Dragonfly

So, I'm back in town... When physicist talk about space, this is the same space that is used in daily usage. The difference is that physicists tell us that there is more to space than meets the eye. The reason that they often refer to space-time is that certain properties of space depend on the time coordinate that is chosen, while the combined space-time is invariant under Lorentz transformations, which gives more general results. That time goes slower the more space-time is curved has been unambiguously demonstrated by countless experiments, only we don't observe that in daily life as the effects are then extremely small, therefore it seems counterintuitive to us (but for the correct functioning of the GPS system it is essential to take this effect into account). It is not true that the physicist defines space as something different from the common concept, he merely shows that our common perceptions are only approximations and that the properties of space and time in reality are not so simple as we'd intuitively believe, they are not the independent absolute entities they may seem to us in daily life.

Still looking. Not yet found. No direct evidence with measurements on Earth, but there is very strong astronomical evidence. The binary system PSR B1913+16, consisting of a pulsar and a neutron star orbiting each other, shows an orbital decay that is exactly conform the predictions of orbital decay due to the loss of energy by emitting gravitational waves, as predicted by the general theory of relativity. Here is a graph of the observed decay (red dots) and the decay predicted by general relativity (blue line). Curved space-time at work for you! But of course there are philosophers who "know" that space-time cannot be curved, although they wouldn't know the difference between a Riemann tensor, a Ricci tensor or a Christoffel symbol, but they've decided from their armchairs that this is all nonsense and no doubt they have a theory that can predict that orbital decay much better than such a rationalistic theory as general relativity.

Does an initial superluminal expansion contradict special relativity? Or is the idea that special relativity doesn't kick in until after the first few nanoseconds, or something on that order? Or? Ellen None of our physical theories work at the instant the expansion started and for a few hundred millionths thereafter. But once the symmetries were broken and the forces separated in to the four forces or interactions we know, the speed of light appears to be constant to within the precision of measurement we can do. Don't forget that special relativity is only valid for flat space-time. In general relativity it is possible that different regions of curved space-time can move in opposite directions with relative speeds greater than the speed of light. The "classical" theory of general relativity does indeed predict a singularity, but that doesn't take into account quantummechanical effects which will become important at very small scales. Although we still don't have a theory that successfully combines GR with QM, it's likely that there is in fact no singularity at the center of a black hole. PS. I'm moving this week to a new place, so I won't have much time for reactions the coming days.

No. I remember that when I was a toddler, my mother told me a bit about our good Lord in heaven (I also remember that I tended to confuse him with a pilot) and I've been baptized ("you never know"), but that's all, no prayers, no church and all that jazz. Today I think my parents were at most some kind of deists. When I was about 12 years old, I'd left all that behind me. Of course not. The agnostic position does take into account established facts. The tooth fairy story is a plain lie told to children: the caregivers state something as fact while knowing their statement to be false. Zeus and Thor as myths haven't stood up to scientific scrutiny either. Neither has the God myth. The only difference with Zeus and Thor is that the latter no longer have many followers, but the number of believers in some supernatural power isn't a scientific argument either...

I don't see why. Measuring rods and tapes are still widely used, even if they're not good enough for high accuracy measurements that you for example need for certain scientific experiments. That we have changed the standards in the course of time is because the newer standard was more accurate than the old one, but, once we had abandoned those standards that were based on the length of human body parts like the cubit or the ell, which had the disadvantage of having a large variability, the basic principle has always been the constancy of atomic structures and elementary physical phenomena. For an ordinary measuring rod it doesn't make any difference if the standard is a platinum rod or a certain number of wavelengths, it's too inaccurate for that anyway. That relation is an average relation with a fairly low accuracy, no more than 2 digits (moreover, it also changes in the course of time), while the elementary physical relations of atoms and subatomic particles are known with an accuracy of 9 to 12 digits, so it would be a poor substitute. But the biggest objection is that if you could describe the expanding universe in terms of a constant total size with shrinking constituents (with a simple homogeneous isotropic model that would be possible, I'm not sure about more complex models), you wouldn't get any new physics, as all the physical laws are based on the constant size of size of atomic and subatomic systems and wouldn't change at all as all elementary building blocks would shrink equally. It would merely be a substitution of words (Hubble expansion → constancy, constancy → Hubble shrinking), the same as if we would agree that from tomorrow the new meter equals two old meters. It would change a lot of numbers but every mathematical relationship between length measurements would remain the same, just as when we switch from inches to centimeters. So the only effect would be that we substitute a very precise standard with a rough and still rather poorly understood one.

I'm certainly equally radical... Are you also agnostic with regard to the existence of Zeus and Thor? Or the tooth fairy?

