Indeed. It is surprising how often I've been chastised for saying that some people are smarter than others. Relatedly I believe that some people are just incapable of learning, for example, college algebra. As an extreme example can a mentally disabled person learn college algebra?
Einstein quite frequently messed up his math. But he was lucky to be surrounded by some excellent minds that regularly pulled him out of holes and kept him on the right track. One person's intelligence doesn't matter at all if they are surrounded by idiots, or they are stuck in environments that focuses their minds on bullshit (eg Google - lot bright people there working on pure shit)
It's worth chastisting a little bit, because "smart" is at best an oversimplification. I wrote at length about this in another post, but the tldr is that, in expectation, most people are good at some things and bad at others. If I'm good at university-level mathematics but terrible at woodworking, am I smarter than someone who is good at woodworking but has a hard time wrapping their head around group theory?
Case in point: I struggled in my algebra class and developed no useful intuition for groups until years later, but by most conventional standards I am a moderately intelligent person.
Of course smart is a vague term and it's not one that can be precisely defined or measured. However, let's consider the question,
Can a mentally disabled person learn college algebra?
The answer is yes or no, or some can but others can't. Within the context of college algebra and considering no other areas is it safe to say that some people are smarter than others? I think clearly the answer is yes. Of course a person not smart in college algebra might have genius level talent in programming, writing, art, or some other area.
I'm smarter than the vast majority of people in the world when it comes to mathematics but am completely useless when it comes to engineering, art, writing, physics, and other areas. Saying one is bad at college algebra is not a denigration, it is an assertion of fact and not in any way a determinant on one's worthiness.
I teach mathematics at a university. A large majority of my colleagues think that everyone is equally capable of learning college algebra. I think they are wrong. I think it is obvious they are wrong. They think any assertion that some people college algebra must be rooted in racism or other terrible biases that one has.
Academicians ought not dogmatically cling to notions that are easily disprovable. Namely, it is clear that some people - mentally disabled for instance - can't learn college algebra. We should not shy away from confronting uncomfortable truths.
>The answer is yes or no, or some can but others can't.
The problem is that the answer isn't yes or no. Performance isn't discrete. Someone who fails college algebra and repeats a semester might do better than their peers next time around. Your oversimplification would mean that no improvement is possible which is at odds with the paper this HN submission is about which is about the fact that the learning rate is the same.
That implies that it isn't a yes or no question. The question is how long will it take. You might bucketize a person that needs 10 semesters to finish his bachelor's (assuming European 6 Semesters) as incapable of learning college algebra.
The problem with this reasoning is that finishing the bachelors could still result in a quite significant improvement in quality of life even for a handicapped person, so acting as an authority telling them they can't do anything is counterproductive.
>. Saying one is bad at college algebra is not a denigration, it is an assertion of fact and not in any way a determinant on one's worthiness.
Now you are moving the topic. Being bad at something is different from being unable to learn something.
People who are capable of learning something can still be bad at it. College freshmen are bad at the things they are about to learn, that is the point of college, to learn new things and get better at them.
Leave mental disability out of it, because it's not relevant to the discussion.
What's clear to me is that people have different learning rates and different need for personalized attention. I also would never argue with the assertion that some people have greater natural aptitude for specific things, meaning their ability to pick up the material at a standard pace without a lot of extra personalized help.
There's plenty of research showing that IQ exists and can be consistently measured, but I would hesitate to ascribe the learning outcomes in a higher-level math class directly to IQ. If assessing general intelligence were easy, we wouldn't need decades of psychology research on the topic. So I personally don't think we should be in the business of trying to assess how smart people are in general. Assessing attitude at specific tasks can of course be practical and useful.
That said, have you asked your colleagues for clarification on what they mean by "everyone can learn"? Are they talking about learning it on a hand-wavy pop science level (eg Numberphile), or learning it well enough to derive results and apply it in new problems? Do they have a timeline in mind for learning, or a specific context? Are you sure your colleagues are being dogmatic for fear of confronting uncomfortable truths, or are they just optimistic? Or have they forgotten that algebra is pretty esoteric and far away from what people normally deal with in their day-to-day lives, and might actually be a specialized topic that does require a bit of specialized natural aptitude?
> A large majority of my colleagues think that everyone is equally capable of learning college algebra.
They have to hold that view, though, else their reason for existence disappears. How can students justify the high cost of hiring a professor, accepted on the premise of being able to make it up with higher future earnings, if they realize that the reason there is a spectrum of incomes is because some people can't rise into higher paying work?
You and I know that the mentally disabled person will never rise into a $500,000 per year job, no matter how hard they try, because of their disability. But your colleagues have to suggest that the mentally disabled person won't only because that person hasn't attended their classes. Their entire marketing strategy of getting students into their seats rests on it. Failure to communicate that to students means they soon find themselves out of job.
