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Adrian Hester

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Everything posted by Adrian Hester

  1. Do you mean "What it does is repeal...restrictions on a right which is already denied" or something similar?
  2. You mean the 1982 Carpenter film, not The Thing from Another World (1951) that it was sorta based on (or that shared the same source, anyway), right? I like the original story most myself, John Campbell's "Who Goes There?"
  3. I'm not Jewish, nor am I very familiar with Judaism, but do you mean Purim here? (Or is Purim counted as part of Passover?)
  4. Reviving this thread to make a couple of additions I should have thought of earlier... And then there's Giannini's student Nicolas Flagello. I recommend him very highly. And Morten Lauridsen has written some very fine choral music.
  5. I agree, but I also consider it a meaningful day in one sense: It's the eve of National Half-Off Chocolate Day!
  6. Cool! Not only will I get to buy myself chocolate and booze (I could hit two birds with one stone with a Brandy Alexander, yum), I'm encouraged to write private letters to myself--and if they're cool enough they'll be made public! How enlightened--public masturbation is illegal in most places.
  7. Hardly. Confucius lived 551-479 BC, Aristotle 384-322 BC, so less than two centuries.
  8. No, in the standard theory a neutrino is considered to have an anti-particle. Photons and the Z-boson are considered to be their own anti-particles, as are nonfundamental particles like the pion (composed of an up or down quark and its antiquark). No it doesn't. No it can't, because an electric dipole field drops off as the cube of the distance. You can sum over a great number of randomly-arranged dipoles to eliminate the angular dependence of each dipole, but you cannot combine all those dipole fields to produce an inverse-square law. (Indeed, you wouldn't even get an inverse-cube force field, since the dipoles would effectively cancel out thanks to the angular dependence of the field symmetrical about the dipolar axis, giving a net field of zero with random brief fluctuarions about zero.) Mathematically impossible to get anywhere near an inverse square field, just won't work. Huh? They look like big clouds in the sky, and they act like small bundles of rock with large accretions of ice and other frozen matter--which is what you'd expect, since that's what they are. "Euphemistically"? Nonsense. Matter vaporizes off the surface as the Sun's radiation heats it and pushes the comet the other way in accordance with Newton's Third Law. There's no euphemism--those are precisely accelerations resulting from non-gravitational forces (reaction forces, to be precise). More nonsense. If it's an electrmagnetic force, then metals will not permit the force to pass through them while non-metals will act like dielectrics or whatever, precisely as they do for the coulomb field of a bare electric charge. Sorry, that's an ineluctable consequence of the nature of electromagnetism. No gravity, sorry. Nonsense. You need high temperature is all, as you'd know if you actually knew any plasma research. Indeed.
  9. Well, I'm much more a hard-bop straight-ahead guy myself and prefer my Hancock in Maiden Voyage territory, and perhaps I'm just a benighted bourgeois fuddy-duddy but I still think Ron Carter is the best bassist. For me, something like Geri Allen's Twenty-One with Ron Carter and Tony Williams is dreamy-good stuff indeed; to me, that's ambrosia. On the other hand, I don't think we have much argument about Wayne Shorter's abilities (though you might laugh at my saying Hank Mobley's under-rated in comparison--not that he's as good, just that he had the misfortune of playing when he did). And notice how it all comes back to Miles Davis? Maybe I'm just not as advanced as you... (Seriously, your dudes are just not my cup of tea, but they don't offend me either, what I've heard. And jazz guitar, I'm just not much of an afficionado apart from Django; but since I don't seek it out, I don't know much beyond Joe Pass and Pat Metheny, both of whom I like, so I don't count my opinion as worth more than a bucket of cold spit.)
  10. Leonard Peikoff has already addressed this issue in a Q&A of 1 Nov 2006. (I believe he asked that his answers not be quoted in other forums so as to avoid being taken out of context. Just scroll down most of the way to the bottom; it's the second question under the date.)
  11. First, you should supplement those readings with a good book on philosophy of language. One suggestion is Bernard Harrison's An Introduction to the Philosophy of Language, which I found clear and interesting (many that I've read are pretty frustrating in not going back beyond or in some cases even as far as Frege; Harrison starts with Locke and then goes to Frege); Harrison leans to the later Wittgensteinian view of things, but he does a good job discussing rival views. You might also look for a book on linguistic semantics as opposed to formal semantics (the theory of meaning common in academic philosophy, which is heavily influenced by Frege and mathematical logic), though again you want a good survey that takes account of philosophical issues without digging too much into purely linguistic matters--one of Sir John Lyons's introductory texts would be good there. Here's how I'd suggest going about analyzing what each philosopher is arguing for. First, what is his theory of meaning? How does it relate to reference? Second, does he reduce meaning to strictly propositional content? Third, which is more basic, sentence meaning or word meaning? Fourth, does he emphasize reference or sense in analyzing word meaning? (Sense, at least in this sense [heh], means how a word contrasts in meaning with other words. That is, in cognitive science terms, does he take a view closer to prototypes or structuralism? Both are necessary in linguistics, but not necessarily in philosophy.)
