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The Innumeracy of Intellectuals (2008)
- ColinWright 14y agoYou want to see "The Two Cultures" by C P Snow: http://en.wikipedia.org/wiki/The_Two_Cultures http://en.wikipedia.org/wiki/The_Two_Cultures http://www.google.co.uk/search?q=CP+Snow+cultures http://www.google.co.uk/search?q=CP+Snow+cultures
- unimpressive 14y agoPart of the problem is seeing Math/Science and The humanities as opposites or opposed to each other.[0] Human knowledge mostly likes to spit in our face when we attempt to label it.[1] [0]: http://www.britannica.com/EBchecked/topic/497891/Renaissance-man http://www.britannica.com/EBchecked/topic/497891/Renaissance... [1]: http://en.wikipedia.org/wiki/Intertwingularity http://en.wikipedia.org/wiki/Intertwingularity
- barrkel 14y agoThe problem is that mathematics and the sciences are useful, while the humanities are largely about social signalling. One may be proud to be ignorant of mathematics precisely because it is useful; being ignorant of it indicates you have sufficient wealth in other areas that you don't need to get your hands dirty, as it were. And on the other hand, being ignorant of something like classical music is looked down upon precisely because it marks you out as not a member of the group.
- zeteo 14y agoPrecisely. Maybe the best way to make math "cool" is to reclaim for it that status of "completely useless but fun knowledge" that Hardy was so proud about in his Apology.
- jinfiesto 14y agoMath is cool, and at least to me is lots of fun. The problem, at least at my university is that all of the lower division math classes have been commandeered by the engineering programs. I enjoy doing a substantial amount of recreational math in my spare time. Unfortunately, the classwork at the lower-levels (basically the calc sequence) basically involves regurgitating formulae over contrived physical problems. At its best, Math can be an extremely entertaining way to spend an evening, or a rainy day; It's at least as much fun as writing or reading poetry, or reading a good novel.
- klipt 14y agoStill true of some parts of pure math...
- dmhdlr 14y agoAmong the Western public this might be true. But among intellectuals the bigger prejudice is that numbers are "hard." I certainly find them to be so, and have felt like this since high school algebra. At root it seems to be an epistemological problem, complicated in higher learning by over-specialization in all disciplines.
- aamar 14y agoBut there are reams of math and many fields of science (astronomy, paleontology) that have no practical utility. It's quite easy to find this sort of material in any university, in books, etc. While I won't directly take on your social signaling claim, there are some humanities which have clear utility (while also functioning as social signals), for example knowing the precise meaning and usage of a large set of words. People in the academy are not disdained for having this practical facility. An adjusted version of your claim: I think that in some countries (including the U.S.) math & hard science are tarnished through their association with poorly-protected and therefore indifferently remunerated professions, such as accounting, pharmacology, and engineering. Most educated people I encounter would, all things being equal, like to be good at math, but some let themselves off a little easy. Trying and being bad at history would make you dumber than a lawyer, which feels okay; trying and being bad at algebra makes you dumber than an accountant, which is humiliating--so better not to try.
- hatcravat 14y ago>But there are reams of math and many fields of science (astronomy, paleontology) that have no practical utility. Really? Just how do you think ships (and airplanes while over water) navigated before GPS? How do you think the radius (and from that and the density, the mass) of the earth was determined? Would you be able to drive your car to work if not for the effort of paleontologists (many of whom work for the oil industry)?
- aamar 14y ago> Just how do you think ships (and airplanes while over water) navigated before GPS? All the astronomy needed for navigation was completed in prehistoric times, as far as I know. Modern astronomy, I think, has nothing to contribute. > How do you think the radius (and from that and the density, the mass) of the earth was determined? Eratosthenes modeled Earth as a sphere and the sun as an infinitely distant light source; what is the astronomy there, other than the common sense idea that the sun is very far away? I think you could also have mentioned how astronomy inspired Newton's work, which has utility. But the point here is really about modern astronomy as a field of study: dark matter, black holes, etc. -- these are not "immediately useful" topics. Studying them does not get "one's hands dirty" because it's preparation for day labor. > Would you be able to drive your car to work if not for the effort of paleontologists (many of whom work for the oil industry)? Yes, I think so; a few paleontological techniques are useful for exploration, but it is not a major (or essential) tool, though many geological techniques are; exploration began far before paleontologists were involved. The standard I was applying was really that certain fields of science are as superficially impractical as humanities like history or literature. A few paleontologists employed in industry wouldn't undermine that; a few historians get picked up by industry too (arts, law, etc.).
- kingkawn 14y agoThere's also social signaling occurring when he includes boozing in his list of reasons he has chosen to remain ignorant of arts and music.
