The continuum hypothesis has nothing to do with the calculus taught in high school, or this article for that matter. I like talking about math, though, so for those who don't know, here's a non-technical explanation of the continuum hypothesis.
(1) "smaller" sets: A set is a particular group of objects (numbers, fruit, names, your Toyota, etc.). Given two sets, we say the first is smaller than the second if (a) we can assign to each object in the first a corresponding, unique object in the second, yet (b) we cannot assign to each object in the second a unique object in the first. For instance, {1, 2, 3} is smaller than {apple, 1, Karen, Jim} since we can pair up 1 with apple, 2 with 1, and 3 with Karen, but any attempt to pair in the other direction will necessarily fail by using one of the numbers 1, 2, or 3 twice, breaking uniqueness. The good part of this definition is that it also makes sense for infinite sets, which is where the "just count it" definition breaks down.
(2) An unintuitive example: The natural numbers are just the numbers 1, 2, 3, 4, 5,.... They form an infinite set. The integers are just the numbers..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.... The integers contain the naturals so one might expect the naturals to be smaller than the integers. This is *not* the case, since I can pair each integer with a unique natural as follows:
0 with 1 1 with 2 -1 with 3 2 with 4 -2 with 5...
Thus (b) cannot be satisfied since the pairing attempt does not always fail.
(3) Real numbers: The real numbers are fractions like 4/5 together with the irrationals like pi or Sqrt(2). These also form an infinite set and again contain the naturals. However, they are "large" enough so that the naturals are smaller than the reals in the sense above; this is the content of Cantor's Diagonal Argument.
(4) The Continuum Hypothesis states that there is *no* set S where both (a) the naturals are smaller than S and (b) S is smaller than the reals. Intuitively, there is no "size" strictly between the naturals and the reals.
It turns out the Continuum Hypothesis is neither provable nor falsifiable under standard but technical assumptions; one can assume either its truth or falsehood without creating contradictions. It's probably the most famous example of an "undecidable" statement. In my experience, though it doesn't come up much among non-set theorists, there's no general consensus on which path to take. I suppose I lean towards accepting the generalized continuum hypothesis since it collapses down the hierarchy in an appealing way while also giving the axiom of choice as a bonus (which I actually "believe").
You're probably talking about the fact that an ordered field with the least upper bound property is equivalent to the real numbers (formal details here). Strictly speaking the axioms don't imply the existence of a system that satisfies them. Some construction is necessary, though several standard approaches can be carried out with only appeals to highly intuitive bits of set theory.
The list of axioms I linked isn't intuitive in the "nigh universally innate" sense. However, I've developed a fair amount of intuition regarding them. Their machine-like formal representation is not even remotely how I think about them, though it offers a compact and above all perfectly clear way to communicate.
While I tend to agree, I've always figured people get around rate limits by having a huge pool of addresses they try brute forcing. Rotate the addresses quickly enough to prevent being rate-limited (possibly using a botnet to spread the IPs around?). The odds of guessing correctly are essentially the same with either strategy (this actually has lower variance, though the expected number of compromised accounts should be the same).
Someone mentioned a good possibility in this vein: he reused his password on a site that got compromised which was then connected to his Hotmail account. He has a strong history of password reuse from the article.
Good point, thanks. He even mentions how he has slight variations on his new password for several accounts only because the sites have different rules. Password reuse motivating (1) makes sense, except that "my PC login [is compromised]" is unexplained in that case. He may have meant PC Pro site login, which would clear up the discrepancy nicely and explain everything.
How is this Microsoft's problem? The possibilities are...
(1) A guy writing articles about his new email address used a relatively weak password and someone guessed it
(2) He logged in on a compromised machine
(3) Microsoft has a genuine security problem
The guy leaped right to (3), which seems the least likely to me. Since "my PC login" has also been compromised, (2) seems right. I can't help but feel this would have been pointed out long ago if the service were Gmail instead of Hotmail.
