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junto 5 days ago

> 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 reality is that this rule applies to everything.

The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s.

I think we do our children a disservice by convincing them that some of their peers are just “born with it”, because it discourages them from continuing to try.

What we should be teaching children is HOW to learn. At the moment it’s a by-product of learning about some topic. If we look at the old adage “feed a man a fish”, the same is true of learning.

“Teach someone mathematics and they will learn mathematics. Teach someone to learn and they will learn anything”.

diffeomorphism 5 days ago | parent | next [-]

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 time to further explore and improve, leading to further success. Students who struggle with the time constraint are forced to take shortcuts like memorizing "magic formulas" without having time to really understand. Trying to close that gap is very hard work.

drbig 5 days ago | parent | next [-]

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).

blackbear_ 5 days ago | parent [-]

I would say that you could generalize this even further outside of education. A few early successes in life can greatly accelerate one's trajectory, while early failures could set one many years back. And this happens independently of whether those events are due to skill or luck.

jvanderbot 5 days ago | parent | prev | next [-]

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 other kids, and a little bump that lets them get started easier and therefore much earlier.

This sets them up for fantastic success very quickly. [1] shows a great example of this.

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 amount of preparation that almost nobody can manage. Starting late, with emotional baggage, kids, and having to spend 5 years relearning how to learn? Forget it.

1. https://danielkarim.com/how-to-become-a-genius-the-polgar-ex...

NoMoreNicksLeft 5 days ago | parent | next [-]

> 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.

jvanderbot 5 days ago | parent | next [-]

I think I have met those folks. Maybe not. And you're welcome!

They're just quick. But the ones I've met, at least, are quick to make associations. When I really dig and ask them to explain themselves or a concept, they usually make analogies to things they know, but I don't. Then I have to go learn that thing. Then they try the analogy again, but I haven't fully learned it from years of making analogies about it.

Years of grad school experience was painful like this, until I got to a point 10 years after grad school, after a PhD, and well into research, that I "just got" things (in my subfield) as well. It's these experiences that made me feel that it's 80% preparation and perspiration (both of which are dominated by time), and 20% "other" mythology. Don't get me wrong, that 20% is what makes a 2 year old read earlier than others, and getting started reading at 2 (and continuing it!) for 4 years before starting school will make you light years ahead of your peers. The same goes for chess, math, etc etc. There is something legendary about Oppenheimer learning enough dutch in 6 weeks to deliver a lecture. Or perhaps learning to translate his lecture and memorizing it. Who knows.

Do we really believe there's a magical "genius" such that they can do anything? No, so what are the limits to their genius? The limits are defined by what they are a genius at. This is a tautological definition.

I'm not saying "Anyone at any time can become a genius at anything". I'm saying "If you take a kid, start early, and cultivate them just right so that you have time to realize compounding effects, - you can let them grow into basically anything" (probablistically speaking - there are learning disabilities and physical issues etc).

StefanBatory 4 days ago | parent | prev [-]

> I think most believe they don't exist for two reasons.

I add third (okay, 2b) - because the pain of coming up with the fact other people are better than you at a deep, fundamental level is too overwhelming.

stonemetal12 5 days ago | parent | prev [-]

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 between people, so some people need less "plasticity and retrainability" to be good at a task. Plasticity is physical characteristic like height and varies between people.

Initial speed usually isn't that important, but speed of learning is important and makes the difference between possible and impossible within a human lifetime.

jvanderbot 4 days ago | parent | next [-]

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.

matwood 4 days ago | parent [-]

I agree with you. I don’t think I’m naturally gifted at much (I’m just average), but I was taught stubborn hard work pretty early on. Unfortunately it took me until my 20s to figure out I could be athletic if I applied that hard work. I could also be good at programming doing the same. I’ve met people who are truly gifted and it’s amazing, but I’m pretty decent at the things I worked hard at.

hilbert42 4 days ago | parent | prev [-]

"Initial speed usually isn't that important, but speed of learning is important and makes the difference between possible and impossible within a human lifetime."

