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The Math Myth

econlog.econlib.org

271–280 of 328 posts

Re: The Math Myth

#271

Few people have to use calculus or advanced probability or number theory, but everyone relies on it. The article missed this point. Need some examples? Public key cryptography, machine learning, physics simulations of the aerodynamic properties of an airplane. I could go on and on. Just because a vast majority of the population never has to think about how this stuff works does not imply that it is somehow useless. W…

I totally agree. I feel like this argument is the equivalent of saying "I'll never need to learn linear programming, I'll just plug it into lpSolve" "I'll never need to learn cryptography, I'll just use the Unix libraries" "I'll never need to know thermodynamics, my car just works!" "Google just works!"

At some point somebody had to be the person that figured out all these things so the other 99% of people can use it and not think about it ever. And I'd much rather be the person solving the interesting problems than the person using the tools without truly understanding them to solve more mundane (but still probably useful and important) tasks, but that is just my personal taste.

Re: The Math Myth

#273

This largely matches my experience - as a software engineer, I spend probably In a market economy, basically all returns come from marginal gains. The vast majority of your lifetime income will come from a dozen or fewer opportunities that you happen to be in a position to take advantage of, whether it's a new job offer or a high-profile project you volunteer for or a startup that takes off. You will qualify for thos…

There is more to math than just calculations, algebra, geometry, etc. Logic, and reasoning through choices & the effects of those choices are vital math skills as well, and for many people in math, they don't manifest until one takes a few rigorous proof-based classes, where one often sees new approaches to arriving at concepts they know, and how to properly get to a conclusion from a particular point. I wish these s…

Logic, and reasoning through choices & the effects of those choices are vital math skills as well, and for many people in math, they don't manifest until one takes a few rigorous proof-based classes

A lot of people I meet don't understand logic and reasoning. A lot of people don't understand rigor. Many people have difficulty thinking systemically or have difficulty thinking about the 2nd and 3rd order effects of their actions. I mean, think about the way people drive and some of the things you've seen other drivers do! People also seem to be much more self centered, less civic minded, and less cognizant of details.

I wish these skills were emphasized more earlier in people's education, they are important skills for maximizing success IMO.

I think American kids would have a better understanding of 2nd and 3rd order effects if they were required to clean their own school bathrooms, like in Japan. (Disclosure: I had to clean my own school bathrooms, but did not go to school in Japan.)

Re: The Math Myth

#274

Earlier quoted context omitted.

> I mean I wonder how many people even understand that 0.999... = 1? To be honest, I think it's unreasonable to expect anybody - even with a Ph.D in a field other than mathematics - to be able to even define the real numbers: My definition is probably very different from yours(I tend to say there's countably many real numbers).

There are not countably many real numbers. How can you claim your definition is correct?

There's nothing special about the definition. Use any construction you like, but do it over a countable model of set theory[1]. Now you have a countable set of real numbers, although there is no correspondence between it and the natural numbers within the model. The statement that 'there is an uncountable set' is also provable, although the set is countable. It's one of those Goedelian tricks, like the statement that is proven true but is unprovable.

That said, I prefer to say that only real numbers that can be emitted by computer programs exist.

[1] Use the Downward Lowenheim-Skolem theorem to get a countable set theory, and choose something like ZFC as your set theory.

Re: The Math Myth

#275
Even if this article were correct that math isn't necessary for employment, it would be wrong that math education is unimportant.

It isn't even correct on the employment front, though, because it is attempting to unimaginatively extrapolate from the current state of employment.

John Nagle's comment at https://news.ycombinator.com/item?id=12422307 probably expresses this better than I can, but if you're going to make an advance in a scientific or engineering field — any advance — you need math. If you're planning to spend your working life as a button-pusher, carrying out algorithms that other people have designed, or proceeding blindly by trial and error, you don't need math.

But those button-pusher and blind blunderer jobs will be automated in five, ten, or maybe twenty years. And the article's comment section suggests that even today they aren't nearly as common as the article asserts.