Before it gets quoted back to me, he justified (3) by saying
although I have to say from anecdotal evidence that Hotmail seems far more susceptible to account hijacking than Gmail.
That's a very weak argument--it's based on anecdotal evidence and ignores possible differences between user populations. You'd think the editor of a magazine would take the time to write a thorough article instead of a knee-jerk one.
And even if there isn't, logic should be in place to suspend account who start mass emailing their contact lists with suspicious links, it shouldn't be that hard to stop.
The same thing was mentioned above, but all a hacker needs is the contact list. They can spoof your email address and bypass Microsoft entirely afterwards. Of course the same is true of all email providers.
In retrospect I wasn't clear, but by "gay sex" I was referring only to the physical act. To be clear, the straw man I intended to invoke might say, "a male inserting his penis into the anus of another male and humping till orgasm is unnatural", which is ridiculous considering the monkey example above.
Exclusive homosexuality is at least very rare in animals, so the reasons behind animal and human gay sex are often very different, as you imply.
But I do support the abolishment of 0 as a concept. It makes coding so much simpler.
Hear hear! I'm sick and tired of all these "null reference exceptions" and "segmentation faults" my programs keep throwing. Each time I debug them I find a 0. If 0 didn't exist, neither would my problems!
They did use base 20, but the way most people count with their hands and feet is in base 1, regardless of whether you use 10 fingers or 20 fingers + toes. You can somewhat reasonably count in binary on your fingers, but only up to 10^10 - 1 = 1023. Adding more states to each finger gets really difficult, and who needs to count so high on their fingers anyway?
According to this page each digit was written as some bars, each with value 5, plus some dots, each with value 1. You could imitate this system on your hands--eg. right hand for bars, left for dots. If you were good enough you could do the same with your feet for a total of two base-20 digits, though counting in binary nets you a larger maximum with hands only.
In case anyone was wondering, the AC's link above is an actual article complaining about ICANN. I thought it might be one of the usual troll pictures, but nope.
(OT: I can cross my eyes which for some reason makes everything very fuzzy; it's useful sometimes when I don't want to see something distinctly like now or when I'm looking through a page with spoilers all over. I've always vaguely wondered if everyone can do that.)
and I've never seen anything but appreciation for these people.
In general I agree, though I've been the "question guy" in some instances where it wasn't universally appreciated.
* In a quantum mechanics course that often lacked mathematical rigor (eg. the completeness property of Hilbert space was never explicitly mentioned) I asked some questions some of the physics students and the instructor viewed as minor details that weren't worth the time or effort to look into (eg. "how can we ignore infinitely many terms? maybe they'll add up to something large").
* In a chemistry course, once an instructor rushed through a derivation mostly by flashing through a bunch of integrals on his PowerPoint. I didn't feel I understood it very well so I asked for details, but it was clear from body language that the rest of the class wasn't interested in the material or derivation so I stopped. The instructor seemed to think discussing the details wasn't important either from his tone of voice and body language.
* I remember bringing up various questions outside of class to friends who sometimes weren't at all interested. As an example, an engineering course on signals did a little work with Fourier transforms, and I wondered if the Fourier series of an arbitrary signal accurately reconstructs that signal. I've since learned that it's a delicate question, and I can understand why the instructors completely ignored it; I did in class as well since it worked for the simple signals we played with.
If anyone's interested in the answer to the above question, there are actually continuous functions whose Fourier series does *not* converge to the original function at each point. In fact, to every continuous periodic function there is another continuous periodic function which differs from the original at each point by an arbitrarily small amount and where the partial sums of the Fourier series are unbounded on some non-empty set E. Still more is true: E can be taken to be dense, i.e. each real number is arbitrarily close to some point in E, and in fact E can be taken to be uncountable, so in some sense the Fourier series does not converge to the original function for points that are infinitely more numerous than the rational numbers. And by now everyone will have lost interest, which illustrates my original point that questions aren't universally appreciated.