How is this supposed to be good faith advice? The mentally disabled person may earn $15/h as a janitor or $25/h in some high productivity job that would usually pay $60/h and requires a college education but also has some accomodations for their disability. Mental disability isn't linear and it isn't a discrete yes or no either.
It's like everyone here is taking some extreme edge case as the baseline for mental disability where it is immediately obvious that they can throw them into the "too dumb" bucket.
We also calibrate our definition of smartness to expectations. I say my cat is smart because he opens the front door to let in his deer friends. That doesn’t mean I think he can learn algebra. (Meanwhile, the beagle never figured out how to walk on the same side of a tree as me while on leash.)
I think that is a very dangerous hole those academicians have dug themselves into. And not even healthy for themselves as they're surely always on the look out for the bogeyman?
I agree, natural aptitude absolutely is a thing. I'm somewhat smart, but maths does not come readily to me no matter what I try. And don't even get me started on music - which I have brute-forced myself into being barely able to play.
Jim Simons is a great example. Has made 28 billion from algorithmic trading, has Chern–Simons form named after him in math but has said he sucks at computer programming because he can't remember syntax well enough.
If he was 50 years younger he probably would just be a very mediocre programmer and not have "wasted" his time with this other intellectual activity.
Einstein would be a data entry clerk trying to get a job writing javascript.
I suspect with so many more educated people we have so many more true genius level minds than a 100 years ago but we have narrowed economically useful intellectual life to such a degree that 99% of them are doing well paid sub-optimal bullshit with their genius unexpressed.
> If I'm good at university-level mathematics but terrible at woodworking, am I smarter than someone who is good at woodworking but has a hard time wrapping their head around group theory
We don't have enough information to say. But what's almost certainly true is that one of you is smarter than the other.
I think a useful analogy is smart = compute, wisdom/knowledge=data.
Your example is not great because "woodworking" is primarily a knowledge game. Nothing is complex to the point you can't understand it.
University-level mathematics is less obvious--there's certainly a knowledge aspect--but I would stay largely a compute game.
Almost all people can become top-tier at knowledge games, not nearly as many at compute games.
> Your example is not great because "woodworking" is primarily a knowledge game.
I think his example is very good if he requires much more effort to understand straightforward woodworking concepts. It might not be that he can't be an average woodworker but that it takes him 5x more effort - and after just 3x more effort he's kind of done.
Sure, if that were true. But it's not. Anyone who can understand college algebra can understand woodworking concepts, because woodworking concepts have virtually no cognitive complexity.
Source: I learned college algebra, and I have my woodshop 20 yards from me.
A better example would be my ability in strategy games such as checkers, chess, bridge, et alia. I'm generally worse at such games than most of my friends, none of whom have any special training or aptitude for strategy games.
Giving an "extreme" example turns your example into a flawed logic or apples/oranges comparison which gives no new insight into the original argument anymore.
I think you don’t understand the what constitutes flawed logic. If gave a counterexample to the statement: Everyone can learn college algebra. Therefore this statement is not true.
We are then left we needing to modify the statement. What is true is the following: Some people, but not everyone, can learn college algebra.
This is an uncomfortable statement for a lot of people because the inevitable follow up is: Who can and who can’t learn college algebra?. Relatedly, one must confront the idea that not everyone is college material. Maybe too many people are going to college and this is why so many in college are struggling in basic courses. I could go on.
Your post appears naive in that you don’t seem to have thought through the implications of the idea that not everyone can learn college algebra.
>Your post appears naive in that you don’t seem to have thought through the implications of the idea that not everyone can learn college algebra.
It is naive in the sense in that it actively tries to discourage people from trying and learning including the ones who can because they will have this brain virus implanted into their minds that they can't do something because of some unchangeable factor and then turn the mind virus into reality where they are unable to perform which then further tells them that they can't perform because they aren't smart enough. It is basically the equivalent of pulling up the ladder under the pretense of avoiding injury in case someone falls. You can tell anyone that they aren't smart enough and tell them to not do something but only people who try and succeed can disprove them.
So you have this constant cheap troll attack about people talking how you can't do things and then you must put in the expensive effort to disprove them which they can only do in a few disciplines.
> It is naive in the sense in that it actively tries to discourage people from trying and learning including the ones who can because they will have this brain virus implanted into their minds that they can't do something because of some unchangeable factor
No one's discouraging anything. Differences in cognitive abilities should be no more surprising than differences in ability to jump and run, thus resulting in differences in one's ability to be a professional basketball player.
It is simply a fact that most people cannot play in the college level basketball, let alone the NBA. This should not be surprising, nor does this fact discourage people from playing basketball causally for fun or fitness. I'm not sure why this exact same argument would suddenly be discouraging when applied to cognitive activities.
