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A Software Engineer’s Adventures in Learning Mathematics

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Re: A Software Engineer’s Adventures in Learning Mathematics

#221

Post by greggman »

hugofirth wrote: post #219
greggman wrote: post #216

Earlier quoted context omitted.

I wish more people would scream this from the rooftops. There's that whole movement trying to get more people into programming like code.org and they all say "If you're good at math you'll love this". I feel like that's scaring away lots of people who would otherwise do just fine. Examples, there's almost no math running Hacker News. There's no math in programming most blogs. There's no math in most apps. There's no…

I would have thought game engines would require a strong grounding in maths across a lot of their "moving parts"? Not being dismissive, just curious how you found working in that environment without strong maths skills.

Modern 3D game engines need math in the renderer, physics, maybe the AI but the majority of a game engine doesn't. Loading files, reading inputs, displaying UIs, the object system, scripting languages, most tools, font rendering, localization systems, game save system, networking system. Nowadays teams either buy middleware for the parts that need math or else they have specialists on the team for those things.

On top of that lots of game engines aren't 3D. 2D Mario? No serious math in there, at least not the SNES/NES ones. The 2D Zeldas? Even less. 2D Metroid? Probably less than Mario. Those games didn't use real maths for physics which is about the only place they could possibly use anything more than basic arithmetic.

Re: A Software Engineer’s Adventures in Learning Mathematics

#222

Post by tokenrove »

decasteve wrote: post #205
tokenrove wrote: post #201

Earlier quoted context omitted.

> Part of the reason I began studying math, is that I felt it was my limiting factor. The range of problems I could tackle as a programmer was limited by math. It turns out this was partly true. I started studying math intensely (doing every exercise in books, etc) when I realized the same thing: math was a limiting factor for my programming ability. Michael Abrash hints about this in some article, and I sneered at i…

It was a big hassle and a big life change. But I've always had in the back of my mind that I wanted to do it and I'm glad I did. I put it off because the money I was making, and the places I was traveling, was too good to pass up at the time. So I saved money with the idea that I would get the chance to go to school. I did try to learn math as an autodidact before I began the degree. The more abstract the math, the h…

Thanks for the reply. My solutions to the problem of not having anyone to reach out to have been to make friends with mathematicians, and to hire grad students as tutors.

Re: A Software Engineer’s Adventures in Learning Mathematics

#223

Post by dsuth »

fnordfnordfnord wrote: post #220
dsuth wrote: post #187

Earlier quoted context omitted.

There's more to it than that. In most places, the title 'Engineer' is a legal entity. In Australia, signing off on a design as an engineer makes you legally responsible for guaranteeing that it has been correctly designed, and is safe for public use. This includes personal liability in the case that it fails (bridge, software, whatever), and can be shown that it was not designed according to appropriate standards, or…

In the US we have the title PE, Professional Engineer, which requires some additional qualifications (exams, supervised apprenticeship, etc), and of course a state license. Most people don't bother any more, which has lead to a much smaller number of PE-Engineers many of whom are relegated to being mere license-holders who sign drawings for others, who do the actual engineering. >So basically, don't call yourself an…

> Most people don't bother any more, which has lead to a much smaller number of PE-Engineers many of whom are relegated to being mere license-holders who sign drawings for others, who do the actual engineering.

To some extent this happens in Australia as well, although there is a movement both to require things to be signed off by a PE (or CPEng here), and to have those engineers provide documented supervision of the work they sign off on.

> As far as that goes, I've met a number of pedigreed folks who can't engineer their way out of a wet paper bag.

No argument there, certification is never proof positive of competence. I've met very good engineers who aren't Engineers with a capital E, and very bad Engineers who knew enough to fool a test board, but not much more.

The existence of these licensing schemes is far from perfect, but better than nothing IMO. Applying the concept to general purpose software is another discussion entirely!

Re: A Software Engineer’s Adventures in Learning Mathematics

#224

Post by qmalxp »

rntz wrote: post #184
qmalxp wrote: post #117

Earlier quoted context omitted.

Re: 4). As a pure mathematician, I would argue Calculus and Linear Algebra are the father and mother of pure math as well (okay maybe not logic).