The relevant journal is a non-traditional "open access journal" where articles are freely available (pseudo-random sample; others here), but article authors pay the publisher to publish. It's similar to self-publishing. I imagine TOISCIJ is not respected at all since in a brief search the only info I could find on it was related to the fake paper incident. While it is technically a "peer reviewed journal" (or at least it calls itself that, present evidence to the contrary), it's misleading not to immediately point out how it differs from most people's idea of traditional "peer reviewed journals".
Some scandals along the same lines:
* The Bogdanov affair, where two French twins, one a mathematician and the other a physicist, published apparent nonsense in respectable journals. Physicist John Baez (singer Joan's cousin, actually) called the papers "a mishmash of superficially plausible sentences containing the right buzzwords in approximately the right order. There is no logic or cohesion in what they write."
* The Schön scandal, where a German physicist claimed breakthroughs and published a number of papers. Journals withdrawing his papers include Science, Physical Review, Applied Physics Letters, Advanced Materials, and Nature.
* The Sokal affair, where a physicist published a rather hilarious paper in the journal Social Text. To be fair, that article was not peer-reviewed by a physicist.
No, the paper was not published and was not accepted at a conference. According to the article, the authors received word that the fake, computer generated paper had "been accepted for publication after peer-reviewing process in TOISCIJ [The Open Information Science Journal]".
They didn't take the hoax any further, though:
Davis said that he considered scraping together the $800 to see if Bentham would actually publish the fake paper, but considered that taking the hoax further would be "unethical."
"I think that the point has been made," he said. "And, I mean, it's $800, and I'm a graduate student."
The paper is clearly nonsense; here's a few lines from the beginning:
"Compact symmetries and compilers have garnered tremendous interest from both futurists and biologists in the last several years. The flaw of this type of solution, however, is that DHTs can be made empathic, large-scale, and extensible. Along these same lines, the drawback of this type of approach, however, is that active networks and SMPs can agree to fix this riddle."
I spent a while searching for a copy of the Yahoo! article and came up with nothing. I did find this story from a local news outlet that probably says about the same as the Yahoo! article did. I also wasn't able to find more than search engine hints of a followup article saying that the guy was released from the hospital. He missed out on a Darwin award, at least. I imagine he recovered mostly or completely.
Warp drive would be awesome. I'm not sure if a new particle (perhaps a new branch of particle physics?) or heavy revision to general relativity would be more satisfying to me as an explanation of dark matter / its purported effects. I'm not really knowledgeable enough in these matters to have a solid opinion either way. I just wanted to mollify what I see as a knee-jerk reaction against exotic dark matter and towards another Einstein-esque revision of previous notions about space and time
About my name, I think I was eating a bowl of Froot Loops when I made this account. Something about 4 o's struck me. I only later noticed the mild irony of a gay man picking a handle with "fruit" in it; it makes me smile from time to time:).
Agreed, atrocious summary and terrible title. Here's an alternate.
Survey Finds Too Little Dark Matter Near Solar System
The existence and approximate distribution of dark matter have become standard assumptions in cosmology. According to Nature, it "explains how structure arose in the Universe, how galaxies formed and how the rapidly spinning Milky Way manages to keep from flying apart." However, a paper recently accepted by the Astrophysical Journal studied stellar velocities in our part of the galaxy in an attempt to infer the amount of dark matter present near our solar system and came up with unsettling results. Moni Bidin, the study's lead author, concluded that "at most, only about one-tenth the amount of dark matter predicted by models could exist in the volume of space they examined." Astronomer Frederic Hessman, who is uninvolved in the study, put things bluntly: "If this is right, it turns everything totally upside-down." Physicists are calling for caution and several note the difficulty and sensitivity to error of the present results. Astronomer Chris Flynn, who approved Bidin's paper for publication, cautioned, "I wouldn’t throw out nearby dark matter quite yet” and “The measurement being made is very challenging, and there are a number of ways for it to miss the dark matter even if is there.”