- jdleesmiller 14y agoA related anecdote: I saw mathematician Andrew Dilnot [1] at a Mathematica users conference a couple years ago, and he asked the audience how many times the size of the world economy had doubled since 1900, given that it had grown at about 5% per year. The audience guesses were in the 2-4 range, but he pointed out that the rule of 72 gives 110/(72/5) ~= 7.6. "Don't feel bad," he said, "last week I gave this talk to the council of European finance ministers, and they did no better!" (I may not have remembered the numbers exactly, but they were something like that.) [1] http://en.wikipedia.org/wiki/Andrew_Dilnot http://en.wikipedia.org/wiki/Andrew_Dilnot
- Locke1689 14y agoYour calculation is way off. You forget that the rule of 72 is how long it takes for the money to double. Thus, the final calculation is 2^7.6 which is, as any good computer scientist knows, a little less than 256
- Tycho 14y agoHuh? At 5% growth per annum, the economy takes 70/5=14 years to double (I prefer the rule of 70). 112 years since 1900, so that's enough time for the economy to double 112/14=8 times.
- adrianN 14y agoThe economy grew by a factor of 1.05^112 = 236. Which is close enough to his number to assume that he missed the "doubling" part of the question. 236 is about 7-8 doublings.
- Locke1689 14y agoWoops, yeah, I thought it asked how many times larger the economy was, not how many times it doubled (which, btw, seems like a weird way to phrase the question to me).
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- _delirium 14y agoThis is a bit of a curious post. I'm not sure the antidote to people being proud of ignorance in science/math (which is a problem) is to be proud of ignorance in the humanities (which is also a problem). I mean, if you'd rather go boozing than read Bertrand Russell, that's a choice you're free to make, but I wouldn't be proud of it. I guess I don't know much about the history of classical music myself, but mostly because one can't study everything, and it isn't currently near the top of my reading list (though the fact that both Douglas Hofstadter and David Cope constantly mention J.S. Bach makes it somewhat relevant to my AI interests). I also don't generally think as scientists we can afford to be ignorant of the humanities in general, though many people can afford to ignore parts. There is a lot of physics that suffers from "bad metaphysics" precisely because of its practitioners reinventing metaphysics, in the guise of "interpretations" of physics, when they are unaware of obvious problems that arise, which even a small amount of reading would've made them aware of. And there's a lot of work in artificial intelligence that makes more sense with a humanities background. Oddly this seems to be a recent phenomenon. Early 20th century physicists were very well-read in philosophy, and their interpretations are accordingly sophisticated and rarely run into novice problems. Same with mathematicians; it's hard to even separate whether someone like Frege was a mathematician or philosopher. Some is unavoidable due to increasing specialization, but if anything that would seem to call for more humility, not extra arrogance that we know how to solve the philosophical problems that we don't time to study in as much depth as Einstein/Planck/Bohr/etc. did... I'd trace some of it (on both sides) to a general academic tendency to want to rationalize why the fields you didn't specialize in and don't know about aren't that important to know about. There's an only half-joke that academics always want to reduce every field to their own: to an economist everything is analyzable with economic tools, to a sociologist everything is culture, to a physicist everything is physics and its minor epiphenomena, to a philosopher everything is philosophy plus implementation details, to a dynamical systems theorist everything is just instantiations of dynamical systems, etc.
- stanleydrew 14y agoThis is only mildly amusing because I know Bertrand Russel more from his work in mathematics than from his work in the humanities. http://en.wikipedia.org/wiki/Principia_Mathematica http://en.wikipedia.org/wiki/Principia_Mathematica http://en.wikipedia.org/wiki/Russells_paradox http://en.wikipedia.org/wiki/Russells_paradox
- cperciva 14y agoI don't mind the innumeracy of so many liberal arts intellectuals... as long as they stick to liberal arts. Alas, they do not. A short time ago, I was involved in debate over instituting a new affirmative action program at my university. "We're failing this group terribly! We must do something about this!" came the rallying cry. I responded with university admissions statistics, high school graduation statistics, and census statistics, showing that the largest reason behind our apparent lack of members of that group was that we were an urban institution which drew students mostly from the local area, and members of that group lived mostly in rural areas where the population as a whole tended to attend more rural institutions. (Canada has far more of a trend towards attending "nearby" post-secondary institutions than the US does.) I was accused of trying to confuse the issue "by introducing numbers and percentages", and the admissions policy was adopted.
- simonsarris 14y agoIs there a good reason to think this is not either a curious outlier or strawman? Is that situation alone actually good reason to demand people "stick to the liberal arts"? Or is there something else here among your reasoning? For the record, I have a degree in CS and Philosophy, so its awfully tough to "stick to the liberal arts".
- cperciva 14y agoThat was the most blatant example, but I see members of the university Senate voting for what they "know" over what they have evidence for on a regular basis. (And the philosophers aren't the problem... although that might be partly because our philosophy department is quite strong on logic.)
