I don't agree with your analogy. Given 16 coin tosses and any length 8 sequence, you'd expect the sequence to appear 8/2^8 = 1/32 of the time. (Simulate it if you don't believe me; proving it is boring statistics.) In general a length k subsequence of a length n sequence of coin tosses appears (n-k)/2^k times. Replace 2 with s if the coin has s sides.
Anywho, I interpret the bit you quoted as saying "our theory's predicted probability distributions have an expected value for 'energy jet clustering about 144 GeV' to be 1/250th of the observed average, and the variance is small enough that this is very highly improbable". There's no mention of trying lots of hypotheses, only the implication that the standard model predictions do not match up to observation. There are several explanatory hypotheses ("new brand of Z boson", "heavy version of a gluon") but they seem to be after-the-fact attempts to explain the discrepancy. Verifying the result by repeating it, preferably at another lab with another team, is important since particle physics experiments are extremely sensitive to error--for instance, the 144 GeV mentioned in the article is about 0.000000023 Joules, and your computer consumes hundreds of Joules per second while running.
Note that IANAPP (particle physicist), though I'm sure one day I'll at least read a technical book on the standard model. I've picked up a small amount of it over the years, and I have an interest in some advanced physics.
The point is that given the amazing plugin support in FF, there's no real usability reason to include ANY social plugins by default.
For some features, like mouse gestures, I agree with this line of reasoning. Almost everyone who uses mouse gestures will be quite comfortable finding and installing addons. To extend the example of my parents, if they used Twitter, they'd have a hard time knowing addons exist or finding ones that they might find useful. If enough users like them would benefit from having a Twitter-interfacing feature, I'd say the rest of us (me included; I dislike Twitter) should just have to suck up the extra bloat.
It's important to note TFA is very vague on what social network integration will actually be offered. The relevant text:
there will be a new paper plane logo in the URL bar that provides access to your social media accounts, such as Facebook, Twitter and we assume other services such as Reddit, Digg or StumbleUpon as well.
It might just be an area for specialized addons, where you enter the site you have an account at, it downloads and installs the relevant specialized addon, and things go from there. The article is unclear on whether or not, say, Facebook will have browser integration by default through this panel. The screenshot doesn't show a Twitter icon, either--it just has the facebook logo and a plus sign.
I am certain that the deciding factor was ad revenue partnerships, not better user interface or core feature integration.
I don't follow--where are the ads and how do they generate extra money for social networking sites? The screenshot doesn't include any ads. Not having to go to the site's page actually bypasses an opportunity to display ads if the browser interface doesn't include them. If I were to guess why social network integration was being offered, I'd say it's because of this statistic (lifted from Wikipedia) and those like it: "According to Social Media Today, in April 2010 an estimated 41.6% of the U.S. population had a Facebook account." If your users use something you think you can help them use, you'll probably add features to support them. I don't see anything necessarily nefarious in that.
not everyone needs a browser on their Linux (not everyone needs social network integration in their Firefox).
Not everyone needs browser tabs--like my parents, who to my knowledge don't know how to visit multiple sites simultaneously. When a large enough fraction of users benefit from a feature more than the feature hurts other users, it should probably be included. I'm not sure if that's the case here, but my point is inclusion of features is complex, and your rather heavy handed example glosses over that complexity.
I'm curious (enough to read a summary of the process, but not enough to find out myself) how these features were chosen. Perhaps they even did some user studies suggesting the majority of their users would like these features. Of course,/. will have a significant "anti bloat" bias. I know I get frustrated at software taking a few seconds to load while most "regular" users don't seem to notice.
You're concluding that he's more advanced in physics than math, because the physics described doesn't use advanced math.
No; sorry I wasn't clearer. I'm concluding that he's more advanced in physics than math since there was no reference whatsoever to math more advanced than calculus, while there were references to branches of physics more advanced than calculus-based mechanics. I tend to put calculus and calculus-based mechanics on the same footing difficulty-wise. Ultimately I suppose this speculation doesn't really matter. You may well be right that he's studying more advanced areas of math that the journalist never mentions--though somehow I think they would have name dropped them. "Jacob is studying analytic number theory and algebraic topology" sounds impressive, even if you have no idea what those things are.
However you don't need to know any math to correctly report that someone is taking graduate-level math, so that statement is likely to be correct.
The bit of the article I think you're referring to,
That did not happen to Jake, thanks in part to a third psychological evaluation done nearly two years ago. It showed that this fifth-grader was not regressing but was simply bored and needed to be stimulated -- in a very big way.