I understand that saying "we don't know what dark matter is" is unsatisfying, but some particles don't interact much with other particles. Neutrinos are a great example, since they only take part in the weak force and gravity (so not the electromagnetic or strong forces). Is it so hard to believe that some matter interacts solely through the gravitational force? That would mean no electromagnetic effects and almost no interactions with other forms of matter. Such matter would only be noticeable at gravity-dominated, cosmological scales.
Who knows? Maybe there's a whole segment of matter humans are unfamiliar with which interacts very little with the matter we know about but interacts with itself in complicated ways. Maybe there are dark matter solar systems populated by dark matter people who are just as confused as we are about the weird gravitational anomalies caused by our otherwise invisible existence. Communicating through gravity would certainly be an interesting challenge! I don't really believe this, but my point is basically the same as Hamlet's: "There are more things in heaven and earth than are dreamt of in your philosophy"--that is, it's arrogant to expect humans to be in a position to observe all the parts of the universe. Perhaps some things are just hidden.
Your post and its high moderation made me feel overeducated, so I wrote a poem in archaic style to reinforce the feeling.
Today I chanced to Look Down from my Ivory Tower;
the Vision horrified me.
I saw the Peasants Clamoring blindly
for the Simplest Certain Knowledge
of the Calculus and of Physicks.
I saw the Depth of Divide betwixt us thus:
One Man's Hidden Knowledge is Offal to th' Other.
P.S. To be fair, the stuff you mentioned is somewhere around the programming equivalent level of "objects can have properties". P.P.S. Also, note the pun on "offal"/"awful" in the last line. It's the only good line of the poem. It's true in at least 4 ways. P.P.P.S. Sorry for such a weird post. Maybe it'll amuse someone.
I should have been clearer and said, "If you had a valid point pertaining to the bit of your post I quoted, what was it?". I agree with you on the part I did not quote.
About the part I quoted, you made a blanket statement about mathematical logic and nature that's clearly false: mathematical logic is highly relevant to how nature actually works, for instance with "time series generalized least-squares regression models" mentioned in the first journal article's abstract. I was just wondering if you had a good point that you didn't quite say correctly.
Premises:
(1) Dinosaurs had some initial size diversity due to environmental factors
(2) Egg sizes were limited because thick shells would be air tight
(3) Egg-laying dinosaurs went through large size variances as they grew to adulthood (compared to mammal-scale)
Reasoning:
* Because of (1), (2), and (3), a particular species would occupy a broader environmental niche, eg. with small juveniles going places adults couldn't reach
* Increased niche breadth would cause species to interact and compete more with other species
* Increased competition results in a size arms race since larger animals get food more, which incidentally increases niche breadth all the more
* The process doesn't continue indefinitely since large sizes eventually hit environmental constraints, though "steady-state" sizes would be larger in egg-laying dinosaurs than eg. mammals. Birds have strong environmental reasons to stay small that tend to overcome increased competition.
[If you're a biologist, preferably one who has read the paper, please correct me if I'm wrong. The Nature article is pretty vague and I can only read the abstract of the journal article.]
Slashdot Mirror
You seem to have misunderstood my post. The phrase "Rotate the addresses" refers to email addresses, not IP addresses; sorry for the ambiguity.
The continuum hypothesis has nothing to do with the calculus taught in high school, or this article for that matter. I like talking about math, though, so for those who don't know, here's a non-technical explanation of the continuum hypothesis.
