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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

#191

Post by Tainnor »

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.

Square roots are not some "mathematical trivia", they're amongst the most fundamental operations in mathematics.

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

#192

Post by NoMoreNicksLeft »

jvanderbot wrote: post #135
diffeomorphism wrote: post #48

Earlier quoted context omitted.

Caveat here is that "talent" and "dedication" is linked to speed at least in the beginning. For instance, any student can learn calculus given enough time and advice even starting from scratch. However, the syllabus wants all this to happen in one semester. This gives you vicious and virtuous cycles: Students' learning speed increases with time and past success. So "talented" students learn quickly and have extra tim…

Indeed, speed is often read as "smarts" whereas I would maintain it's much more often "preparation". We can't on one hand believe in the plasticity and retrainability of the mind, while simultaneously believing that speed is something only a few are born with. On the nature/nurture scale, I think it's 20/80 or so - but prodigies and geniuses have an interest that keeps them thinking and learning 10x or 100x more than…

> I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and

I was having a problem agreeing with this subthread, and I have you to thank for putting it into words that I can finally formulate my disagreement against.

Have you never met one of those people for whom they did not need to "want"? They could literally phone it in and still do better than anyone else, no matter how dedicated they were. Even should practice/study be necessary for them, they benefited from it to some absurd proportion that I couldn't even guess to quantify. I've known more than one of these people.

I think most believe they don't exist for two reasons. The first is the ridiculous number of television shows and movies that depict motivation as being the key to success. We're just inundated with the (unsupported by evidence) that this is the means to extraordinary genius. Second, I would say that this is the most comforting theory. "Why yes, I could have been a gifted whatever or a talented something-or-other if I had put the time in, but I chose this other thing instead."

Maybe some would say we all need to believe this, that a society that doesn't believe in it is harsher or more unkind.

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

#193

Post by sourcepluck »

bloqs wrote: post #154
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…

This is mostly correct. Working memory plays a huge component in grokking more complicated mathematical components, and IQ itself is separated into performance and verbal IQ (which together constitute your IQ score) and its demonstrably robust. Some people find this easier than others and that is OK. I dont disagree with the premise that mathematical thinking can benefit anybody, but its absurd notion that everything…

Imagine our world was extremely similar to how it is now in any way you'd care to imagine, except two things were different.

1. Everyone (young, old, poor, rich) thinks that maths is interesting and fun and beautiful and important. Not important "to get a good job" or "to go to a good college" or "to be an impressive person", but rather important because it's fun and interesting. And maybe it also helps you think clearly and get a good job and all these practical things, but they're secondary to the tremendous beauty and wondrousness of the domain.

2. Everyone believes that barring actual brain injuries people can learn mathematics to a pretty high level. Not Ramanujan level, not Terrence Tao, not even a research mathematician at one of the smaller universities, but a level of extreme comfort, let's say a minimum level of being able to confidently ace the typical types of exams 17 and 18 year olds face to finish secondary school in various countries.

Would you claim that in that world - people think maths is great, and that anyone can learn it - we'd see similar levels of ability and enjoyment of mathematics?

My claim is that we don't live in "Math-World", as described above, but "Anti-Math-World". And further, that anyone suggesting things have to be the way they are in Anti-Math-World is not only wrong, but also fundamentally lacking imagination and courage.

Kids are told week in week out that maths is stupid, that they are stupid, that their parents themselves are stupid, that the parents hated maths, that the teachers are stupid, and then when they end up doing poorly, people say: "ahhh, some kids just aren't bright!"

Parents who like things like learning and maths and reading and so on, have kids that tend to like those things. And parents that don't, usually don't. Saying that this somehow tells us something concrete and inalterable about the nature of the human brain is preposterous.

It's a card that's used by grown-ups who are terrified by the idea that our education systems are fundamentally broken.

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

#194

Post by delta_p_delta_x »

This is pretty interesting. I did reasonably well in maths up to the A-levels, and then absolutely collapsed in university. I never got a grade better than B- in any maths-adjacent class. Discrete maths was my worst topic, I barely scraped a pass. And the irony was that I majored in CS and physics.

I should probably find a time machine and re-do everything.

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

#195

Post by noqc »

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 have never disagreed more with a comment. You can fully decide that you're not interested in mathematics, after having taken all of the math classes that you could possibly be offered before university, without ever encountering a proof, or even a mathematical definition.

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

#196

Post by itissid »

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't.

I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

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

#197

Post by XajniN »

Reading most of the answers here, I can only conclude most of you were home schooled or went to some fancy schools for gifted children.

An average human is unable to even write properly. Even basic mathematical operations like multiplication and division are too complicated from their perspective.

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

#198

Post by kristopolous »

atribecalledqst wrote: post #119
kristopolous wrote: post #56

there's thinking mathematically and then there's being able to fluently read math articles on wikipedia as if they're easier than ernest hemingway. I can do the former and the latter I will insist until my grave is impossible for me.

I used to judge myself for not understanding everything in math articles on Wikipedia, but as time has gone on I've realized that their purpose isn't really to be an introduction , but a reference . Especially as the topics become more esoteric. So they're not really there for you to learn things from scratch, but for people who already understand them to look things up. Which is why you'll sometimes see random obscu…

I've heard that and I think it's silly. They handwave away why nothing should ever be explained. Wikipedia doesn't work like that for any other topic.

You'll see something like a mathematical proof with no explanation and it's end of article. The edit history will have explanations aggressively removed.

The equivalent would be the article for say, splay tree, to have no diagrams and just a block of code - feeling no obligation to explain what it is or if you looked up a chemical and it would just give you some chemical equation, some properties and feel no obligation to tell you its use, whether it's hazardous or where you might find it... Or imagine a European aristocrat and all that is allowed is their heraldry and genealogy. Explanations of what the person did or why they're important are forbidden because, it's just a reference after all.

Nope, these math people are a special kind of bird and I'm not one of them.

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

#199

Post by itissid »

itissid wrote: post #196

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

One thing I can agree with is that if one is stressed out and have poor psychological habits you will suffer and be miserable regardless.

I would say focusing on mindfullness(like vipasaana) can go a long way in this. But mindfulness is not an intellectual exercise, one has to live it. Do multiple hours of meditation a day and it gets you somewhere good in a few months.

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

#200

Post by notepad0x90 »

itissid wrote: post #196

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

I must disagree. I consider art same as entertainment to the most part. I would want to be good at math and I also disagree that it has anything to do with mental capacity. It's not a competition, I don't need to be better at math than others but my pursuit of other things like cryptography, better algorithms, and understanding physics is limited by my primitive understanding of mathematics.

If I was a multi-millionaire, learning lots of math on my free time would be one of the things I would pursue while chilling at my beach house.

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