goodmath en Moving on <span>Moving on</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> Finally, at long last, I can tell you what I've been up to with finding a new home for this blog. I've created a new, community-based science blogging site, called Scientopia. With the help of many wonderful people, we're ready. We launched this morning. So to continue following GM/BM - along with the work of many other wonderful bloggers, like Scicurious, Grrlscientist, Mike Dunford, Dr. Skyskull, and lots of others, come on over to <a href="">Scientopia</a>, the new home of <a href="">Good Math/Bad Math"/a&gt;.</a></p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Mon, 08/02/2010 - 04:41</span> Mon, 02 Aug 2010 08:41:49 +0000 goodmath 92812 at Goodbye, Scienceblogs <span>Goodbye, Scienceblogs</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> So my decision is made. I'm closing up around here. I'm in the process of working out exactly where I'm going to go. With any luck, Seed will leave this blog here long enough for me to post an update with the new location. But I'm through with Seed and ScienceBlogs.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Wed, 07/07/2010 - 16:01</span> Wed, 07 Jul 2010 20:01:49 +0000 goodmath 92811 at Seed, Conflicts of Interest, and Sleaze <span>Seed, Conflicts of Interest, and Sleaze</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> As my friend <a href="">Pal wrote about</a>, Seed Media Group, the corporate overlords of the ScienceBlogs network that this blog belongs to, have apparently decided that blog space in these parts is now up for sale to advertisers.</p> <p> We've been advertiser supported since I joined up with SB. I've never minded that before. Providing a platform and bandwidth takes money, which has to come from somewhere. The way that ads have been handled before has been no problem: the ads are clearly distinguished from the content. There's no way that you're going to mix up one of my posts with a paid advertisement.</p> <p> Until now.</p> <p> Seed has, in its corporate wisdom, decided to let Pepsico buy its way into a blog on ScienceBlogs. Pepsi writes SMG a nice check, and suddenly their content gets mixed in to the ScienceBlog RSS feeds, the ScienceBlog feed to Google News, etc., <em>exactly</em> the way that my blog posts do.</p> <p> This is <em>not</em> acceptable.</p> <p> For now, I'm suspending my blog for a few days. If Seed decides to back out of this spectacular stupidity, then I'll start posting here again. If not, then I'll go looking for a new home for GM/BM. The money that I've made from the ads that Seed has sold has been nice - but it's not worth my integrity.</p> <p> If Blogs here are for sale, then I'm gone.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Tue, 07/06/2010 - 14:47</span> Tue, 06 Jul 2010 18:47:04 +0000 goodmath 92810 at Searching for Topics <span>Searching for Topics</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> As regular readers have no doubt noticed by now, posting on the blog<br /> has been slow lately. I've been trying to come back up to speed, but so<br /> far, that's been mainly in the form of bad math posts. I'd like to get<br /> back to the good stuff. Unfortunately, the chaos theory stuff that I was<br /> posting just isn't good for my schedule right now. Once you get past<br /> the definitions of chaos, and understanding what it means, actually<br /> analyzing chaotic systems is something that doesn't come easily to me - which<br /> means that it takes a <em>lot</em> of time to put together a post. And<br /> my work schedule right now means that I just don't have that amount of<br /> time.</p> <p> So, dear readers, what mathematical topics would you be particularly<br /> interested in reading about? Since I'm a computer scientist, my background<br /> obviously runs towards the discrete math side of the world - so, for the<br /> most part, the easiest topics for me to write about are from that side. But<br /> don't let that limit you: tell me what you want to know about, and I'll take<br /> the suggestions into consideration, and figure out which one(s) I have the time<br /> to study and write about.</p> <p> I don't want to limit you by making suggestions. I've tried that in the past, and<br /> the requests inevitably end up circling around the things I suggested. But I really want to<br /> know just what you want to know more about. So - fire away!</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Mon, 06/28/2010 - 05:02</span> Mon, 28 Jun 2010 09:02:24 +0000 goodmath 92809 at Saturday Recipe: Ginger Scallion Sauce <span>Saturday Recipe: Ginger Scallion Sauce</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> Today's recipe is something I made this week for the first time, and trying<br /> it was like a revelation. It's simple to make, it's got an absolutely<br /> spectacularly wonderful flavor - light and fresh - and it's incredibly<br /> versatile. It's damned near perfect. It's scallion ginger sauce, and once you<br /> try it, it <em>will</em> become a staple. To quote David Chang, whose cookbook<br /> I learned this from: if you've got ginger scallion sauce in the fridge, you'll<br /> never be hungry.