http://www.amusingplanet.com/2011/09/jonathan-hardesty-9-yea... (the original forum thread seems to be down at the moment) - but it chronicles a guy who started to learn to draw and over the course of 9 years you can see the improvement.
I started playing guitar when I was 11...did I suck then...yes...I could barley hold a full sized guitar...and over the years I have learned new techniques and practiced endlessly...and now people would say I am pretty good.
Writing and math are no different - to peg them as just "talent you are born with" deprives the subject of all the work they have done throughout their lives.
The first couple of drawings are terrible, primary school level drawings - the perspective, shading etc. are all completely off.
If you honestly believe you couldn't pull something like that off given 30 minutes of dedicated drawing...well I don't believe you.
Some more examples of skills that are learned:
* Programming
* Public Speaking
* Estimation
* Throwing
* Juggling
Or are you going to start telling me that some babies are born with an innate ability to juggle? or programming?
I am not saying these skills are easy or trivial, they require thousands of hours of dedicated practice. It sounds to me you think most people are simply good at something and do that...when in fact people spend thousands of hours honing and perfecting skills.
You can't jump into the water and start swimming until you lean how to control your body through crawling, standing and lifting...with maths...you may be unable to grasp theorems because you lack basic training in propositional logic (something that is rarely taught before undergraduate unfortunately - it is so simple and provides a grounding that would make any additional mathematics teaching a whole lot easier) - what is your mathematical background? what books have you studied? what lectures/courses have you taken? Lets see if we can't fix this!
Do you honestly think your genetics is playing against you in your study of mathematics? Which bits are you struggling with? What have you tried to fix it? What courses have you taken? Have you tried private tutoring? khan academy? Have you tried anything for longer than a couple of a days? weeks? How many hours of deliberate practice do you think you have put into studying mathematics?
It sounds like you have a grudge against basic mathematics because you think isn't important, you're afraid of it, and it affected your life in an adverse way. Unfortunately that has little to do with a human's ability to learn.
The truth is that talent means nothing in comparison with practice.
Exactly. Most people don't realize how unnatural and difficult written language actually is, yet here we are. There's a great book on the subject called 'Proust and the Squid'[1]; it looks into the history, development and neuroscience of reading and it's quite eye-opening. There's really no reason to believe why math/music/programming/etc should be any different.
[1] http://www.amazon.com/Proust-Squid-Story-Science-Reading/dp/...
Also, you have a pretty skewed idea of how evolution works. How long do you think it took for evolution to "wire our brains" to learn to write quickly?
As long as the time it took for evolution to rewire our brains, I'd say more than a thousand of years, it's not like writing was invented yesterday.
Difficulty and ability are orthogonal matters, but you seem to be trying to defend a hard/static correlation between them. Of course difficulty affects ability, but it doesn't limit/promote anything. As long as you keep exposing yourself to something, your brain will adapt to get more used to it (i.e. 'get better' at it). That doesn't indicate how fast you'll be at it, nor does it mean you can't start at a lower/higher point than other people (which in itself doesn't dictate whether you up superior/inferior to them) -- it just means it's possible.
'math-inclined'... so in other words, interested/experienced in math?
Um, yeah?
You don't like math, we get it. But you can't justify matters of taste 'scientifically' like that. There is no other way we can quantify these 'inclinations' you speak of other than taste, so there's nothing really new here.
Not everybody born with perfect pitch wants to be a musician, and I can guarantee you there are plenty of musicians without it that can run circles around some of those that do have it.
I'm interested in programming and music, and confidently feel I'm good at both, does that mean I'm "musically/programmatically-inclined"? If so, how might I be? Or instead, how would you define a person that isn't musically-inclined? You could argue that a literally tone-deaf person isn't, but not that !musical_inclination == tone_deafness; so how would you define it? The simplest definition that would catch the most cases here would just be the lack of interest. So in other words:
if (interests.contains(some_subject)) {
return POTENTIAL_SUCCESS;
}
else {
return null; // because it is 'undefined', not necessarily FAILURE
}
Well, I'd argue this is a bad place to start out. The better questions are:
1. What do these equations represent?
2. Why do we care about what they represent?
3. What does "solving them" mean for the things they represent?
You can do so much of this without the formalisms of classroom mathematics and, honestly, it's what "real" mathematicians do. The formalisms are just a high-bandwidth way of communicating these ideas between mathematicians. They're just a highly technical map of the terrain, not the terrain itself.
