tag:blogger.com,1999:blog-1466552513513999074.comments2015-06-13T15:07:47.396-07:00Even More Grumbine Science!quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-1466552513513999074.post-67948627728359778632008-12-15T13:09:00.000-08:002008-12-15T13:09:00.000-08:00I think it depends on what's forgotten. If one has...I think it depends on what's forgotten. If one has no idea what a derivative or an integral means, one should probably take calculus again. If one can't recall which trig substitution to use for e.g. int(sqrt(1+x^2)), one should do a few problems in the relevant section of a calculus text. If one doesn't recall the exact formulation of Green's Theorem, one can use the Google.<BR/><BR/>As far as the actual doing of the math, most things (including symbolic differentiation and integration of anything that can be done comfortably by hand) can be done with a calculator. Virtually everything can be done by computer. The key though, in both of those, is that you have to know how to set up the problem, which requires a not-insignificant level of understanding and skill. Having learned how to do a decent amount of math by hand and by computer, I have to say it's actually <I>harder</I>, in a lot of ways, to do calculus by computer if you're only doing it once (unless you're doing iterated integrals of nauseatingly complex multivariable expressions clearly never intended for human consumption). The main advantage is that if you want to run the same sort of procedure over and over using different functions or constants or whatever, or if you want to do relatively simple numerical computation on large quantities of data, the process is automated.<BR/><BR/>I'd be distinctly surprised, in other words, to find out that a significant number of scientists whose field of work involves doing symbolic math on a regular basis have forgotten how to do it. Not only did most working scientists grow up before the technology to do this sort of stuff was widely available, but the technology in its current form just doesn't have any advantages for one-off problem-solving unless the problem involved is hideously complex. Of course, many modern scientists deal mostly with statistical analysis of large amounts of numerical data, but then even without computers their calculus skills might still get rusty without practice.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-43816986716931114772008-12-14T23:56:00.000-08:002008-12-14T23:56:00.000-08:00Much of math post-calculus level you simply lose i...Much of math post-calculus level you simply lose if you don't use it enough. I'm sure a lot of scientists forgot many of the "integration techniques" such as trig. substituions, integration by parts, etc....the vital part is that they know what an integral means and why they or someone else should use it. "Solving for x" can be done with a calculator. I wonder what the recommended approach is for someone who forgot some of the stuff that is assumed in higher-level courses.Chris Colosehttp://www.chriscolose.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-47059509347455542042008-12-11T06:22:00.000-08:002008-12-11T06:22:00.000-08:00I have to second your notion that too much math in...I have to second your notion that too much math instruction falls into the "rote" mode of cranking out problem after problem with no real application attached.<BR/><BR/>Higher math is not my strong suit to begin with, but undergrad Calc II made no sense whatsoever to me until I took my first Graduate Physical Oceanography class, and we started doing motion equations for water parcels in differing sized basin. I still claim no math expertise as a result of that, but at least then I could see how it all came together. Perhaps we should have folks from non-math disciplines ( who are never the less trained in math) teach the calc I and II classes - if only so students don't get lost in the letters.kcsphilhttp://www.blogger.com/profile/12049875206738422083noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-57737008200097241252008-12-06T14:03:00.000-08:002008-12-06T14:03:00.000-08:00The problem I've seen a lot of is not so much what...The problem I've seen a lot of is not so much what I'd call a math weakness, but a math applications weakness. Many math instructors and most math textbooks seem to try very, very hard to teach specific skills in sequence and in isolation. They are also generally very artificially consistent with notation, using the same letters for the same things almost every time. Applications problems in math classes are almost invariably a matter of "take the formula, theorem, or process you just used on the last 50 problems, figure out where the given information fits into it, and crank the problem out in exactly the same way." <BR/><BR/>This does help students remember the processes well enough to progress in math courses, but it's not what's needed as preparation for science courses. When dealing with a science problem, one has to have one's math memories cross-referenced, not just sequentially ordered; one has to be able to reach back and pull out some techniques from pre-algebra, some from calculus, some from trigonometry, and some unique to science, and one has to be able to decide how to put them all together. In the process, one has to deal with scientists' peculiar notation habits and different variable names and moving coordinate systems, which tend to fail to "trigger" the correct process in students who have been well-conditioned by math departments.