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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#211

Post by SomeStupidPoint »

alejohausner wrote: post #95
soVeryTired wrote: post #70

Earlier quoted context omitted.

Limits use a construction that's pretty similar to an infinitesimal. The epsilon-delta definition of a limit is no joke for students.

Oddly enough, I never understood the epsilon-delta description of limits until I read David Foster Wallace's book on infinity. All through my degree in math I was taught about things without learning the historical context that created those things.

I'm always super happy that I stumbled in to taking topology before real analysis.

It meant that I understood the topological idea of limits before I had to do proofs using just the epsilon (for sequence) or epsilon-delta (for functions) definition, and so could translate the logic of showing things about neighborhoods in to the terminology of (real analysis) limits.

Limits, in the abstract, are a fairly simple concept: in the case of sequences, for any neighborhood of the limit, the entire tail of the sequence (past some point) is contained in the neighborhood; in the case of functions, for any neighborhood of the limit at f(x), there's a neighborhood around x, such that every point in that neighborhood maps to the neighborhood around the limit.

Re: The Math Myth

#212

Post by JoeAltmaier »

morgante wrote: post #192
rohit89 wrote: post #189

Earlier quoted context omitted.

I believe the OP's exercise was to do the division manually not mentally. Basic mental arithmetic is probably the most used in day-to-day life. It feels weird having to whip out a calculator/phone every time you need to make a quick estimate.

> I believe the OP's exercise was to do the division manually not mentally. That's equally useless. Why would I try to figure out the result manually when I have a computer in my pocket at all times? If anything, doing things manually when we have computers seems weirder.

With only a little practice, I found I can add up a column of 4-digit numbers in seconds. Faster than you can whip out your calculator app.

Its the impression that computers are easier, that gets me. Why not practice for 2 minutes and learn a better way? Instead of limping along with the computer all your life.

Re: The Math Myth

#213

Post by morgante »

JoeAltmaier wrote: post #212
morgante wrote: post #192

Earlier quoted context omitted.

> I believe the OP's exercise was to do the division manually not mentally. That's equally useless. Why would I try to figure out the result manually when I have a computer in my pocket at all times? If anything, doing things manually when we have computers seems weirder.

With only a little practice, I found I can add up a column of 4-digit numbers in seconds. Faster than you can whip out your calculator app. Its the impression that computers are easier, that gets me. Why not practice for 2 minutes and learn a better way? Instead of limping along with the computer all your life.

Good for you. Do whatever you want.

I have a phone with me at all times. It's hardly an inconvenience to use it.

Re: The Math Myth

#214

Post by _asummers »

superuser2 wrote: post #173
treehau5 wrote: post #157

Earlier quoted context omitted.

For software engineers specifically -- every time you are coding formalized programmatic logic, you are using math. If you took a logics and proofs course, it would help you formalize logic better. Every time you write a "for" loop you are essentially using summations. There is a book called Concrete Mathematics and one of the primary authors is Donald Knuth, basically it's "Programmers math" and in my opinion, would…

>every time you are coding formalized programmatic logic, you are using math Almost no one (outside of those who were friends with math majors) are actually familiar with the nature of proof-based mathematics. When you hold out "programming is math" the general public, policymakers, admissions offices, kids who might want to be programmers, etc. don't make the association to Analysis and Abstract Algebra, they make i…

What you speak of is a failure of mathematics education, frankly. I meet too many people with this viewpoint, and regularly have to explain that there's all sorts of math out there that would align with one of their skills. People are not taught mathematics from a problem solving interactive puzzle perspective, they're taught it from a rote computational perspective, removing all the sense of wonder and pleasure from doing things within a system of axioms.