  12. Don't go into it expecting the book (novella, actually) to answer those questions: It's very different from either this movie version or The Omega Man.
  13. Well yeah, I'd probably be uncomfortable if something made me squamish too. Especialy if it's a game of Naked Squamish growing out of Naked Twister. That would be even twistier and more twisted than Twister.
  14. Dude. DUDE. Alaska to Mexico to start--Pan Am Highway all the way!
  15. Smugling free will in by the back door here: If your thoughts are determined, then the fact that they might be changed in the course of blind, determined interactions with other blind, determined humans doesn't make your thoughts any less determined. Billiard balls change direction after colliding with other billiard balls--that doesn't change the fact that their motions are still all determined. Either one's thought processes change in a completely determined manner under the influence of others, in which case Peikoff's argument still fully holds, or else there's something else that does allow one to change one's thought processes (how? blank-out)--in which case, again, Peikoff is correct and there is free will. No, this is fallacious--if your thought is just like everything else in the universe, fully determined, then there's no way for evolution to introduce something non-deterministic; it's simply impossible, just as evolution couldn't equip a species with the ability to violate the Law of Conservation of Energy. In any case, the concepts of "advice" and "information" assume some degree of free will--the ability to weigh and choose among alternatives in the first case, a selective sorting and integration of data in the other. Only in the sense that "blind" is a better description of a deterministic mind. First, note the fact that if this argument even addresses Peikoff's argument, then once again free will has been smuggled in the back door here through the word "influence." If influence is used in the sense of a planet deterministically influencing the motion of another one through its gravitation, the resulting motion is still deterministic, as is the thought of the person influenced. If influence is used in the looser sense of the result of a simple interaction that might or might not sway someone's decision, then this means the person influenced has free will--he is able to choose to follow the influence or advice or take cognizance of information or to do otherwise. The basic error is a stubborn refusal to recognize that determinsim is all or nothing--the mind is just as much a part of the material world as a billiard ball, and if the world is deterministic, then that means that what you think was determined for all time by the conditions at any time in the past, and that fully includes the mind of the determinist. Adding in the influence of other minds is a red herring.
  16. Take a number in base 2 like 1110111001. First, add up the digits in boldface, that is, alternate ones starting with the last digit; call that sum A (here=3). Then add up the other digits; call that B (here=4). Then add A and two times B (here giving 11). If this sum is divisible by three, then the original number is as well. In this case, 11 is not divisible by 3, so neither is the original number (which is, if my addition is right, 953).
  17. It has been answered already, in case you missed it, in Laure's posting up the thread, and expanded on by hunterrose. First, there are other rectangles that meet the given requirement, an infinite number of them, in fact. (For example, the rectangles with sides x=2.1, y=42; x=2.5, y=10; and x=2.8, y=7.) If you mean why are there no other rectangles with integer sides, that too has been abnswered. For x between 0 and 2, the formula gives y<0, which is physically meaningless. For x=2, y is undefined (division by 0). For x>4, you get the same results as for x between 2 and 4, just with the roles of x and y reversed; thus, for integers x>4, you get the same rectangle as for a value of x between 2 and 4, just rotated 90 degrees. So, the only integers for which you can have distinct rectangles are for x=3 and x=4. In this case, both possibilities work.
  18. At the coffee shop I go to, it'll buy you three cups of coffee with a dime tip left over.
  19. But then again, the Greeks themselves had a fondness for finding integer solutions to equations (Diophantine equations)--essentially solving problems involving countable things. And when you think about it, it's pretty gruesome to consider the real-world significance of non-integer solutions to word problems about the number of cattle in two herds, say. On the other hand, there's nothing gruesome or unnatural about rectangles with non-integer sides.