Likely so, but is suggest that personality, drive and motivation are also very important factors. I know from experience that stuff I had little interest in as a youngster and that I've still little in I still know little about.

Yes, my interests have grown and broadened over the years but simply I regard some stuff so irrelevant to my life that it's not worth a second thought and I am much better off applying my limited number of neurons to matters of greater importance and enjoyment.

Of course, no one has the luxury of just learning about what one finds interesting and or enjoyable, life's knocks and experiences along with utilitarian-like imperatives force one to learn stuff they'd rather not know about.

1980phipsi 5 days ago | parent | prev [-]

I find it is good to go back to things you struggled with in the past and come at them with a new and broader understanding.

sdeframond 5 days ago | parent | prev | next [-]

> 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. Which is good already!

wtetzner 5 days ago | parent | next [-]

> 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.

Being tall isn't a skill. I suspect you could be skillful enough at basketball to overcome the hight disadvantage. However, I think most people who might become that skillful see the high disadvantage (plus the general difficulty of becoming a pro basketball player) and take a different path through life. It's also possible that the amount of time that would be needed to grow your skill past the height disadvantage is too long, so it's not feasible to do it to gain a position in the NBA.

rafaelero 5 days ago | parent | next [-]

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.

nemo 5 days ago | parent [-]

>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.

samatman 4 days ago | parent [-]

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.

goatlover 4 days ago | parent | prev [-]

Height is one physical attribute that helps, and professional players are mostly above average height for a reason. But also hand-eye coordination and fast-twitch muscles help even more. Many basketball players are very explosive athletes, because it's a sport with a relatively small play area and lots of quick movements are needed.

Track and swimming are where innate physical attributes have the most obvious benefits. Michael Phelphs had the perfect body for swimming. There is no amount of trainingg that 99.999% of the population could do to get close to what Usain Bolt ran. Most humans could not train to run under 4 minutes in a mile or under 2:30 in a marathon. They just don't have the right muscular and cardiovascular physiology.

Team sports are of course more complicated as other qualities come into play that aren't as directly physiological.

wtetzner 3 days ago | parent [-]

> Most humans could not train to run under 4 minutes in a mile or under 2:30 in a marathon.

Of course, but I don't think anyone was seriously suggesting that. The vast majority of humans can become pretty good at swimming though. And that was my interpretation of the original claim about cognitive tasks, mathematics, etc.

nradov 5 days ago | parent | prev | next [-]

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

nolamark 4 days ago | parent [-]

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.

benjijay 4 days ago | parent [-]

Most people have an above-average number of legs.

sdeframond 4 days ago | parent [-]

What's the average number of legs for humans ?

cutemonster 4 days ago | parent [-]

A bit less than two

sdeframond 4 days ago | parent [-]

What about Frank Lentini ?

https://en.m.wikipedia.org/wiki/Frank_Lentini

nolamark 3 days ago | parent [-]

Seems like he has more than the average number of legs as well.

The fact that he has a wiki page, and that many folks with born without or who have lost legs (~500,000/year Americans experience limb loss or are born with a limb difference https://amputee-coalition.org/resources/limb-loss-statistics...) do not, suggest that the number of people with < 2 is far greater than the number of people with > 2. So the average is still less than 2.

For better or worse, number of legs (or number of arms) is canonical example people use to demonstrate the statistical principal a significant majority of a population can be above average of some metric.

cutemonster 9 hours ago | parent [-]

He must have been an amazing person. I imagine one easily gets bullied, when looking that different. But, from Wikipedia:

> Lentini was so respected among his peers that he was often called "The King".

samatman 4 days ago | parent | prev [-]

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

shrubhub 5 days ago | parent | prev | next [-]

So you're saying success at maths isn't an inbuilt ability. Instead, it depends on an (inbuilt) ability to hyper focus... Which you are just born with?

elbear 5 days ago | parent [-]

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).

air7 5 days ago | parent [-]

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.

card_zero 5 days ago | parent | next [-]

Hey, that doesn't have to be what "natural curiosity" means. Besides which it makes no sense to say people are born with complex interests. I mean, OK, your genes might incline you a certain way, but that's not the same thing.