<BR/><BR/>Now, obviously this isn't the main problem for your students in intro astronomy courses who are barely functioning at a pre-algebra level. It may, however, have been an issue for your grad school office-mate.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-83185344647885911322008-12-06T08:29:00.000-08:002008-12-06T08:29:00.000-08:00My first inkling about the importance of not makin...My first inkling about the importance of not making too many assumptions came when I was in grad school. My office-mate was having a hard time with a homework problem that was a simple (if you understood multivariate calculus -- which one does rather assume of graduate students in math-heavy sciences) matter of integrating terms that were given to us in the problem. Her comment "Just because I passed a class doesn't mean that I learned the material."<BR/><BR/>On one hand, it rather <I>should</I> mean exactly that. On the other, reality intervenes and even if a student has had a course that I as a teacher of some later class would think sufficient to understand my stuff, I really should not assume that it is the case.<BR/><BR/>I had a more extensive introduction the last time I taught astronomy (100-level at a local community college). Though the class did have a math requirement, and my nominal expectations were well below that, I wound up giving my own in-class math placement test. I made a number of changes after discovering that few in the class could operate at a jr. high to high school pre-algebra level. <BR/><BR/>Next time I teach, whenever and whatever that is, I'll have some math and other in-class placement (or maybe I should call them warning?) tests in hand.<BR/><BR/>For the non-math sides, I've also started looking at the cultural assumptions. That, for instance, students will know what the path of a ball through air looks like. (I already know that this can't be assumed.) There are many such things. Some lend themselves to being labs (ok, go toss some balls, drop some and see how high they rebound, ...).Penguindreamshttp://www.blogger.com/profile/10783453972811796911noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-19385478092343905202008-12-02T22:17:00.000-08:002008-12-02T22:17:00.000-08:00um, are you there?i guess this thread is done. wh...um, are you there?i guess this thread is done. what a shameRickr0llnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-85735531674259053192008-12-01T19:57:00.000-08:002008-12-01T19:57:00.000-08:00you mean the CTC's and such (you can ignore th...you mean the CTC's and such (you can ignore the God/gods discussion)? Those aren't metaphysical entitites, but interesting manefestations of the "wild side" of general relativity. There was a paper, like i said, on this verey topic, by J. Richard Gott, III and Li-Xin Li (Can the Universe create itself?):<BR/>http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Aastro-ph%2F9712344.<BR/><BR/>After that discussion, cwfong gets into the whole "time is only a metaphor" argument, and i think it is important to note this beforehand:<BR/><BR/>Posted by: John Morales- #211- http://scienceblogs.com/pharyngula/2008/11/siwoti_syndrome_open_thread.php<BR/><BR/>RickrOll, I suppose cwfong seems to be saying that, if the Universe is but one of many embedded in some Metaverse, and if the Metaverse is eternal, it "says little" to investigate any given universe's origin or end.<BR/><BR/>I don't see how it follows, even granting the premises, and the light beams example doesn't seem relevant.<BR/><BR/>cwfong seems to be poo-pooing the very concept of time's arrow as relevant.Rickr0llnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-7029455475529768352008-12-01T17:31:00.000-08:002008-12-01T17:31:00.000-08:00I do agree on providing stronger backgrounds. Requ...I do agree on providing stronger backgrounds. Requiring stronger backgrounds, as you note, is tricky; in theory, women and men entering these classes have the same background in formal education. My guess is that women's background gaps are more informal; many don't spend as much time building and designing things, playing with rockets and projectiles, and generally doing things that provide an informal, intuitive understanding of physical concepts that can serve as a background on which to build the formal knowledge. This is of course not universal, but my guess is that it can account for a significant portion of the gender gap for students entering the introductory physics and engineering sequences.<BR/><BR/>On calculus: the amount of calculus required for the level of physics the studies were investigating is really quite trivial. Waves and especially fields require significantly more, but the research focused on introductory mechanics courses, which can be handled with basic algebra and a minimal understanding of how to take a derivative of a simple polynomial and do an occasional integral of the same. However, an algebra weakness (which is in my admittedly anecdotal experience quite common) can be a killer. I don't think that's a problem that can be solved with a more "applied" teaching methodology, though; if anything, the weakness seems to lie in basic symbolic manipulation.