- mangler 14y agoYeah, the next time you go to your local yoga class and the local bleached bimbo starts babbling on about quantum physics (for some reason, a favourite subject), ask them if they can solve a quadratic equation. Guess what, they can't. But that is not a reason to desist! The quantum physics banter lives on... So, learn from these smart people. Fake it and bask in it!
- evincarofautumn 14y agoPerhaps the sciences are just harder to pretend to care about. I don’t mean that derisively—it’s just that the arts are very approachable because you don’t need to understand everything in order to appreciate it. I’m a designer at heart, but my work is firmly in the hard sciences. I’m excited about what I do, and it shows. That’s what gets people interested—ferocity, passion. You have to be able to describe your work in accessible terms, so that other people can appreciate it without having to understand it in depth. Not all people want to understand everything—it’s hard work. Work that we hackers can take for granted because, by our nature, we enjoy it.
- _delirium 14y agoThat's probably true for some parts of science, but I think the general public pays at least as much attention to science as to art, when something catches its attention. How many people who don't know the first thing about particle physics were tweeting about the Higgs Boson? Probably more than the number who tweet about Damien Hirst! Astronomers are good at getting public attention and cultivating a sense of "astronomy appreciation" among laypeople as well.
- evincarofautumn 14y agoSure. But we’re not all Neil DeGrasse Tyson or Bill Nye, and we don’t all work in fields that make it to “pop science” status. My work is in compilers—not exactly well known outside academia and the programming community. It doesn’t come for free.
- DanBC 14y agoI think that's worrying - people don't have the language to begin to understand the Higgs boson. Not just that they don't know what a boson is, but they don't really know what particles are, or what energy is, or what mass is. And so when you need to explain what the Higgs Boson is you need to give the simple lies we tell people when we explain physics I live in the UK. BBC Radio 4 has a "flagship" news and current affairs programme called 'Today'.[1] Science is routinely handled as if the audience are idiots, while arts are given free range to be reasonably esoteric. [1] Today website (http://news.bbc.co.uk/today/hi/default.stm http://news.bbc.co.uk/today/hi/default.stm)
- hsmyers 14y agoI was lucky enough to spend a fair amount of time in college with a senior citizen who was aiming for a fine arts degree in painting. As in most colleges, this does not require algebra which she thought was a shame as she had been home schooled and had a thorough background in mathematics as was expected of a young lady of her class and social standing. That 'woke' me up to the decline in education standards in the second half of the 20th century. Not only in this country but around the world. If you think I'm wrong, just compare the textbooks available now with what was available in say 1910! Would you even be allowed to use a text book by Hilbert? I doubt it. I will grant you that she was exceptional and typically excelled in any endeavor she chose---she was I believe the first American woman to be allowed a role on stage at the Abbey Theatre in Dublin as an example. Decline and Fall are us I guess...
- neutronicus 14y agoYou're comparing educational standards for the wealthy to educational standards for everyone.
- wpietri 14y agoBut he's doing it across a couple generations. Our material wealth is so much greater that it's reasonable to ask whether our level of education has kept up.
- ef4 14y agoBy 1910 universal compulsory education was already in full swing in many places. Take Massachusetts, for example. If you examine the textbooks being used in Massachusetts at that time you'll see the same phenomenon -- they're much more advanced than modern textbooks. And they were not just for the rich, Massachusetts already had compulsory education. And by the same argument: where are today's equivalent textbooks for the rich? Our wealth gap is as big as ever, yet I see no books even for the rich that are so advanced.
- abecedarius 14y agoI'd be curious to see an example. I seem to recall a 19th-C. MIT entrance exam as comparable to or maybe behind what my better high-school classmates learned.
- rickmb 14y ago"our economy is teetering because people can’t hack the math needed to understand how big a loan they can afford" That is not so much caused by a lack of math as it is a surplus of delusional optimism. No amount of math will ever beat that. Not only is it a bad example, I can't think of any better examples, and apparently neither can the author. It may be that my utter incompetence in math makes me less than objective, but I fail to see any convincing argument in the entire article.
- SagelyGuru 14y agoBeing an intellectual ought to be primarily a matter of attitude of respect towards knowledge of all kinds and, above all, a strong curiosity and interest in learning. Thus what is particularly sad is not the fact that some subject or another is avoided and ignored by (intellectually) lazy people but that such people, proud of their ignorance, nowadays pass for intellectuals. 'My subject is more important than yours, so I am not going to waste time learning from you' is just a post-justification for being a dullard and a bigot.
- pessimizer 14y agoCase in point: http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-... I find it a bit sad how he thinks that people should be taught long division, which is what we have calculators for, but algebra is a step too far. The only reason I think people should be taught arithmetic is so that they understand algebra. After algebra, Calculus I for people who want to actually be knowledgeable about the world around them (No heavy series and no multivariate), and then I don't care what they do, because I trust that they understand how the world works. Instead, Hacker suggests that we drill those future artists and writers on duplicating the functions of a calculator for 12 years, and then throw them into the voting booth. Bleah.