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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

#221

Post by notepad0x90 »

itissid wrote: post #207
notepad0x90 wrote: post #200

Earlier quoted context omitted.

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-milliona…

Thanks. > art same as entertainment Could you volunteer me how much time you spend on it? And how is your day job? > my pursuit of other things like cryptography, better algorithms, and understanding physics is limited by my primitive understanding of mathematics. Could you volunteer why you would want to learn these subjects? Is it your day job or is it something you would like to pursue in the future. > If I was a…

I don't think UBI is feasible, it is anathema to the human condition to be content with the bare minimum. if not for our own selves, we would want the best life possible for our loved ones (present or future). my "UBI" would be a couple of million dollars.

I want to learn those subjects because I enjoy learning and understanding. Life should be lived with knowledge applied through wisdom.

> Could you volunteer me how much time you spend on it? And how is your day job?

On entertainment? I can't tell you, I like to watch a movie or a tv show whenever I have time for it. There are more enjoyable pursuits in life, and most worthy pursuits involve adversity and require perseverance.

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

#222

Post by intelVISA »

nradov wrote: post #206
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.

Come on, get real. If people had all of their needs covered a lot more of them would sit around getting high and playing video games than perfecting their art.

Is that not better than the current alternative where they're forced to become grifters?

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

#223

Post by tgv »

llm_trw wrote: post #164
tgv wrote: post #163

Earlier quoted context omitted.

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.

Are you an LLM? You brought up the point of mathematicians not knowing what a square root is yourself. Anyway, the square root is is so many levels below maths as done by mathematicians, it's laughable.

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

#224

Post by samatman »

sdeframond wrote: post #137
junto wrote: post #23

Earlier quoted context omitted.

> I agree with the sentiment of this. I think our obsession with innate ~~mathematical~~ skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. The author of the book has picked out mathematics because that was what he was interested in. The r…

> I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. It might be different for intellectual skills but I am not that sure. Almost anyone can become decent at almost anything though.…

Simpson's Paradox[0] is the reason people are so easily seduced by the tempting, but dead wrong, illusion that humans are in any sense equal in their innate capacity for anything.

Because it turns out that, in the NBA, height does not correspond with ability! This of course makes sense, because all the players are filtered by being NBA professional basketballers. A shorter player simply has more exceptional ability in another dimension, be that dodging reflex, ability to visualize and then hit a ball trajectory from the three point line, and so on. Conversely, a very tall player is inherently useful for blocking, and doesn't have to be as objectively good at basketball in order to be a valuable teammate.

Despite this lack of correlation, when you look at an NBA team you see a bunch of very tall fellows indeed. Simpson's Paradox.

We see the same thing in intellectual pursuits. "I'm not nearly as smart as the smartest programmer I know, but I get promoted at work so I must be doing something right. Therefore anyone could do this, they just have to work hard like I did". Nope. You've already been selected into "professional programmer", this logic doesn't work.

[0]: https://en.wikipedia.org/wiki/Simpson's_paradox

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

#225

Post by openrisk »

agentultra wrote: post #167
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...

There is this long-running (and quite fascinating I think) debate about the different "types" of mathematical thinking. Logical vs Intuitive, Geometric vs Algebraic etc. Can't recall where exactly but I remember reading about a 19th century mathematician that crowed they had not a single figure in their masterpiece.

Visualization is probably not a silver bullet but a lot of people are visual thinkers so maybe it would help a few more to reach a higher level in mathematical thinking.

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

#226

Post by samatman »

nemo wrote: post #188
rafaelero wrote: post #182

Earlier quoted context omitted.

Intelligence is also not a skill, but the thing that makes you skillful in all cognitive tasks. Just like what height does to basketball players.

>Intelligence is also not skill, but the thing that makes you skillful in all cognitive tasks. Careful with that "all", even the most highly intelligent humans still have peaks and deficits in different domains.

