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Everyone is capable of, and can benefit from, mathematical thinking

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Re: Everyone is capable of, and can benefit from, mathematical thinking

#161

Post by tgv »

chipdart wrote: post #147
tgv wrote: post #121

Earlier quoted context omitted.

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

> cannot agree. It's just "feel-good thinking." Not really. There's nothing inherently special about people who dedicated enough time to learn a subject. > "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. What a bad comparison. So far in human history there were less than 200 people who ran 10…

> Not really. There's nothing inherently special about people who dedicated enough time to learn a subject.

"You didn't work hard enough." People really blame you for that, not for lacking talent.

> So far in human history there were less than 200 people who ran 100m in less than 10s.

And many millions have tried. There may be 200 people who can run it under 10s, but there are thousands that can run it under 11s, and hundreds of thousands that can run it under 12s. Unless you've got clear evidence that those people can actually run 100m in less than 10s if they simply try harder, I think the experience of practically every athlete is that they hit a performance wall. And it isn't different for maths, languages, music, sculpting (did you ever try that?), etc. Where there are geniuses, there also absolute blockheads.

That's not to say that people won't perform better when they work harder, but the limits are just not the same for everyone. So 'capable of mathematical reasoning' either is some common denominator barely worth mentioning, or the statement simply isn't true. Clickbait, if you will.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#163

Post by tgv »

llm_trw wrote: post #148
tgv wrote: post #121

Earlier quoted context omitted.

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

There's a difference between being able to memorize what a square root is and being able to do math - which to mathematicians means being able to organize a proof. I've found that the people who most believe in math being a genetic ability are the ones who do not work in the symbolic world of modern math, but in the semantic world of whatever the field the math describes is. The two are rather different.

Strangely enough, you'd be hard pressed to find a mathematician who doesn't know what a square root is.

And I didn't mention genetics. Nature is complicated.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#164

Post by llm_trw »

tgv wrote: post #163
llm_trw wrote: post #148

Earlier quoted context omitted.

There's a difference between being able to memorize what a square root is and being able to do math - which to mathematicians means being able to organize a proof. I've found that the people who most believe in math being a genetic ability are the ones who do not work in the symbolic world of modern math, but in the semantic world of whatever the field the math describes is. The two are rather different.

Strangely enough, you'd be hard pressed to find a mathematician who doesn't know what a square root is. And I didn't mention genetics. Nature is complicated.

You'd also be hard pressed to find one who doesn't know how to flush a toilet.

Neither trivia has anything to do with being good at mathematics as done by mathematicians.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#165

Post by e79 »

sureglymop wrote: post #114

I think for most people the issue is that they never even get to the fun stuff. I remember not really liking math right until university where we had set theory in the first semester, defined the number sets from scratch went on to monoids, groups, rings etc. That "starting from scratch" and defining everything was extremely satisfying!

If you’re interested in computer science, have you ever looked at the Software Foundations course by UPenn? It follows a similar approach of having you build all sorts of fascinating math principles and constructions from the ground up. But then it keeps going, all the way up to formal methods of software analysis and verification.

https://softwarefoundations.cis.upenn.edu/

Re: Everyone is capable of, and can benefit from, mathematical thinking

#166

Post by vundercind »

penguin_booze wrote: post #139

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

I'm an adult who's been programming computers professionally for 20 years, and went to school for it, and I've lost most mathematical skills past what I'd learned by 6th grade or so, from lack of use.

People who aren't even working in a field that's STEM-adjacent have even less use for stuff past simple algebra and geometry (the latter mainly useful just for crafting hobbies and home-improvement projects) and a handful of finance-related concepts and formulas.

I expect to go to my grave never having found a reason to integrate something, at this rate.

The result is that any time I try to get back into math (because I feel like I should, I guess?) it's not really motivated by an actual need. The only things that don't bore me to tears for sheer lack of application ends up being recreational math problems, and even that... I mean, I'd rather just read a book or do almost anything else.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#167

Post by agentultra »

openrisk wrote: post #64

There is this element of abstract mathematical thinking that many young people get exposed to at some point in the educational system but just never "get it" and they disconnect. This is where it goes awry as the gap only widens later on and its a pity. Working with symbols, equations etc. feels like it should be more widely accessible. Its almost a game-like pursuit, it should not be alienating. It might be a failur…

I don't know how widespread this phenomenon is but in the book Do Not Erase [0] it seems that there are quite a few prominent mathematicians who do use visual representations in their work.

[0] https://en.wikipedia.org/wiki/Do_Not_Erase:_Mathematicians_a...

Re: Everyone is capable of, and can benefit from, mathematical thinking

#168

Post by vacuity »

LoganDark wrote: post #150
sethammons wrote: post #120

Earlier quoted context omitted.

It is the sum of costs and advantages that lead to reproductive success. The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives. I'm not sure what you are trying to say.

> I'm not sure what you are trying to say. I'm saying, if it doesn't ruin lives to the point of preventing reproduction, then it stays in the gene pool. Basically, I'm saying this: > The trait is still here and still prevalent meaning people are still getting laid and starting families and presumably leading fulfilling lives.

As long as an organism isn't performing too badly, it stays in the gene pool. It can persist and even share its genes more broadly, if in diluted form, to the other more successful organisms. And then some of those mixed-genes organisms may occasionally express more strongly, but again not enough to affect reproductive success across the population.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#169

Post by agentultra »

And yet it is flame-bait to suggest that programmers benefit from mathematical thinking. I've not met a more passionate and divided crowd on the issue. Most traditional engineers wouldn't disagree that they use and benefit from mathematical thinking. Programmers though?

I don't think there's a single answer as to why many dislike it so much. Some folks view it as a way to gate-keep programming. Others view it as useless ("I've been a successful programmer all my life and I've never used math").

On the other side of the coin there are many who view our craft as a branch of applied mathematics -- informatics if you will.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#170

Post by kdfjgbdfkjgb »

air7 wrote: post #92
elbear wrote: post #41

Earlier quoted context omitted.

Not even that. It depends on the learned ability to stop pushing yourself when your focus is wavering. That's how you develop aversion towards the topic. Let your natural curiosity draw you to particular topics (that's why you might have a winding road through the subject).

parent comment was a bit tounge-in-cheek but I'll continue the sentiment: You're saying that the curiosity is "natural" hence one is either born with it or not. I think that there is no way around the fact that it will be hard and uncomfortable to mimic the progress of someone that has an innate inclination towards a subject (be it talent or focus or curiosity) artificially.

> You're saying that the curiosity is "natural" hence one is either born with it or not.

Why does curiosity being natural necessarily mean some people are born without it? It could also mean everyone (or every average human) is born with it, and overtime it gets pushed out of people.

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