What do you mean by a shrinking photon? A really monochromatic photon would be infinitely long (a plane wave), a photon with a finite spectral breadth would have a finite length that depends on its spectral content. Or do you mean a photon with a smaller wavelength? That would in standard theory correspond to a more energetic photon. But the point is of course: smaller compared to what? Length is defined by the wavelength of photons with a certain frequency, so it is meaningless to talk about shrinking photons (or shrinking atoms for that matter).

If you choose a unit for a measurement, or perhaps I should say a standard on which that unit is based (the unit "meter" is used already for centuries, but the standards have been changed several times, for increasing accuracy), you choose a standard that is as invariant as possible, compared to elementary physical units like the Bohr radius of the hydrogen atom. Therefore the platinum bar that was used first, was kept in controlled conditions at a certain temperature etc. Later more accurate standards were chosen, like a certain number of wavelengths of a particular spectral line. Now there isn't any reason to think that the distance between two galaxies, whether between the centers or the perimeters, has a constant relation to the distances defined in elementary physical systems like atoms (which correspond to our notion of distance that we use in daily life), so such a distance would be a bad unit. We prefer to consider the elementary building blocks of the universe, the atoms and elementary particles, to be constant instead of the whole universe, as that would enormously complicate matters. After all, all hydrogen atoms are equal, as are all iron atoms etc., while stars and galaxies are continuously changing. The galaxies may for example in general move away from us, but some of them are moving towards us. I suspected that already...

Ah, a snake in disguise!

Certain, certain... it's normal to assume that if someone presents a carefully prepared article (I think we may trust Rand in that regard), that you take his or her statements in that article seriously and don't assume that the writer in fact meant something different, unless there are compelling reasons for that, e.g. an obvious error as I indicated in my previous post, or additional evidence that the writer does not always write what he or she means. I've seen no evidence for that. It's the other way around: if she did say or imply something different elsewhere, we might suppose that she expressed herself badly this time, but without such evidence it's normal to assume that she wrote what she meant, the more so as she's reputed to be painstakingly precise in such things. If you think that she said something silly here, you cannot just assume "oh, she must have meant something different". Do you do the same thing with other philosophers and writers?

There is no such thing as an absolute size. Size is measured with respect to a unit. That can be a platinum bar or a certain number of wavelengths of the light of a certain transition between two levels of a certain atom, or still another definition, but in your scenario the size of a galaxy remains the same, as the relation between the galaxy and the measuring unit doesn't change. On the other hand, when the distance between two galaxies was at first n units, it now becomes m units, with m > n. We call the increase in the number of units an increase in size, and not a decrease of the unit, as the unit is defined to be unchangeable. That we in the course of the history have chosen different units is because the original units were not really constant with respect to more elementary physical phenomena and the increasing accuracy of our measurements made units based on more elementary phenomena necessary.

I didn't read the next paragraph a while ago. In any case, she didn't write "words at all" or "any words" like you try to cram in her mouth, did she? She may have meant "those words" or "the words", meaning the words to express the thoughts, but it didn't reach the book that way. Typesetters and proofreaders do make errors! Of course, I don't expect you to ever give her any slack about anything, even considering that English wasn't her native language. If Rand writes "he has, as yet, no knowledge of words" and "the process which his mind performs wordlessly", her meaning is clear and unequivocal. You cannot just claim that she meant something different if you don't agree with those statements, nor blame typesetters and proofreaders or her poor command of the English language more than 20 years after she wrote Atlas Shrugged. You can only do that if there is an obvious error, like a missing negation or an unintended double negation, when it is clear from the context that the intended meaning is the opposite of the expressed meaning. There isn't any indication of such an error here, the rewrite squad is not needed in this case. This was no off-the-cuff remark, if she wrote it, she did mean it. I don't think she would have liked the idea that self-proclaimed clairvoyants would later claim that she in fact meant something different than she wrote. It depends on the definition of "concept", but while I think that you might perhaps defend the notion that you can have concepts for concrete entities without having a word for them (like "man", "cat", "food"), it seems to me that you cannot grasp an abstract concept like "length" without language. It may make sense to attribute to animals the ability to have concrete concepts, but no animal will understand the concept "length". That doesn't mean that animals or the child in the preverbal phase cannot distinguish different lengths and use those differences to their advantage, but those animals and those children cannot form the abstract notion of "length". You can point to a man or a cat, to a long object or a short object, but you cannot point to "length", you need a description in a language to grasp such an abstract concept.

Yeah, that's rather obvious... As you no doubt can prove. Boy, you should see my long comings! I know very well what Pross stands for: plagiarism.

And now one for that volcano in Iceland, the Eyjafjallajökull.

What does that matter? The discovery of plagiarism in that book is recent and that is what counts. Plagiarism doesn't become out-of-date. Hard work? Then you should use cut and paste, that's more efficient. And although I like to work in the garden, I also have other activities. In Pross' circles, no doubt. There they tend to write exactly the same sentences as Ayn Rand or Will Thomas. Justice and a dislike of sweeping things under the carpet. No, sorry, you'll have to look for another partner. Why should I? Plagiarism is plagiarism, even if he could paint better than Rembrandt (which he doesn't). As Chris Grieb would say: why don't you tell us what you really think? So, you know that for a fact? Then I'm curious to hear how you know that. Forewards? I can imagine that. With the right sources to steal from, you can get a nice text. Ah, another Atlas Shrugged movie project!

