Tuesday, November 25, 2008

The Dark Compliment

I’m reading about the philosophy of physics (see previous post), so I happen to be thinking of Bohr's wave-particle complimentarity... and resonance:
......An empty bottle, for example, emits a low tone when you blow over it because the tiny vibrations that are the disturbance of the air caused by that blowing all mount up if (and only if) they have a wavelength that fits nicely into the extent of the bottle (much as how, when you give a swing a sequence of little pushes, the swing swings with a larger and larger amplitude). I’m thinking that because the universe has a finite size, so there might be resonance. Maybe the universe is still ringing like a bell from the Big Bang. It is clearly permeated by background radiation (the lingering whisper of that explosion), so maybe there is also resonance. (The universe is growing, so the resonant notes would be lowering their tone.)
......Where is the resonant ringing? Well if the resonance was like a sound wave, we would expect to see bands of denser particles and less dense particles (that being what sound is), those particles being galaxies perhaps, or clusters of galaxies. And if you think of the waves being in spacetime then again, matter would tend to congregate in the troughs. Small ripples move over ocean swells much as they do over calm seas, so we would not necessarily notice anything locally; but such clustering as though in troughs is indeed observed at the largest scales. And most of the wave energy is in those huge swells, which reminds me of the dark matter that, whilst being unobservable (whence the term 'dark'), is thought to make up over 80% of the matter of the universe.
......Galaxies seem to need more mass than we can see, in their stars and dust, to account for how compacted together are those stars and that dust. So my thought is that dark matter might be the energy associated with such huge universal swells. It would be directly unobservable as matter because such swells would be too big to look much like particles to us, much as electrons are too small to look like waves (except when that aspect proves invaluable, e.g. in electron microscopy). Maybe not of course, but I was wondering if any reader knows whether or not the maths of that analogy works out?

Monday, November 24, 2008

Thinking things through thoroughly

An atom with stationary electrons positioned around a positive nucleus would be unstable, because the electrons with their negative charge would be irresistibly pulled towards it. If they moved around the nucleus, like planets orbiting the sun, the atom would still collapse. Newton had shown long ago that any object moving in a circle undergoes acceleration. According to Maxwell’s theory of electromagnetism, if it is a charged particle, like an electron, it will continuously lose energy in the form of electromagnetic radiation as it accelerates. An orbiting electron would spiral into the nucleus within a thousandth of a billionth of a second. The very existence of the material world was compelling evidence against Rutherford’s nuclear atom.
That's (p. 81) from Quantum, an exceptionally good account of the revolution in physics in the first half of the last century (the physics is nicely explained (the author studied philosophy as well as physics) and most importantly, the biography is as engaging as in a novel (if a literary one))... I quoted the paragraph above because of its combination of logical clarity, scientific support and falsity. The resolution begins to emerge in 1913 (p. 96):
Whereas others had interpreted these problems of instability as damning evidence against Rutherford’s nuclear atom, for Bohr they signalled the limitations of the underlying physics that predicted its demise. His identification of radioactivity as a ‘nuclear’ and not an ‘atomic’ phenomenon, his pioneering work on radioelements, what Soddy later called isotopes, and on nuclear charge convinced Bohr that Rutherford’s atom was indeed stable. Although it could not bear the weight of established physics, it did not suffer the predicted collapse. The question that Bohr had to answer was: why not?
Bohr’s electron shell model of the atom was ready to explain chemistry by 1922, and in 1923 it was physically justified by a French prince who had earlier failed his physics exams (p. 149):
If viewed as a standing wave around the nucleus instead of a particle in orbit, an electron would experience no acceleration and therefore no continual loss of radiation sending it crashing into the nucleus as the atom collapsed. What Bohr had introduced simply to save his quantum atom, found its justification in de Broglie’s wave-particle duality. When he did the calculations, de Broglie found that Bohr’s principal quantum number, n, labelled only those orbits in which electron standing waves could exist around the nucleus of the hydrogen atom. It was the reason why all other electron orbits were forbidden in the Bohr model.
In late 1925 Schrodinger read of de Broglie’s idea in a footnote to one of Einstein’s papers, and by early 1926 he had obtained his famous wave equation (p. 206):
Schrodinger knew exactly where to start and what he had to do. De Broglie had tested his idea of wave-particle duality by reproducing the allowed electron orbits in the Bohr atom as those in which only a whole number of standing electron wavelengths could fit. Schrodinger knew that the elusive wave equation he sought would have to reproduce the three-dimensional model of the hydrogen atom with three-dimensional standing waves. The hydrogen atom would be the litmus test for the wave equation he needed to find.
Schrodinger disagreed with the probabilistic interpretation of his wave equation introduced by Max Born that same year; but Bohr was more perceptive (p. 219):
Niels Bohr would soon argue that until an observation or measurement is made, a microphysical object like an electron does not exist anywhere. Between one measurement and the next it has no existence outside the abstract possibilities of the wave function. It is only when an observation or measurement is made that the ‘wave function collapses’ as one of the ‘possible states of the electron becomes the ‘actual’ state and the probability of all the other possibilities becomes zero.