As in dropping out of school.
"Indeed, it would not be in Jacob's best interest to force him to complete academic work that he has already mastered," clinical neurophysiologist Carl S. Hale, Merrillville, said in a report provided by the Barnetts.
"He needs work at an instructional level, which currently is a post college graduate level in mathematics, i.e., a post master's degree. In essence, his math skills are at the level found in someone who is working on a doctorate in math, physics, astronomy and astrophysics."
is from a neurophysiologist. It doesn't say that Jacob is taking graduate-level courses, just that he should. It's difficult for outsiders to recognize the difference between undergraduate math and serious graduate/PhD level math, though to specialists the difference is huge. I also suspect the statement for a few other reasons. "post college graduate level" is a non-standard phrase in my experience; most people would simply say "graduate level". Doctorates in those fields require vastly different amounts of math, which also varies greatly by specialty:
Experimental physicists and theoretical physicists are usually on completely different levels in their math ability (and conversely in their ability to perform experiments). One of my old physics professors is a fantastic theoretician, but from what I've heard is absolutely terrible in the lab. He once told us how he almost didn't get in to his doctoral program because of his poor experimental skills. I remember a story about some physicists (I don't remember the names) in the early days of quantum. They found experimental evidence for the existence of the spin of electrons. One of them turned to the other and said "we need another degree of freedom", and the other said "what's a degree of freedom?". He must have been a good experimentalist, but clearly he was not into developing theory. Anyway, it just seems that if the neurophysiologist knew what they were talking about they would have been clearer and more accurate.
Haha. I would have happily been the reporter's interpreter. I'm sure they could have found someone if only they knew what circles to look in. It would have been so refreshing if the article had been truly well-informed. I suppose it goes to show how huge the gap between most people and technical specialists is.
GR is pretty good at fending off attacks, except that it doesn't mesh with quantum mechanics. Best of luck with your reinterpretation of SR; it sounds interesting.
My interpretation is the kid is more advanced at math than he is at physics. Nothing unusual about that.
Maybe. The article mentions quantum mechanics and relativity (whether it's special or general is unclear, showing just how little the journalist knew about what they wrote), which are both more advanced than calculus-based mechanics (which is what I take the calculus-based physics reference to mean). It doesn't mention any math more advanced than calculus. From these sparse references I come to the opposite conclusion--that he's more advanced in physics than math, and like most physicists his command of math flows from describing physics.
Calculus is an interesting branch of math in that it's relatively easy to have a very strong intuitive grasp of it, but it's difficult to make rigorous. Historically, Newton and Leibnitz developed calculus using infinitesimals in the 1600's, but their methods required a lot of intuition. It wasn't until Robinson's development of non standard analysis in the 1960's that their version was put on rigorous foundations. Calculus was first made rigorous by the incremental development of mathematical analysis, particularly by Weierstrass, in the ~1800's--but this took a different view from the historical infinitesimal approach. I suspect his grasp of calculus is the intuitive one that's common among technical people, and not the rigorous one that's common among modern mathematicians/math grad students.
His video reminded me of myself when I first learned calculus (which was also at a young age, and to be honest also far better than most of my peers). I would love to know if he could come up with a counterexample to the integration by parts formula where the functions involved aren't well behaved. I wouldn't have been able to. I suspect he couldn't, but it's difficult to say. Certainly his grasp of calculus is deep compared to 99% of people.
Jean-François Champollion was a prodigy who went on to decipher the Rosetta Stone. Évariste Galois founded the mathematical field that became known as Galois theory as a teenager. I don't know any other examples; I suspect they are quite rare. There's a big difference between being able to understand material at an early age and having the creativity/staying power to make lasting contributions to a technical field. Plus, there just aren't that many child prodigies.
but there's no such equivalent as "hello world" in calc, geometry, etc.
I disagree. u-substitution and integration by parts are "hello world"-level in calculus, IMO. Some basic geometry results are similar, like how angles formed by intersecting pairs of parallel lines relate to one another. I'd say the Pythagorean theorem cast into the language of trig and solving an equation like "x - 9 = 10" are also both "hello world"-level for trig and algebra, respectively.
Each of these subjects builds and builds to far more advanced material, while a programming language levels off in difficulty relatively quickly. In that sense the analogy is flawed, but I think it's still worthwhile.
