And the connection to Cal Tech’s distribution requirements?
See my updated post above.
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I have found that when you can make cross-curricular connections that students get excited. For example, one of my sub-units is called “Functional Melodies” and shows how math and music overlap. The music kids can find the math and the math kids can learn to listen to things in the music. It touches on geometry, trig, sequences/series, waves, graphing, etc.
The problem I think we often have in the classroom as that we draw our courses too narrowly- so if it’s trig year, the students don’t look at algebra or geometry. Keeping the formal subjects narrowly focused makes it harder to connect the interdisciplinary big ideas which seem to get students excited.
When I was looking at a residential science and math high school program for one of my children, I asked about music. I was told, “Oh, yes, some students bring instruments!” No band, no orchestra, no lessons… no thank you!
Agreed.
I don’t know if this is true; a kid can buy a Rasberry Pi and figure out how to program it for $15; that’s less than a hard cover book sells for.
An interesting aside - the best predictor of a child’s literacy level later in life is the number of books in the house the child grew up in, not how much time was spent reading to the child. I think this is quite fascinating and probably relevant to the curiosity part of this discussion and how it plays with the ability to learn hard things, or important things.
And math - my math kid like topology and statistics and geometry. Not so much calculus- calculus is a tool that useful, but the others topics have more layers. I actually think of non-applied math as requiring more the type of thinking skills than those one associates with most STEM courses.
I think this does a disservice to students. They should study the humanities not as a means to an end(which makes them an applied engineering unit), but so that they can go to the Vatican and understand the artistic and historical importance of the Cathedral. This may lead them to do better work in their chosen field, but in a much less direct way.
There is a lot of handwringing in this country about underfunded schools and all that, but the simple truth is that to study math at the world class level you just need a blackboard, a damp cloth, and a piece of chalk.
I would know. I grew up in a country where that was all we had.
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Does it have to be Hagoromo chalk?
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Yes, sociology is applied psychology, etc. But that XKCD cartoon is mocking scientists on the right who think they belong to a more “pure” or objective field and look down on the scientists to their left.
This is a well-known joke amongst scientists.
Whereas in fact sociology is as pure and objective as abstract algebra?
I think you’re missing a fairly critical piece of equipment.
I’m so used to this forum being actively and strictly moderated that I’m quite surprised to see that since my last visit we’ve worked our way unfettered to comparing which studies are more objective than others. Why does this matter?
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Thanks. I think I have it now:
Humanities majors don’t have to take math and science. Science majors have to take humanities. Therefore, science majors know more about humanities than humanities majors know about science. This explains why so many humanities majors have a much broader definition of science; and by “much broader,” I take that to mean inaccurate, which then leads to presumably inaccurate stereotypes.
I’m still not sure why you needed the second premise, but I get what you’re saying.
I have just a few observations about all this and then will move on, since this thread is close to jumping the shark.
I have frequently observed that technical people often overlook and oversimplify what it takes to master other forms of learning. It is not easy, for example, to become a good writer.
I also believe, with supporting evidence in this very thread, that a lot of technical people assume that other people who don’t pursue technical studies make that choice because they can’t hack it. For those who subscribe to this view, I think you’re overlooking a lot of smart people who are simply not interested in what you or your kid is studying or doing. It just doesn’t turn them on. And you also have to account for the cohort of humanities kids at highly selective schools. To have a reasonable shot at admission to those places, you have to take calc and other hard science courses in HS, and excel in them. These are not by and large the dummies who can’t handle quant, which is also a stereotype.
I do concede that the hard sciences take a lot of work and are easier to fail, where road blocks stay road blocks until they’re overcome. Less true for many / most other areas of intellectual inquiry.
As I said upthread, stereotyping is caused by the lack of familiarity, and often bi-directional. I should add a third element: some in the group being stereotyped do seem to, at least partially, fit the description. The problem lies in the generalization to the entire (or a majority of the) group.