I see the argument about chemistry, but I do think there's a very strong crossover of doing math and building software (in the large). In math, you begin with a set of base known statements. Whether starting from the axioms, or working within some system, you begin to build a vocabulary of the system, a feel of the way objects within the system interact, and an understanding of the limitations of the system you're currently in. Through the course of needing to get things done, you combine these various abstractions together to create more useful ones, constantly making your system a little bit more powerful. Often, taking steps back from your system and combining things into elegant ways gives insight into other patterns present in the system, and recasts solutions in slightly different lights with hints as to what they could have been, had you known what you know now. Then over the course of time, you begin to bring in new foreign systems, which you might not understand fully, and you use inelegantly. But again, working through issues, you build up that vocabulary and intuition to solve problems in your space, constantly putting tools and tricks into your belt on how things could fit together. Occasionally something will be insufficient in your tool belt, or a concept you weren't quite clear on will come up in your problems, causing you to go back, learn a thing, and come back armed ready to keep making progress.

To me, that all sounds like what I do when I'm building software.

Re: The Math Myth

#215

Post by astazangasta »

yummyfajitas wrote: post #183
astazangasta wrote: post #154

Earlier quoted context omitted.

I think we have a disagreement about epistemology. I say, you can't believe in truth if you don't believe it is knowable. In any case, statisticians are not interested in learning the truth, either, and the goal of their enterprise is not access to it.

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.

Re: The Math Myth

#216

Post by petra »

JackMorgan wrote: post #36
sp527 wrote: post #19

This has so much more to do with the lack of easily monetizable applications of complex mathematics. I'm sure a significant number of engineers and STEM professionals feel (as I do) that they're deliberately eschewing those subjects not for a lack of interest, but rather as a response to market demand. The market of people who are genuinely passionate about complex subjects in math and science is saturated relative t…

What would you study instead to remain valuable in the next two decades? I've gotten pretty deep into engineering: worked on games, mobile, web, FP, legacy code revival, a half dozen popular languages, automated testing, and people management. I'm looking for something new to study to add flexibility and "luck surface area" to my career. I was thinking ML would be another area of valuable study. Do you have any alter…

Not him, but:

It's clear that the trend in software is towards higher abstraction, and that's what makes selecting what to learn so hard.

But maybe a heuristic: learn thing that could not be abstracted(unless AI appears), or at least choose a few abstractions up ahead.

One such thing is desinging and developing domain-specific-languages, which also looks to be an important tool in some systems.

Another thing is prototyping with very high-level tools, because it gains you experience in working with customers, extracting requirements, product management, etc.

Re: The Math Myth

#217

Post by doozy »

I was a maths minor and dropped out of a MSc in Applied Maths. I took many courses that would be considered advanced by most, such as Stochastic Calculus, Partial Differential Equations, Multivariate Statistics, Time Series Econometrics, etc.

But I left academia over a decade ago, and have never used any of that. I have, however, used a few things above 8th grade maths, such as linear algebra, regression analysis, and some basic numerical analysis. I used once a FFT.

All in all the author is spot on. And I believe an advanced degree in maths is not a legitimate requirement for anything but a handful of positions, and most of those aren't particularly desirable.

I still remember fondly my days studying Baby Rudin, though. Definitely one of the courses that made an impact in my education. But in hindsight, it's been as useful in my career as my study of Latin.

Re: The Math Myth

#218

Post by petra »

nostrademons wrote: post #88

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…

But if that's the case, the fact that we all learn the same thing(even something as powerful as math), doesn't sound ideal at all, and a multidisciplinary knowledge strategy should serve us better, right ?

Re: The Math Myth

#220

Post by hackaflocka »

The author in 1885:

"People say that we should train people for factory jobs, but everyone I know is gainfully employed in agriculture, and we don't have any factories where I live."

As a college professor, let me assure the author that statistics and programming is not a standard part of an eighth graders program. In fact, the ones I teach have passed the 12th grade, and most are woefully unprepared in algebra, statistics, probability and programming.

For me, understanding slightly advanced math (the type discussed in Taleb's Fooled By Randomness) helped me realize that Financial academic math is complete B.S. (in its use of the Gaussian Dist. in non-Gaussian processes). Yes, that's how learning more math has benefited me: it helped me discover how math is used to support complete B.S.

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