I agree that his knowledge is likely superficial. I hope he gets to the more rigorous material (analysis, linear algebra, algebra,...) he needs to expand beyond basic calculus, or that he's already started it. To be blunt, it's easy to impress most people with calculus, but it's hard to impress real mathematicians that way since it's so simple to people with an aptitude for it.
The PhD level quote you gave was from "clinical neurophysiologist Carl S. Hale". To outsiders, graduate/PhD level and undergraduate level math look pretty much equally inscrutable (eg. this vs. this). None of the information in the two articles (TFA's or The Indianapolis Star's) or in the video suggests to me that this assessment is accurate. Perhaps they just left it out, but in the video Jacob doesn't give me the sense of "this is incredibly basic; my goodness this is basic; I've gone so much further than this" that I'd expect if he were really at the graduate/PhD level.
He also made more mistakes than I would expect--messing up dx's, messing up constants, and messing with notation. I didn't get the sense that he understood the underlying real analysis backing up his calculus, or that he was as familiar with formal proofs as he would need to be to actually be at the graduate/PhD level. He seemed to be performing the usual algorithmic manipulations and modifying part of a lecture he was given. Certainly he understood the basic calculus he was describing, but it's unclear to me how deep it goes. Relatively few people are qualified to judge his ability, so it would be easy to overstate when faced with lots of magic symbols. I wish I could talk to him for 5 minutes and just determine his general ability level myself.
I find it difficult to sort out the journalist's inexperience from their sensationalism. For instance, The Indianapolis Star version mentions a "calculus-based physics class he has been taking this semester" but then says "he needs work at an instructional level, which currently is a post college graduate level in mathematics". There is a big gap between calculus-based physics and graduate level math--at least serious graduate level math. Differential geometry would seem to be right up his alley, but there's no (even horribly obfuscated) mention of it.
The highest level of math directly mentioned in the article that I was able to figure out was "funky letters and upside-down triangles", presumably meaning Greek and the gradient symbol (it has other uses), which are undergraduate level. The video only discusses basic calculus at a level that perhaps one in a thousand high school freshmen reach; it's remarkable, but not "12-Year-Old Rewrites Einstein's Theory of Relativity" remarkable. The article mentions a YouTube video on quantum mechanics but I couldn't immediately find it. I agree with previous posters that the subtext of the quotes of the letter from Prof. Tremaine is "I want to encourage you, but, aside from your age, your ideas are unremarkable at my level of physics."
Without more info, my opinion (FWIW) is that he's got a great memory and is at a relatively advanced undergraduate level in physics and math. He'll probably make a great researcher after a few more years of maturation, which is probably why he's been offered a research position--for his potential, not for his current work, as some of the article text implies. I wish him the best of luck, and all the creativity he'll need to make truly interesting discoveries.
I think it must vary a lot by country. In the US the new movie would easily beat out 4 for popularity in the general population. From Wikipedia, "The film's total international gross is $127,764,536, for a total worldwide gross of $385,494,555"; 4 grossed ~$133,000,000 worldwide. Even inflation adjusted the new one is much higher.
Re:Can't agree with him on the alternative univers
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Leonard Nimoy Turns 80
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I'm on the fence about the reboot. We've had a ton of material from the old universe--something like 29 seasons and 10 movies, not to mention a massive number of books. Expanding on the original 5 year mission seems like a pretty good direction. The past didn't work out (Enterprise), the future (post-TNG-era) doesn't seem that interesting because the Federation would probably become overpowered, and the present (TNG-era) has been done, a lot. TOS was cut short and this could be a chance to see what we missed from a time period many people liked. It would probably have been very constraining to do a second TOS series while respecting the mounds of material from that era and TNG. Enterprise had to do that and wasn't terribly successful. I hope they don't turn the franchise into another sci-fi action series, though.
But, I am annoyed they blew up Romulus in the old universe and Vulcan in the new one. They should have left the old one alone and confined all major changes to the new universe, making clear that the two run in parallel so the new universe doesn't "overwrite" the old one.
Nimoy as a psychic race car driving detective: http://www.imdb.com/title/tt0068248/. A friend of mine bought it and (after we found a VCR) we enjoyed it. Nimoy does a good job no matter what, it seems.
I don't agree that 2 was the best TOS movie. I actually prefer both 6 and 4 (in that order) to 2. The final scenes of 2 are definitely the saddest in all of Star Trek (including all 11 movies and all episodes of the 6 series), though.