</p> <p> There are two main variations of this: there's a cooked version, and a raw version. Mine is the raw version. I love the freshness of flavor, and while cooking it will intensify some of the flavors, it will also detract from that delightful freshness.</p> <p><b>Ingredients</b></p> <ul><li> Fresh ginger - roughly one inch, peeled.</li> <li> A bunch of fresh scallions.</li> <li> A teaspoon, give or take, of coarse salt.</li> <li> 1 tablespoon of soy sauce.</li> <li> 1 tablespoon rice vinegar.</li> <li> 1/4 cup oil - peanut oil, canola oil, or something<br /> other neutral oil. </li><li> A dash of sesame oil.</li> </ul><p><b>Instructions</b></p> <ul><li> Mince the ginger. Toss the minced ginger into a food<br /> processor.</li> <li> Cut the roots off of the scallions, cut them coarsely, and<br /> add them to the food processor.</li> <li> Add the rest of the ingredients to the food processor.</li> <li> Run the food processor until everything is finely ground into a<br /> smooth sauce.</li> </ul><p> That's it. Ginger scallion sauce. Taste it - make sure it's<br /> got enough salt. Don't add any soy sauce - just use plain salt if it<br /> needs any. </p> <p> So what can you do with it? Just about anything. A few<br /> great ideas:</p> <ol><li> Ramen noodles. Just cook up a batch of ramen, and toss it<br /> with a tablespoon of the sauce. You can also add some stir<br /> fried meat and veggies to make it a bit more filling. </li> <li> Grilled meats. Use a bit of the sauce as a marinade,<br /> then grill it, and dress it with a bit of the sauce<br /> when it's done.</li> <li> Use it instead of mayo on a sandwich.</li> <li> Add a bit more vinegar, and use it as a vinaigrette<br /> over a salad.</li> <li> Sautee some shrimp, and toss some ginger-scallion<br /> sauce in just before they're done.</li> <li> Get a nice whole fish, steam it cantonese style<br /> with just a bit of salt, soy, and sake. Spoon<br /> a bit of the sauce over it when it's done.</li> </ol><p> If you wanted to try to cooked version, you take the ginger, scallions, and salt, and puree them in the food processor. Then put them into a large pot. In a <em>different</em> pot, heat the oil up until it just starts to smoke, and then pour it over the ginger/scallion/salt mixture. When it cools, whisk in the rest of the ingredients.</p> <p> But like I said - I think it's best to just stick with it raw.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Sat, 06/26/2010 - 11:19</span> Sat, 26 Jun 2010 15:19:41 +0000 goodmath 92808 at The Surprises Never Eend: The Ulam Spiral of Primes <span>The Surprises Never Eend: The Ulam Spiral of Primes</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> One of the things that's endlessly fascinating to me about math and<br /> science is the way that, no matter how much we know, we're constantly<br /> discovering more things that we <em>don't</em> know. Even in simple, fundamental<br /> areas, there's always a surprise waiting just around the corner.</p> <p> A great example of this is something called the <em>Ulam spiral</em>,<br /> named after Stanislaw Ulam, who first noticed it. Take a sheet of graph paper.<br /> Put "1" in some square. Then, spiral out from there, putting one number in<br /> each square. Then circle each of the prime numbers. Like the following:</p> <p><img src="" alt="i-0afef8236fdd3fea23fbcfb35f81eeb6-ulam.png" /></p> <p> If you do that for a while - and zoom out, so that you can't see the numbers,<br /> but just dots for each circled number, what you'll get will look something like<br /> this:</p> <p><img src="" alt="i-aa21847004619e9491df4d005b0ce86c-ulam200.png" /></p> <p> That's the Ulam spiral filling a 200x200 grid. Look at how many diagonal<br /> line segments you get! And look how many diagonal line segments occur along<br /> the same lines! Why do the prime numbers tend to occur in clusters<br /> along the diagonals of this spiral? I don't have a clue. Nor, to my knowledge,<br /> does anyone else! </p> <p> And it gets even a bit more surprising: you don't need to start<br /> the spiral with one. You can start it with one hundred, or seventeen thousand. If<br /> you draw the spiral, you'll find primes along diagonals.</p> <p> Intuitions about it are almost certainly wrong. For example, when I first<br /> thought about it, I tried to find a numerical pattern around the diagonals.<br /> There are lots of patterns. For example, one of the simplest ones is<br /> that an awful lot of primes occur along the set of lines<br /> f(n) = 4n<sup>2</sup>+n+c, for a variety of values of b and c. But what does<br /> that tell you? Alas, not much. <em>Why</em> do so many primes occur along<br /> those families of lines?</p> <p> You can make the effect even more prominent by making the spiral<br /> a bit more regular. Instead of graph paper, draw an archimedean spiral - that<br /> is, the classic circular spiral path. Each revolution around the circle, evenly<br /> distribute the numbers up to the next perfect square. So the first spiral will have 2, 3, 4;<br /> the next will have 5, 6, 7, 8, 9. And so on. What you'll wind up with is<br /> called the <em>Sack's spiral</em>, which looks like this:</p> <p><img src=" spiral.png" alt="i-8e4cdfc0a83e388851408bd4b44fd1e4-Sacks spiral.png" /></p> <p> This has been cited by some religious folks as being a proof of the<br /> existence of God. Personally, I think that that's silly; my personal<br /> belief is that even a deity can't change the way the numbers work: the<br /> nature of the numbers and how they behave in inescapable. Even a deity who<br /> could create the universe couldn't make 4 a prime number.