There are other categories of work, such as child care, elder care, sex work (which, defined broadly, includes trophy wives, Hollywood, and a substantial fraction of secretaries and maids), sales, and family counseling. So there will probably still be employment that doesn't require math as long as there are humans, even if it's not the kind of employment the article discusses.

But the bigger question is whether education should be directed at employment. Is being an employee what you aspire to in your life? It is very good to be useful to other people. Allowing other people to employ me has benefited me greatly, and that's true for most people I know. But being used by others is not the only or even the primary good in life.

Education is what makes us human. Education is a process of personal evolution from a dumb beast into a human being. Education gives us control over our impulses and prevents us from being suckered by predatory salespeople, politicians, lawyers, preachers, and others. At its best, education makes democracy possible despite such predators, although democracy is rarely possible because the people is nearly always sufficiently uneducated to vote it down unintentionally. Education begins before schooling and doesn't end when schooling ends, but I, like many people, have found that schooling can speed education up considerably.

And mathematics is fundamental to education in all of these senses. Even if mathematics isn't necessary for someone else to use you — which is all this "Math Myth" article tries to show — mathematics is necessary for you to judiciously choose when and how you will be used, and mathematics is necessary for citizenship.

Re: The Math Myth

#276
post #87

This is not just Math. I learnt chemistry, physics, biology and all that from middle to high school. Now as a software engineer they're totally useless and I have long forgotten all those details that I spent months and years to memorize and master. Even reading a science-101 book in one day now will teach me more than what I can remember. Unless you plan to major in those fields, should we just take some introductio…

Matching people with the professional roles that are best for each other is highly valuable - so even if most people forget chemistry, it's often worth teaching, because the introductory chemistry class is how chemists decided to become chemists.

Re: The Math Myth

#277
post #18

I think society would be a lot better if BASIC math and statistics would be better understood. How many times do you see a study posted here with N=23 and people say "the sample size is too small" when it's clearly not? How many people ask for a card deck change to change their luck? How many times do people read a poll like 49% +/- 3% vs. 43% +/- 3% and conclude the two candidates are statistically tied? I could pro…

> I mean I wonder how many people even understand that 0.999... = 1? To be honest, I think it's unreasonable to expect anybody - even with a Ph.D in a field other than mathematics - to be able to even define the real numbers: My definition is probably very different from yours(I tend to say there's countably many real numbers).

It's a definitional issue. "God created the integers. All else is the work of man." The theory of reals is a convenient abstraction defined by axioms. It's not created by construction.

Re: The Math Myth

#278
post #210

Earlier quoted context omitted.

I'll believe that there is a correlation of more than 0.5 to 0.7 between good at software development and good at abstract math. But hardly higher -- there are also some other talents needed, I don't know what. I saw a few people that had no problems with the math courses in CS but that never really got the programming part. (No names or details, people might be recognized.) But this is of course anecdotal. (My surpr…

> But hardly higher -- there are also some other talents needed I'm not going to deny the presence of some built-in preferences for formalized thinking among some subset of the general population, however the cognitive resources and preferences that would lead one to enjoy or excel at math, are about the same as those correlated with programming. e.g. a noticeable interest in understanding mechanical systems. So give…

I thought so too, it was surprising to see intelligent people struggle for years with the simpler parts of programming.

Maybe those guys were just unmotivated? Or they were hardworking idiots which had gotten a good math background by sheer will and hard work? It didn't seem so.

The alternative is the existence of basic cognitive talents you need for coding which aren't needed for math? Like for us color blind, that really can't appreciate some art?

None chimed in with support, so I'd guess my sample was unusual; a lot of the guys here should have teaching experience from academia.

(Category theory makes for better Org Mode? I'm curious, too!)

Re: The Math Myth

#280
I am OK with these articles for a selfish reason: keeps my competitive edge with those who do not know deep mathematics. Being able to see the interconnections of seemingly disparate concepts is highly valuable, and not an easily "Google-able" skill, which is something people should strive for.
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