The Math Myth • Hacker News Board

Re: The Math Myth

#251

Post by sn9 » Sun, Sep 04, 2016, 1:29 AM UTC

axlprose wrote: post #246

berntb wrote: 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…

> P.S.: as an anecdote, I just recently used my (minimal) category theory knowledge to change the way I take notes, so that I can smoothly use outlining tools (like org-mode) more like mindmaps when taking notes on complex topics.

I, and likely many others, would love to see a writeup of this if you ever felt inclined to write one.

Re: The Math Myth

#252

Post by yequalsx » Sun, Sep 04, 2016, 1:32 AM 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.

It depends on where you want to start your axioms. We can go the Whitehead/Russell route or just use this as an axiom.

We convince children that 1+1 =2 without delving into the Peano axioms. It's ok to not delve too deeply into the axiomatic structure of the reals.

Re: The Math Myth

#253

Post by mattmcknight » Sun, Sep 04, 2016, 1:35 AM UTC

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…

>Almost no one (outside of those who were friends with math majors) are actually familiar with the nature of proof-based mathematics

Hmm...when I was a CS major, a discrete math course was required, and it was all proofs. I believe that is still common. I don't find the proof aspect that relevant to programming, but the concepts of discrete math, such as sets, graphs, definitely are.

As far as things that aren't programming go in relation to programming, contest math, with its focus on efficient and creative problem solving, is probably more similar to the daily experience of writing software than any course I took. The exception would be Math Modeling and other courses that actually required programming.

Re: The Math Myth

#254

Post by nhebb » Sun, Sep 04, 2016, 1:39 AM UTC

In defense of math:

Statistics was the one ongoing use of math in my former roles as a manufacturing engineer. Beyond that I haven't used much math directly. However, I have replied upon my knowledge of engineering core courses to understand and solve problems. I needed to understand calculus-based math in order to understand that coursework. So math is important.

There is a saying among teachers that in K-3 you "learn to read" and from then on you "read to learn". The same principle holds for math. Math itself may not be the end goal for many degrees, but after you "learn to math", you "math to learn".

Re: The Math Myth

#255

Post by mempko » Sun, Sep 04, 2016, 2:10 AM UTC

Jimmy wrote: post #244

mempko wrote: post #242

Earlier quoted context omitted.

The reason for it is because the vast majority of jobs college people get are bullshit jobs. I blame capitalism and it's tendency to create useless positions in hierarchical organizations. If you think the gov makes all the useless and pointless paper pushing jobs, you have never been in a large company. In fact, market capitalism creates all kinds of pointless soul sucking jobs like lawyers, police, and insurance br…

I said "intellectually intensive", not "meaningful". The majority of people throughout history worked manual labor jobs that weren't intellectually intensive, but they were often quite necessary. >If you think the gov makes all the useless and pointless paper pushing jobs, you have never been in a large company. I'm currently employed at a large company doing mostly pointless work, so I'm not sure where you got this…

In Adam Smith's wealth of nations he talks about division of labor and how it makes people "as stupid as a creature can be". I would argue the work a farmer and people in tribal societies do is more intellectually stimulating and varied than in the modern world. Unless for a select few engineering jobs, we mostly damn people to do the same narrow set of tasks every day.

Also about the gov bit. I was talking to the larger HN readers than just you. Sounds like you know exactly what I am talking about.

Re: The Math Myth

#256

Post by Animats » Sun, Sep 04, 2016, 2:11 AM UTC

I used to write physics engines for animation, back in the 1990s when nobody had one that worked right. That required reading books on nonlinear differential equations and getting consulting from experts at Stanford. I had to learn about quaternions. I had more of a classical computer science education - number theory, mathematical logic, combinatorics, proof of correctness - but not enough number crunching.

Before that, I'd worked on automatic theorem proving and proof of correctness. I still like Boyer-Moore theory. I recently revived the old 1970s-1992 Boyer-Moore theorem prover and put a working version on Github. It's fun to run that again; it's a thousand times faster than it was in the early 1980s.

