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The Math Myth

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Re: The Math Myth

#301

Post by sriram_malhar »

autokad wrote: post #299
sriram_malhar wrote: post #296

This argument, that "higher math" is only for those few who are interested and capable, is infuriating. I detest utilitarian arguments, that something is worth learning only because it is useful in my day-to-day. I haven't had the faintest use in my daily life for knowing anything about igneous rocks, sorghum, golgi bodies, Chandragupta Maurya, black holes, playing hockey. Yet, it would be singularly depressing to no…

knowing about gogi bodies, hockey, and black holes is a personal choice, and it wouldnt be efficient to teach these topics in depth to everyone. needing higher level math is absolutely unnecessary for 99% of the working population, so the argument that our economy will fall to pieces unless we force high level calculus and trig on every student seems suspect. however, it is hurting america in an indirect way. we have…

The specifics of hockey and golgi bodies are not important. Practically everything we learn in high school is unimportant for 99% of the working population.

My point is that it is important for a culture to aim high. There is a reason why Israel produces way more innovation than Saudi Arabia, although most of the population in both countries has no use for calculus or igneous rocks.

Re: The Math Myth

#302

Post by JoeAltmaier »

morgante wrote: post #213
JoeAltmaier wrote: post #212

Earlier quoted context omitted.

With only a little practice, I found I can add up a column of 4-digit numbers in seconds. Faster than you can whip out your calculator app. Its the impression that computers are easier, that gets me. Why not practice for 2 minutes and learn a better way? Instead of limping along with the computer all your life.

Good for you. Do whatever you want. I have a phone with me at all times. It's hardly an inconvenience to use it.

Its not a point of pride, you know, to remain unskilled in the ordinary things of life. It takes only a few minutes to learn these things. I wonder why anyone would resist?

Re: The Math Myth

#303

Post by heydenberk »

rudedogg wrote: post #285
heydenberk wrote: post #77

I have relatively little mathematical education and have been seeking to correct that by self-educating over the last year, so I have a certain bias. Nonetheless, I disagree with the key points of this article. The article asserts that most modern professional jobs requires only "Excel" and 8th grade programming. In my experience, over-reliance on software like Excel rather than a basic competency in numerical progra…

What are you using to self-educate? I'm kind of doing the same. I decided to start with "Mathematics for the Nonmathematician", which so far is good (only on chapter 3 though). Someone in the comments shared https://betterexplained.com/ - which I hadn't heard of and looks great.

I'm cobbling it together — I looked at what the requirements were for various universities' math degree programs and then found classes on Coursera, MIT OCW, etc., which matched those as well as possible.

I've also found QuantStart's guide[0] to be a particularly good resource, but bear in mind that is oriented toward learning quantitative finance (in which I have no particular interest per se).

[0] https://www.quantstart.com/articles/How-to-Learn-Advanced-Ma...

Re: The Math Myth

#304

Post by yummyfajitas »

astazangasta wrote: post #245
yummyfajitas wrote: post #237

Earlier quoted context omitted.

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 neg…

Irrational numbers are also "fundamentally inaccessible" in the exact same (infinite limit) sense that statistical convergence is. It's not a useless concept at all, it's actually the fundamental concept.

What your real world example describes is something different entirely. That's just pragmatically choosing the wrong model due to computational or human tractability. That's not fundamental to statistics, that's just a cheat you made because it's good enough.

Statistics is about acknowledging that cheat and quantifying how much it hurts you; fundamentally such a thing is not possible if truth doesn't exist.

Re: The Math Myth

#305

Post by JoeAltmaier »

nilkn wrote: post #225
banach2 wrote: post #195

Earlier quoted context omitted.

What? Why -0.9?

Because that's exactly what the argument above does. It simply subtracts away the decimal part of 9.999.... This is always wrong except in the case of infinitely many repeated digits, and the proof does not explain this. More rigorously, let 9.999{n} denote an expansion with n 9s after the decimal point, where n can also be infinity. The subtlety with the argument is that it needs X to be the same as everything after…

Yeah, yes and no. The premise is, that 0.9999... repeating CAN be represented as a decimal number, so that means it CAN be used in arithmetic. If we deny that 0.999... minus 0.999... is zero, then the premise is broken and the question is kind of moot.

Re: The Math Myth

#306

Post by TheOtherHobbes »

Digital Signal Processing - the kind of programming that makes your phone and your MP3 player work - is math.

3D rendering and animation and 2D browser transforms are math.

AI and ML have large math components.

Speech recognition is math.

Industrial electrical power distribution engineering is math.

Bridge and other kinds of structural engineering are math.

Analog circuit design is math. Once you get past the op-amp cookbook stage it can get quite complicated, especially if you need to handle RF issues.

Rocket science and aerospace design is math.

Supply chain process optimisation is math.

Traffic modelling is math.

Quant fintech is math.

Encryption and security are math.

At the absolute minimum these need geometry and trig/complex numbers. Many are impossible without differential equations/calc.

So this is one of the most idiotic comment pieces I've ever read. But unfortunately it proves that many people don't understand professional engineering at all, which makes it very hard for them to value it.