</p> <p> Even just working with simple integers, and as simple a concept of<br /> the prime numbers, there are still surprises waiting for us.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Tue, 06/22/2010 - 05:58</span> Tue, 22 Jun 2010 09:58:52 +0000 goodmath 92807 at Metaphorical Crankery: a bad metaphor is like a steaming pile of ... <span>Metaphorical Crankery: a bad metaphor is like a steaming pile of ...</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> So, another bit of Cantor stuff. This time, it really isn't Cantor<br /> crankery, so much as it is just Cantor muddling. The <a></a> href=""&gt;post<br /> that provoked this is not, I think, crankery of any kind - but it<br /> demonstrates a common problem that drives me crazy; to steal a nifty phrase<br /> from, people who can't count to meta-three really shouldn't try<br /> to use metaphors.</p> <p> The problem is: You use a metaphor to describe some concept. The metaphor<br /><em>isn't</em> the thing you describe - it's just a tool that you use. But<br /> someone takes the metaphor, and runs with it, making arguments that are built<br /> entirely on metaphor, but which bear no relation to the real underlying<br /> concept. And they believe that whatever conclusions they draw from the<br /> metaphor must, therefore, apply to the original concept.</p> <p> In the context of Cantor, I've seen this a lot of times. The post that<br /> inspired me to write this isn't, I think, really making this mistake. I think<br /> that the author is actually trying to argue that this is a lousy metaphor to<br /> use for Cantor, and proposing an alternative. But I've seen exactly this<br /> reasoning used, many times, by Cantor cranks as a purported disproof. The<br /> cranky claim is: Cantor's proof is wrong, because <em>it cheats</em>. </p> <p> Of course, if you look at Cantor's proof as a mathematical construct, it's<br /> a perfectly valid, logical, and even beautiful proof by contradiction. There's<br /> no cheating. So where do the "cheat" claims come from?</p> <!--more--><p> Muddled metaphors.</p> <p> A common way of describing Cantor's proof is in terms of games. Suppose<br /> I've got two players: Alice and Bob. Alice thinks of a number, and<br /> Bob guesses. Bob wins if he guesses Alice's number.</p> <p> If Alice is restricted to a finite set of integers, then Bob will<br /> win in a bounded set of guesses. For example, if Alice is only allowed<br /> to pick numbers between 1 and 20, then Bob is going to win within 20 guesses.</p> <p> If Alice is restricted to natural numbers, then Bob will win - but it<br /> could take an arbitrarily long time. The number of steps until he wins is<br /> finite, but unbounded. His strategy is simple: guess 0. If that's not it, guess 1. If<br /> that's not it, guess 2. And so on. Eventually, he'll win. And, in fact, after<br /> each unsuccessful guess, Bob's guess is <em>closer</em> to Alice's number.</p> <p> If Alice can use integers, then it gets harder for Bob - but it doesn't<br /> really change much. Still, in a finite but unbounded number of guesses, Bob<br /> will get Alice's number and win. Now, the "closer every guess" doesn't really<br /> apply any more - but something very close does: there are no steps where Bob<br /> gets <em>further away</em> from the absolute value of Alice's number; and<br /> every two steps, he's guaranteed to get closer to the absolute value of<br /> Alice's number.</p> <p> We can make it harder for Bob - by saying that Alice can pick any<br /> fraction. Now Bob's strategy gets much harder. He needs to work out a system<br /> to guess all the rationals. He can do that. But now the properties about<br /> getting closer to Alice's number no longer apply. He's no longer doing things<br /> in an order where his value is converging on Alice's number. But still, after<br /> a finite number of steps, he'll get it.</p> <p> Finally, we could let Alice pick any <em>real</em> number. And now,<br /> the rules change: for any strategy that Bob picks for going through the<br /> real numbers, Alice can find a number that Bob won't even guess.</p> <p> There's a fundamental asymmetry there. In all of the other versions of the<br /> game, Alice had to pick her number first, and then Bob would try to guess it. Now,<br /> Alice doesn't pick her number until <em>after</em> Bob starts guessing - and she<br /> only picks her number after knowing Bob's strategy. So Alice is cheating.