[HN Gopher] The Math Myth
___________________________________________________________________
The Math Myth
Author : paulpauper
Score : 34 points
Date : 2022-06-06 21:52 UTC (1 hours ago)
(HTM) web link (www.econlib.org)
(TXT) w3m dump (www.econlib.org)
| 8bitsrule wrote:
| I've used calculus very little, algebra quite a lot. One of the
| side-benefits of learning calculus (apart from reading others'
| work) is how much solving those problems reinforces your algebra
| skills.
|
| Solving one scary calculus problem thrown at me as an undergrad -
| an integral - resulted in a solution which broke it into 16
| separate integrals. _Days_ of algebra were involved.
| eli_gottlieb wrote:
| What in the actual fuck? Apparently I must be in "the 10%".
| xqcgrek2 wrote:
| I have a hard time believing the claims in the article. I use
| vector calculus and linear algebra everyday and so do my
| colleagues
| rrss wrote:
| I'd like a job where I used more math - can you share your job
| & industry?
| Manuel_D wrote:
| You might not be writing out integrals and derivatives by hand,
| but I think most engineers use calculus a lot more frequently
| than they realize it.
|
| * If daily user growth is increasing linearly, total user count
| is exponential over time.
|
| * If I have a radially symmetric shape it's center of gravity is
| going to be centered on the axis of symmetry - if the density is
| uniform. But if the density isn't uniform, where will the center
| of balance shift?
|
| This is single dimension and multi-dimensional calculus,
| respectively. I bet most engineers use at least the former, at an
| intuitive level, on a regular basis.
| flopquads wrote:
| "total user count is exponential over time" No, it's quadratic
| over time.
| xvedejas wrote:
| If daily user growth is increasing linearly, total user count
| is squaring over time.
|
| Exponential growth would be when daily growth is proportional
| to the current number of users, which is different.
| majormajor wrote:
| American high school education does seem still unfortunately
| calculus mono-focused, with little of even what makes calculus
| interesting considered, just ram a bunch of rules for derivation
| and integration into your head.
|
| A broad base of at least some of stats, linear algebra, and
| others seems like it would be more useful to most even in STEM to
| me. I've met folks who were great at those who struggled with
| geometry and/or calculus, and vice versa. Yet plenty of need for
| people good at all sorts of those.
| discreteevent wrote:
| I originally studied EE and we did a lot of math. Fourier series,
| Laplace transforms ... Never used any of it. The most I've used
| has been some simple statistics and a cubic spline for some curve
| fitting. Even ML seems to just use basic linear algebra. That
| said, trigonometry can be quite useful for DIY jobs.
| devnulll wrote:
| I've used more Geometry & Trig working on my Model Train Set
| than I have as a professional software engineer. Figuring out
| table spacing, track radius, overhang from trains, is basic
| stuff.
|
| I needed to buy a bunch of precisely cut curved wood for a 2nd
| level (laser cut wood! So Awesome!), and had to actually re-
| learn the basics of trig in order to provide the details to
| have everything made.
| t_mann wrote:
| I find it hard to believe that anyone working as a programmer /
| software engineer wouldn't be using any actual computer science
| (as in data structures, algorithm complexity,...). I could
| believe that most people working as engineers in civil/mechanical
| engineering would mainly use Excel, but not that they wouldn't be
| using exponential functions.
|
| But I guess his point is rather that most graduates of
| engineering schools don't even work as engineers at all, which
| might be true, I don't know (I even have difficulty believing
| that given the number of people I know who weren't even trained
| as engineers and are now working as software engineers).
| contravariant wrote:
| > This is a conjecture that desperately needs resolving with
| solid statistics and in-depth interviews.
|
| Ironic that a hypothesis that most people won't need mathematics
| should require solid statistics to resolve.
| AlbertCory wrote:
| I was curious about Bryan Kaplan, since he seemed hard to
| categorize, so I did some research.
|
| Hate to say it, but he looks like a Malcolm Gladwell wannabe with
| some attention-grabbing book titles. Perfect for a TED talk.
| orzig wrote:
| I disagree with many things he says, but don't think he can be
| dismissed so easily. How many other public intellectuals have
| even attempted, let alone nailed, anything like this?