If you do anything serious with graphics, you need to understand 4x4 matrix transformations throughly. I have the whole shelf of Graphics Gems books, and they're mostly math. At one point I rewrote many of the C code in C++, and got rid of their start-at-one arrays. (The original was Graphics Gems in FORTRAN, and the C version used a horrible hack to make arrays start at 1.)

I didn't know enough filter theory when we were doing the DARPA Grand Challenge. We had a lot of trouble integrating the GPS and AHRS data into a good position and orientation. We had about 3 degrees of heading noise, which kept messing up the map-making function. We really need 3D SLAM, but didn't know how.

Now I need more math to understand machine learning.

I'm also looking at designing a specialized switching power supply for the antique Teletypes I restore. You can get enough energy from a USB port to drive the big selector magnet if you use and store it properly. Fortunately I can get LTSpice to do most of the number crunching.

I think I've used all the math I was ever taught. And I'm not really into math.

Re: The Math Myth

#257

Post by eli_gottlieb » Sun, Sep 04, 2016, 2:13 AM UTC

See, if you tell me this is actually true, then to my ears, it just says that people who can actually wield real math in anger have a massive advantage over everyone else.

Re: The Math Myth

#258

Post by Camillo » Sun, Sep 04, 2016, 2:18 AM UTC

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…

#2 is spot on. That is also why going to university no longer guarantees a "good job". A degree used to be a pretty decent proxy for intellectual talent. For many degrees, that was actually most of the value to potential employers, rather than the specific skills learned. You could get an English degree and get a job in an unrelated field not because your English education made you particularly valuable as an employee, but because the fact that you had made it through college was proof of the value that you had to begin with.

But now, since more and more people are pushed towards college, the value of a degree as a proxy for talent has been debased. On top of that, there happens to be some correlation between the actual economic value of the skills taught in a degree and its power as a proxy for intellectual talent. For example, a degree in engineering teaches economically useful skills, and is also less accessible to those of middling intelligence. But a degree in English, on top of teaching skills of little economic utility, also lacks a strong filter for intelligence. So more of its value was in its role as a proxy, and it took a bigger hit to it.

And that is why you see so many people with English degrees working as baristas. But the key point is that those are mostly people who would have been baristas anyway. The magical feather was fake; the employability, or lack thereof, was within them all along.

Re: The Math Myth

#259

Post by mistercow » Sun, Sep 04, 2016, 2:25 AM UTC

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 problem with looking at other countries is always that you can't control the other variables. Numerous economic and cultural factors affect the outcomes you're talking about, so we end up learning almost nothing about the specific factor we care about.

Re: The Math Myth

#260

Post by eli_gottlieb » Sun, Sep 04, 2016, 2:34 AM UTC

quantumhobbit wrote: post #222

sidlls wrote: post #81

Earlier quoted context omitted.

I want everyone to read and re-read your bit about data science and machine learning. Many times. I think even people in the software industry underestimate both how accurate and how difficult it is to employ statistics to produce something truly meaningful. My current job is on a data science team. I find it amusing that the business folks are able to sell our product, and then sigh to myself and do a little crying…

To most people machine learning and data science are magic. They either believe in magic or they don't. Once you learn it with sufficient mathematical sophistication, it stops being magic and starts being a tool that works in some situations and not in others. You are surrounded by people who believe in the magic and will buy anything whether it works or not. Equally frustrating is being surrounded by non-believers w…

Well, as someone who took a solid class in machine-learning, has an understanding of why it works, and regards it far more as science than magic, "we" who know it damn well committed a sin and sold our souls for funding if "we" just told everyone else it was magic.

Now, admittedly, I think the deep-learning folks are so glad to finally have their faith in neural networks vindicated that they've let themselves buy into their own propaganda, but that doesn't mean there's any actual magic!