(1) "smaller" sets: A set is a particular group of objects (numbers, fruit, names, your Toyota, etc.). Given two sets, we say the first is smaller than the second if (a) we can assign to each object in the first a corresponding, unique object in the second, yet (b) we cannot assign to each object in the second a unique object in the first. For instance, {1, 2, 3} is smaller than {apple, 1, Karen, Jim} since we can pair up 1 with apple, 2 with 1, and 3 with Karen, but any attempt to pair in the other direction will necessarily fail by using one of the numbers 1, 2, or 3 twice, breaking uniqueness. The good part of this definition is that it also makes sense for infinite sets, which is where the "just count it" definition breaks down.
(2) An unintuitive example: The natural numbers are just the numbers 1, 2, 3, 4, 5, .... They form an infinite set. The integers are just the numbers ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, .... The integers contain the naturals so one might expect the naturals to be smaller than the integers. This is *not* the case, since I can pair each integer with a unique natural as follows:
0 with 1 ...
1 with 2
-1 with 3
2 with 4
-2 with 5
Thus (b) cannot be satisfied since the pairing attempt does not always fail.
(3) Real numbers: The real numbers are fractions like 4/5 together with the irrationals like pi or Sqrt(2). These also form an infinite set and again contain the naturals. However, they are "large" enough so that the naturals are smaller than the reals in the sense above; this is the content of Cantor's Diagonal Argument.
(4) The Continuum Hypothesis states that there is *no* set S where both (a) the naturals are smaller than S and (b) S is smaller than the reals. Intuitively, there is no "size" strictly between the naturals and the reals.
It turns out the Continuum Hypothesis is neither provable nor falsifiable under standard but technical assumptions; one can assume either its truth or falsehood without creating contradictions. It's probably the most famous example of an "undecidable" statement. In my experience, though it doesn't come up much among non-set theorists, there's no general consensus on which path to take. I suppose I lean towards accepting the generalized continuum hypothesis since it collapses down the hierarchy in an appealing way while also giving the axiom of choice as a bonus (which I actually "believe").
You're probably talking about the fact that an ordered field with the least upper bound property is equivalent to the real numbers (formal details here). Strictly speaking the axioms don't imply the existence of a system that satisfies them. Some construction is necessary, though several standard approaches can be carried out with only appeals to highly intuitive bits of set theory.
The list of axioms I linked isn't intuitive in the "nigh universally innate" sense. However, I've developed a fair amount of intuition regarding them. Their machine-like formal representation is not even remotely how I think about them, though it offers a compact and above all perfectly clear way to communicate.
While I tend to agree, I've always figured people get around rate limits by having a huge pool of addresses they try brute forcing. Rotate the addresses quickly enough to prevent being rate-limited (possibly using a botnet to spread the IPs around?). The odds of guessing correctly are essentially the same with either strategy (this actually has lower variance, though the expected number of compromised accounts should be the same).
Someone mentioned a good possibility in this vein: he reused his password on a site that got compromised which was then connected to his Hotmail account. He has a strong history of password reuse from the article.
Good point, thanks. He even mentions how he has slight variations on his new password for several accounts only because the sites have different rules. Password reuse motivating (1) makes sense, except that "my PC login [is compromised]" is unexplained in that case. He may have meant PC Pro site login, which would clear up the discrepancy nicely and explain everything.
How is this Microsoft's problem? The possibilities are...
(1) A guy writing articles about his new email address used a relatively weak password and someone guessed it
(2) He logged in on a compromised machine
(3) Microsoft has a genuine security problem
The guy leaped right to (3), which seems the least likely to me. Since "my PC login" has also been compromised, (2) seems right. I can't help but feel this would have been pointed out long ago if the service were Gmail instead of Hotmail.
Before it gets quoted back to me, he justified (3) by saying
although I have to say from anecdotal evidence that Hotmail seems far more susceptible to account hijacking than Gmail.
That's a very weak argument--it's based on anecdotal evidence and ignores possible differences between user populations. You'd think the editor of a magazine would take the time to write a thorough article instead of a knee-jerk one.
And even if there isn't, logic should be in place to suspend account who start mass emailing their contact lists with suspicious links, it shouldn't be that hard to stop.