Friday, November 21, 2008

Richards' paradox again

Upon reflection, I don’t think much of my previous resolution of Richards’ Paradox, which was as follows: Such finite strings of words as specify real numbers between 0 and 1 can be listed in order of increasing number of symbols used in the description and then, within each length of description, in alphabetical order. Given that list, one may seem able to define a real number between 0 and 1 and not in that list using a diagonal procedure: The digit in its nth decimal place is the final digit of d + 1, where d is the digit in the nth decimal place of the nth number on the list. Richards’ paradox is that such a number has such a finite description (so it is in our list, whence that procedure is contradictory, where it is, so there is no such number, in our list, whence that procedure is not contradictory, and so on).
......My previous resolution was just to note that our list includes anything that anyone could possible say (in finitely many words) that would specify a real number between 0 and 1. So in order to specify a number via that list, any (finitely describable) diagonal procedure must explicitly exclude its own entries in the list. But that now seems patently inadequate. Given such a list, we have its diagonal, and so a real number not on that list is clearly indicated. And we can say that it is. What we say cannot be in the list, but that just means that such a list—of all the finite specifications of such real numbers—is impossible. I would not be surprised if it was impossible, because words are typically a bit vague and variable in meaning. But it does seem odd that we can deduce that they must be fuzzy or incomplete, which is why I am not very fond of that resolution either. All in all, I find Richards’ paradox very puzzling.

Monday, November 17, 2008

How We Reason

*......Either Jane is kneeling by the fire and she is looking at the TV, or else Mark is standing at the window and he is peering into the garden.

*......Jane is kneeling by the fire.
Does it follow that she is looking at the TV?
......Most individuals say, “yes”, see Walsh, C., and Johnson-Laird, P.N. (2004: Co-reference and reasoning. Memory & Cognition, 32, 96–106). Given the first premise, they think of two possibilities: in one, the first conjunction is true; and in the other, the second conjunction is true. They overlook that when the second conjunction is true, the first conjunction is false, and that one way in which it can be false is when only its first clause is true, i.e., Jane is kneeling by the fire but not looking at the TV. Hence, the correct answer to the question is: “no”.
That’s from ‘How We Reason: A view from Psychology’ in The Reasoner 2(3), 4–5. Philip Johnson-Laird’s book ‘How We Reason’ is out in paperback next month.
......Maybe that was an example of a fallacy, rather than a paradox, but I’ve labelled it under ‘paradox’ in view of how easy it is to see through those I’ve been looking at recently; and after all, I’d said “yes” myself. (There’s a nice list of fallacies in The Reasoner 2(5), 7–8.)

