What is talent?


Victor Pross

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Offering my own two cents in the area of my interest, I can say this: Some people are "visually illiterate" and some aren't. Those who aren't, have a talent. This is innate, but it needs to be honed. Practice perfects or sharpens that which nature gave us.

For those who are visually illiterate, it can be said they lack the mental/visual aptitude necessary to translate lines and colors into meaningful images. They may have talents in other areas, but they lack the talent of being visually literate. I heard that Pre-industrial aboriginal tribes cannot make sense of two-dimensional renderings of a three-dimensional object so it is unlikely they'll be hiring me soon.

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In trying to understand the dynamics of the psyche in relation to the concept of talent, I find it helpful to set the meaning of the word "talent" in the context of two other words: skill and discipline. A person can have talent without yet having developed the skills or disciplines to unlock its potential. Equally, a person can be very skilled and/or disciplined at an activity without showing any particular talent that might set him apart from other skilled and/or disciplined people.

I'm not going to look at a dictionary (that would require discipline) but I would like to state the meaning these words conjure up in my mind:

Talent– the ability to creatively access the resources of one's experiential imagery, generate, manipulate and even distort perceptual models of the world that is experienced, create an action sequence that will express these models objectively, and put that action sequence in motion while monitoring the results for producing the models one has created.

Skill– the ability to manipulate some aspect of reality to produce a desired result. (Clearly, having skill would help the expression of talent.)

Discipline– (my greatest weakness) The ability to act within the structures of some system– whether created by oneself or others.

When Rand turned away from writing fiction, she turned away from her creative talent as I have described it. She embraced her discipline and skill for further developing and expressing the structures she had already created.

Paul

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It is only your maximum potential and maximum capacity that is limited by any innate talent and I think it is important to add to this discussion that the vast majority of people never come anywhere *near* their potential, so to speak of a higher innate potential or capacity is really beside the point.

Even Einstein immersed himself in scientific papers and publications for years on end, and still his most productive years were the years he left his wife and children in another country. The point being, unless you spend nearly 100% of your waking moments, and then even go with less sleep to have more waking moments, on doing that thing you are trying to excel at, you will not ever come anywhere near your own maximal potential in it, so stop thinking about your potential and innate capacities and just get off your butts and do the things you are interested in!

I find more often than not that the people who appeal to innate differences are just looking for ways to excuse their own laziness. If you can't draw well, go to the book store and buy a book on 'learning how to draw' or take an art class at a local community college, or grab a pencil and just try.

I was not born with a gene to weld, but I bought books on it and practiced for hours on end, now I am a decent welder. I have no gene for composite construction, 3D animation, computer modeling, aluminum casting, home remodeling, plumbing, electrical, drawing, sketching, designing, etc etc etc. But a lot of practice at all of these things makes me better and better at them, and also makes it perpetaully easier to learn newer skills. Again I suggest reading the article I posted in an earlier comment.

The human mind, unlike all other computers, actually gets faster with the more information that is stored in it.

Michael F Dickey

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Matus,

You make some very interesting points.

There is no question that practice makes perfect. It is also true that repetition, devotion and applying yourself are the foundations to acquiring a skill. But I do argue that some people seem to be wired at birth and are more apt at a given area—such as math, drawing or music. In many cases, you see it from the very beginning. Let’s take the question of drawing again: I exhibited an advance skill at a very young age and this spot lighted me as far back as I can remember. But this is not to say that what I am doing today is similar to what I was doing at the age of three. Of course there is room for improving on one’s ability. In fact, I do believe anybody can take a series of drawing classes and later walk away with marginally improved skills, but these people will never—never—be able to paint like Michael Angelo or Rembrandt. I don’t care if you take a random child and train him from an early age till he’s fifty—some people will never paint, compose music, etc, like the masters. Why not? Because they don’t have “the gift” and it’s this innate ability that fascinates me. This is what I’m trying to understand.

Victor

Edited by Victor Pross
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It is only your maximum potential and maximum capacity that is limited by any innate talent and I think it is important to add to this discussion that the vast majority of people never come anywhere *near* their potential, so to speak of a higher innate potential or capacity is really beside the point.

...