The same thing was mentioned above, but all a hacker needs is the contact list. They can spoof your email address and bypass Microsoft entirely afterwards. Of course the same is true of all email providers.
In retrospect I wasn't clear, but by "gay sex" I was referring only to the physical act. To be clear, the straw man I intended to invoke might say, "a male inserting his penis into the anus of another male and humping till orgasm is unnatural", which is ridiculous considering the monkey example above.
Exclusive homosexuality is at least very rare in animals, so the reasons behind animal and human gay sex are often very different, as you imply.
Which never happens in humans? I'm not sure what your point is, but I'm curious to know.
...the high ranking males mounting the lower ranking males.
And people say gay sex isn't natural why again?
But I do support the abolishment of 0 as a concept. It makes coding so much simpler.
Hear hear! I'm sick and tired of all these "null reference exceptions" and "segmentation faults" my programs keep throwing. Each time I debug them I find a 0. If 0 didn't exist, neither would my problems!
They did use base 20, but the way most people count with their hands and feet is in base 1, regardless of whether you use 10 fingers or 20 fingers + toes. You can somewhat reasonably count in binary on your fingers, but only up to 10^10 - 1 = 1023. Adding more states to each finger gets really difficult, and who needs to count so high on their fingers anyway?
According to this page each digit was written as some bars, each with value 5, plus some dots, each with value 1. You could imitate this system on your hands--eg. right hand for bars, left for dots. If you were good enough you could do the same with your feet for a total of two base-20 digits, though counting in binary nets you a larger maximum with hands only.
The site was loading very slowly so I scraped the 2012 rankings for the curious but impatient:
1 - C - 17.555% .NET - 0.978%
2 - Java - 17.026%
3 - C++ - 8.896%
4 - Objective-C - 8.236%
5 - C# - 7.348%
6 - PHP - 5.288%
7 - (Visual) Basic - 4.962%
8 - Python - 3.665%
9 - JavaScript - 2.879%
10 - Perl - 2.387%
11 - Ruby - 1.510%
12 - PL/SQL - 1.373%
13 - Delphi/Object Pascal - 1.370%
14 - Visual Basic
15 - Lisp - 0.951%
16 - Pascal - 0.812%
17 - Ada - 0.783%
18 - Transact-SQL - 0.760%
19 - Logo - 0.652%
20 - NXT-G - 0.578%
In case anyone was wondering, the AC's link above is an actual article complaining about ICANN. I thought it might be one of the usual troll pictures, but nope.
(OT: I can cross my eyes which for some reason makes everything very fuzzy; it's useful sometimes when I don't want to see something distinctly like now or when I'm looking through a page with spoilers all over. I've always vaguely wondered if everyone can do that.)
and I've never seen anything but appreciation for these people.
In general I agree, though I've been the "question guy" in some instances where it wasn't universally appreciated.
* In a quantum mechanics course that often lacked mathematical rigor (eg. the completeness property of Hilbert space was never explicitly mentioned) I asked some questions some of the physics students and the instructor viewed as minor details that weren't worth the time or effort to look into (eg. "how can we ignore infinitely many terms? maybe they'll add up to something large").
* In a chemistry course, once an instructor rushed through a derivation mostly by flashing through a bunch of integrals on his PowerPoint. I didn't feel I understood it very well so I asked for details, but it was clear from body language that the rest of the class wasn't interested in the material or derivation so I stopped. The instructor seemed to think discussing the details wasn't important either from his tone of voice and body language.
* I remember bringing up various questions outside of class to friends who sometimes weren't at all interested. As an example, an engineering course on signals did a little work with Fourier transforms, and I wondered if the Fourier series of an arbitrary signal accurately reconstructs that signal. I've since learned that it's a delicate question, and I can understand why the instructors completely ignored it; I did in class as well since it worked for the simple signals we played with.