Saturday, November 15, 2008

Curry's Paradox

A sentence is true insofar as it describes reality, ordinarily (and adequately enough here), so consider the following sentence:
(C)......If this sentence is true then so is the sentence (S).
Suppose that (C) is true. We would have, not only that (C) was true but also—from (C)’s definition—that from (C) being true we would have the truth of (S), so we would have, consequently, that (S) is true. That is, if (C) is, as we supposed, true then (S) is true. But that means—from (C)’s definition—that (C) is true.
......It seems that, logically, (C) is true, which is a paradox because (C) cannot be true, of course, because (S) was arbitrary, and some sentences are certainly false. If there was (as there seems) nothing wrong with our logical steps, then there was something wrong with our original sentence. And note that (C) says (of itself) that contradictions—e.g. (S) = “2 + 2 = 5”—follow from its truth, so essentially it says (of itself) that it is not true. That is, (C) is a Liar-style sentence, and the traditional resolution of such sentences is that they are senseless, a bit like such nonsense as “I met a man who wasn’t there” (can be).
......The propositional content of a Liar sentence such as “This sentence is not true,” which I shall call ‘(L),’ is essentially the same as that of the clearly empty “Disobey this command!” Such an utterance from one’s superior would naturally prompt the thought: What command? And note that just as (L) can seem true—since it seems to say that (L) is not true, and (L) is senseless so it is not—paradoxically because it is not, so similarly (C) can seem true: If (C) is false then it is false that from a falsehood—that (C) is true—we might deduce a contradiction—via all sentences being true—whereas such a deduction is plausibly alright.

Thursday, November 13, 2008

Berry's Paradox

The natural numbers are one, two, three and so forth. They can grouped by the number of syllables it takes to say them: {one, two, three, ...}, {seven, thirteen, fourteen, ...}, {eleven, seventeen, twenty-one, ...}, ... . So we can easily find, for example, the smallest natural number that cannot be given to us, in that way (by saying its English name), in fewer than three syllables; it is eleven.
......Let us now allow any method of verbally specifying a natural number—e.g. “two hundred and thirty-four times fifty thousand and fifty” (saving us six syllables on simply saying its name)—and consider the following specification:
(B)......The smallest natural number that cannot be specified in less than twenty-five syllables.
Berry’s paradox (which is over a hundred years old) is that (B) is itself only twenty-four syllables long. It seems paradoxical because we expect (B) to specify a number, in at least twenty-five syllables (much as earlier we got eleven, in three syllables), and yet whichever number it is has therefore been given to us by (B) in less than twenty-five syllables.
......However, since we have allowed any method of verbally specifying a natural number, we have allowed that I might take any number and say it at a certain time and date and then refer to it (and hence specify it) in less than twenty-five syllables as, for example, “The number mentioned by me between two and two thirty on the first of June two thousand and eight.” It is quite indeterminate which numbers one might do that for, and hence the number specified by (B) is also indeterminate.
......And if we don’t generalise completely, but instead limit to some extent the ways in which the numbers considered by (B) may be specified, then (B) will either give us some specific number with no problem (much as the specification above gave us eleven), or else it will be rather more obviously self-contradictory (much as Richard's paradox is), so that we would hardly expect it to give us a number (whence it should stop appearing paradoxical).

The Possibility of Free Will

Consider a real object in the world around you, e.g. a brown chair. Maybe the chair is really made of atoms, but if so then that underlying chair is not so much brown as capable of reflecting photons in certain ways. And since there is only one chair not two, out there in the real world—where you can see that the brown chair is—so there is no atomic chair. But of course, we need not become Idealists for that reason.
......Why should there not be many different but equally sound ways of regarding things? That there appears to be a puzzle may just be due to our being in the world that we are thinking about. So we might expect greater puzzles when thinking about ourselves, due to our being them identically. Therefore the following argument—that we couldn’t have morally significant free wills—shouldn’t convince us that we don’t.
......The argument is that, whatever a free choice between at least two alternatives—say, X and Y—is, either something beyond one’s power to choose determines that choice or else nothing does. One chooses, say, X; but why? If some reason for choosing X appealed to one, then something in one’s nature must have been predisposed to be so appealed to (and if that thing was chosen, then the regress just goes one step back, to why one so chose), but if nothing does then one’s choice was made randomly, irrationally, irresponsibly and so forth.

