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The Math Myth

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Re: The Math Myth

#241

Post by tnecniv »

hibikir wrote: post #191
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…

You seem to describe a very different world of programming than the one I live in. I have no dislike for logic, formal proofs, category theory and such: I can live in that world just fine. However, almost none of the problems I've ever had to dealt with in my 15 years programming made me wish for large amounts of that: I've used bits here and there, but going all in never made any sense. The hard part of most tasks I…

When all you have is a hammer, the world is full of nails. In my experience, knowing more math will allow you to tackle harder problems in a more sophisticated manner.

> Great!... Except, not so, because his proof only worked in a mythological environment where there is no latency between nodes. Under real conditions, the algorithm's properties led to unacceptable results, and he just hid behind the proof.

Then he did a bad job. His failure does not undermine the power of taking a formal approach to a problem. He should have accounted for this latency in his initial model. What he did is the equivalent of someone working on an autonomous car and assuming that a noisy GPS signal is good enough to do control with.

Re: The Math Myth

#242

Post by mempko »

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…

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 brokers. This is because nobody trusts each other.

You can blame gov regulation, except most regulation is written by lobbyists for mega corps

Re: The Math Myth

#243

Post by whybroke »

kazinator wrote: post #181
whybroke wrote: post #169

Earlier quoted context omitted.

Cassius Clay differs from Mohamed Ali on the name property therefore they are not identical?

Good grief ... If we have an entity X and we use the function name(X) to inquire about its name property and obtain "Mohamed Ali". And then if elsewhere we use name(X) and it evaluates to "Cassius Clay", then name() is not a mathematical function. You have to find a way to reason about an object and its properties so that they are functions. If it can have multiple names, you have to model that appropriately.

Or a name is not an attribute and .999... and 1 name the same thing.

I would humbly submit that if your code is showing Cassius Clay is not the same person as Mohammed Ali, it is your code that would be in error rather than the universe.

Re: The Math Myth

#244

Post by Jimmy »

mempko wrote: post #242
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…

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 assumption from.

Re: The Math Myth

#245

Post by astazangasta »

yummyfajitas wrote: post #237
astazangasta wrote: post #215

Earlier quoted context omitted.

>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.

This is like saying real analysis is not concerned with irrational numbers since they can only be constructed as limits of sequences of rational ones.

No, it's not. The fact that observation is a limit on our apprehension of the real world means the "truth" is fundamentally inaccessible, and is a useless concept to the statistician. All you can hope to do is test your model against the observation, you'll never, ever get access to the truth.

As a real-world example that I deal with every day, we frequently model the expected distribution of gene expression as a negative binomial. It doesn't matter how closely we observe the actual distribution of gene expression, it is never going to perfectly fit a negative binomial (it won't even get close), even though this is what we test our observation against, because the 'truth' is something different and far too complex for us to apprehend.

Re: The Math Myth

#246

Post by axlprose »

berntb wrote: post #210
Bahamut wrote: post #202

Earlier quoted context omitted.

I disagree, as someone coming from a math background - from no formal CS training, but 4 years of math at a top graduate program, I fully believe that a large percent of my peers from there could be extremely successful developers. In fact, I ran into a fellow former peer once at a conference who joined Google after exiting academia - he is currently on the Angular team. To take myself as an example, I have been very…

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 given that set of preferences that would produce an interest in math/cs, if a person was raised by a mathematician parent, they'd likely be "good at math", but possibly still struggle with programming when they reach their CS classes in college. Meanwhile another person with the same set of preferences but raised by a hacker, might be good at programming by the time they reach college, but still have a hard time with math.

The issue is less about "can this CS person be good at math?" or vice versa, and more about "will this person be motivated to learn these complementary skill-sets?". Because it's not just a one-way street, mathematicians can also learn from thinking programatically, as shown by the growing popularity of automated theorem provers like Coq. And mathematics being helpful for programming is nowhere better epitomized than by the huge trend of nearly every popular language slowly adopting functional features (and even "optional" typing), because everyone is slowly discovering that mathematically sound programming principles actually are practical (just a bit more abstract and difficult to grasp at times).

Both of those examples should be pretty good evidence of these two fields being pretty helpful towards each other. The large show-stopping issue here making this relationship non-obvious, is education. If complex subjects that are already difficult get taught poorly, it's only natural that we don't expect people to make connections and think "oh hey, this [math/cs] concept I learned about might be helpful in this [totally unrelated] situation".

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.

Re: The Math Myth

#247

Post by mruniverse »

Not confined to math, but it's helped me become aware that problems can be solved by reasoning.

Also to be measured in how sure I am about something being right.

Re: The Math Myth

#248

Post by [deleted] »

anthk wrote: post #145
moron4hire wrote: post #49

Earlier quoted context omitted.

You are discarding an essential part of the representation. You are moving the goal post to make yourself right. Just because people don't always understand infinitesimals doesn't make them right. It's the reason they are wrong. There just plain don't know what they are talking about. You can't represent 0.2 exactly using IEEE floats, either, but that doesn't mean the representation 0.2 is not exactly equal to 1/5th.

Scheme has (exact->inexact x) and (inexact->exact x) for those issues.

[deleted]

Re: The Math Myth

#249

Post by justinlardinois »

I'm not surprised that this article is pretty divisive on Hacker News.

> I find it difficult to find anyone who uses more than Excel and eighth grade level mathematics (=arithmetic, and a little bit of algebra, statistics and programming)

I think even that's a bit optimistic; I think people whose further studies or jobs don't require that level of mathematics forget it pretty quickly. For a base level of "everyday life," you probably only need basic arithmetic operations.

As anecdotal evidence, look to all those times that a relatively convoluted expression is posted on Facebook or Reddit and people argue for weeks about what the proper solution is. Of course there's plenty of people who get it right, but the wrongs range from a subtle misunderstanding of order of operations to a complete lack of knowledge about it.

Re: The Math Myth

#250

Post by ambicapter »

NhanH wrote: post #129
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…

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 to be handsomely rewarded.
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