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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#231

Post by hackuser »

cs702 wrote: post #114

I think this essay asks the wrong question, and then reaches doubtful conclusions from it. We should not be asking whether most individuals today use higher-level math in their daily lives, because the answer we get will depend on the degree of math literacy of the people with whom those individuals must interact every day. The level of discourse is often dictated by the 'lowest common denominators' -- that is, the p…

I agree, and also wonder if the concepts of more complex mathematics and how to apply them are beyond most people, at least in the way they are taught. They are designed by professors for professors, sort of like that software that nobody can use effectively because it's designed by its developer (who has deep expertise in that application) for her/himself.

Re: The Math Myth

#232

Post by lisper »

kazinator wrote: post #178
lisper wrote: post #134

Earlier quoted context omitted.

> add another digit But you can't. All of the places where you might want to add a digit are already occupied by 9's.

So you're saying a countable infinity can be occupied, so that there is no room for one more. You must then disbelieve concepts such as that the even integers can be put in 1:1 correspondence with all integers; i.e. that there are exactly as many even integers as there are integers.

> So you're saying a countable infinity can be occupied, so that there is no room for one more.

No. I'm saying that a countable infinity doesn't have room for one more at the end. There is no end.

You can obviously stick a 1 in the middle, but then you have a number strictly less than 0.999...

Re: The Math Myth

#235

Post by burrows »

mmmBacon wrote: post #149
analog31 wrote: post #25

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations. The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math a…

Worked in HW design for 16 years and I've never seen a design that was done by trial and error. Usually lots and lots of simulation and calculation up front followed by a DOE (design of experiment) to provide insight in areas which are difficult or impossible to simulate well. It's most certainly not trial and error.

Designing and running a simulation sounds like a trial. Observing the results of the simulation then making a correction, seems to imply a sort of error.

Re: The Math Myth

#236

Post by pjscott »

morgante wrote: post #160

His conjecture is correct, but his conclusion is not. Advanced mathematics are rarely used for any professional position (including software engineering), but that doesn't mean that technical degrees are irrelevant. In my experience, such filters (like an MIT degree in CS) are invaluable for two reasons: 1. Math does teach you to think logically, which is an invaluable skill in all careers and essential in some (soft…

> [...] try teaching programming to a bunch of math majors and a bunch of sociology majors, see how learns more easily.

That doesn't necessarily mean that teaching math to people makes them better at programming. It could also mean that the kind of people who major in math (and then don't drop out in the first year) tend to be better at the kind of thinking used in programming than people who go into sociology.

It's hard to tell what causes what, and that's what the author is talking about when he says that the matter of skill transfer isn't settled.

Re: The Math Myth

#237

Post by yummyfajitas »

astazangasta wrote: post #215
yummyfajitas wrote: post #183

Earlier quoted context omitted.

The entire goal of statistics is to build approximations which converge to truth in some manner or another. E.g., a Bayesian posterior ideally converges to a delta measure on truth as N -> infty. A frequentist point estimate converges to truth (with P = 1) as N -> infty. The entire purpose of statistics is to quantify the difference between our beliefs and actual truth.

>A frequentist point estimate converges to truth (with P = 1) as N -> infty. Since we are never at infinity, our observations are always finite, all this is saying is "we always deal with approximations of reality," i.e., statistics is never, in fact, about the "actual truth", it is about testing the set of our limited observations of reality against a model.

This is like saying real analysis is not concerned with irrational numbers since they can only be constructed as limits of sequences of rational ones.

Re: The Math Myth

#238

Post by unabst »

Context is the problem. This myth applies to all subjects. But it also applies to Excel, because it's not the subject, it's the context. What they still teach at school is the "Excel" of their time. They thought it would be most useful.

But even with excel spreadsheet, if you leave out the "why" you still end up with a boring class of formulas and UI work through tutorials that will leave you questioning relevance just the same. And your school paid MS how much?

If you're developing a game, or designing a building, or analyzing online sales, or trying to build a web site, you now have the context, but you probably don't have the education unless you took special courses in higher education which is practically the only place they teach with context. Maybe they just need to add more context to lower and general levels as well?

Anecdotally, it's fair to say good students manage to identify context beforehand and keep things relevant. It really helps with learning when you're driven by purpose, not obligation.

Re: The Math Myth

#239

Post by mamcx »

morgante wrote: post #161
mamcx wrote: post #158

I think that in the pursuit of higher levels of understanding, some people miss what is even more important to know. Is better to have strong basic skills, than high-level skills. I was (supposedly) of the bests student of my college. However, terrible at math? Of course. My grandmother was able to do arithmetic in his head like nothing , yet I even have trouble with sum and rest. She only have 3 years of education a…

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic arithmetic is almost entirely useless as a skill. Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

Ok, so what could be the true "base-skill" in math?

And is possible to achieve knowledge of it, without a strong foundation of arithmetic?

Truly, I don't know, as I say I'm bad at math.

However, the point is that without strong basics the rest is a lost cause (IMHO). What is the basic, I'm open to know, however, I think arithmetic is part of it...

Re: The Math Myth

#240

Post by Jimmy »

100000% accurate article. It frustrates me when I see even professional programmers perpetuating the "Math Myth", as it's called here. "It's important for all programmers to have a foundation in CS theory!" No, it's not.

The vast majority of human beings will never do anything intellectually intensive post-college. Even those in STEM fields. Not that an undergrad degree is "intellectually intensive" anyway.

EDIT:

>The second argument is the one I always hear around the mathematics department: mathematics helps you to think clearly. I have a very low opinion of this self-serving nonsense. In sports there is the concept of the specificity of skills: if you want to improve your racquetball game, don't practice squash! I believe the same holds true for intellectual skills.

Dear God, I'm so happy to see this in writing. For a while, I was afraid that I was the only one who had realized this. This observation has several useful immediate corollaries. For one, it shows that those "brain training" games that some people like to play are a waste of time. Also, it shows that if you ever catch yourself saying "I'm working on my X to help with Y", it probably means that you're just afraid of the failure that will inevitably come when you initially begin to practice Y, and that fear can only be ameliorated if you just dive in and start doing Y.

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