Wednesday, November 12, 2008

The Action of Free Will

Materialism, in its most plausible forms (e.g. property dualism, cf. this old crosspost), implies that something like micro-psychokinesis should be observable, via the likelihood of Gaia as a self-aware wielder of such of its parts as us, self-aware and language (and other tool) using as we are; because if we are purely material, if matter is such that amongst its properties it includes those that give rise to us as we are—much as sunlight is such that amongst its properties it includes those that allow lasers to blast rocks to smithereens—then it is surely indicated, by our existence, that a more complex and unitary structure such as the Earth’s ecosphere would be more like the goddess Gaia than, say, a car or a crystal.
......Similarly theism, in its most plausible form (e.g. as indicated by the most plausible theodicy), indicates that something akin to micro-psychokinesis would occur within living brains, if not elsewhere, as the soul-brain interaction. Reports of such things as micro-psychokinesis are therefore most interesting philosophically, because their empirical details should have—or so one might expect upon reflection upon what we know pretty well nowadays—the potential to discriminate between the most plausible materialisms (not, e.g., Humean supervenience) and theisms (not, e.g., Islamist fundamentalism). It is therefore sociologically interesting that there is so little professional interest in making rigorously objective observations of such things, even though there are reports by scientists of such things.
......How many other ways are there, whereby 'collapse' and 'no-collapse' interpretations of Quantum mechanics could be distinguished (the true from the false) empirically? If there was micro-psychokinesis then minds would not just be occupying slices through a world described by the wave function, since in that latter case the external events would have to seem random to us. A possible reason why there is a lack of professional scientific interest in such experiments is that 'collapse' interpretations seem to need an observer external to the entire physical universe, e.g. a God, and many scientists prefer to presume that there is no such being. They would say that since there is no such being, so 'collapse' interpretations are false, and hence there is no micro-psychokinesis to look for. Really a rather unscientific attitude (hardly letting the world itself tell you what is true of it).

Wednesday, November 05, 2008

Theism implies Open theism

According to theism there is a God who has, for example, the most understanding that anyone could possibly have. Open theism is the thesis that God’s future is to some extent open. It is not that God exists within time, but that time—or rather, changeability—is another of God’s attributes. The temporal dimension is certainly implicit in much of our ordinary talk of ordinary things (changeable continuants), but it is only our imperfect, quasi-spatial reification of change. Changeability itself originates with God’s power to change (e.g. to choose to create contingent continuants like us) should he wish to. The following shows that changeability is indeed a power, rather than a liability.
......It is one of several arguments I produced in response to Mawson’s recent argument that, since a temporal God would not know all about the future, if we had free will, whereas a timeless God would, and since God is maximally knowledgeable, so God is timeless. It is based on the observation that if God could be timeless—if a timeless divinity could create a world of people like us, while being above and beyond our personal and physical temporalities (or ways of being changeable)—then surely an everlasting (or Open theistic) God could have created such a world in a single moment of his relatively transcendental time. He would just have been creating things whose temporalities differed that much from his own, just as a timeless divinity would have been doing.
......Now, there are lots of possible worlds, which God would know all about even if he did not actually create all of them. Not creating some of them would hardly be a failure of omnipotence, as being unable to create them would. So suppose that God is everlasting and that he has chosen not to instantaneously create such a world as ours would be were God timeless, but has instead made it as Open theists believe it is. If God was timeless he could not do that, because he would have to know all about the future of any world that he could possibly create. So an everlasting God knows about (and is able to create) all the possible worlds of a timeless God, and more besides.
......God being maximally knowledgeable (and maximally powerful), we should be Open theists, at least according to Mawson’s methodology (and given the validity of such possible-worlds-talk).
......It is perhaps more clear that we should not conclude that God is timeless just because he could then be completely knowledgeable (and powerful) in respect of ourselves. That is because 100% of a little could be much less than 1% of a lot. To see that even more clearly, let RoboGod be an infinite computer that can create arbitrarily complex virtual beings, about which it would know (insofar as computers can know) everything, and over which it would have complete control. One might think that one might be such a creature (e.g. because Functionalism is conceivable) but even so, RoboGod might not know as much as (and is clearly less powerful than) someone who could create such a computer in the first place.