  20. Okay, I can still give a stripped-down version of what I wrote while it's still fresh. You should look at it this way--there's a numerical view of numbers (in which numbers are written in digits and decimals) and a geometrical view (in which numbers are represented by lengths), and each has its strengths. The numerical view is very convenient for arithmetic and is very easily suited to treating questions of precision naturally--for one thing, the number of digits you list tells you how precise the measurement is. The problem is that numbers have to be written out in base notation, corresponding to the number of subdivisions you make to represent the fraction geometrically, and there is no base in which all fractions terminate (have a finite number of digits), essentially because there are infinitely many prime numbers. Changing the base allows you to represent some of these fractions as terminating, but changing the base is a bit of a pain compared to just choosing a different subdivision for your unit of length in geometry. (Plus, if you've been taught math using our decimal notation, base 10, the other bases are not at all natural to handle.) Then there's the question of numbers with infinitely many non-repeating digits, which are called irrational numbers. Rational numbers are those that are equivalent to a ratio of two whole numbers, or more precisely of integers* (and have either a finite number of decimal places or else repeat infinitely), while irrational numbers are not. Irrational numbers are not too much of a problem for the numerical view of numbers, especially for all practical uses, since they are exactly parallel to rational numbers--the rules and procedures for handling them in arithmetic are completely unchanged for rational and irrational numbers, and you just have to write them out to the precision needed so the question of how all later digits act is irrelevant. (They're not so convenient as rational numbers for number theory or just plain curiosity, however, since you have to calculate later digits than you might have written down with a formula--they're not as easily specified as rational numbers, in other words.) [* "Counting numbers" are 1,2,3... (Some people also call these the "natural numbers," which is what I know them as, while apparently others equate natural numbers and whole numbers.) "Whole numbers" are the counting numbers and 0. "Integers" are the whole numbers and the negatives of the counting numbers: ...-3,-2,-1,0,1,2,3...] However, irrational numbers are a bit troublesome philosophically for the geometrical view because they can't be measured in the same way as rational numbers. To represent a fraction, you subdivide a unit and add up some of the subdivisions--in other words, you reduce measurement to straightforward counting. 3/8 would be rpresented by dividing the unit into equal eights and taking the length of three of them, for example. You can't do that with irrational numbers. Take a square of side 1 and consider the diagonal across it; the length of that diagonal is irrational. What that means is that there's no finite subdivision of the side of the square that you can add up so many times to give the length of the diagonal (more precisely, add to the length of the side, since it's greater than 1), but it's quite easy to construct that length geometrically in other ways. (That is, the two lengths are said to be "incommensurable"; neither one can be measured by a finite number of finite subdivisions of the other.) What this means for the numerical view of numbers is that there is no base, no subdivision of numbers by thirds or fifths or hundred-thirteenths or what-not, in which an irrational number will be infinitely repeating--it's always infinitely non-repeating. He was one of the Sophists before Socrates; his most famous statement is "Man is the measure of all things." I know all this because I read a lot about the history and philosophy of science and also like to play around with number theory. (That's the study of integers, prime numbers, fractions, decimal representations, rational and irrational numbers, and so on; like geometry, it's a fine hobby if you want a mathematical hobby because you can go from simple basics to very interesting results without having to make a career out of it.) Yes, though a better, simpler example is the area of a right triangle--cut a rectangle in two across one pair of diagonals. The area is A=x*y/2; the 2 would never have a decimal because it's a pure number (essentially it results from counting one of the two halves of the rectangle, if you want to look at it that way). In pure math, that's all you need to say, but if you're talking about the area of a real triangle whose sides you've measured, you have to take a bit more trouble. First, you can only measure the length of each side to a certain precision; if the shortest division on your ruler is d, then you only know for sure that the real length of each side is within half that distance d from the measured value (x and y). (Well, in many cases that's the only significant imprecision--if the hatch marks on the ruler are about the same size as the division between them, that adds a comparable source of imprecision, and there's also the question of how straight the ruler edge is and how accurate the measurement of the right angle is. Sometimes these have to be taken into account in the final result, sometimes not. And then if you're doing calculations on a computer you have round-off error as well. No doubt SoftwareNerd or one of the other regulars could tell you some tales about that.) So, x is no longer than x+d/2 and no shorter than x-d/2, and the same with y, so the largest area the triangle can have is (x+d/2)*(y+d/2)/2, and the smallest (x-d/2)*(y-d/2)/2. (All of those 2's are pure numbers because they result from the geometry of the situation, not from measurement.) If you expand the products, you find that the area can be no more than (x+y)*d/4+d^2/8 larger than A (calculated from the x and y you measured), and no more than (x+y)*d/4-d^2/8 smaller than A. Then, if d is very much smaller than x and y, d^2 is very much smaller still, so you can ignore the term in d^2 (if it's the last step in your math) to that degree of precision and say that the precision (to be exact, the maximum error) in the area is (x+y)*d/4. You can do the same thing for the error formula for the length of the hypotenuse of a right triangle from the Pythagorean Theorem, but you'd have to know the series expansion for the square root of a sum to follow it, which I suspect you're not familiar with. In the geometrical view you don't have to worry about all that, and to get the result in pure math, you just set d=0.