I think you meant to limit yourself to movies 1 through 6 or 1 through 10. 11 (JJ Abrams') was very much an action movie geared toward general audiences. Compare 11 to, say, 8 (First Contact)--8 tends to assume you care about Data and Picard and such, while 11 builds its characters while only assuming vague background knowledge of Kirk and Spock.
I don't think we were supposed to take the plot seriously. I viewed it as an intentionally thin excuse to get the crew of the Enterprise to 1980's San Francisco where they could interact with each other and their strange environment in amusing and unique ways without spending much time on the plot. It was able to focus on very strong Kirk-Spock interactions immediately following Spock's resurrection and also develop several subplots for other characters who normally don't get much screen time without spending much time on actual plot. The silliness of the plot also lent itself to quite a bit of memorable comic relief that would have been inappropriate elsewhere, like all the things you listed. (Imagine a "nuclear wessels" type joke in Wrath of Khan!) I wouldn't want several movies in the same series following this plot style, but I'm glad they went for it with this one.
That said I agree with you that the movie felt odd without an Enterprise. I also find the intro sequence with the alien probe to be too long. (OT: the actor who played Sisko's dad from DS9 is featured prominently in the intro, which is strange to see.) Somehow I've always been willing to overlook the implausible wrap-up at the end. The environmentalist subtext has also always been fine with me, though I agree that the androgynous alien/Riker episode was pretty heavy handed.
I thought it was "A Study in Dramatic Camera Shaking". (Apologies to anyone who didn't notice how shaky the camera was and, upon rewatching, gets really distracted like some friends of mine have after I mentioned it.)
Your post reminds me of a game a friend of mine and I "designed" (at least in our heads) a few years back. Its main ideas were
(1) players can change the world permanently
(2) the world progresses with player-made technological innovation
(3) the player factions' purpose is to organize technical progress and labor for a common purpose
You could dig a hole and it would stay there, or make a plateau for defense, or burn down a forest, or plant one, or set up mining operations. The natural world would basically be developer-made (probably largely auto-generated). From there, you could build a wheel, then a cart, then a computer, then a computer game, etc, and distribute your designs. Player-made technical innovation produces mounds of content and an economy, adding tons of gameplay that developers alone could never hope to create due to its sheer volume. Technical advances of course would tend to change the world--a warmongering faction with an air force might cause another faction to go underground, creating massive earth moving operations. (3) hopefully prevents chaos and adds overarching goals to create structure. Factions can also "pool" labor to create large projects like building city gates or casting a gigantic levitation spell to create a mobile city. There would of course be a magic creation system comparable to the technical creation system.
I suppose the main idea was to simulate the interesting large-scale parts of human interactions, making them easier and more fun, and adding in standard fantasy elements. Developer work would be in creating systems of content creation and enabling basic player actions from which more could be built, instead of creating static content that's obsolete in a few months. Of course, such a game won't technically be possible for a long time. Even then, creating a good "technology creation" system would be very difficult, as would managing the amount players can change the world. Relying on player content is risky, but look at MineCraft--some people really enjoy building things, even if there's little reward.
As I understand it, the usefulness of this system is in ordering the urgency of calls before a human gets to consider them, for when all operators are busy. Since natural language processing is hard, they instead analyzed the mechanics of the sound itself. Certainly a human could distinguish between the cases I listed by text alone, but the question is whether or not this system could distinguish between them if all human operators are busy, forwarding the more urgent case to humans first. I'm sure during a major disaster a good implementation of this system would be useful. Perhaps there are other common use cases--I'm certainly not in emergency dispatching.
If the mother is hysterical in your situation, I'm unsure how my brain would order the two callers. I would have to train it, I suppose, and see if I could pick up on common properties of calm-but-urgent calls and not-calm-but-urgent calls.
It mentions those parameters, but the article doesn't say specifically how they were used. (It only vaguely implies they were used to do something like distinguish "highly stressed" from "not stressed" callers.) Perhaps their machine learning algorithms used those same parameters to deal with the "calm caller" case, as in my slow, careful speech example. Whether or not this is the case would require more information than TFA or TFAbstract gives.
I can easily imagine a mother calling about her kid's cat in a tree, and an EMT calling about a serious accident. My own neural net has no trouble distinguishing the seriousness of the two cases from sound alone so long as the mother isn't hysterical (which seems unlikely in general). The EMT would be more casual and less businesslike in a less serious situation, which I can also distinguish from sound alone.
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You seem to have pulled those numbers from nowhere....