</p> <p> The game metaphor demonstrates the basic idea of Cantor's theorem. The<br /> naturals, integers, and rationals are all infinite sets, but they're all<br /> countable. In the game setting, <em>even if</em> Alice knows Bob's strategy,<br /> she <em>can't</em> pick a number from any of those sets which Bob won't guess<br /> eventually. But with the real numbers, she can - because there's something<br /> fundamentally different about the real numbers. </p> <p> Of course, if it's a game, and the only way that Alice can win is<br /> by knowing exactly what Bob is going to do - by knowing his complete<br /> strategy from now to infinity - then the only way that Alice can win is<br /> by cheating. In a game, if you get to know your opponent's moves in advance,<br /> and you get to plan your moves <em>in perfect anticipation</em> of every<br /> move that they're going to make --- you get to <em>change</em> your move<br /><em>in reaction to</em> their move, but they don't get to respond likewise<br /> to your moves --- that is, by definition, cheating. You've got an unfair<br /> advantage. Bob has to pick his strategy in advance and tell it to Alice, and<br /> then Alice can use that to pick her moves in a way that guarantees that<br /> Bob will lose.</p> <p> The problem with this metaphor is that <em>Cantor's proof isn't a<br /> game</em>. There are no players. No one wins, and no one loses. The<br /> whole concept of fairness <em>makes no sense</em> in the context of Cantor's<br /> proof. It makes sense in <em>the metaphor</em> used to explain Cantor's<br /> proof. But the metaphor isn't the proof. A proof isn't a competition.<br /> It doesn't have to be <em>fair</em>; it only has to be <em>correct</em>.<br /> The fact that what Cantor's proof does would be cheating if it were a game<br /> is completely irrelevant.</p> <p> This kind of nonsense doesn't just happen in Cantor crankery. You see the<br /> same problem <em>constantly</em>, in almost any kind of discussion which uses<br /> metaphors. There are chemistry cranks who take the metaphor of an electron<br /> orbiting an atomic nucleus like a planet orbits a sun, and use it to create<br /> some of the most insane arguments. (The most extreme example of this in my<br /> experience was a guy back on usenet, who called himself Ludwig von Ludvig,<br /> then Ludwig Plutonium, and then <a></a> href=""&gt;Archimedes Plutonium. He went<br /> beyond the simple orbit stuff, and looked at diagrams in physics books of<br /> "electron clouds" around a nucleus. Since in the books, those clouds are made<br /> of dots, he decided that the electrons were really made up of a cloud of dots<br /> around the nucleus, and that our universe was actually a plutonium atom, where<br /> the dots in the picture were actually galaxies.) There are physics bozos who<br /> do things like worry about the semi-dead cats. There are politicians who worry<br /> about new world orders, because of a stupid flowery metaphorical phrase that<br /> someone used in a speech 20 years ago. </p><p> It's amazing. But there's really no limit to how incredibly, astonishingly<br /> stupid people can be. And the idea of an imperfect metaphor is, apparently,<br /> much too complicated for an awful lot of people.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Thu, 06/17/2010 - 07:45</span> Thu, 17 Jun 2010 11:45:15 +0000 goodmath 92806 at The Unfalsifiable Theory Of Everything from viXra <span>The Unfalsifiable Theory Of Everything from viXra</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> Today is <a href="">another bit of rubbish from viXra!</a> In the comment thread from the<br /> last post, someone (I presume the author of this paper) challenged me to<br /> address this. And it's such a perfect example of one of my mantras that I<br /> can't resist.</p> <p> What's the first rule of GM/BM? <b>The worst math is no math</b>.</p> <p> And what a whopping example of that we have here. It's titled "Spacetime<br /> Deformation Theory", by one Jacek Safuta. I'll quote the abstract in its entirety, to<br /> give you the flavor.</p> <blockquote><p> The spacetime deformations theory unifies general relativity with quantum<br /> mechanics i.e. unifies all interactions, answers the questions: why particles<br /> have mass and what they are, answers the question: what is energy, unifies<br /> force fields and matter, implies new theories like spacetime deformations<br /> evolution. </p> <p>This is a theory of principle (universal theory delivering description of<br /> nature) and not constructive theory (describing particular phenomenon using<br /> specific equations).</p> <p> The theory is falsifiable, background independent (space has no fixed<br /> geometry), not generating singularities or boundaries.</p> <p> This is hard to believe but a belief has nothing to with it. The real<br /> intellectual challenge is to falsify the theory.</p> </blockquote> <!--more--><p> So, we've got what the author claims is a grand unification theory - the<br /> one thing that has evaded the best minds of the last hundred years! And it's<br /> falsifiable! Wow!</p> <p> Unfortunately, as we'll see, it's <em>not</em> falsifiable in any<br /> meaningful way, because <em>it doesn't make any predictions</em>.</p> <p> One of the important qualities of a genuine scientific theory is that<br /> it makes predictions. That is, a theory isn't a vague bundle of words; it's<br /> something precise, which describes some aspect of reality to a sufficient<br /> degree of details that it allows a scientist to make predictions, and then<br /> perform a test in reality that checks whether or not the prediction is<br /> correct. The most important property of a prediction is its potential to<br /> be <em>wrong</em>. A testable theory makes a prediction <em>which isn't guaranteed<br /> to be correct</em>.