  21. I just spent an hour replying to this, and the damn computer ate it. Sorry, I'm not up to doing it again.
  22. Your error in reading has already been corrected--in yards and square yards they are equal in value. But think about the question of yards and feet a bit more. How long is four feet in yards? 1.333333.... Four feet, by your argument, is precisely four feet and precisely measurable. Yet in yards it's not what you consider a measurable number--it's a number you say can't be used in measurement. Yet yards too are precisely measurable by your argument--three feet exactly. (And in fact, since a yard is defined as three feet, then it is precisely three.) If it's precisely measurable in one unit (feet), then if you change to a second unit (yards) precisely measurable in terms of the first unit, then surely it should be precisely measurable in that unit too, right? Yet suddenly by changing from feet to yards you get a (supposedly) unmeasurable length. No, that would be 4--without a decimal expansion it's the symbol for the integer in counting, not a measurement. If you write out the decimal expansion, then you're admitting a finite degree of precision, and no matter how many zeroes you write out, it's not infinitely precise. Again, false. You're being thoroughly misled essentially by the fact that we have ten fingers. As I already mentioned, it's quite easy to trisect a line segment, which means that you can divide a ruler into thirds, ninths, twenty-sevenths, and so on right down as far as you want with as much precision as you want (there's nothing special at all about dividing a ruler into tenths, hundredths, and so on instead or thirds), so in fact 2.6666.... is a number you can measure with just as readily as 4.000... The thing is, 3 is not a divisor of 10, so its decimal expansion is infinitely repeating. (And it's because it's infinitely repeating, roughly, which is what "rational number" means, that you can base a ruler on units of three. The case is different if they're infinitely many non-repeating digits.) But it still corresponds to a definite length precisely measurable by trisecting a unit if that unit is precisely measurable (though not one that will match up with any of the lengths ticked off on a ruler by subdividing it forever and ever by tenths, which is what the infinitely repeating threes means geometrically); otherwise you're in the position of saying that only some lengths can be precisely and meaningfully trisected, all others being meaningless lengths (essentially any lengths not formed from the original unit by combinations of repeated subdivisions by halves and fifths)--and this by simple virtue of the fact that you've chosen one essentially arbitrary length as your basic unit of length. If you choose a different unit, then many of these unmeasurable lengths will in general suddenly become measurable. This isn't meant to give you a hard time. Rather, it's worth going through because all of this has been an issue in the philosophy of mathematics since the Ancient Greeks, though in a slightly different form. How do mathematical entities connect to reality? How does abstract geometry relate to actual measurements? A common Greek reply was essentially Platonic, that they are pure forms or what-not imperfectly reflected in reality. (Though at least one Greek, Protagoras, took essentially your approach, which is to say that only what is concretely real is true--thus, he argued that because in physical reality all circles and lines have finite thickness, then no lines or circles can really intersect in only one point.) With the adoption of decimal notation, we moderns have additional questions--how do numbers in general relate to the integers, and more generally how do algebra and geometry connect up with each other? The way it's handled in modern mathematics is to use bare numbers--integers and pure fractions--to indicate what is countable and hypothesized to be precisely measurable, decimal expansions to indicate measurements to a certain degree of precision; and the pure, abstract mathematics is tied to real measurements by indicating the degree of precision in any subsequent measurement in terms of the precision of the first measurement.
  23. I just wanted to add that I think all of SN's choices were quite good ones.
  24. That depends on the person, but one good candidate would be Shelley's "Hymn to Intellectual Beauty." (I'm especially fond of the fifth stanza.) You might also want to point them to Coleridge's "Frost at Midnight." Both might be longer than you had in mind, however. A good one (if a bit dark) by Robert Frost is "Once by the Ocean ." On a less serious note, a fun one I loved when I was little was Robert Louis Stevenson's "The Dumb Soldier."
  25. Doesn't matter; you can always exactly trisect any given line segment in geometry. Take a line segment eight units long, trisect it with compass and straight-edge, project that length perpendicular to the two ends of the original line segment, and connect the other ends of the two perpendicular segments. The resultant rectangle, which is very easily constructed, will have the same perimeter in units of length as its area in units of length squared. Alternately, take a rectangle 8 feet by 24 feet--its area in square yards will have the same value as its perimeter in yards. In any case, the same objection holds for a square of side 4--either you accept an infinite precision in measurement (which is usually indicated by writing 4 and not 4.0), in which case 8/3 is just as valid a length as 4, or else you cannot say the side of your square is exactly 4.00000... units and its perimeter 16.00000... units and area 16.00000... units squared.
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