I don't agree with your analogy. Given 16 coin tosses and any length 8 sequence, you'd expect the sequence to appear 8/2^8 = 1/32 of the time. (Simulate it if you don't believe me; proving it is boring statistics.) In general a length k subsequence of a length n sequence of coin tosses appears (n-k)/2^k times. Replace 2 with s if the coin has s sides.
Anywho, I interpret the bit you quoted as saying "our theory's predicted probability distributions have an expected value for 'energy jet clustering about 144 GeV' to be 1/250th of the observed average, and the variance is small enough that this is very highly improbable". There's no mention of trying lots of hypotheses, only the implication that the standard model predictions do not match up to observation. There are several explanatory hypotheses ("new brand of Z boson", "heavy version of a gluon") but they seem to be after-the-fact attempts to explain the discrepancy. Verifying the result by repeating it, preferably at another lab with another team, is important since particle physics experiments are extremely sensitive to error--for instance, the 144 GeV mentioned in the article is about 0.000000023 Joules, and your computer consumes hundreds of Joules per second while running.
Note that IANAPP (particle physicist), though I'm sure one day I'll at least read a technical book on the standard model. I've picked up a small amount of it over the years, and I have an interest in some advanced physics.
The point is that given the amazing plugin support in FF, there's no real usability reason to include ANY social plugins by default.
For some features, like mouse gestures, I agree with this line of reasoning. Almost everyone who uses mouse gestures will be quite comfortable finding and installing addons. To extend the example of my parents, if they used Twitter, they'd have a hard time knowing addons exist or finding ones that they might find useful. If enough users like them would benefit from having a Twitter-interfacing feature, I'd say the rest of us (me included; I dislike Twitter) should just have to suck up the extra bloat.
It's important to note TFA is very vague on what social network integration will actually be offered. The relevant text:
there will be a new paper plane logo in the URL bar that provides access to your social media accounts, such as Facebook, Twitter and we assume other services such as Reddit, Digg or StumbleUpon as well.
It might just be an area for specialized addons, where you enter the site you have an account at, it downloads and installs the relevant specialized addon, and things go from there. The article is unclear on whether or not, say, Facebook will have browser integration by default through this panel. The screenshot doesn't show a Twitter icon, either--it just has the facebook logo and a plus sign.
I am certain that the deciding factor was ad revenue partnerships, not better user interface or core feature integration.
I don't follow--where are the ads and how do they generate extra money for social networking sites? The screenshot doesn't include any ads. Not having to go to the site's page actually bypasses an opportunity to display ads if the browser interface doesn't include them. If I were to guess why social network integration was being offered, I'd say it's because of this statistic (lifted from Wikipedia) and those like it: "According to Social Media Today, in April 2010 an estimated 41.6% of the U.S. population had a Facebook account." If your users use something you think you can help them use, you'll probably add features to support them. I don't see anything necessarily nefarious in that.
not everyone needs a browser on their Linux (not everyone needs social network integration in their Firefox).
Not everyone needs browser tabs--like my parents, who to my knowledge don't know how to visit multiple sites simultaneously. When a large enough fraction of users benefit from a feature more than the feature hurts other users, it should probably be included. I'm not sure if that's the case here, but my point is inclusion of features is complex, and your rather heavy handed example glosses over that complexity.
I'm curious (enough to read a summary of the process, but not enough to find out myself) how these features were chosen. Perhaps they even did some user studies suggesting the majority of their users would like these features. Of course, /. will have a significant "anti bloat" bias. I know I get frustrated at software taking a few seconds to load while most "regular" users don't seem to notice.
You're concluding that he's more advanced in physics than math, because the physics described doesn't use advanced math.
No; sorry I wasn't clearer. I'm concluding that he's more advanced in physics than math since there was no reference whatsoever to math more advanced than calculus, while there were references to branches of physics more advanced than calculus-based mechanics. I tend to put calculus and calculus-based mechanics on the same footing difficulty-wise. Ultimately I suppose this speculation doesn't really matter. You may well be right that he's studying more advanced areas of math that the journalist never mentions--though somehow I think they would have name dropped them. "Jacob is studying analytic number theory and algebraic topology" sounds impressive, even if you have no idea what those things are.
However you don't need to know any math to correctly report that someone is taking graduate-level math, so that statement is likely to be correct.
