The Math Myth • Hacker News Board

Re: The Math Myth

#321

Post by antod » Mon, Sep 05, 2016, 10:48 AM UTC

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…

> Truth be told, outside of a few life-support-critical applications, most design is done by trial and error. Very little real engineering gets done.

I think people don't even realise when all that extensive math they studied is even helping them. They may have forgotten or not used the specifics in real life, but if they originally understood it well then they probably gained an important subconscious intuition that shapes, optimises and/or narrows that design trial and error. And the best engineers have a great subconscious intuition for finding solutions.

Note: I studied Civil Engineering, so my math background was nearly all Trig and Calculus rather than the Discreet Math, Logic or Number Theory etc that a Computer Science degree might entail. I've forgotten nearly all of it and never really used it IRL, but I can still appreciate having a 'feel' for relationships between changing quantities etc that others without that math background don't seem to have. And having spent far longer working with software (self taught) than I ever spent with Civil Engineering, I often wonder what subconscious intuition of CS style math I'm missing that would help me.

Re: The Math Myth

#322

Post by hzhou321 » Mon, Sep 05, 2016, 2:27 PM UTC

You can't always use results to justify cause. Given the situation that most adults (even with higher education) are not good at math (possibly due to the failure of education) -- in particular, most adults are infused with the perception that math is hard -- you will find them naturally trying to avoid math as much as they can. So you find that eighty percent of adult rarely ever use beyond Excel and 8th grade math.

Can you use this result to go back and justify that we don't need math beyond 8th grade?

I beg to differ. I only can provide anecdote. As myself are not bad at math, I find myself use calculus and linear algebra all the time. In fact, I think differently. As another anecdote, my son, who I consider is not nearly good at math, he is in middle school and he uses trigonometry all the time.

You use what you have. Knowledge changes the way we think and work. With knowledge, you simply see the world differently.

Re: The Math Myth

#323

Post by Aenima » Mon, Sep 05, 2016, 6:31 PM UTC

Bahamut wrote: post #132

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…

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…

I agree. The majority of engineers may not utilize higher level math. However, all engineers learn how to analyze a problem and attempt to achieve an unknown solution. The solution may include known components that already solve a particular problem, e.g. authorize website users with the Spring Security library. Yet the key is synthesizing these pieces into a new solution for the problem domain. Most mathematics teach students to solve known problems and memorize formulas. Students will get far more mileage by learning to problem solve through logic, reasoning, and synthesis. Not to mention developing the willpower needed to keep working through failures and the social skills to work with others towards solving a problem.

Re: The Math Myth

#324

Post by soVeryTired » Wed, Sep 07, 2016, 9:50 AM UTC

kazinator wrote: post #147

soVeryTired wrote: post #127

Earlier quoted context omitted.

But the "example from real analysis" section in your link uses exactly the same limiting technique to construct e. That section shows that 0.999... is constructible.

First we have to agree on what 0.999 is, then we can call it constructible or not. Numbers formed by repeated 9's appended to 0.9 are certainly Turing computable. Which has the meaning that we have a terminating algorithm which, given a natural number N, will compute the N-th digit of the infinite sequence 0.999... This is the same way that pi is computable. Given an N, we can compute the N-th digit of pi in a finite…

But that's exactly what the ellipsis means. What other interpretation is there? I might as well argue that 1 = 1 only if we agree on the convention that = means "equals".

Re: The Math Myth

#325

Post by JadeNB » Thu, Sep 08, 2016, 3:29 PM UTC

ryanmonroe wrote: post #153

yequalsx wrote: post #56

Earlier quoted context omitted.

Property of real numbers: between distinct real numbers is at least one other number. Now try to find a decimal representation of a number bigger than 0.9999999... but less than 1.0. You clearly can't. They must be equal. No need for infinitesimals.

Okay, so it follows from completeness. Now prove that real numbers are complete (or provide a construction of the reals that uses completeness as an axiom) without using concepts foreign or confusing to someone with a middle school level exposure to math.

> Okay, so it follows from completeness.

There is nothing to do with completeness here; 0.999… = 1 is a statement about a series of rational numbers summing to a rational number, and the convergence of the series is established by the fact that it sums to the right-hand side, not by an abstract appeal to completeness.

Re: The Math Myth

#326

Post by rntz » Sat, Sep 10, 2016, 2:11 PM UTC

MichaelBurge wrote: post #274

Ar-Curunir wrote: post #267

Earlier quoted context omitted.

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…

I think you are confusing the object-level and the meta-level (and incidentally confusing everyone who doesn't know advanced set theory).

In any case, if you want to talk about the computable reals, then call them computable reals. Don't say "reals" for "computable reals", even if you think the former don't exist. Unicorns don't exist either, but that doesn't justify defining "unicorn" as "a horse".

Re: The Math Myth

#327

Post by SZJX » Sun, Sep 11, 2016, 3:18 PM UTC

The problem with the American mass has never ever been the lack of "advanced math" or whatsoever. They're missing the point. It's the tremendous gap between elite education and "common" education, as well as the lack of very basic scientific common sense among the population. It's not required for people to possess outstanding advanced skills like a PhD, but when many get even some of the most basic facts wrong, and even believe the earth is 4000 years old for example, then there's a massive problem.

Of course I know it's the elites among the upper echelons of the society who are more than happy to see and maintain such a situation, and unfortunately this article might well be another addition, a so-called academic/think-tank publication that serves their agenda. It can't get more obvious at the end of the article: "leave elite education to those who 'need' it! Keep the mass ignorant!" Yeah, sure, so that the children of the elites always stay powerful and the mass keep remaining ignorant. It doesn't matter for the massive power wielded by the US, the state terrorism employed by Uncle Sam, but it matters, a lot, for genuine empowerment of the people and true democracy, which people including the author here doubtlessly want to stop at all costs.

Re: The Math Myth

#328

Post by pdm55 » Wed, Sep 14, 2016, 2:41 PM UTC

graycat wrote: post #68

The OP is a special case of the old, big question of what to teach. It is fair to say that there is an old and strong belief that a person who has studied broadly, and deeply through, say, college, in math, physical, biological, medical, social, and computer science, and the humanities will have a significant advantage in much of the rest of life. Lacking a better name, here I call such study a broad education . To a…

As a Math/Science teacher who has to make decisions every day about who and what to teach, I agree that "with a broad education we are fishing for advantages in the future". I see a similarity with playing sport. When we are young, we play various sports. Some will make a career out of a sport they are good at. Some will continue to play occasionally just for enjoyment it brings. Most will probably benefit health-wise from the experience. Similarly with Math/Science education. It may become a career, an occasional interest, or simply a memory that gives some quantitative insight into what goes on around us.