If anyone's interested in the answer to the above question, there are actually continuous functions whose Fourier series does *not* converge to the original function at each point. In fact, to every continuous periodic function there is another continuous periodic function which differs from the original at each point by an arbitrarily small amount and where the partial sums of the Fourier series are unbounded on some non-empty set E. Still more is true: E can be taken to be dense, i.e. each real number is arbitrarily close to some point in E, and in fact E can be taken to be uncountable, so in some sense the Fourier series does not converge to the original function for points that are infinitely more numerous than the rational numbers. And by now everyone will have lost interest, which illustrates my original point that questions aren't universally appreciated.
The relevant journal is a non-traditional "open access journal" where articles are freely available (pseudo-random sample; others here), but article authors pay the publisher to publish. It's similar to self-publishing. I imagine TOISCIJ is not respected at all since in a brief search the only info I could find on it was related to the fake paper incident. While it is technically a "peer reviewed journal" (or at least it calls itself that, present evidence to the contrary), it's misleading not to immediately point out how it differs from most people's idea of traditional "peer reviewed journals".
Some scandals along the same lines:
* The Bogdanov affair, where two French twins, one a mathematician and the other a physicist, published apparent nonsense in respectable journals. Physicist John Baez (singer Joan's cousin, actually) called the papers "a mishmash of superficially plausible sentences containing the right buzzwords in approximately the right order. There is no logic or cohesion in what they write."
* The Schön scandal, where a German physicist claimed breakthroughs and published a number of papers. Journals withdrawing his papers include Science, Physical Review, Applied Physics Letters, Advanced Materials, and Nature.
* The Sokal affair, where a physicist published a rather hilarious paper in the journal Social Text. To be fair, that article was not peer-reviewed by a physicist.
No, the paper was not published and was not accepted at a conference. According to the article, the authors received word that the fake, computer generated paper had "been accepted for publication after peer-reviewing process in TOISCIJ [The Open Information Science Journal]".
They didn't take the hoax any further, though:
Davis said that he considered scraping together the $800 to see if Bentham would actually publish the fake paper, but considered that taking the hoax further would be "unethical."
"I think that the point has been made," he said. "And, I mean, it's $800, and I'm a graduate student."
The paper is clearly nonsense; here's a few lines from the beginning:
"Compact symmetries and compilers have garnered tremendous interest from both futurists and biologists in the last several years. The flaw of this type of solution, however, is that DHTs can be made empathic, large-scale, and extensible. Along these same lines, the drawback of this type of approach, however, is that active networks and SMPs can agree to fix this riddle."
I spent a while searching for a copy of the Yahoo! article and came up with nothing. I did find this story from a local news outlet that probably says about the same as the Yahoo! article did. I also wasn't able to find more than search engine hints of a followup article saying that the guy was released from the hospital. He missed out on a Darwin award, at least. I imagine he recovered mostly or completely.
Warp drive would be awesome. I'm not sure if a new particle (perhaps a new branch of particle physics?) or heavy revision to general relativity would be more satisfying to me as an explanation of dark matter / its purported effects. I'm not really knowledgeable enough in these matters to have a solid opinion either way. I just wanted to mollify what I see as a knee-jerk reaction against exotic dark matter and towards another Einstein-esque revision of previous notions about space and time
About my name, I think I was eating a bowl of Froot Loops when I made this account. Something about 4 o's struck me. I only later noticed the mild irony of a gay man picking a handle with "fruit" in it; it makes me smile from time to time :).
Agreed, atrocious summary and terrible title. Here's an alternate.