The bit of the article I think you're referring to,
That did not happen to Jake, thanks in part to a third psychological evaluation done nearly two years ago. It showed that this fifth-grader was not regressing but was simply bored and needed to be stimulated -- in a very big way. As in dropping out of school. "Indeed, it would not be in Jacob's best interest to force him to complete academic work that he has already mastered," clinical neurophysiologist Carl S. Hale, Merrillville, said in a report provided by the Barnetts. "He needs work at an instructional level, which currently is a post college graduate level in mathematics, i.e., a post master's degree. In essence, his math skills are at the level found in someone who is working on a doctorate in math, physics, astronomy and astrophysics."
is from a neurophysiologist. It doesn't say that Jacob is taking graduate-level courses, just that he should. It's difficult for outsiders to recognize the difference between undergraduate math and serious graduate/PhD level math, though to specialists the difference is huge. I also suspect the statement for a few other reasons. "post college graduate level" is a non-standard phrase in my experience; most people would simply say "graduate level". Doctorates in those fields require vastly different amounts of math, which also varies greatly by specialty:
Experimental physicists and theoretical physicists are usually on completely different levels in their math ability (and conversely in their ability to perform experiments). One of my old physics professors is a fantastic theoretician, but from what I've heard is absolutely terrible in the lab. He once told us how he almost didn't get in to his doctoral program because of his poor experimental skills. I remember a story about some physicists (I don't remember the names) in the early days of quantum. They found experimental evidence for the existence of the spin of electrons. One of them turned to the other and said "we need another degree of freedom", and the other said "what's a degree of freedom?". He must have been a good experimentalist, but clearly he was not into developing theory. Anyway, it just seems that if the neurophysiologist knew what they were talking about they would have been clearer and more accurate.
Haha. I would have happily been the reporter's interpreter. I'm sure they could have found someone if only they knew what circles to look in. It would have been so refreshing if the article had been truly well-informed. I suppose it goes to show how huge the gap between most people and technical specialists is.
GR is pretty good at fending off attacks, except that it doesn't mesh with quantum mechanics. Best of luck with your reinterpretation of SR; it sounds interesting.
My interpretation is the kid is more advanced at math than he is at physics. Nothing unusual about that.
Maybe. The article mentions quantum mechanics and relativity (whether it's special or general is unclear, showing just how little the journalist knew about what they wrote), which are both more advanced than calculus-based mechanics (which is what I take the calculus-based physics reference to mean). It doesn't mention any math more advanced than calculus. From these sparse references I come to the opposite conclusion--that he's more advanced in physics than math, and like most physicists his command of math flows from describing physics.
Calculus is an interesting branch of math in that it's relatively easy to have a very strong intuitive grasp of it, but it's difficult to make rigorous. Historically, Newton and Leibnitz developed calculus using infinitesimals in the 1600's, but their methods required a lot of intuition. It wasn't until Robinson's development of non standard analysis in the 1960's that their version was put on rigorous foundations. Calculus was first made rigorous by the incremental development of mathematical analysis, particularly by Weierstrass, in the ~1800's--but this took a different view from the historical infinitesimal approach. I suspect his grasp of calculus is the intuitive one that's common among technical people, and not the rigorous one that's common among modern mathematicians/math grad students.
His video reminded me of myself when I first learned calculus (which was also at a young age, and to be honest also far better than most of my peers). I would love to know if he could come up with a counterexample to the integration by parts formula where the functions involved aren't well behaved. I wouldn't have been able to. I suspect he couldn't, but it's difficult to say. Certainly his grasp of calculus is deep compared to 99% of people.
Jean-François Champollion was a prodigy who went on to decipher the Rosetta Stone. Évariste Galois founded the mathematical field that became known as Galois theory as a teenager. I don't know any other examples; I suspect they are quite rare. There's a big difference between being able to understand material at an early age and having the creativity/staying power to make lasting contributions to a technical field. Plus, there just aren't that many child prodigies.
but there's no such equivalent as "hello world" in calc, geometry, etc.
I disagree. u-substitution and integration by parts are "hello world"-level in calculus, IMO. Some basic geometry results are similar, like how angles formed by intersecting pairs of parallel lines relate to one another. I'd say the Pythagorean theorem cast into the language of trig and solving an equation like "x - 9 = 10" are also both "hello world"-level for trig and algebra, respectively.
Each of these subjects builds and builds to far more advanced material, while a programming language levels off in difficulty relatively quickly. In that sense the analogy is flawed, but I think it's still worthwhile.