It's a matter of the definition. The general factor of intelligence, which is measured through various somewhat lossy proxies like IQ tests, is exactly the degree to which someone exceeds expectation on all cognitive tasks (or vice versa).

The interesting finding is that this universal correlation is strong, real, and durable. Of course people in general have cognitive domains where they function better or worse than their g factor indicates, and that's before we get into the fact that intellectual task performance is strongly predicated on knowledge and practice, which is difficult to control for outside of tests designed (successfully, I must add) to do so.

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

#227

Post by jvanderbot »

stonemetal12 wrote: post #217
jvanderbot wrote: post #135

Earlier quoted context omitted.

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…

Bobby Fisher won his first US Championships at 14 against people who had been playing chess longer than he had been alive. Suggesting they didn't want it more, or practice more than some kid is silly. "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." Sure we can, the initial orientation of neurons differs b…

I think there's a probabalistic argument I'm making that's more in line with the article.

Yes - there will be 10x-ers. And that group will have a 10x-er iside it, and so on given exponential dropoff of frequency of talent. Bobby Fisher is a few std dev above even the best, perhaps.

Generally speaking, "You can do anything you want, but wanting (enough, and naturally) is the hardest part" might need a three standard deviation limit.

Have you heard the phrase: Being average among those who practice makes you 9X% among the population? I think that's what I'm saying - you can be a top performer if you dedicate yourself, especially early enough, but almost nobody will.

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

#228

Post by fluoridation »

j7ake wrote: post #181
physicsguy wrote: post #136

Earlier quoted context omitted.

Well, I guess what I mean is that most people have some level of general intelligence that when applied correctly can generally give good results in most subjects. In general the people who do well in school do well in everything, even if they have a preference, and as such could do well in most of those subjects if they went on to further study. The evidence tends to be that in lower income countries people push tow…

The extreme case does not imply a binary scenario ie that there are those that can those that cannot. Rather, learning ability is a continuum. people have varying degrees of ability to learn mathematics. Couple this with environmental factors and society generates a huge variability in mathematical ability that crosses income levels and other demographics. This view is rejected by many because it is against the push…

You get a huge variability if you consider the absolute extreme outliers. Most people should be able to reach a level of competence where they can understand mathematical concepts abstractly and apply that same reasoning to other areas, and not feel a visceral rejection at the mere idea. I think that's a modest enough standard that a good portion of any given population should be able to reach, and yet education is failing at achieving that.

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

#229

Post by nolamark »

nradov wrote: post #210
sdeframond wrote: post #137

Earlier quoted context omitted.

> I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. I respectfully, but strongly, disagree. There's a reason most NBA players are over 2 meters tall, and one does not become taller with time, dedication nor focus. It might be different for intellectual skills but I am not that sure. Almost anyone can become decent at almost anything though.…

Most NBA players are under 2 meters tall. The average height is 1.99 meters. https://www.lines.com/guides/average-height-nba-players/1519

Since we are being pedantic, your statement may be true but it is unsupported by the data you presented. To make it simple, let's talk about the imaginary basketball league with four players, of unit less heights of 4, 4, 4, and 1. The average height is 3.25, yet 3/4 the players are taller than average.

A paid promotion of International Median is not Average Association.

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

#230

Post by diffeomorphism »

mr_mitm wrote: post #113
benreesman wrote: post #2

I’m far from being any kind of serious mathematician, but I’ve learned more in the last couple years of taking that seriously as an ambition than in decades of relegating myself to inferiority on it. One of the highly generous mentors who dragged me kicking and screaming into the world of even making an attempt told me: “There are no bad math students. There are only bad math teachers who themselves had bad math teac…

Wouldn't it then follow that all students of the same teachers end up with the same skill level in math? Not sure that's the case.

Doesn't follow. Bell curve in, shifted bell curve out. Ideally this also tweaks the variance a bit.

In other words: Some students flourish despite their teachers, some flourish because of them.

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