</p> <p> As a quick aside, this is the difference between intelligent design and<br /> evolution. ID can take <em>any</em> evidence, and say "That's what the<br /> designer wanted". Mike Behe can predict that there are no "irreducibly<br /> complex" systems. But when push comes to shove, he never defines irreducibly<br /> complex in a testable way. He can conclude that some system is IC; but if<br /> it's proved that it's not, that doesn't invalidate ID. It just shows that that<br /> one system isn't IC - and he'll just wave his hands and point at another<br /> dozen that he claims are. Even if you could get him to accept the idea that IC isn't<br /> a proof of anything, ID remains perfectly fine: there's <em>nothing</em> that<br /> can invalidate it.</p> <p> Evolution is thoroughly falsifiable. It predicts, for example, that all living<br /> things have a common ancestor. And test after test has supported that. If you can<br /> show a single species that <em>isn't</em> derived from the common ancestor,<br /> evolution goes down. If you can show a single feature of a single species that<br /> really couldn't have been the result of evolution, then evolution goes down.</p> <p> In the case of our friend Jacek, he's got a non-falsifiable "theory". It's<br /> so woefully vague that there's nothing in the world that could possibly<br /> falsify it. It's got plenty of problems, but due to its vagueness, any problem<br /> that could potentially be used to falsify it can be handwaved away.</p> <p> So what's his theory? Basically that <em>everything</em> is a distortion<br /> of spacetime. What appears to be a particle is really just a distortion of<br /> spacetime - a sort of pinch in the fabric of space around the location of the<br /> point. Forces are also distortions in spacetime - they're just shaped<br /> differently.</p> <p> To quote him:</p> <blockquote><p> Any interaction between spacetime deformations we notice as a force: we<br /> named them gravitational, strong and weak nuclear and electromagnetic. Any<br /> spacetime deformation (a physical object) interacts (a force) with all other<br /> objects (being the force itself!) </p> <p> A differentiation of forces depends only on gradient and size of the<br /> deformation subject to our detection. (see exemplary Figure 1). </p> <p>Read: <b>all<br /> interactions (forces) are only spacetime deformations with different geometry!</b></p> </blockquote> <p> So - all forces are the <em>same</em> deformations of spacetime. The<br /><em>only</em> distinction between the forces comes from the gradient and<br /> size of the spatio-temporal distortion.</p> <p> OK, here's one potential falsifier: he's claiming that gravity and<br /> electromagnetic forces are exactly the same thing. Why does a magnet only<br /> attract <em>certain</em> things, instead of everything? It's just a distortion<br /> in spacetime, right? He specifically claims that the differentiation of forces<br /> depends <em>only</em> on the gradient and size of the deformations. Gravity<br /> attracts everything equally. Magnetism attracts some things, and repels<br /> others. How can the same distortions behave so differently if they <em>only</em><br /> differ in gradient and size?</p> <p> Of course, he can wiggle out of that. Throw in a couple of extra dimensions,<br /> and claim that different dimensions distort differently. So the difference<br /> between forces could be their size and gradients <em>in different dimensions</em>.<br /> Presto! Easy.</p> <p> After this, he gets to something that he seems to believe is<br /> profound:</p> <blockquote><p> 3.11. Finally, we can ask the question: what is pressure? And answer: it is a<br /> spacetime deformation. </p></blockquote> <p> I'd love to know who asked that question? Or rather, who asked that<br /> question without knowing the answer? Since when is the nature of<br /><em>pressure</em> a problem?</p> <p> Now, we move on to the very best part. He's got an entire section<br /> that's titled "Mathematics". It starts off with the statement:</p> <blockquote><p>Hooke's law in simple terms says that strain is directly proportional to stress. </p> <p> Tensor expression of Hooke's Law</p> </blockquote> <p> (The incomplete second sentence is exactly as it appears in the<br /> paper.)</p> <p> What does Hooke's law have to do with anything? He never says. The rest of<br /> the "mathematics" section is essentially content free.</p> <p> There's one drawing that is supposedly<br /> an example of a particle in spacetime. What kind of particle? Unspecified.<br /> What are the axes? Unspecified. What's the magnitude? Unspecified.</p> <p> Then, there's a couple of bell-curves, which supposedly illustrate the<br /> "spacetime density of nuclear matter". They're just absolutely traditional<br /> illustratory statistical bell-curves, with no unit on the Y-axis, and the<br /> x-axis measured in standard deviations. Standard deviations from what? He doesn't<br /> bother to say. (In fact, in the bibliography, he credits the bell-curve<br /> illustrations to wikipedia.)