I agree that his knowledge is likely superficial. I hope he gets to the more rigorous material (analysis, linear algebra, algebra, ...) he needs to expand beyond basic calculus, or that he's already started it. To be blunt, it's easy to impress most people with calculus, but it's hard to impress real mathematicians that way since it's so simple to people with an aptitude for it.
The PhD level quote you gave was from "clinical neurophysiologist Carl S. Hale". To outsiders, graduate/PhD level and undergraduate level math look pretty much equally inscrutable (eg. this vs. this). None of the information in the two articles (TFA's or The Indianapolis Star's) or in the video suggests to me that this assessment is accurate. Perhaps they just left it out, but in the video Jacob doesn't give me the sense of "this is incredibly basic; my goodness this is basic; I've gone so much further than this" that I'd expect if he were really at the graduate/PhD level.
He also made more mistakes than I would expect--messing up dx's, messing up constants, and messing with notation. I didn't get the sense that he understood the underlying real analysis backing up his calculus, or that he was as familiar with formal proofs as he would need to be to actually be at the graduate/PhD level. He seemed to be performing the usual algorithmic manipulations and modifying part of a lecture he was given. Certainly he understood the basic calculus he was describing, but it's unclear to me how deep it goes. Relatively few people are qualified to judge his ability, so it would be easy to overstate when faced with lots of magic symbols. I wish I could talk to him for 5 minutes and just determine his general ability level myself.
I find it difficult to sort out the journalist's inexperience from their sensationalism. For instance, The Indianapolis Star version mentions a "calculus-based physics class he has been taking this semester" but then says "he needs work at an instructional level, which currently is a post college graduate level in mathematics". There is a big gap between calculus-based physics and graduate level math--at least serious graduate level math. Differential geometry would seem to be right up his alley, but there's no (even horribly obfuscated) mention of it.
The highest level of math directly mentioned in the article that I was able to figure out was "funky letters and upside-down triangles", presumably meaning Greek and the gradient symbol (it has other uses), which are undergraduate level. The video only discusses basic calculus at a level that perhaps one in a thousand high school freshmen reach; it's remarkable, but not "12-Year-Old Rewrites Einstein's Theory of Relativity" remarkable. The article mentions a YouTube video on quantum mechanics but I couldn't immediately find it. I agree with previous posters that the subtext of the quotes of the letter from Prof. Tremaine is "I want to encourage you, but, aside from your age, your ideas are unremarkable at my level of physics."
Without more info, my opinion (FWIW) is that he's got a great memory and is at a relatively advanced undergraduate level in physics and math. He'll probably make a great researcher after a few more years of maturation, which is probably why he's been offered a research position--for his potential, not for his current work, as some of the article text implies. I wish him the best of luck, and all the creativity he'll need to make truly interesting discoveries.
I think it must vary a lot by country. In the US the new movie would easily beat out 4 for popularity in the general population. From Wikipedia, "The film's total international gross is $127,764,536, for a total worldwide gross of $385,494,555"; 4 grossed ~$133,000,000 worldwide. Even inflation adjusted the new one is much higher.
I'm on the fence about the reboot. We've had a ton of material from the old universe--something like 29 seasons and 10 movies, not to mention a massive number of books. Expanding on the original 5 year mission seems like a pretty good direction. The past didn't work out (Enterprise), the future (post-TNG-era) doesn't seem that interesting because the Federation would probably become overpowered, and the present (TNG-era) has been done, a lot. TOS was cut short and this could be a chance to see what we missed from a time period many people liked. It would probably have been very constraining to do a second TOS series while respecting the mounds of material from that era and TNG. Enterprise had to do that and wasn't terribly successful. I hope they don't turn the franchise into another sci-fi action series, though.
But, I am annoyed they blew up Romulus in the old universe and Vulcan in the new one. They should have left the old one alone and confined all major changes to the new universe, making clear that the two run in parallel so the new universe doesn't "overwrite" the old one.
Nimoy as a psychic race car driving detective: http://www.imdb.com/title/tt0068248/. A friend of mine bought it and (after we found a VCR) we enjoyed it. Nimoy does a good job no matter what, it seems.
I don't agree that 2 was the best TOS movie. I actually prefer both 6 and 4 (in that order) to 2. The final scenes of 2 are definitely the saddest in all of Star Trek (including all 11 movies and all episodes of the 6 series), though.