Being interested in a subject is massively helpful to learning it. But interest arises circumstantially, it's an emotion. The grim reality that it would be really useful to you to learn a certain subject does not necessarily make you interested in the subject, unfortunately. (Perhaps "financially interested", but that's something else.)

ericd 4 days ago | parent [-]

I think there is some natural inclination towards abstract thinking versus more grounded in reality, just judging based on kids I know. Some of them really enjoy playing with ideas in their heads, some enjoy playing with things they can touch more. It seems likely that those different attractions would express themselves in how much they practice different things as time goes on.

elbear 4 days ago | parent | prev | next [-]

I was talking about curiosity in general not curiosity about something in particular. We are naturally inquisitive to the point we have to be restrained by our parents. The problem is some of the restraints are based on the fears of our parents and not on actual dangers. Also, it's hard to develop an appreciation for something when it's forced fed to you.

kdfjgbdfkjgb 5 days ago | parent | prev [-]

> 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.

Retric 5 days ago | parent [-]

Some infants explore vastly more than others.

So the minimum might not be zero, but it isn’t some fixed quantity.

elbear 4 days ago | parent [-]

That's not because it doesn't exist, it's because it's restrained

Retric 4 days ago | parent [-]

How?

People do studies on weeks old babies, it seems unlikely curiosity has been restrained at that point.

dennis_jeeves2 5 days ago | parent | prev | next [-]

>I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus.

And this also gives the proponent (you in this case) an excuse to blame a person for not focusing hard enough or not being dedicated enough if they don't grasp the basics, let alone excel.

Gimpei 4 days ago | parent | prev | next [-]

I don’t know if I agree. Grad school was profoundly humbling to me because it really showed me that there are a LOT of people out there that are just much much better than me at math. There are different levels of innate talent.

Malidir 5 days ago | parent | prev | next [-]

>The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s.

Nonsense!

The brain you are born with materially dictates the ceiling of your talent. A person with average ability can with dedication and focus over many years become reasonably good, but a genius can do the same in 1 year and at a young age.

We have an education system which gives an A Grade if you pass the course, but 1 person may put on 5 hours a week and the other works day and night.

PittleyDunkin 5 days ago | parent [-]

What makes you think that "genius" is nature and not nurture? I'd love to see the evidence for this; i'm deeply skeptical.

Edit: I don't mean to argue that there aren't genetics involved in determining aptitude on certain tasks, of course, but the assumption that genius is born and never made feels like a very shallow understanding of the capacity of man.

Malidir 4 days ago | parent [-]

> I'd love to see the evidence for this; i'm deeply skeptical.

Cool, come and have a coffee with me :) I have older and younger siblings and was the one randomly blessed.

Whereas most recognised talents are associated with hard work and so there is then this visible link, I am a good example as I did the bare minimum throughout education (and beyond...).

The way my brain processes and selectively discards/stores the information it receives is very different to majority of the population. I have no control over it.

I take zero credit for any of my achievments - I regularly meet intelligent people near to retirement who have been to a tier 1 university, may have PHDs, worked 60 hours a week since they were born, been on course and what not and cannot reach the levels I can.

My nurturing was no different to siblings/peers (and was terrible!)

Note: I have my weaknesses too, but as a whole, I am exceptional. Not through effort!! Completely random - neither of my parents are intelligent and nothing up the ancestary tree as far as I know.

PittleyDunkin 3 days ago | parent [-]

I am also exceptional in many ways, (some of them negative), and some of this is clearly inherited and likely genetic. I share too many innate strengths with my father and, to a lesser extent, my siblings to disagree with this. But I just don't know how you could preclude developmental factors like "when you started reading as a child", "what sort of puzzles and games you played as a child", "lack of trauma as a child", etc.