Even if the math is packaged and hidden (CAD etc) someone still has to write and check the software. If math isn't taught properly at school, the number of people capable of that shrinks.

Because these people are disproportionately valuable, that's a very bad policy indeed.

Re: The Math Myth

#307

Post by astazangasta »

yummyfajitas wrote: post #304
astazangasta wrote: post #245

Earlier quoted context omitted.

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 neg…

Irrational numbers are also "fundamentally inaccessible" in the exact same (infinite limit) sense that statistical convergence is. It's not a useless concept at all, it's actually the fundamental concept. What your real world example describes is something different entirely. That's just pragmatically choosing the wrong model due to computational or human tractability. That's not fundamental to statistics, that's jus…

Irrational numbers can be represented exactly; integrals allow us to perform exact calculation using them. In what comparable way does truth (e.g. the true process underlying gene expression) have a role in statistics? We neither measure the truth nor model it; it is absent.

Re: The Math Myth

#308

Post by yummyfajitas »

astazangasta wrote: post #307
yummyfajitas wrote: post #304

Earlier quoted context omitted.

Irrational numbers are also "fundamentally inaccessible" in the exact same (infinite limit) sense that statistical convergence is. It's not a useless concept at all, it's actually the fundamental concept. What your real world example describes is something different entirely. That's just pragmatically choosing the wrong model due to computational or human tractability. That's not fundamental to statistics, that's jus…

Irrational numbers can be represented exactly; integrals allow us to perform exact calculation using them. In what comparable way does truth (e.g. the true process underlying gene expression) have a role in statistics? We neither measure the truth nor model it; it is absent.

Integrals themselves are, except in very special cases (piecewise functions with rational values), only definable as limits - specifically the limit of the Riemann sum. (You can also use measure theory, but measures themselves are only definable on sigma algebras, which in the non-finite case are also not explicitly constructable.)

In what comparable way does truth (e.g. the true process underlying gene expression) have a role in statistics? We neither measure the truth nor model it; it is absent.

I don't quite understand. You are arguing that statistics doesn't care about truth simply because some biologists are using a model they know to be wrong? That doesn't even make sense.

In applied math in general (which includes but is not necessarily limited to statistics), the following equation holds:

    error = |true model - actual approximated model|
We can use the triangle inequality to show:

    error
Presumably you all have decided that |true - best| is adequately small via scientific investigation. Or maybe not, maybe your workplace just doesn't care, I don't really know.

Various mathematical techniques, or increasing sample size in a statistical scenario, can be used to reduce |best - actual|. Due to the triangle inequality, this brings you closer to truth.

Statistics is also concerned with expanding class X in such a way as to more easily reduce the model error.

I really feel like I'm missing something, because I truly can't comprehend what you are trying to argue.

Re: The Math Myth

#309

Post by wolfgke »

mattmcknight wrote: post #253
superuser2 wrote: post #173

Earlier quoted context omitted.

>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 prog…

> I don't find the proof aspect that relevant to programming

By Curry-Howard isomorphism proofs in some particular proof system are equivalent to computer programs.

Re: The Math Myth

#310

Post by nzp »

mamcx wrote: post #239
morgante wrote: post #161

Earlier quoted context omitted.

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic arithmetic is almost entirely useless as a skill. Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

Ok, so what could be the true "base-skill" in math? And is possible to achieve knowledge of it, without a strong foundation of arithmetic? Truly, I don't know , as I say I'm bad at math. However, the point is that without strong basics the rest is a lost cause (IMHO). What is the basic, I'm open to know, however, I think arithmetic is part of it...

Nope. There are people (I'm one of them) who have sometimes extreme difficulty doing basic arithmetic manually and in the head. In my case it's not the full-blown dyscalculia[1] but to this day I haven't been able to learn full multiplication table for example, so forget about multiplying numbers in my head. I can do it on paper, but the whole process looks like a computer under heavy swapping. I even have hard time adding and subtracting numbers mentally. If I'm expected to produce a numerical result while being watched it all becomes a catastrophe because then I also get substantial anxiety for not being able to do what for most people is a simple thing. There's something about operations with concrete numbers (although I have no problem with numbers themselves) that turns my mind into mush.

OTOH, I have basically little problem with any other branch of mathematics. The more advanced the better, actually. In school it got easier as it got more advanced (although geometry was always easy no matter what level). Getting calculus in high school felt like I could suddenly breathe with full lungs. And I studied theoretical physics later at university. Apart from the basic reality that the math required is hard and needs a lot of work no matter how smart/gifted/whatever you are, I had no substantial problem with most of it. Abstract algebra, group theory, vector spaces and manifolds... oh the joys! Because none of it requires you to do any kind of mental arithmetical computation. This is not a unique experience, I once saw a TV report on a young successful astrophysicist with basically the same problem: Calculus on manifolds, GR field equations? Pfff... All day and every day. But, give her some numbers on a blackboard to multiply and she gets completely lost.

[1]: https://en.wikipedia.org/wiki/Dyscalculia

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