Tensorman

Indeed, what the first ball "did to it", in other words, an action. Neither the "nature" of the first ball nor the "nature" of the second ball can generate motion without the specific action of the first ball striking the second ball. If there is no action, nothing will happen. The "nature" of the second ball may determine what exactly happens after it has been struck (in other words, how it moves), but the cause of the movement is the event of the first ball striking the second one.

Ayn Rand, Art and Cognition (II), The Objectivist volume 10 number 5, May 1971, page 1 and page 6.

There seems to be a misunderstanding about Rand's use of "periodic" in her discussion of music. She does not mean that certain musical elements (motives, themes) are repeated in a composition, she's talking about periodic vibrations, i.e. sounds that have a definite pitch. A few quotes: It's clear that she distinguishes here periodic vibrations, which we hear as a musical tone with a definite pitch and non-periodic vibrations, sounds which don't have a clear pitch and which she calls noise. This is a physical and not a musical distinction, i.e. it doesn't concern the structure of the music (like: does it have repeating notes, motifs, rhythms), only its elementary building blocks themselves.

Periodic is by definition repeating. And a sine wave is one of the simplest periodic functions. Most music instruments produce much more complex periodic functions, which can be seen as the sum of a series of sine waves (with Fourier analysis any periodic function can be described as an infinite series of sine functions), with a ground tone that defines the base frequency and a series of overtones, the values and the amplitudes of which determine the timbre of the instrument.

A characteristic of any tone that can be recognized as such is that it is periodic, while non-periodic sound is perceived as noise with which we cannot associate a tone. For example the "concert A" is defined as an oscillation with frequency 440 Hz. That in practice such tones are not exactly periodic is in my view not essential. It is like saying that the Earth is a sphere, which is also only an approximation, but that is also true for a billiard ball. Further, periodic does not necessarily mean a sine wave, in general a tone will be a mixture of more or less audible sine waves with different frequencies, in which the lowest in general is the strongest and defines the tone. Even most percussion instruments produce periodic vibrations, only these are of short duration and often have different and strong overtones, so that the tonal quality is less obvious, but in most (not all) cases still a tone (defined by the periodic character of the sound) can be discerned. That in music tones change continuously in frequency and volume doesn't change the fact that the building blocks are periodic - even if not exactly, still quite accurately as we can hear quite small deviations of frequency, which if they are unintended (as in a string vibrato, a kind of second-order periodicity) can be experienced as "out of tune".

A modern axiomatic mathematical theory of Euclidean geometry is given by Hilbert's axioms. These formal axioms are chosen so that they correspond to our more intuitive notion of geometry, just as Peano's axioms are a formalization of our intuitive notions of natural numbers.

The answer is trivial. There is no single "correct" definition of "sound". One of the definitions refers the physical phenomenon of sound waves, another one to that what is perceived by a human being as sound. These are two different things, although they are related. The first one is a physical concept, the second one a physiopsychological concept. With the first definition the answer is yes, with the second one no. It is simply a semantic issue, because of the ambiguity in the meaning of the word "sound".

I haven't followed that thread, but the fact that 1 = .9999...repeating follows by elementary logic from the mathematical definitions and notation, it's no nonsense, on the contrary, it's the only logical answer. But perhaps you don't like logic...

Neither is there a quantity as +1 in real life. Things like 1 cow or 1 dollar do exist in real life, but not the number 1. The latter is an abstraction that can be useful in counting real things, so that an abstract concept like natural number has a useful application in real life. Exactly the same holds for other abstract notions like negative numbers, rational numbers, real numbers or complex numbers. These can all be used for real-life applications, in the case of negative numbers for example for bookkeeping (an extension of the notion of counting) and in the case of complex numbers for example for electrical circuits. In general the connection between the abstract concept of a certain kind of number will be more "complex" (no pun intended) for more general categories, like complex numbers, than for natural numbers (counting things). That in the latter case the link between number and real object is simple (counting) does not mean that the number (an abstract concept) and the object (cow, dollar, real objects) are the same. So when you realize that all numbers are abstract and there doesn't exist any number in reality, but that those numbers and the corresponding theories can be applied to real life situations, there isn't any problem.

Rats and flies are still much too large, but such experiments have been done successfully with atoms and even relatively large molecules. Those can be brought in a superposition of states, also called 'cat states'. For larger systems the phenomenon of decoherence makes the existence of such states practically impossible. That is also the modern answer to the riddle of Schrödinger's cat: QM does not predict that a macroscopic system like a cat can exist in a superposition of two different states (alive and dead), it will always be either alive or dead. At Schrödinger's time this was not yet known, but today the fate of his cat is no longer a riddle, it has been solved years ago. But of course popular books still like to present such old ideas because they sound so mysterious. The same for the problem of a consciousness that seems to seal the fate of the cat (Wigner's friend theories), thanks to the decoherence explanation consciousness is no longer needed in the explanation, the cat is already dead or alive before anyone looks, in accordance with our macroscopic intuition (which works well for macroscopic systems, but fails at atomic scales, as we've never experienced those directly in our lives).