InDubioProRubio 5 days ago | parent | prev | next [-]

The boostrap skill is the ability to obsess over something. To focus and self-reward on anything is a heaven sent. Good thing we do not medicate that if we are unable to get that energy on the road, that base skill.

hilbert42 4 days ago | parent | prev | next [-]

"What we should be teaching children is HOW to learn."

Absolutely correct. And that begins with getting their interest, thus their attention; and that's a whole subject in and of itself.

ponderings 5 days ago | parent | prev | next [-]

I've had some success converting people by telling them others had convinced them they were stupid. They usually have one or two things they are actually good at, like a domain they flee to. I simply point out how everything else is exactly like [say] playing the guitar. Eventually you will be good enough to sing at the same time. Clearly you already are a genius. I cant even remember the most basic cords or lyrics because I've never bothered with it.

I met the guitar guy a few years later outside his house. He always had just one guitar but now owned something like 20, something like a hundred books about music. Quite the composer. It looked and sounded highly sophisticated. The dumb guy didn't exist anymore.

shrubhub 5 days ago | parent [-]

But also, some people are stupid, right?

yawpitch 5 days ago | parent | next [-]

Intellect is like a gas, it will expand to fill its container. The container, in humans, is epigenetic and social — genetics only determines how hot or cold your gas is, ie how fast and how fluidly it expands, but you’re taught your limits — it’s best to see stupid as not how limited you are relative to other but what limits you have now and may abandon in the future.

That said, some people received a smaller starting container, and might need some help cracking it. That’s the work of those who think they’ve found a bigger one.

ajuc 5 days ago | parent | prev | next [-]

The inborn part is how quickly you get results (good or bad). Stupidity is the results.

If we spent 50% of time thinking productively - inborn thinking speed would matter. But in my estimate even 5% is generous.

So it matters far more what kind of feedback you have to filter out the wrong results, and how much time you spend thinking - than how quickly you can do it.

Also practice helps with speed.

5 days ago | parent | prev [-]
[deleted]
red75prime 4 days ago | parent | prev | next [-]

> The belief that some people have an innate skill that they are born with is deeply unhelpful.

In practice your views result in stinting access of non-existent (in your opinion) talented children to a faster education track. They don't exist therefore they don't need different treatment (finer points get lost when the idea disseminates). Quite a hot theme in American education two (or so) years ago.

myworkinisgood 4 days ago | parent | prev | next [-]

Math is a stepping stone to critical thinking skills. And while one can probably learn those skills in any way, math forces you to learn those skills by learning the method of writing proofs. No other field forces you to push your critical thinking skills to the limit that math does.

LoganDark 5 days ago | parent | prev | next [-]

> 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.

yawpitch 5 days ago | parent [-]

> a side effect of experiencing the world differently

A side effect for which there is a substantial, lifelong, and most importantly wide cost, even if it occasionally confers usually small, usually fleeting, and most importantly narrow advantage.

sethammons 5 days ago | parent | next [-]

At such cost with such narrow advantage, why has it persisted so pervasively? I would counter that the advantage is wider and the cost narrower than your current value system is allowing you to accept.

LoganDark 5 days ago | parent [-]

Natural selection doesn't care about cost or advantage, only reproduction.

sethammons 5 days ago | parent [-]

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.

LoganDark 5 days ago | parent [-]

> 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.

vacuity 5 days ago | parent [-]

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.

LoganDark 5 days ago | parent | prev [-]

Yes, there is a significant cost to being built differently regardless of perceived advantages (by one's self or others). For example, as an autistic, I have to cope with finding interaction with non-autistics quite difficult for me, even if detail-oriented thinking can make certain tasks seem easier to me.

graemep 5 days ago | parent | prev | next [-]

> The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything.

My first thought when the article got to the dialog between logic and intuition bit was that the same is true for school level physics.

scubbo 4 days ago | parent | prev [-]

> an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s.

I see you're familiar with Ryan North.