The problem with the lack of sufficient, or even basic, skills in math and statistics in the general population, and among many in the humanities majors, is well known. What’s less known is their lack of sufficient, or even basic, knowledge of the sciences. This lack of understanding of what sciences are has many consequences, including its role in helping to facilitate the spread of conspiracy “theories” (across the full political spectrum) on the internet and other media channels. However, it would be stereotyping to say that all, or nearly all, members of the group have this issue.
There’s also stereotyping in the other direction. Some perceive that many STEM majors lack understanding of nuances in a world full of nuances, that they lack critical thinking skills, or that they’re just “numbers guys” or even robotic. I don’t dispute that some of them may fit that description, but that surely is an erroneous generalization if applied broadly.
As to the question of whether the best of the humanities majors can do well in STEM if they had become interested in STEM, it depends on many factors, including 1) they almost had to become interested in math/sciences early in their lives; and 2) what “doing well” in STEM means (becoming a engineer in some engineering discipline, or an elite mathematician or scientist in physical or natural sciences). Regardless, the question is so hypothetical that we’ll never know the full answer, partly because none of our elite schools (other than MIT/Caltech) requires their humanities majors to take serious math and science courses. The few students who major in the humanities at MIT/Caltech didn’t distinguish themselves in STEM, however. But it’s a very small sample.
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I’m not arguing about which field actually is more pure or objective. I’m arguing that the purist attitude is worthy of mocking, and that it is indeed mocked by scientists of all fields.
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I was responding to a comment that “STEM is not objective” by pointing out how broad an umbrella STEM is, and that at the far end of the spectrum (such as it is) M is indeed as objective as things ever get, since it deals with neither opinions nor theories, but only with necessary truths - so much so that some philosophers even consider it a tautology.
The included comic was just the icing on the cake. It’s not funny if you have to explain it.
(But do note the traditional second punchline in the mouseover text on the xkcd website I didn’t include in my initial post;)
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…But there’s also this guy for your amusement.
Anyone knows who that is?
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Mr. Feynman who also said, “To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”
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These experts that he refers to call themselves intellectuals. And they are proud to call themselves intellectual. Shouldn’t it be seriously embarrassing to call yourself an intellectual? Some of them are public intellectuals. Somehow distinguishing themselves from private intellectuals – whoever those are.
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The posts above about Richard Feynman reminds me of a couple of other titbits about Feynman related to this thread topic:
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Although I’m not in the legal profession, I’ve had chances to work with law partners from many of the nation’s most premier law firms, from NYC to LA, from DC to Chicago. They were undoubtedly highly intelligent, and proud of their abilities to understand and connect the minutiae in documents thousands (or even millions) of pages long, often written in torturous English. However, I highly doubt that they would be able to fully understand the first 100 pages of The Feynman Lectures on Physics, which are three-volume long and based on his lectures given to all Caltech freshmen (some freshmen could have skipped the course by testing out of it, but probably none of them did with Feynman teaching that course), even though the physics was described in the books in plain English in great and insightful details, with remarkably few formulae/equations. These books are still considered by many to be the most insightful introduction to physics.
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Stephen Hawkin may be better known to an average American than Feynman, because of his popular books and his physical conditions. He was certainly a great physicist/scientist, but he was no Feynman. Feynman was widely regarded among physicists and other scientists as the most brilliant, iconoclastic and revered figure in science since WW2, and the greatest native-born American scientist, ever. He once taught a cross-disciplinary course on physics, computer science and biology at Caltech, along with Prof. Carver Mead, a famed pioneer in microelectronics and semiconductor. The back of the classroom was filled with faculty members from many different disciplines, hoping to gain some insights from listening to Feynman.
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His BBC interview series “Fun to Imagine” should be required viewing for all school kids (and their parents, especially those thinking imagination is an exclusive domain of liberal arts).
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He is such a great communicator !
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Apparently, it is not impossible for a poet to become a mathematician. Hilbert may not have had a large enough sample size.
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