</p> <p> And that's the end of the paper. That's it.</p> <p> For a supposed GUT, it's really missing a lot of things. For example,<br /> it claims to explain the nature of particles - they're distortions<br /> in spacetime. But the problem for the theory is, particles only occur<br /> in certain, very limited forms. There are only 12 kinds of particles. If it's<br /> all just continuous distortions in spacetime, then why aren't there a<br /> continuum of particle sizes? Why does charge come in discrete units? Why<br /> do electrons only exist in discrete energy levels, instead of a continuum?<br /> The theory doesn't explain this. It <em>seems</em> like it predicts<br /> a continuum of particle sizes/strengths. But we can't falsify it that<br /> way, because it's too vague. He can wave his hands, and claim that there's<br /> some reason for it.</p> <p> He clearly states that there's no wave-particle duality: "The<br /> wave-particle duality notion is not necessary any more as wave and particle<br /> are the same thing. We can assume a particle to be a transverse or<br /> longitudinal wave." And yet, there are very concrete experiments - the dual<br /> slit experiment - that can demonstrate both non-particle wave behavior, and<br /> non-wave particle behavior. As described, his theory can't explain that. But<br /> we can't say that it falsifies it either, because once again, there's just not<br /> enough precision here to say, definitively, what he means by "assume a<br /> particle to be a transverse or longitudinal wave".</p> <p> It's really quite an astonishingly bad pile of rubbish. And despite<br /> the author protestations to the contrary, it's a perfect example of a<br /> non-falsifiable pile of rubbish, because it lacks anything approaching the<br /> precision or completeness that would allow it to make a falsifiable<br /> prediction.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Fri, 06/11/2010 - 08:29</span> Fri, 11 Jun 2010 12:29:53 +0000 goodmath 92805 at Gravity, Shmavity. It's the heat, dammit! <span>Gravity, Shmavity. It&#039;s the heat, dammit!</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> Sorry for the ridiculously slow pace around here lately; I've been<br /> ridiculously busy. I'm changing projects at work; it's the end of the school<br /> year for my kids; and I'm getting close to the end-game for my book. Between<br /> all of those, I just haven't had much time for blogging lately.</p> <p> Anyway... I came across <a href="">this lovely gem</a>, and I couldn't<br /> resist commenting on it. (Before I get to it, I have to point out that it's on<br /> "". viXra is " is an e-print archive set up as an<br /> alternative to the popular service owned by Cornell University. It<br /> has been founded by scientists who find they are unable to submit their<br /> articles to because of Cornell University's policy of endorsements<br /> and moderation designed to filter out e-prints that they consider<br /> inappropriate.". In other words, it's a site for cranks who can't even post<br /> their stuff on arXiv. Considering some of the dreck that's been posted an<br /> arXiv, that's pretty damned sad.)</p> <p> In my experience, when crackpots look at physics, they go after one of two<br /> things. Either they pick some piece of modern physics that makes them<br /> uncomfortable - like relativity or quantum mechanics - and they try to force <em>some</em><br /> argument that their discomfort with it must mean that it's wrong. The other big one<br /> is free energy - whether it's perpetual motion, or vacuum energy, or browns gas - the<br /> crackpots claim that they've found some wonderful magical process that defies the laws<br /> of thermodynamics in order to make limitless free energy. The cranks rarely (not never,<br /> but rarely) go after the kinds of physics that we experience every day.</p> <p> Well, this is something different. This guy basically wants to claim that<br /><em>gravity</em> doesn't really exist. And along the way, he claims to have solved<br /> the problems of dark matter and dark energy. See, we've all got it totally wrong<br /> about gravity! Gravity isn't a force where matter attracts other matter. It's<br /> a force where <em>warm things</em> attract other warm things! Gravity is actually<br /> a force created when things radiate heat.</p> <!--more--><p> As evidence of this, the author claims to show how heating a copper sphere<br /> changes its apparent mass! The author claims that if you put a 1068 gram<br /> copper sphere above a 1000 watt heat element for 400 seconds will<br /><em>increase</em> its mass by 20 grams - almost two percent! And <em>no<br /> one</em> has ever noticed this before!</p> <p> Even better - if you put a copper hemisphere placed concave side up, below<br /> two spheres full of ice, and you turn on a 1000W heat element for 500 seconds,<br /> the mass will change by nearly <em>10 percent</em>! And once again, <em>no<br /> once noticed it</em> before our intrepid author!