I would say that anybody without an intellectual disability can learn college algebra. There is a lack of motivation and a lack of training that prevents people from succeeding.
> I would say that anybody without an intellectual disability can learn college algebra.
I think that's a stretch, unless you expand the meaning of "intellectual disability". I would agree that considerably more people can succeed than currently do because effort can make up for a lot, but that's a different claim.
People have different working memory capacity, different abilities to reason deductively and considerably more differences on various other metrics of cognitive performance. There are as many dimensions to cognitive performance as there are ways to measure athletic performance, and people fall on very different parts of this spectrum.
With significant effort over time, I can make up for athletic deficiencies and become a pretty good basketball player, but being 5'9" I almost certainly would never be able to make a college basketball team let alone the NBA. I'm not sure why this same logic applied to cognitive abilities is so controversial.
Not at all. In my experience, many people of mediocre intelligence but a background that has sufficient education think they're geniuses. The variability in intelligence achievable by tutoring vastly exceeds the difference in their intelligence vs. that of the average inner-city high school dropout without a disability.
> People have different working memory capacity
Multiple studies have shown how this is easy to train.
> different abilities to reason deductively
This is also very easy to train by example.
> I almost certainly would never be able to make a college basketball team let alone the NBA
Being able to do college algebra isn't equivalent to making the NBA, which means being in the top fraction of a percent in basketball ability. Being able to do college algebra is equivalent to being able to dribble.
> Multiple studies have shown how this is easy to train.
Running ability is also easy to train, that doesn't mean everyone can run a marathon. Some people have flat feet or poorly proportioned limbs unsuited to long-term running. These aren't disabilities preventing them partaking in such activities, but nevertheless limits their potential.
> Being able to do college algebra is equivalent to being able to dribble.
No, it's being able to at least dunk. Again, a common skill but not one everyone can achieve.
> Running ability is also easy to train, that doesn't mean everyone can run a marathon.
Everybody without a disability can run a 5k. High schools used to require students to do a mile run to pass physical education.
> Some people have flat feet or poorly proportioned limbs unsuited to long-term running.
And some people have microencephaly. We're not talking about outliers. We're talking about the vast majority of people.
> No, it's being able to at least dunk.
Look, you're not special for being able to learn college algebra. 95% of Koreans and Singaporeans can do it today, but this wasn't the case 60 years ago. It just requires a basic level of education.
> And some people have microencephaly. We're not talking about outliers. We're talking about the vast majority of people.
No, you specifically said "people without a disability". Unless you're going to expand the meaning of "disability", various permutations within the range of "normal" physical characteristics will impose different limits on athletic abilities, and analogously, the range of cognitive qualities (memory, focus, spatial reasoning, etc.) will do the same for cognitive tasks.
The fact that these qualities can be improved via training doesn't change the basic fact that those limits will be quite different for different people, even within the normal range. We can quibble all day about whether college algebra falls under that category, but this basic fact won't change.
> the range of cognitive qualities (memory, focus, spatial reasoning, etc.) will do the same for cognitive tasks.
And that range is smaller than the difference between your ability to perform cognitive tasks and the average high school dropout's ability to perform those tasks. Education makes a much larger difference.
I disagree. Education boosts IQ scores by 1-5 points [1], where 1 standard deviation from the mean IQ score is +/-15 points. The spread on cognitive abilities is clearly broader than education can cover.
Education has improved the average IQ of multiple East Asian countries by 15 points over two decades. That's an entire standard deviation improvement for the whole population. One-on-one tutoring has been shown to make a two standard deviation difference. That's the difference between median intelligence and genius. https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem
Your study is about the effect of an extra year of badly done education on people who drop out of school, which is worth 1 IQ point. That same study shows that the effect of mediocre education on people who don't drop out of school is an increase of 5 IQ points.
You have defined a too narrow definition of "flawed logic" in order to make a counterargument which still doesn't defy the argument the original comment has made. Then you make a baseless assumption in your last sentence that the commenter has not thought through the implications of the idea that not everyone can learn college algebra. Your writing is also honestly a bit difficult to understand so i assume you're learning English.
> Your writing is also honestly a bit difficult to understand so i assume you're learning English.
His argument seemed like a pretty straightforward logical deduction to me. If his argument doesn't refute the claim that everyone can learn college algebra, then you must have some unusual definition for one or more of "everyone", "learn" and "college algebra".
I think you don’t understand what assumption means. I made no assumption in my last sentence. I wrote how your post appears. This is an opinion of mine. This ought to have been clear because I used appears and don’t seem. The reason I phrased things the way I did is precisely because I was not making an assumption. You might be an expert on this topic. I don’t know your background. I was telling you how your post came across to me.
What is funny and ironic is that you falsely accuse me of making a baseless assumption and then in the next sentence explicitly say you are assuming I’m learning English. I think it’s clear that I’m not learning English.