|
| https://www.econlib.org/my-complete-bet-wiki/
| culi wrote:
| Nice you managed to categorize the work of this person who's
| been around 20 years longer than Gladwell. The important thing
| is that you found a way to place yourself above them without
| ever making a real criticism :)
| blip54321 wrote:
| Since finishing school, I've used very little of the math I
| learned in school.
|
| I've used a lot of math. Most of it built on high school algebra
| and geometry. Does that mean that's all I needed to learn?
|
| No.
|
| The key thing I do use is more ephemeral: Mathematical maturity.
| In my current job, I use math I never learned in graduate school.
| I'm able to learn it quickly because I learned a lot of math back
| then. My math classes were a way to develop mathematical
| maturity.
|
| Which specific math I learned in graduate school was almost
| incidental. What I picked up was the ability to learn new math.
| kazinator wrote:
| In programming, you're doing math whenever you convince
| yourself that a rewritten piece of code means the same thing as
| the original (by thinking about it, rather than just running
| it).
| culi wrote:
| I mean, at a certain point, you're just abstracting logical
| thinking in general and calling it "math". You can say the
| same about baking, working out your schedule ahead of time so
| you can pick up your kids and have time to buy groceries, or
| trying to sort your playlist of non-album singles in a way so
| that you optimally position each song in a way that minimizes
| how jarring the switch from one track to the next is
|
| I feel like the whole point of "math" is to abstract these
| natural patterns so we can like... write them down and
| investigate them further. We have a limited mental capacity
| so we abstract it into a syntax/system of meaning so that we
| can let the paper or the computer do some of the memory work
| for us.
|
| If you're doing it in your head, sure that's a skill, but is
| it really math?
| burrows wrote:
| Do you use "math" and "deductive reasoning" to refer to
| distinct activities?
| jfengel wrote:
| Deduction is used in a lot more than just the classes
| labeled "mathematics". Which makes one question just to
| what degree the mathematics classes are even useful.
| Perhaps deductive reasoning could've been taught to do
| more useful things than factoring polynomials.
| obviouslynotme wrote:
| I am one of the exceptions that uses higher level mathematics on
| a regular basis at work. I agree with his theory that teaching
| everyone calculus, or preparing to take it, is not necessary for
| most.
|
| The problem I have is that he is looking at averages. In my
| experience, there are five tiers: counting, arithmetic, algebra,
| calculus, and higher math. The USA is simultaneously sending more
| people to the top two and bottom two, with the bottom two going
| from a small few to a real population segment. I don't even know
| if the worst public schools teach anything anymore or if they are
| just pseudo-prisons to capture taxes.
|
| I won't even go into the woeful state of logical and statistical
| knowledge. I don't know why those aren't core requirements for
| graduating high school.
| yunyu wrote:
| I have used very little algebra/calculus/pre-college content, but
| have used a lot of linear algebra/discrete mathematics. Would
| this be a common exception to the rule?
| samus wrote:
| I think the author had purely calculus in mind. Discrete
| mathematics is indeed crucial to understand computer science.
| Statistics are very important too, especially in our post-fact
| world, to be able to call out obvious bull**** when you see it.
| devnulll wrote:
| > Discrete mathematics is indeed crucial to understand
| computer science.
|
| FAANG engineer here, having worked in multiple companies you
| would recognize as a principle (or higher) engineer. I've
| also taken Discrete math when I was a CS undergrad.
|
| I've never used any of the advanced math learned in school,
| and I've had the pleasure of working on some of the largest
| and most complex systems ever made. Lots of basic Excel. The
| "math" I have needed for work (such as TLA+ modeling,
| percentile distributions, etc) was always learned "on
| demand".
| contravariant wrote:
| That makes sense to me. I find that calculus requires quite a
| lot of additional knowledge to make it applicable, whereas it's
| often relatively straightforward to rephrase a problem in terms
| of linear algebra or discrete mathematics.
| kenjackson wrote:
| He discusses how specificity is key in sports, but actually the
| consensus now is to avoid specialization for as long as possible.