I find more often than not that the people who appeal to innate differences are just looking for ways to excuse their own laziness. If you can't draw well, go to the book store and buy a book on 'learning how to draw' or take an art class at a local community college, or grab a pencil and just try.

You hit the nail on the head. And raised a good question too: what is the point of deciding that someone's drawing ability is innate? Is it in order to "help" someone figure out when they should give up? What's the practical purpose of knowing the answers to that kind of question?

And that's what the talent people here are doing: deciding. They have no facts to prove their claims. They are obviously biased. E.g., Victor says that if someone doesn't become a good artist, then they must have had no inborn talent. The thing is you can't get inside someone's head (and a person that's inside his own head isn't necessarily good at introspecting). Maybe they used their minds to their fullest and that was as good as they could do, or maybe they had a bunch of hang-ups that in subtle ways made them less able to learn. Maybe some guy *would* have been the next Michelangelo if he had only dug a little deeper. You just can't know. But Victor presumes he knows and decides that the guy must not have had inborn talent.

Shayne

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...In fact, I do believe anybody can take a series of drawing classes and later walk away with marginally improved skills, but these people will never—never—be able to paint like Michael Angelo or Rembrandt. I don’t care if you take a random child and train him from an early age till he’s fifty—some people will never paint, compose music, etc, like the masters. Why not? Because they don’t have “the gift” and it’s this innate ability that fascinates me. This is what I’m trying to understand.

Victor

Maybe, Victor, but you don't know that for sure. It's not like millions of people spend most of their waking life perfecting their abilities to paint or sculpt, and many artists are not judged by objective criteria anyway (Jackson Pollack anyone?) But it could very well be that you might be a much much better violinist than Yo Yo Ma but you'd never know because you never picked up a violon to find out, let alone spent 100,000 hours perfecting your ability to play it (the average time it takes a person to become an 'expert' at something) Same goes for long distance bicycling, skeet shooting, basketball, or memorizing long strings of numbers. We could have millions of people walking around who are better composers than Mozart (who was a pop musician of his day anyway) or better scientists than Einstein but are way too busy watching survivor, gossiping, and shopping to ever find out.

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(...) what is the point of deciding that someone's drawing ability is innate? Is it in order to "help" someone figure out when they should give up? What's the practical purpose of knowing the answers to that kind of question?

And that's what the talent people here are doing: deciding. They have no facts to prove their claims. They are obviously biased.

Shayne,

I would have to look up something to give you some facts music-wise, but I once read studies of brain-waves that show that people with high innate musical ability have more interaction between their left and right neocortex lobes than other people do. I have not looked into this for drawing, but I have no doubt there are many studies of this nature for a whole slew of things for the curious.

We should be careful to remember that a word has more than one definition and that the word "talent" is used (not by Rand, but in the culture at large) to indicate both innate potential and developed capacity. This is a case where a lot of polemics happen over semantics.

I don't think people who see that innate ability exists in a small child and say so are on some kind of evasion campaign to blank out their own laziness. Some people might do this, but certainly not all and I would say not even the majority. (I am not saying you hold this view, either. I am merely mentioning it because it is a popular view among several posters with whom I have interacted.)

As to your question about practical purpose, I can give you a very practical purpose for deciding if a person has a strong innate potential or not: to avoid ignoring reality. Correct identification.

I find that correctly identifying the reality I observe is enormously practical, especially in evaluating it.

:)

Michael

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As to your question about practical purpose, I can give you a very practical purpose for deciding if a person has a strong innate potential or not: to avoid ignoring reality. Correct identification.

I find that correctly identifying the reality I observe is enormously practical, especially in evaluating it.

Thanks MSK. This is exactly it. This subject is of particular interest to me, and for more than obvious reasons. I happen to be writing a novel where these questions are covered by some of central characters. But it’s also a matter of intellectual curiosity. This question could also be significant to those who are raising children, don’t you think? It also helps understand the human potential, the human mind, etc. Knowledge is good.

I can see that a defensive position has taken place, and I admit I was taken aback as to why that would be so. I am not married to the points I have made --and I am open to arguments or contrary views—if presented with respect. What I have said is based on observation and experience. But I could be wrong.