<BR/><BR/>On my own ideas - it depends on the science, and it depends on the women. As I noted, I think that most women who make it to college-level physical science and engineering courses have gender-atypical learning styles to begin with - the filtering starts in early high school or possibly even earlier. <BR/><BR/>And I think that any question phrased as "how do we teach (insert subject) to (insert group)?" is founded on some pretty tenuous assumptions about the homogeneity of that group. Women taking calculus-based physics are different from women taking physics for flautists, and both are different from middle-school girls taking introductory earth science. Even worse, the variations within each group are probably enormous, especially in the middle-school group which hasn't yet self-selected into different science tracks.<BR/><BR/>More on this later - I have calculus homework :)quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-3122443077437957312008-12-01T16:06:00.000-08:002008-12-01T16:06:00.000-08:00As many a journalist has lamented, the headline wr...As many a journalist has lamented, the headline writers may not even have read the article. Much less the issues we have with journalists not hearing the science.<BR/><BR/>The weaker background issue has an obvious and readily addressed solution -- provide stronger backgrounds. And, harder to implement, <I>require</I> stronger backgrounds. In taking the physics (et al.) classes, you are going to be in trouble if taking a derivative was something you passed in your calculus class only with a great deal of struggle, and which remains a struggle. In later classes, it's assumed that you can do all that material well. <BR/><BR/>There are also serious issues with calculus being taught by people who have no consideration of their students ever trying to (gasp!) <I>use</I> the subject to solve problems. Hard to get the strong background in that case, and then success in physics et al. turns to more a matter of who thinks more in applied mode than taking the appropriate background classes.<BR/><BR/>Maybe in some later posts you can put up some of your own ideas about how to teach science to women.Penguindreamshttp://www.blogger.com/profile/10783453972811796911noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-70269461855773820812008-12-01T14:19:00.000-08:002008-12-01T14:19:00.000-08:00Ah :)Seriously, I honestly don't know. I have been...Ah :)<BR/><BR/>Seriously, I honestly don't know. I have been working on developing a level of understanding of the math behind the theories. From a purely conceptual point of view, I find the multiverse quite compelling, but without understanding the math I'm not really able to take a position and stand behind it.<BR/><BR/>As far as the comment thread there, I think I agree pretty solidly with you on this point:<BR/>"i have to agree that the only life we know of is us, so the universe being "primed for life" seems excruciatingly ad hoc. We don't even know if the paramenters can be changed in the first place, like jim harrison said."<BR/><BR/>However, I had a little trouble following the rest of the thread, which seemed to get bogged down with a bit too much metaphysics.<BR/><BR/>(for anyone else reading, we're talking about this post/thread:)<BR/>http://scienceblogs.com/evolutionblog/2008/11/is_the_multiverse_real.php#commentsquasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-79391024396181597882008-12-01T13:23:00.000-08:002008-12-01T13:23:00.000-08:00i was agreeing with you. It is from the evolution...i was agreeing with you. It is from the evolutionblog article, which paraphrased the other. The original stated that the facts fit the theory, but it is quite ther reverse, as the multiverse hypothoses has made no predictions other than 'anything and everything.' I think that there is a multiverse, simply from a eternal inflation perspective. The "fine tuning" line of reasoning is a red herring, and should be recognized as such. <BR/>Now honestly, i don't care about your qualifications quasar, i just want to know where you stand. I have no qualifications either. In particular, what are your thoughts on my comments and those of cwfong? they are great fodder for discussion, after all.Rickr0llnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-81054951802546093792008-12-01T10:17:00.000-08:002008-12-01T10:17:00.000-08:00I think you may be misunderstanding - I liked the ...I think you may be misunderstanding - I liked the EvolutionBlog post (which I only found some days after I wrote this one - I'm not responding to it or any of the comments in it). I just think the Discover article was a disaster.<BR/><BR/>I'm not sure where you got the quote "The hypothesis of a multiverse explains a lot of data" but as far as I can tell, it's not from me - with whom are you arguing?<BR/><BR/>Re: multiverse, I'm not yet qualified to have an opinion.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-56111096955790447652008-11-30T23:46:00.000-08:002008-11-30T23:46:00.000-08:00come on, aren't you being a little bit too critica...come on, aren't you being a little bit too critical, quasar? If you take it, in and of itself, the article isn't very strong, but the post in it's entirety is quite good. Many comments offer the same criticisms that you point out. I am talking of course about the EvolutionBlog post, not the article, or meta-article. That article only made some claims, nothing doncrete. "The hypothesis of a multiverse explains a lot of data"- flat out wrong, the multiverse is something which comes from the information, and makes no predictions as of yet.