| Playing other sports helps you in your primary sport, especially
| when it comes to injury reduction. The book Range by Epstein
| covers this well.
|
| The article also seems to be focused on a certain kind of math.
| Boolean algebra is a type of math that is used regularly in CS
| and EE. It is so fundamental that if you don't get it you
| probably can't code anything non trivial.
| natly wrote:
| Range is kind of a niche book I'm not sure it represents the
| consensus yet.
| lynguist wrote:
| I've read that the Olympic gold medalist in archery
| specifically practiced the piano, basketball, and painting just
| to improve his archery skills. Skills translate.
| epgui wrote:
| Wow, this is exactly the sort of anti-intellectualist drivel that
| makes me lose faith in humanity.
|
| And oh, the irony of dismissing the case for mathematics as a
| thinking aid as "self-serving nonsense" for which the author has
| "a very low opinion"!
|
| Perhaps if the author had a better attitude towards education and
| was capable of appreciating the value of mathematics (or more
| generally, science) in everyday life (to say nothing about the
| importance of this in democracies), then he would not hold this
| infantile opinion.
|
| Sorry, not sorry.
|
| Edit: the point is not whether you "use it" when you're out and
| about doing your groceries. If you're judging the value of maths
| and science by this measure, you're missing the point, and you're
| at such a low level of insight that your perspective is useful to
| nobody. Rule of thumb: don't listen to anti-intellectualists.
| B1FF_PSUVM wrote:
| > anti-intellectualist drivel
|
| You're barking up the wrong tree. At worst it's elitist, not
| anti-intelectual:
|
| _" The math myth is the myth that the future of the American
| economy is dependent upon the masses having higher mathematics
| skills."_
|
| Just doubting the need for higher math skills to be massified,
| not against their being necessary, perhaps to an elite.
| barry-cotter wrote:
| > Perhaps if the author had a better attitude towards education
| and was capable of appreciating the value of mathematics (or
| more generally, science) in everyday life (to say nothing about
| the importance of this in democracies), then he would not hold
| this infantile opinion.
|
| The author has a doctorate, teaches at a university, has
| written several books and home educated two of his sons to a
| level where they published academically before they entered
| university. He's also more well read in philosophy and
| literature than average though that is a low bar to clear.
|
| If you have an argument more compelling than name calling you
| should share it.
| epgui wrote:
| My argument is that the value of mathematics is not in
| whether it's useful in everyday life (the first-order
| utility), but that it is in fact in how it helps you to think
| better (the higher-order utility).
|
| The author, as decorated as he may be, seemingly fails to
| appreciate the latter: in his own words, he has a "very low
| opinion of this self-serving nonsense". The exercise of
| fleshing out the argument against the higher-order value of
| mathematics, you will note, is left as an exercise to the
| reader.
|
| This is by definition an anti-intellectualist position:
| defending such a position, which goes contrary to what should
| be the default position in general, should require a very
| high burden of proof, not an offhand dismissal.
| kazinator wrote:
| A lot of people wouldn't be able to muster 8th grade math skills
| and do something usefl with Excel. Maybe there is a non-strawman
| version of the Math Myth is that the economy would benefit if
| more people could do that.
| vsareto wrote:
| There is a lot of statecraft behind governments promoting this
| myth, so I wouldn't be reading into it too much. The countries
| listed want as high as possible of a population of scientists,
| and they will forecast doom and gloom to try and convince anyone
| with a passing amount of patriotism to work in those fields.
| There never was a clear proof that we needed more.
| nicodjimenez wrote:
| I started a math tools company (mathpix.com) and I could not
| agree more! US needs humanities far more than STEM. US is
| extremely strong at STEM and extremely weak at humanities. This
| includes understanding of the real world and human affairs. Young
| people now have zero understanding of religion, the military,
| geopolitics, or really how to think critically about ANYTHING
| related to social sciences. The truth about the reason for the
| death of social sciences in the US is a dark and complex one, I'm
| not even so sure that truth is even important. What matters is
| what's next, and it had to start with a little bit of realist
| humanities education for young people.
___________________________________________________________________
(page generated 2022-06-06 23:00 UTC)