Victor

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I would have to look up something to give you some facts music-wise, but I once read studies of brain-waves that show that people with high innate musical ability have more interaction between their left and right neocortex lobes than other people do. I have not looked into this for drawing, but I have no doubt there are many studies of this nature for a whole slew of things for the curious.

There are also studies that demonstrate how the physical structure of the brain is modified by the individual's own choices. And anyways, you can't have an legitimate study of "people with high innate musical ability" unless you've already demonstrated "innate musical ability". I asked for facts and you gave me circular logic.

As to your question about practical purpose, I can give you a very practical purpose for deciding if a person has a strong innate potential or not: to avoid ignoring reality. Correct identification.

Looking for something that's not there is a form of evading reality not adhering to it.

http://www.cordair.com/carlyle/selfmademan.php

Shayne

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Michael:

I am curious, do people who have had their corpus collusum severed (a type of epilepsy treatment includes severing the bundle of nerves that connect the two hemispheres with amazingly few side effects) have any problems playing or composing music? Of course having more communication between the right and left hemispheres might be consequence of studying and developing musical capabilities, and not the source of the abilities or trigger point for them. Music is both creative and logical (extremely mathematical) so it’s clear it would require both specialization areas of the brain to accomplish. That’s akin to saying people that have a larger pre-frontal cortex are more intelligent, when using your intelligence obviously encourages the growth and development of the brain in this area, likewise martial artists, gymnasts, and ballet dancers probably see much more communication between the areas of the brain responsible for musculature control and the rest of the brain. It is easy to confuse the cause and effect in these cases.

I certainly do not think a random mother who appreciates her 2 year olds colored drawings and comments on it is trying to blank out her own laziness either, nor do I think it is appropriate to attribute such a sentiment to me (if that was your intention) it’s rather disingenuous. It’s clear that some people start doing things earlier, perhaps they have physiological mechanisms making them able to start and get better at those things earlier on, or perhaps they happen to do something and enjoyed it more than other young children and thus did it more, thus developing those physiological differences as they grew. Case in point, I read about a young girl, some 18 years old now, who is the best female rock climber in the world. She blows away all competition, rushing past the second best with no problems. What’s her secret? She grew up in Africa with her missionary parents and had as a best friend a spider monkey, she spent much of her childhood playing in trees with monkeys, doing much of this while she was physiologically growing and developing. In effect, she changed her own body structure because of this activity, her arms with respect to her other body proportions are longer than 90% of people, and her fingers as well. She can do pull ups with just two fingers. One could certainly look at her and say ‘Aha, look at all that natural talent and potential she was born with’ but they would be wrong as her difference was entirely environmentally induced. Just like Tiger Woods, who was playing golf before he could walk.

However, the tendency for us to attribute other peoples accomplishments to some ‘innate’ talent, some natural extra capacity for music, art, or sports, is just a form of mass psychological deferral. It is implicitly a tendency to simply forgive ourselves for not accomplishing those things. No, the mother is not explicitly forgiving herself for never developing her artistic interests, but she is advocating a world view in which ‘natural talent’ plays the predominant role. In reality, in ALL of these cases of the most accomplished people in the world, they ALL required extremely hard work and long term dedication, they constantly worked to develop and refine their abilities, pushing themselves always beyond their existing limitations.

I cant count how many times someone has told me ‘wow, you’re so smart’ when I go on some tangent about physics or what not, 'how do you know all this stuff!' as I am sure many people here have experienced. It annoys me because I know I am not, I have no greater capacity than an average person, I don’t remember things quicker or better. I just read, a lot, and they do not. They are lazy, they sit around and watch TV every night, all night. They gossip for hours on end on the phone. They play video games all weekend. There is a reason they are not smarter people, because they never challenge and develop their own minds and ideas. To think of all the great things they could accomplish if they stopped insisting they were stupid mesmerizes me. At a explicit and conscious level, no they are not forgiving themselves their laziness, nor are parents who recognize an ‘innate’ talent of a child doing so, (I still doubt there is such a thing beyond a child engrossing themselves in something they enjoy) but at a subconsiouss level, to some degree, every time we think something like that or say something like that, we are, again, advocating that world view and to some degree are integrating its consequences into our own minds.