Number theory. Set theory. Category theory. Combinatorics. Graph theory. Linear algebra certainly has applications in some of the above. But I don't think that calculus & linear algebra can be fairly described as "father & mother" to these areas. (Am I wrong? I could be missing some connections; I'm not a mathematician.)

I probably should've thrown in combinatorics, which certainly existed before calculus or linear algebra, and certainly plays a role in applied math.

I would say graph theory is part of combinatorics, and set theory is part of logic.

Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fair to say the parents of abstract algebra are combinatorics and linear algebra.

Number theory at an elementary level is combinatorics, but at higher levels branches into analytic number theory (Calculus) and algebraic number theory ((Linear) Algebra).

Re: A Software Engineer’s Adventures in Learning Mathematics

#225

Post by rntz »

qmalxp wrote: post #224
rntz wrote: post #184

Earlier quoted context omitted.

Number theory. Set theory. Category theory. Combinatorics. Graph theory. Linear algebra certainly has applications in some of the above. But I don't think that calculus & linear algebra can be fairly described as "father & mother" to these areas. (Am I wrong? I could be missing some connections; I'm not a mathematician.)

I probably should've thrown in combinatorics, which certainly existed before calculus or linear algebra, and certainly plays a role in applied math. I would say graph theory is part of combinatorics, and set theory is part of logic. Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fai…

Thanks! That's quite illuminating.

Re: A Software Engineer’s Adventures in Learning Mathematics

#226

Post by numo16 »

greggman wrote: post #216
decasteve wrote: post #48

This topic comes up every so often. I think my previous comment applies here [1]: I started a Math degree after 16 years of programming without any Math beyond high school (the highest being high school calculus). Most of my work as a software developer didn't require any "higher" Maths. Once I began studying math, including Modern Algebra, Analysis, Graph Theory, Category Theory, etc., I realized I understood many t…

I wish more people would scream this from the rooftops. There's that whole movement trying to get more people into programming like code.org and they all say "If you're good at math you'll love this". I feel like that's scaring away lots of people who would otherwise do just fine. Examples, there's almost no math running Hacker News. There's no math in programming most blogs. There's no math in most apps. There's no…

> I feel like that's scaring away lots of people who would otherwise do just fine.

I am much in agreement with this. I know that the guidance counselor on staff when I was in high school would heavily steer people away from going into computer science/programming if they hadn't completed the entire catalog of math classes available at our school. Her assumption was that you needed to be some sort of math wizard in order to be successful in a CS or programming degree.

Re: A Software Engineer’s Adventures in Learning Mathematics

#227

Post by drcomputer »

cosmoharrigan wrote: post #208
drcomputer wrote: post #148

Earlier quoted context omitted.

Thanks for writing this. Over the last 4 years I switched from studying computer science with applications in mathematics, to studying math and symbolic logic with applications in computation. I did this alone, without interacting with anyone in the field. I thought I was going insane because of how many direct 'abstract' connections there are from computer science to mathematics and back again. I know these abstract…

> meticulously constructed symbolic reasoning world (...) connect such disparate symbols together and maintain that connection strongly for long periods of time Out of curiosity, could you give an example?

The construction and maintenance of my psychology using mathematics and symbolic logic to model, explain, extrapolate, analyze, and manipulate it.

I use computer science to explain psychology, in a way the makes the person being judged correct, instead of requiring their behavior to be altered based on personal opinion.

Imagine you have two conflicting sets of data from observation in your mind, and you have to process this data quickly. Taking an arbitrary and insufficient amount of data is selective and results in bias. Over time this results in contradiction even though both instances of inference are correct with regards to the logical model they rely on, and the data fed to the model. Now imagine that you received this data because over a short period of time, you have experience such a wide range of life experience that your observations allow you to collect both sets of data simultaneously and with correctness. Both data models model the world correctly, but when separated into distinct models of 'knowing things' instead of 'one confusing mass of data', you get contradiction.

So imagine someone endures trauma in their life, and has their mind molded in a specific way based on the current state of psychology, because over time the thoughts in the patients mind are shortly transformed to the thoughts in the therapists mind. Psychology did not experience the trauma, so how can psychology have an opinion on the consequences of bad things happening?

Making inferences adds to data and alters future data models and inferences. How people are judged while they are being 'helped' affects whether that help harms or helps them. I was in a group therapy for victims of domestic abuse and my "counselor" told me that she hated people like me.

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