</p> <p> Now, a sane person, looking at this, would immediately say that this<br /> is almost certainly an error. I mean, think about what it means: you can,<br /> using the burner on your stove, change the mass of an object by<br /> nearly 10 percent in five minutes. Mass, which at non-relativistic<br /> speeds is effectively constant - can be varied by a <em>huge</em><br /> amount just in your kitchen!</p> <p> And yet... No one has ever noticed this before! Chemists, doing precise<br /> measurements, have <em>never noticed</em> that the mass of their experimental apparatus<br /> change when they heat them. Rockets, with precisely calculated thrusts to achieve particular<br /> orbits, have actually changed their masses when they're heated, and <em>no one noticed</em>.<br /> The space shuttle gets dramatically heavier during re-entry - and <em>no one noticed!</em>.</p> <p> These things are obvious. The magnitude of the changes that he claims to observe are<br /> absolutely <em>staggering</em>. And yet, no one else has every observed them.</p> <p> So, where's the bad math? It's an issue of magnitude and scale. On the one hand, he's<br /> producing absolutely <em>huge</em> numbers about how mass changes with moderate temperature<br /> change - heating a piece of copper over your kitchen stove can produce a<br /><em>ten percent</em> change in mass! But he doesn't consider the large-scale impacts<br /> that this would have.</p> <p> He works out, based on his observation of apparent mass changes in<br /> his copper spheres, how much heat you need to radiate to create a particular<br /> "gravitational" force. And he then uses that to work out how much difference you<br /> would need in the amount of heat radiated by the daylight side of the earth<br /> versus the night side of the earth to produce the earths orbit - according<br /> to him, it works out to about 0.08% difference. According to his computations,<br /> 8 ten-thousandths difference in the amount of heat being radiated is enough<br /> to produce the earths orbit.</p> <p> And yet - differences of similar or greater magnitude <em>don't make a difference</em>. He<br /> treats the entire daylight side of the earth as being completely uniform in heat<br /> radiation - when, in fact, it's not. The parts of the earth close to the day-night<br /> terminator actually radiate more heat that the parts of the earth close to the night-day line.<br /> So shouldn't the earths direction of acceleration be <em>different</em> because of that? </p> <p> Why does the moon orbit the earth? Why doesn't it show less attraction to<br /> the earth when it's on the dark side of the earth? Why doesn't a new moon<br /> (where the side radiating significant amounts of heat is faced away from the<br /> earth) have less gravitational attraction than a full moon (where the radiating face<br /> is full towards us)?</p> <p> He simply doesn't have a clue of what the numbers he's (mis-)measuring <em>mean</em>. So<br /> he's drawing nonsense conclusions that make absolutely no sense. Any attempt to actually<br /> understand the meaning of the mathematical results that he's computing would show<br /> that they can't possibly be right. But he never does that.</p> <p> Pathetic.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Tue, 06/08/2010 - 05:47</span> <div class="field field--name-field-blog-categories field--type-entity-reference field--label-inline"> <div class="field--label">Categories</div> <div class="field--items"> <div class="field--item"><a href="/channel/free-thought" hreflang="en">Free Thought</a></div> </div> </div> Tue, 08 Jun 2010 09:47:36 +0000 goodmath 92804 at Big Number Bogosity from a Christian College Kid <span>Big Number Bogosity from a Christian College Kid</span> <div class="field field--name-body field--type-text-with-summary field--label-hidden field--item"><p> I know that I just posted a link to a stupid religious argument, but I was sent a link to<br /> another one, which I can't resist mocking.</p> <p> As I've written about quite often, we humans <em>really</em> stink at<br /> understanding big numbers, and how things scale. <a></a> href=""&gt;This<br /> is an example of that. We've got a jerk who's about to graduate from a dinky<br /> christian college, who believes that there <em>must</em> be something special<br /> about the moral atmosphere at his college, because in his four years at the<br /> school, there hasn't been a <em>single</em> murder.</p> <p> Yeah, seriously. He really believes that his school is special, because it's gone four whole<br /> years without a murder:</p> <blockquote><p> Considering that the USA Today calculated 857 college student deaths from 2000<br /> to 2005, how does one school manage to escape unscathed? It's certainly not<br /> chance or luck. For Patrick Henry College, it's in our Christian culture.</p> <p> Critics mock us for our strict rules - like no dancing or drinking on campus,<br /> no members of the opposite sex permitted in your dorm room, nightly curfew<br /> hours - and the lack of a social atmosphere it creates. We have been the<br /> subject of books (God's Harvard), television shows, op-eds, and countless<br /> blogs who rant against our brand of overbearing right-wing Christianity that<br /> poisons society's freedom.