I think you meant to limit yourself to movies 1 through 6 or 1 through 10. 11 (JJ Abrams') was very much an action movie geared toward general audiences. Compare 11 to, say, 8 (First Contact)--8 tends to assume you care about Data and Picard and such, while 11 builds its characters while only assuming vague background knowledge of Kirk and Spock.
I don't think we were supposed to take the plot seriously. I viewed it as an intentionally thin excuse to get the crew of the Enterprise to 1980's San Francisco where they could interact with each other and their strange environment in amusing and unique ways without spending much time on the plot. It was able to focus on very strong Kirk-Spock interactions immediately following Spock's resurrection and also develop several subplots for other characters who normally don't get much screen time without spending much time on actual plot. The silliness of the plot also lent itself to quite a bit of memorable comic relief that would have been inappropriate elsewhere, like all the things you listed. (Imagine a "nuclear wessels" type joke in Wrath of Khan!) I wouldn't want several movies in the same series following this plot style, but I'm glad they went for it with this one.
That said I agree with you that the movie felt odd without an Enterprise. I also find the intro sequence with the alien probe to be too long. (OT: the actor who played Sisko's dad from DS9 is featured prominently in the intro, which is strange to see.) Somehow I've always been willing to overlook the implausible wrap-up at the end. The environmentalist subtext has also always been fine with me, though I agree that the androgynous alien/Riker episode was pretty heavy handed.
My order of TOS movies: 6 > 4 > 2 > 3 > 1 ~= 5.
I thought it was "A Study in Dramatic Camera Shaking". (Apologies to anyone who didn't notice how shaky the camera was and, upon rewatching, gets really distracted like some friends of mine have after I mentioned it.)
Your post reminds me of a game a friend of mine and I "designed" (at least in our heads) a few years back. Its main ideas were
(1) players can change the world permanently
(2) the world progresses with player-made technological innovation
(3) the player factions' purpose is to organize technical progress and labor for a common purpose
You could dig a hole and it would stay there, or make a plateau for defense, or burn down a forest, or plant one, or set up mining operations. The natural world would basically be developer-made (probably largely auto-generated). From there, you could build a wheel, then a cart, then a computer, then a computer game, etc, and distribute your designs. Player-made technical innovation produces mounds of content and an economy, adding tons of gameplay that developers alone could never hope to create due to its sheer volume. Technical advances of course would tend to change the world--a warmongering faction with an air force might cause another faction to go underground, creating massive earth moving operations. (3) hopefully prevents chaos and adds overarching goals to create structure. Factions can also "pool" labor to create large projects like building city gates or casting a gigantic levitation spell to create a mobile city. There would of course be a magic creation system comparable to the technical creation system.
I suppose the main idea was to simulate the interesting large-scale parts of human interactions, making them easier and more fun, and adding in standard fantasy elements. Developer work would be in creating systems of content creation and enabling basic player actions from which more could be built, instead of creating static content that's obsolete in a few months. Of course, such a game won't technically be possible for a long time. Even then, creating a good "technology creation" system would be very difficult, as would managing the amount players can change the world. Relying on player content is risky, but look at MineCraft--some people really enjoy building things, even if there's little reward.
Haha, thanks for that. Good laugh!
As I understand it, the usefulness of this system is in ordering the urgency of calls before a human gets to consider them, for when all operators are busy. Since natural language processing is hard, they instead analyzed the mechanics of the sound itself. Certainly a human could distinguish between the cases I listed by text alone, but the question is whether or not this system could distinguish between them if all human operators are busy, forwarding the more urgent case to humans first. I'm sure during a major disaster a good implementation of this system would be useful. Perhaps there are other common use cases--I'm certainly not in emergency dispatching.
If the mother is hysterical in your situation, I'm unsure how my brain would order the two callers. I would have to train it, I suppose, and see if I could pick up on common properties of calm-but-urgent calls and not-calm-but-urgent calls.
It mentions those parameters, but the article doesn't say specifically how they were used. (It only vaguely implies they were used to do something like distinguish "highly stressed" from "not stressed" callers.) Perhaps their machine learning algorithms used those same parameters to deal with the "calm caller" case, as in my slow, careful speech example. Whether or not this is the case would require more information than TFA or TFAbstract gives.
I can easily imagine a mother calling about her kid's cat in a tree, and an EMT calling about a serious accident. My own neural net has no trouble distinguishing the seriousness of the two cases from sound alone so long as the mother isn't hysterical (which seems unlikely in general). The EMT would be more casual and less businesslike in a less serious situation, which I can also distinguish from sound alone.