Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The Math Myth

econlog.econlib.org

Post reply on HN
Print view View original

261–270 of 328 posts

Re: The Math Myth

#261

Post by Twisol »

lisper wrote: post #232
kazinator wrote: post #178

Earlier quoted context omitted.

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...

You might be able to do something funny with a series whose terms are indexed by ordinals. The last `1` would then be indexed by `omega` (the first transfinite ordinal). I can't claim that the ordinary rules of arithmetic would make much sense, but it's certainly an idea that you can attempt to formalize.

Re: The Math Myth

#262

Post by eli_gottlieb »

Jimmy wrote: post #240

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: >Th…

> 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.

It's important for enough programmers, and their managers, to have enough of a foundation in CS theory that they can understand and believe when they've encountered an intractable, impossible, or research-level problem. Otherwise you're just going to spend time sputtering to your business people about why you can't solve the Traveling Salesman Problem before lunch and the Halting Problem by dinner.

http://xkcd.com/1425/

Re: The Math Myth

#263

Post by WhitneyLand »

The author has a point on the benefit of transference, but he's too extreme in his conclusions.

Trigonometry is useful in so many ways. It's even useful for projects around the house, let alone for a lot of careers. Last I checked it comes after 8th grade.

On the other end of the spectrum he concedes Harvard philosophy undergrads might want to read "The Road to Reality". Bullshit - No undergrad can understand all the math in this book and no one is proposing that they should. Reductio ad absurdum.

And don't forget gaming. Lots of young people these days dream about a career at a game studio and there are a lot more options if you have good math.

He mentions Sputnik but it's not the 1950's anymore. The number of careers that benefit from math will only continue to grow.

Re: The Math Myth

#264

Post by mark-r »

ambicapter wrote: post #250
NhanH wrote: post #129

Earlier quoted context omitted.

Wah. >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 Is this really true? I'm still way too early in my career to know. But I'd have thought if you stick with the more "traditional" route, your income would be fairly con…

He's talking about opportunities. For sure, if you keep doing what you're doing, you will have consistent income. But what if, one day, your boss came to you with a novel, difficult problem that no one in the company, and perhaps in your industry, had already solved? The argument goes, having an arsenal of advanced math at your disposal would make you more likely to solve that difficult, novel problem, and set you up…

You don't often get "handsomely rewarded" for doing what people consider to be your job, even if you do it much better than anybody else. The opportunities are when you get to jump to a different role, getting promoted or going to a different company or using your insight to start your own company.

Re: The Math Myth

#265

Post by mistermumble »

initram wrote: post #159
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…

Can't we look at places where that is the case today and see? I always hear about how in places like Russia, every student learns much harder math than here in the US, and they learn it better. But I don't see other countries like Russia producing better engineered products or better science than we do here. Same with China or Japan, or whoever is supposedly the best this year.

The good ones come to the US to get better paying jobs. I ran a team of 25 software engineers. I tried to hire the most talented programmers in a tight job market. All but one of the engineers I hired were born outside the US.

Re: The Math Myth

#267

Post by Ar-Curunir »

MichaelBurge wrote: post #32
iopq wrote: 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).

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

Re: The Math Myth

#268

Post by ap22213 »

mistermumble wrote: post #265
initram wrote: post #159

Earlier quoted context omitted.

Can't we look at places where that is the case today and see? I always hear about how in places like Russia, every student learns much harder math than here in the US, and they learn it better. But I don't see other countries like Russia producing better engineered products or better science than we do here. Same with China or Japan, or whoever is supposedly the best this year.

The good ones come to the US to get better paying jobs. I ran a team of 25 software engineers. I tried to hire the most talented programmers in a tight job market. All but one of the engineers I hired were born outside the US.

It could be because people who immigrate here are significantly more motivated than people in general.

I read somewhere that many of the most successful entrepreneurs in the US are foreign born. That doesn't necessarily mean that foreign born people are better than American born people (which would be unlikely). It probably just means that people who have tenacity to immigrate also have tenacity to do bigger things than average.

Re: The Math Myth

#269

Post by mturmon »

treehau5 wrote: post #157
Bahamut wrote: post #132

Earlier quoted context omitted.

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…

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…

The introduction to Concrete Mathematics expands on some of the themes here: http://cs.ioc.ee/yik/lib/1/Graham1pre.html

Teaser:

"When DEK taught Concrete Mathematics at Stanford for the first time he explained the somewhat strange title by saying that it was his attempt to teach a math course that was hard instead of soft. He announced that, contrary to the expectations of some of his colleagues, he was not going to teach the Theory of Aggregates, not Stone's Embedding Theorem, nor even the Stone-Cech compactification. (Several students from the civil engineering department got up and quietly left the room.)"

Re: The Math Myth

#270

Post by xapata »

spdionis wrote: post #197
xapata wrote: post #170

Earlier quoted context omitted.

Even if you stick with the traditional route, having a tiny initial advantage for your first job will have compounding results over your lifetime. This is significant enough that people who graduate college during a recession on average have a 9% lower salary during the first 10 years of working [0]. Many people can tell you about their "big break". That one success that seemed to cascade into other successes. Whethe…

The big break has also an important psychological effect that acts basically like compound interest.

It certainly feels like I have had a series of lucky events in my own life, but who knows...
Post reply on HN