In fact, if I was teaching someone and they invented their own bizarro syntax for "solving" equations I'd be ecstatic. Whatever it was that happened in their head that made them
> but the effort to get there will be a power of that needed by a "math-inclined" person.
This is fine and true, perhaps, but if so it's true of all things, not just mathematics. You can replace "math" with "writing" or "running" or "playing a kazoo."
What do you think makes mathematics special?
You think of language as a basic skill because you have taken it for granted your whole life, but the same kinds of mental abilities used for language are what is needed for mathematics. There are heaps of scientific evidence supporting this. [1]
Again, you are putting mathematics on a pillar because it's foreign to you, not because of any inherent difficulty in the subject itself. You're "acknowledging" a myth as fact.
[1] http://www.amazon.com/The-Math-Gene-Mathematical-Thinking/dp...
Never a falser word spoken.
To put on my logician's hat for a second, the great grandparent said, "You can't teach a person to paint, or to write, because you can't teach them talent, the same is true with math." The unstated assumption in this sentence is that one must be talented at, say, writing in order to learn how to write. Of course, this depends entirely on what one means by "writing", "talented," and "learning."
If "being able to write" means being able to write as well as the best writers do then, yes, I'd agree that takes talent. If "being able to write" means having a command of written language above the mere mechanical act of putting words on a page, e.g., humor, irony, structure, flow, etc., then no, I don't think that requires talent. It requires interest and deliberate practice, but I don't think it requires talent.
This word "talent" is kind of a boogey man, anyhow. On the one hand folks plenty of folks say I'm "talented" at math. On the other hand, there were years in college where I spent 40+ hours a week studying it.
I think anyone who chooses could become a decent at mathematics, swimming, playing the guitar, or baking pies if they really wanted to, regardless of talent.
The formalisms aren't the point. For example, I wouldn't stress out if a student couldn't follow Newton's * Principia Mathematica*. I've tried and I can't, really.
This is why the way we introduce "proofs" in high school in the US (via tedious and seemingly arbitrary geometric arguments) is so destructive. It's all formalism and, honestly, very little mathematics.
I can and have explained the Pythagorean theorem to folks with virtually no mathematical training. The only prerequisite is the ability to find the area of a rectangle and perhaps a little but of high school algebra.
We're not talking about diagram chasing, here.
http://www.amazon.com/Talent-Code-Greatness-Born-Grown/dp/05...
Success/fame/fortune/happiness/etc are another matter, but skill acquisition has been shown to be generally straightforward. Some things may have higher learning curves for some people (e.g. math for a person with dyscalculia[1]), but that doesn't mean it's impossible.
Hoping that practice alone in any given subject will get you wherever you want, is just wishful thinking. Think of all the kids that play piano, or write poems or generally do something great at a very young age. You can ascribe their skills to practice or experience, given their age, you just have to acknowledge that it's talent, an innate ability. They don't learn how to play piano, they just get it. The same is true with math people, their brains are wired to comprehend a complex subject, arguably impenetrable for most of the population.
Neuroscience supports the ability to acquire skills. The combination of epigenetics, GMOs, neuroplasticity, and many other advances make it even more apparent that adjusting ourselves is possible; even without a 'free will'[1].
If people don't feel like trying to learn/improve, that's fine; but they shouldn't try going around loosely justifying their actions with 'science' just because it makes themselves feel better.
[1] I only bring this up because determinism seems to be the biggest argument against this for some reason, but it really doesn't counter anything. Hell, I actually agree with it, and have written on the matter: https://news.ycombinator.com/item?id=6235628