Your assumption is wrong. Of course I'm referring to Beethoven and his view of life that is expressed in his music, and that is not a belief that man has no chance of winning, as Rand said, but that struggles can be won. If that's idiotic, that's because these are your words, not mine. That shows that you know nothing about Beethoven's music, it's completely nonsense. A composer that would fit that description is Tchaikovsky, now there you have a composer whose music reflects a malevolent universe.

Rand: "It is the view that has been called Byronic...it is the belief that man must struggle even though he has no chance of winning, and that he must perish heroically...and that is what I hear in practically everything Beethoven has ever written. " This is absolute nonsense. If there is any composer who personifies winning struggles, it is Beethoven. See for example his 3rd, 5th and 9th symphony. Sorry, but Rand had here no idea what she was talking about.

The horizon must be lower than the hills at the left side, somewhere between the hill/air border and the hill/water border at the left, it would intersect the figure somewhere at her left breast. That implies that the perspective of the figure is also wrong, unless you suppose that she's leaning to her left side, which is contradicted by the position of the rest of her body. From the figure alone you'd guess that the horizon is somewhere at the lower part of her neck.

Yup. The flow of the water in the right upper corner is impossible, it's the same "sloping platform" error.

Here are some examples (it may take some time before the pictures appear in full resolution) http://uofugeron.files.wordpress.com/2009/...nce-of-time.jpg http://z.about.com/d/arthistory/1/0/c/i/da...oma_0708_02.jpg http://z.about.com/d/arthistory/1/0/h/i/da...oma_0708_07.jpg http://z.about.com/d/arthistory/1/0/i/i/da...oma_0708_08.jpg http://z.about.com/d/arthistory/1/0/u/i/da...oma_0708_20.jpg http://tinyurl.com/n48v7g They all have some platform or a similar structure that logically would be horizontal, but that has the perspective of a strongly sloping surface (in most cases sloping upward seen from the viewer).

You're right, this is one of the greatest marvels in music! I think you should explore further, then you'll discover that there is a lot of classical music that is far from boring. Live concerts can be a revealing experience! I've more than once been converted hearing a work in a concert which I knew from radio or cd and which I didn't care for.

Oh no, then you still don't know Bach... I don't know Shine, but I know Rachmaninoff's music very well. The comparison Rachmaninoff - Bach is somewhat like the comparison Spillane - Hugo. For quick and easy trills Spillane is fine, but for the real work you'll have to read Hugo, which may not reward you much however, if you haven't already built up the necessary reading skills. Of course you shouldn't take this comparison too literally, it's just to give an idea what I mean. Well, the fact that I've played a lot of Bach myself of course will have helped, which also prompted me to read books about his music, such as a monograph on the WTC. On the other hand I also deeply enjoy a work like St. Matthew's Passion which I cannot play myself (well, apart from playing through a piano transcription and singing along with "Mache dich mein Herze rein"). While Bach always had an immediate appeal to me, studying his music (active and passive) has immensely deepened my appreciation.

Bach is a giant, he is the alpha and omega of music. Rachmaninoff is a composer of some beautiful music but he certainly doesn't belong in the class of Bach. But to appreciate Bach's music you'll have to know more than a few popular pieces like the Toccata and Fuga in d minor (it isn't even certain that this is a work by Bach!). His range of emotions is enormous, from the most sorrowful to the most joyful of music, from monumental to very intimate. It takes many years to begin to appreciate the richness and complexity of for example the WTC with its often subtle connection between each prelude and fugue. So don't dismiss Bach if you hardly know him.

Rounin: good posts, you have a good grasp of the problem. The point is that determinism isn't incompatible with what we call "free will". The possibility of deliberating and making choices does not imply that these choices are not determined.

In a previous post you said that it didn't have a horizon line at all. Now that was hardly something new in painting, as indoor scenes, still lifes and portraits for obvious reasons don't have a horizon line in most cases. Perhaps you meant that the background is very sketchy. But that isn't anything new either, already for centuries portraits often had only sketchy backgrounds. See for example many of Rembrandt's portraits, or compare the Fifer with this painting by Velazquez, which was painted more than 200 years earlier:

No, that wouldn't be logical. We're looking down on their backs, so the horizon must be higher. When the people in the painting would straighten up to a standing position, their heads would be approximately at the height where the horizon now is, in other words, at normal eye level. So there is nothing wrong with the height of the horizon, and it's certainly not "absurdly high".

I think that the idea behind the Matrix is very interesting and that it could in principle be the basis of a great film. Unfortunately they botched it and made it into a third rate action movie.

I prefer a good old movie which takes its time and has a good plot over most modern movies with all their silly chases and fights and special effects.

I agree wholeheartedly. A few weeks ago I saw the first movie for the first time (I haven't seen the other ones, and I don't intend to see them), and I found it a terribly bad movie, in fact it was so childish that it was laughable.

No, the lack of an upper bound is the definition of infinity, they are exactly the same things. So we can for example prove that there are infinitely many prime numbers by showing that the hypothesis that there is a largest prime number (i.e. the set of prime numbers has an upper bound) results in a contradiction.