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

quantamagazine.org

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

#61

Post by drbig »

diffeomorphism wrote: post #48
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…

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…

Thank you for the insight that academic (in a very broad sense) bulk-fixed-time approach does in fact produce both of the cycles, and the gap indeed only widens with time (speaking from personal experience, especially from my life as an undergrad student).

Reminds me of my personal peeve that "studying" should not be "being taught", studying is pursuit of understanding, "being taught" is what happens in primary school (and I'm aware I'm simplifying here).

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

#62

Post by namaria »

cen4 wrote: post #11
agtech_andy wrote: post #6

I used to get very frustrated that others could not intuit information the way I could. I have a lot of experience trying to express quantities to leaders and policymakers. At the very minimum, I ask people to always think of the distribution of whatever figure they are given. Just that is far more than so many are willing to do.

Waste of time. Just talk in terms of what they want to hear. They are just interested in the payoffs (not in the details). As info explodes and specialists dive deeper into their niches, info asymmetry between ppl increases. There are thousands of specialists running in different directions at different speeds. Leaders can't keep up. Their job is to try to get all these "vectors" aligned toward common goals, prevent…

> Their job is to try to get all these "vectors" aligned toward common goals, prevent fragmentation and division.

This is overthinking it. People with power tend to be interested in outcomes. They can't evaluate all the reasoning of all their reports. It comes down to building credibility with a track record and articulating outcomes, when you want to advise decision makers.

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

#63

Post by namaria »

te_chris wrote: post #22

Agree. I’ve been trying to learn ML and data for a few years now and, around 2021 I guess, realised Maths was the real block. I’ve tried a bunch of courses (MIT linalg, Coursera ICL Maths for ML, Khan etc etc) but what I eventually realised is my foundations were so, so weak being mid 30s and having essentially stopped learning in HS (apart from a business stats paper at Uni). Enter a post on reddit about Mathacademy…

Too often people think of learning as accumulating knowledge and believe blockers are about not enough knowledge stored.

That would be like strength training by carrying stuff home and believing that the point is to have a lot of stuff at home.

Intelligence is about being able to frame and analyze things on the fly and that ability comes from framing and analyzing lots of different things, not from memorizing the results of past (or common forms of) analysis.

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

#64

Post by openrisk »

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 failure of educators recognizing what are the pathways to get the brain to adopt these more abstract modes of representing and operating.

NB: mathematicians are not particularly interested in solving this, many seem to derive a silly pleasure of making math as exclusive as possible. Typical example is to refuse to use visual representation, which is imprecise but helps build intuition.

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

#65

Post by chipdart »

hehehheh wrote: post #60
chipdart wrote: post #42

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 would argue something different. The "skill" angle is just thinly veiled ladder-pulling. Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the…

I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.

> I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.

I don't agree. First of all, ladder-pulling in math is observed at all levels, not only cutting-edge stuff. Secondly, it's in applied mathematics where pure math takes a queue onto where to focus effort. See how physics drives research into pure math.

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

#66

Post by purplethinking »

quus wrote: post #44

I’m actually interested in the “can benefit from” claim in this title. I don’t particularly doubt that most people could become reasonably good at math, but I wonder how much of the juice is worth the squeeze, and how juicy it is on the scale from basic arithmetic up to the point where you’re reading papers by June Huh or Terry Tao. As anti-intellectual as it sounds, you could imagine someone asking, is it worth devo…

Pure math is probably not worth the squeeze. I think more important to everyday life is systems thinking and a bit of probability/stats, mainly bayesian updates. "Superforecasting" was an eye-opening book to me, I could see how most people would benefit massively by it.

Similar to systems thinking, just the ability to play out scenarios in your head given a set of rules is a very useful skill, one which programmers tend to either be good at because of genetics or because we do it every day (i.e. simulate code in our head). You can tell when someone lacks this ability when discussing something like evolutionary psychology. Someone with a systems thinking mindset and an ability to simulate evolution tend to understand it as obvious how evolutionary pressures tend to, and really must, create certain behavior patterns (on average), while people without this skill tend to think humans are a blank slate because it's easier to think about, and also is congruent with modern sensibilities.

This skill applies in everyday life, especially when you need to understand economics (even basic things like supply and demand seems elusive to many), politics etc.

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

#67

Post by sureglymop »

faangguyindia wrote: post #35
gsabo wrote: post #15

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've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

[flagged]

"A loser in societal view"... What does that objectively mean? That only reads like you had or have a low sense of self worth. It must've been your perceived definition of what society is because how could you have come to such a conclusion? I think I'd actually subconsciously tend more to viewing someone as "a loser" if they made such a statement because it comes off as self victimization (without an apparent explanation to an outside observer).

And what's the shtick about girls? What are and were you looking for, love and a genuine relationship or attention to compensate for something? Personally I think your values and personality are what matter most and personality is usually what people fall in love with. Though charisma can help a lot to get the ball rolling. Most of what it takes is to treat people normally and nicely and you will have as much of a chance to find love as most people.

Though respect from peers and attention from women ideally shouldn't be your driving force. I think curiosity and passion are much better driving forces that don't involve such external factors and possibilities for insecurities.

Your post reads as if it expresses a frustration and a sense of entitlement. You may not be intrinsically entitled to the things you think you are. Think about that for a bit and try to be rational.

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

#68

Post by fifteen1506 »

But, is that profitable? I'm both being sarcastic and real with this question.

If I can earn an extra 1 million being 'dumb' and thus ensure quality healthcare, education, housing, is it smart to try to be smart?

This is the true tragedy of the commons (or the reverse tragedy, to be precise).

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

#69

Post by ggm »

I want to say yes, but I have two counters. One is that math nerds at school insisted on intimidating for the win and I just hated it.

The second is notation. I had a snob teacher who insisted on using Newton not Leibniz and at school in the 1970s this is just fucked. One term of weirdness contradicting what everyone else in the field did. Likewise failure to explain notation, it's hazing behaviour.

So yes, everyone benefits from maths. But no, it's not a level playing field. Some maths people, are just toxic.

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

#70

Post by LoganDark »

junto wrote: post #23
gsabo wrote: post #15

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've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

> 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…

> Whilst some people (mostly spectrum) do seem have an innate talent

I think the only thing in autism that I'd call an innate talent is detail-oriented thinking by default. It'd be the same type of "innate talent" as, say, synesthesia, or schizophrenia: a side effect of experiencing the world differently.

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