existence of the H and the L causes the wind to blow at right angles to the line joining them. You might mention my name when you explain it to your teacher.'
Ref. 24 A force actually is a good explanation for the features on a weathermap. Modern physics says that all forces - gravity, electricity, radioactivity, and so on - are inventions of the human mind, and the force preventing the wind from blowing directly from a High to a Low on weathermaps is also in this category. This 'Coriolis force' arises because air moving roughly in the North-South direction, or vice versa, gets closer to or further away from the Earth's axis of rotation. If you move further from an axis of rotation, you need to whiz faster to keep above the things below you. If you don't take steps to increase your rate of whizzing, you will lag behind the people below you. The people down there will attribute your lagging to a 'force' pushing you back. That's the 'force' the air feels. Lisa was correct in assuming the air wanted to move directly from the H to the L. The air started doing this, but found itself getting further from the axis of the Earth's rotation. (We are assuming the air is moving towards the equator.) This caused the Coriolis force to kick in, getting stronger as the air moved faster. Eventually this force caused the wind to blow almost at right angles to the direction it wanted to go.
Ref. 25 Raymond Smullyan in Forever Undecided: A Puzzle Guide to Godel (1988) demonstrates the close connection between belief and logic. His book is a derivation of the theorems of Godel (and others) on provability, consistency, completeness, etc, using intuitive reasoning rather than jargon. Smullyan's trick is to use 'correctly believe' instead of 'know' (p 71). This introduces the action of believing into logic. He gives it the symbol B (p74). Thus Bp is the proposition that the reasoner believes the proposition p. (The proposition p&Bp is the proposition that the reasoner correctly believes p.) Later, Smullyan makes Bp the proposition that p is 'provable within the system' (p76). (i.e., we are no longer talking about reasoners believing things, we are talking about mathematical systems proving things.) Apparently it was Godel who introduced the symbol B for 'provable', it standing for the German 'beweisbar' (p108). The usual modal logic symbol these days (instead of B) is a little square box, meaning 'necessarily'.
Smullyan derives Godel's theorems via both the 'belief' and the 'provability' interpretations of B, suggesting a close connection between belief and logic. Indeed, he says (p206, his italics): 'Modal logic enables one to give a unified treatment of reasoners who believe propositions .... and mathematical systems that can prove propositions.'
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Ref. 26 Roger Penrose, The Emperor's New Mind, p 445
2006 May 26, 14:14
2007 June 26, 15:00
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