<BR/><BR/>Additionally, i am confused: multiverse- yes or no?Rickr0llnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-76139191450745423492008-11-29T07:45:00.000-08:002008-11-29T07:45:00.000-08:00I was giving them the benefit of the doubt on that...I was giving them the benefit of the doubt on that particular assumption, which, I agree, is not a great one to make. The puddle is an excellent analogy.<BR/><BR/>But I am aware of legitimate scientists outside the pop-science-writing universe who make actual arguments about the essential arbitrariness of the fine structure constant, and while I'm not 100% sure I agree with them, I'm also not 100% equipped to argue with them, not knowing everything they used to come to that conclusion.<BR/><BR/>On the other hand, if there are any scientists actually trying to make the argument that the article outlined...I don't know what to say. Even granting the possibility that they're right about the fine-tuning being a matter of chance, which I'm prepared to concede for the sake of debate, their argument still falls apart.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-59881043656631995642008-11-29T04:32:00.000-08:002008-11-29T04:32:00.000-08:00I'd back up the mistake(s) further. How do we kno...I'd back up the mistake(s) further. How do we know that the universe as it is is improbable? To define probability you divide the number of times the experiment (tossing a coin, whatever) came out the way that you wanted by the total number of trials. For the universe, we have 1 trial and it came out with us. Insofar as you can talk about probability, which you can't really about a singular event, the probability of a universe like ours is 1.<BR/><BR/>Slightly more generally, there's nothing that says that, say, the fine structure constant really could be very different from what it is. The apparent 'fine tuning' is that we've chosen a particular set of units and <I>assume</I> that the variable can range from zero to infinity. Yet we've never observed a universe where it's different. Until we do, it's ... er, premature to talk of the present universe being improbable.<BR/><BR/>For now, we're in the situation of Douglas Adams' puddle -- surprised that the hole we're in matches our size so well.Penguindreamshttp://www.blogger.com/profile/10783453972811796911noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-79032127567597275212008-11-24T01:37:00.000-08:002008-11-24T01:37:00.000-08:00While I do admit that it's pretty weird, the Stand...While I do admit that it's pretty weird, the Standard Model of particle physics isn't really in the same domain as string theory; it makes testable predictions, so even though we can't see the little beasts directly, we can test aspects of their behavior, and it turns out they do exist and behave as predicted.<BR/><BR/>The first main line of experimental evidence for the existence of quarks came out in the 1960s and '70s, and was the subject of the Nobel Prize in physics in 1990.<BR/>http://tech.mit.edu/V110/N43/nobel.43n.html<BR/>It had to do with the way electrons behave when you bounce them off a proton.<BR/><BR/>Since then all sorts of quarks and leptons have been produced and detected in particle accelerators, and all kinds of experiments have been done on them. One of the really neat thing about quarks bound together by gluons is that the force pulling them together increases with distance - this was discovered experimentally.<BR/><BR/>It's also a confirmed fact that energy has mass. This is what makes a nuclear reactor, or a nuclear bomb, work.<BR/><BR/>String theory is, in contrast, not only experimentally unverified but as far as anyone can tell experimentally unverifiable because it doesn't predict anything in particular (it seems to be able to predict just about anything you'd want). Which doesn't mean it's necessarily wrong, but what sets it apart from random conjectures is not its correctness but its mathematical elegance. Mathematical elegance is, in itself, a questionable criterion for a physics theory.<BR/><BR/>As far as black holes, I don't see why they would need any special time domain to behave the way they do, except insofar as they sort of create their own (remember that time slows down in a gravitational field).<BR/><BR/>I'll refrain from arguing about UFOs, since that's not properly a science discussion.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-22168165557930735992008-11-23T18:26:00.000-08:002008-11-23T18:26:00.000-08:00This whole scenario is still theoretical, just as ...This whole scenario is still theoretical, just as superstrings or wormholes are. I asked a question about parallel universes, existing alongside ours so that they are hidden. Speculation by some is that it explains the strange behavior of UFO's. I propose that there may be time domains which cannot be perceived, but could enable UFO's or black holes to behave as they do, all conjectural, naturally. <BR/>It sounds weird, but no moreso than the description of subatomic or particle physics theories.Reveriehttp://www.blogger.com/profile/05867116287549975106noreply@blogger.com