Survey Finds Too Little Dark Matter Near Solar System
The existence and approximate distribution of dark matter have become standard assumptions in cosmology. According to Nature, it "explains how structure arose in the Universe, how galaxies formed and how the rapidly spinning Milky Way manages to keep from flying apart." However, a paper recently accepted by the Astrophysical Journal studied stellar velocities in our part of the galaxy in an attempt to infer the amount of dark matter present near our solar system and came up with unsettling results. Moni Bidin, the study's lead author, concluded that "at most, only about one-tenth the amount of dark matter predicted by models could exist in the volume of space they examined." Astronomer Frederic Hessman, who is uninvolved in the study, put things bluntly: "If this is right, it turns everything totally upside-down." Physicists are calling for caution and several note the difficulty and sensitivity to error of the present results. Astronomer Chris Flynn, who approved Bidin's paper for publication, cautioned, "I wouldn’t throw out nearby dark matter quite yet” and “The measurement being made is very challenging, and there are a number of ways for it to miss the dark matter even if is there.”
I understand that saying "we don't know what dark matter is" is unsatisfying, but some particles don't interact much with other particles. Neutrinos are a great example, since they only take part in the weak force and gravity (so not the electromagnetic or strong forces). Is it so hard to believe that some matter interacts solely through the gravitational force? That would mean no electromagnetic effects and almost no interactions with other forms of matter. Such matter would only be noticeable at gravity-dominated, cosmological scales.
Who knows? Maybe there's a whole segment of matter humans are unfamiliar with which interacts very little with the matter we know about but interacts with itself in complicated ways. Maybe there are dark matter solar systems populated by dark matter people who are just as confused as we are about the weird gravitational anomalies caused by our otherwise invisible existence. Communicating through gravity would certainly be an interesting challenge! I don't really believe this, but my point is basically the same as Hamlet's: "There are more things in heaven and earth than are dreamt of in your philosophy"--that is, it's arrogant to expect humans to be in a position to observe all the parts of the universe. Perhaps some things are just hidden.
Your post and its high moderation made me feel overeducated, so I wrote a poem in archaic style to reinforce the feeling.
Today I chanced to Look Down from my Ivory Tower;
the Vision horrified me.
I saw the Peasants Clamoring blindly
for the Simplest Certain Knowledge
of the Calculus and of Physicks.
I saw the Depth of Divide betwixt us thus:
One Man's Hidden Knowledge is Offal to th' Other.
P.S. To be fair, the stuff you mentioned is somewhere around the programming equivalent level of "objects can have properties".
P.P.S. Also, note the pun on "offal"/"awful" in the last line. It's the only good line of the poem. It's true in at least 4 ways.
P.P.P.S. Sorry for such a weird post. Maybe it'll amuse someone.
It would take a lot longer to look up Romney. You'd have to search all 5 or 6 of his houses.
Five or six? You don't know how many houses he has?
It flip-flops.
I should have been clearer and said, "If you had a valid point pertaining to the bit of your post I quoted, what was it?". I agree with you on the part I did not quote.
About the part I quoted, you made a blanket statement about mathematical logic and nature that's clearly false: mathematical logic is highly relevant to how nature actually works, for instance with "time series generalized least-squares regression models" mentioned in the first journal article's abstract. I was just wondering if you had a good point that you didn't quite say correctly.
As near as I can tell, the argument is...
Premises:
(1) Dinosaurs had some initial size diversity due to environmental factors
(2) Egg sizes were limited because thick shells would be air tight
(3) Egg-laying dinosaurs went through large size variances as they grew to adulthood (compared to mammal-scale)
Reasoning:
* Because of (1), (2), and (3), a particular species would occupy a broader environmental niche, eg. with small juveniles going places adults couldn't reach
* Increased niche breadth would cause species to interact and compete more with other species
* Increased competition results in a size arms race since larger animals get food more, which incidentally increases niche breadth all the more
* The process doesn't continue indefinitely since large sizes eventually hit environmental constraints, though "steady-state" sizes would be larger in egg-laying dinosaurs than eg. mammals. Birds have strong environmental reasons to stay small that tend to overcome increased competition.
[If you're a biologist, preferably one who has read the paper, please correct me if I'm wrong. The Nature article is pretty vague and I can only read the abstract of the journal article.]