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"Now", as in an immensely tiny blink in the human evolutionary time-scale? Sorry, that's more wishful thinking than the notion of skill acquisition. Surely you

"Now", as in an immensely tiny blink in the human evolutionary time-scale? Sorry, that's more wishful thinking than the notion of skill acquisition. Surely you're aware of feral children, and more 'normal' dyslexics; what's the deal with those? Clearly we should be reading straight out of the womb by now, so what gives?

cliveowen 13y ago
Feral children by definition aren't exposed to anything resembling writing and dyslexia only proves that neurological differences play a major role in our ability to comprehend and parse information.
- oblique63 13y ago
  Exactly, but dyslexics can still read, because they can learn how to. Their genetics may not have given them a good start, but evolution certainly didn't make their lives any easier either; they still had to learn things 'the hard way' like the rest of us -- just with a bit more resistance. 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.
  - cliveowen 13y ago
    I'm not saying that if you start out without being able to solve basic equations and then spend 10 years learning math you still won't be able to solve those basic equations, you will, but the effort to get there will be a power of that needed by a "math-inclined" person. And once there the math-inclined will still run circles around you.
    - oblique63 13y ago
      > ...but the effort to get there will be a power of that needed by a "math-inclined" person. '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 } Pretty novel idea there. Who would've thought you needed to be interested in something to excel in it?
    - jfarmer 13y ago
      > I'm not saying that if you start out without being able to solve basic equations 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? So, maybe a more important muscle to exercise is the one that lets us go up and down the ladder of abstraction. A huge part of mathematics is seeing a class of (relatively) concrete things, finding commonalities and drawing out abstractions, reasoning about the abstractions, and then drawing conclusions about the more concrete things. 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?

cliveowen 13y ago

Feral children by definition aren't exposed to anything resembling writing and dyslexia only proves that neurological differences play a major role in our ability to comprehend and parse information.

oblique63 13y ago
Exactly, but dyslexics can still read, because they can learn how to. Their genetics may not have given them a good start, but evolution certainly didn't make their lives any easier either; they still had to learn things 'the hard way' like the rest of us -- just with a bit more resistance. 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.
- cliveowen 13y ago
  I'm not saying that if you start out without being able to solve basic equations and then spend 10 years learning math you still won't be able to solve those basic equations, you will, but the effort to get there will be a power of that needed by a "math-inclined" person. And once there the math-inclined will still run circles around you.
  - oblique63 13y ago
    > ...but the effort to get there will be a power of that needed by a "math-inclined" person. '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 } Pretty novel idea there. Who would've thought you needed to be interested in something to excel in it?
  - jfarmer 13y ago
    > I'm not saying that if you start out without being able to solve basic equations 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? So, maybe a more important muscle to exercise is the one that lets us go up and down the ladder of abstraction. A huge part of mathematics is seeing a class of (relatively) concrete things, finding commonalities and drawing out abstractions, reasoning about the abstractions, and then drawing conclusions about the more concrete things. 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?