I have not transcribed the complete DIM lecture, only some of the most egregious examples (see this post), so I can't tell you if they mentioned other things about them, but as far as I remember that was the gist of it. After all they were categorizing ex cathedra several scientists according to Peikoff's DIM scheme.

Sometimes even SOLO has interesting news: our good friend Victor Pross has published a book, and... it's full of plagiarisms (surprise, surprise)! Here is the Amazon link for this book.

They believe in the steady benevolent universe.

From my earlier post about Peikoff's DIM-nonsense: Peikoff and Harriman: a folie à deux. Why should we take the nonsense of these two fools seriously? They've really no idea what they're talking about.

Typically a stupid Harriman argument. Newton was a theologian, so his physical theories must be wrong too? And Mendel was also a priest - does that invalidate his discoveries?

Franky, I have no idea what this is. I know what a mathematical projection of a physical sphere is, but not what a mathematical sphere per se is. Especially as it is defined by the same person as "the set of points that lie within a 3-dimensional spherical area." So what the hell is a "spherical area"? That is defined in the next line: By mathematical sphere, I mean the set of points that lie within a 3-dimensional spherical area in ℜ3, where ℜ is the set of all real numbers. For simplicity, let's assume a radius of 1, so our sphere would be the set: S = {(x,y,z) | x2+y2+z2 <= 1 } No, it is a mathematical definition, as I've said so often, mathematics may be applied to physical problems, but in itself doesn't tell us anything about reality. The Banach-Tarski paradox is a good example of an exact mathematical result that has no counterpart in the physical world and also a good illustration of the essential difference between an analytical truth and a synthetic truth. Well, if you think that mathematics is equivalent with word games and tooth fairies... Anyway, the Banach-Tarski paradox is not a real paradox, it's only called a paradox while it is so counterintuitive, but it is in fact an exact result of a mathematical theory that uses the (so very intuitive) Axiom of Choice.

The electric field of the Earth's atmosphere is only approximately static, it can be considered as a leaky capacitor (the Earth has a negative charge and the atmosphere a positive charge) that is continually recharged by thunderstorms (which transport by lightning negative charge to the Earth) all over the world. It is possible to draw some power from the quasi-electrostatic field of the atmosphere, but to get some appreciable power you need huge constructions that are hundreds of meters high or alternatively tethered balloons with all their practical disadvantages and still a relatively low output. With constructions with a size of only a few meters you can only get microscopic currents, the energy density is just far too low and that's the end of it.

The first thing one should ask oneself is "what is exactly meant by reality"? The notion of something called reality is the result of the fact that our experiences are not random but seem to reflect some invariant "core", where invariant doesn't mean that there are no changes in that core, but that those changes follow regularities, in contrast for example to our experiences in a dream. So we formed the abstraction "reality" as that reliable and dependable core that is behind our experiences. That core would be the noumenal world and our experiences the phenomenal world. By definition the noumenal world is unknowable, it is an abstraction that we form on the basis of our experiences, that show systematic regularities that we can formalize as physical laws. We can make models of which we assume that these are representative of reality, but these remain models that are based on empirical evidence, but that are not reality itself, just as we can draw a figure that is representative of the concept "circle", but that is not itself a circle, which is an abstract notion. In modern physics this difference between "reality" and our models of reality is even much more pronounced than in the "Newtonian" world of the past. This is illustrated by the fact that there exist many different "interpretations" of quantum mechanics that are completely different, but that lead to exactly the same formalism that allows us to make experimental predictions of unparallelled precision. That can only mean that those interpretations are irrelevant, there is no way to conclude that a certain interpretation is the correct one as there is no way to test one interpretation against another one. Such interpretations are merely crutches to help us conceiving that model in images that we more or less intuitively can relate to. Nevertheless there remains always a certain "weirdness" that we cannot reason away. Different interpretations merely shift that weirdness to different images, so that the choice of interpretation becomes a personal preference. From our intuition formed by living in a macroscopic world we'd like to imagine the world as consisting of exactly localized masses, as that is the way we perceive the world in our daily life. Nevertheless that image is wrong. So we cannot merely not know "reality", but we cannot even assimilate our experiences via scientific experiments at atomic scales by integrating them to a clear intuitive picture, we can only use our instruments and logic to describe them (just as we cannot perceive spaces of higher dimensions, only reason about them). That is also why Feynman said that nobody understands quantum mechanics, that doesn't mean that nobody could understand the technical details, but that the world they reveal is not well conceivable to us.

Be careful, Brant.

That was exactly my point...