</p> <p> Yet, what is the cost of students being able to "express" themselves? Is that<br /> freedom worth the cost of drunk driving deaths, drug related violence, and<br /> love affairs turned fatal?</p> </blockquote> <p> There were <em>857</em> college student deaths in the five-year period from 2000 to 2005! Therefore,<br /><em>any</em> college where there weren't any murders in that period must be something really<br /> special. That christian culture must be making a really big difference, right?</p> <p> Well, no. </p> <p> <a href="">According<br /> to Google Answers</a>, the US Census Department reports that there are 2363<br /> four year colleges in the US. So, assuming the widest possible distribution of<br /> student deaths, there were 1506 colleges with no student deaths in a five-year<br /> period. Or, put another way, more than 60% of colleges in the US went that five-year period<br /> without any violent student deaths.</p> <p> Or, let's try looking at it another way. According to the census, there are 15.9 <em>million</em><br /> people currently enrolled in college. The school that, according to the author, is <em>so</em><br /> remarkable for going without any murders in the last four years? It has <em>325 students</em>. Not<br /> 325 per class - 325 <em>total</em>.</p> <p> In other words, among a group making up less than 2/1000ths of one percent of the college<br /> population, there were no murders. Assuming that the distribution of violent deaths is perfectly<br /> uniform (which it obviously isn't; but let's just keep things simple), given that there were<br /> 857 violent deaths in the student population as a whole, how many violent deaths<br /> would you <em>expect</em> among the student body at his dinky christian college?</p> <p> That would be a big, fat zero. </p> <p> The fact that there were no violent deaths at his school isn't remarkable,<br /> not at all. But to a twit who's incapable of actually understanding what<br /> numbers mean, that's not the conclusion to be drawn. It's also not that the<br /> violent death among college students is actually remarkably rare. Nor is it<br /> that <em>most</em> college students will go through college without any<br /> violent deaths on campus. No - according to a twit, with <em>857</em> violent<br /> campus deaths over five years, the <em>only</em> reasonable conclusion is that<br /> there must be something special about the ridiculous religious rules at his college<br /> that prevented the great rampaging plague of violence from touching the students<br /> at his school.</p> <p> I actually spent five years as an undergraduate at Rutgers University in NJ. During that<br /> time, there were no violent student deaths. (There was one death by alchohol poisoning; and there<br /> was one drunk driving accident that killed four students.) But <em>zero</em> violent deaths.<br /> Gosh, Rutgers must have been an absolutely amazingly moral university! And gosh, we had<br /> all of those horrible sinful things, like <em>dancing</em>, and <em>co-ed dorms</em>!<br /> How did we manage to go all that time with no violence?</p> <p> It must have been the prayers of the very nice Rabbi at the Chabad house<br /> on campus. Yeah, that must be it! Couldn't just be random chance, right?</p> <p> Ok, now let me stop being quite so pettily snide for a moment. </p> <p> What's going on here is really simple. We <em>hear</em> a whole lot about violence<br /> on campus. And when you hear about eight-hundred and some-odd violent deaths on campus,<br /> it <em>sounds</em> like a lot. So, intuitively, it sure seems like there must be a whole<br /> lot of violence on campus, and it must be really common. So if you can go through your<br /> whole time in college without having any violence occur on campus, it <em>seems</em><br /> like it must be unusual.</p> <p> That's because, as usual, we really suck at understanding big numbers and scale. 800 sounds<br /> like a lot. The idea that there are nearly <em>sixteen million</em> college students is just<br /><em>not</em> something that we understand on an intuitive level. The idea that nearly a thousand<br /> deaths could be a tiny drop in the bucket - that it really amounts to just one death<br /> per 100,000 students per year - it just doesn't make <em>sense</em> to us. A number like 800 is,<br /> just barely, intuitively meaningful to us. One million isn't. Fifteen million isn't. And a ratio with a<br /> number that we can't really grasp intuitively on the bottom? That's not going to be meaningful<br /> either.</p> <p> Bozo-boy is making an extremely common mistake. He's just simply failing<br /> to comprehend how numbers scale; he's not understanding what big numbers really mean.</p> </div> <span><a title="View user profile." href="/goodmath" lang="" about="/goodmath" typeof="schema:Person" property="schema:name" datatype="">goodmath</a></span> <span>Tue, 05/04/2010 - 14:34</span> <div class="field field--name-field-blog-categories field--type-entity-reference field--label-inline"> <div class="field--label">Categories</div> <div class="field--items"> <div class="field--item"><a href="/channel/social-sciences" hreflang="en">Social Sciences</a></div> </div> </div> Tue, 04 May 2010 18:34:19 +0000 goodmath 92803 at