We are because it really doesn’t matter what one’s innate talent is, if you want to do something and learn it, just do it. What practical reason could a rational adult who obsesses over such things really have? If they want to excuse themselves out of learning something they might want to learn ‘oh, I could never be as good as such and such’ or ‘oh, no matter how hard I try, I could never make that sculpture or write that book, I just wasn’t born with that sculptor or author gene’ well now they have a perfect excuse. Why are we obsessing over it, are we looking maybe for things we ourselves or our children might be naturally better at? Are we in the business of pushing our children to do things because we think they might excel at it? My point is, it really doesn’t matter, if ‘natural’ talent plays a role, the major role it plays is defining your ultimate limit, so if your goal is to be better than everyone else in the world at something, then it is worthwhile looking into your ‘natural’ differences, gifts or talents. If your goal is to give up before your start because you wont be the best, then it makes sense to attribute much of people’s levels of accomplishment to natural talent. But if you have an interest in doing something, regardless of your 2nd handed place in the world, then just learn it, do it, and enjoy yourself, what role does natural talent play in that?

If I walked up to a body builder and said ‘wow, lucky you born with all those big muscles!” how do you think he would react? He wasn’t born with them, he had to life weights, just like every other guy there, over and over again, hours and hours and hours on end. And here I come and suggest to him how lucky he is, basically, to have been born with big muscles. The ‘muscles’ you develop in your mind devoted to particular tasks are no different.

Additionally, the human species differs genetically less than any other species on the planet, a random group of 1000 chimpanzees will contain more genetic variation than the whole of the human population. In that very limited room for genetic variation, how much of it do you really think plays a significant roll in how well someone plays an instrument or swings a club and hits a ball?

As for your practical purpose, how does it apply? If there is an influence of ‘innate’ talent, it is extremely difficult to identify and would come from a complex interplay of many different genes. You would hardly be able to decipher its influence until you learn what your ultimate limitation was, which will still require thousands of hours of unceasing hard work and dedication. How is not concerning one’s self with ‘natural’ talent ‘limitations’ (which are hardly more than pseudoscientific ascertains at the moment anyway) an evasion of reality? Would you really not want to take up art if someone put you in an MRI and did a genetic screening and pronounced “Well, I am sorry Michael but you have very little chance of being the best sculptor in the world” Would you quite your pursuit?

Well, as Homer (Simpson) said, “The first step of failure is trying!”

Michael F Dickey

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I can see that a defensive position has taken place,

Ad hominem.

and I admit I was taken aback as to why that would be so. I am not married to the points I have made --and I am open to arguments or contrary views—if presented with respect. What I have said is based on observation and experience. But I could be wrong.

What you are detecting is not a "defensive position" but incredulity at the arbitrary assertions being made by the "talent" people. Your entire position is totally fabricated, without one iota of evidence. There's nothing about it to even refute so far. You've essentially just said "In my experience, people are born with the ability to play music". The only way to respond to that is with either the politically-correct "Interesting perspective" or incredulity at the fact that you think you're following a process of reason here.

Shayne

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Victor, I am not sure if you are referring to me, but I did not pick up on any disrespectful tones here nor did I attempt to convey any. I seem to be accused of that frequently on this forum for hardly more than disagreeing. Michael, are disagreements not welcome on this forum? If so I shall depart as unwelcome. I have not been abusive of harsh or disrespectful, I have only disagreed with your and stated what I think is the underlying predominant cultural philosophical reason behind the attitude of embracing the ‘natural talent’ myth when hard science shows it, at most, barely relevant.

Michael F Dickey

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Looking for something that's not there is a form of evading reality not adhering to it.

Shayne,

But this has not been demonstrated yet, I don’t know that it isn’t there or not. You have decided ahead of time and without any substantive argument that talent is not innate. Also, keep in mind: I am NOT saying that man is not “self-made”. Of course he is—in terms of ethical questions. I am speaking of aptitude, abilities, and talents—acquired or developed or innate. That’s what this thread is about. Ethical questions can apply to this topic, but it’s not what I’m addressing at the moment. So I don't understand the tone of reproach in your posts.

Edited by Victor Pross
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For all of those who are interested in the question of talent, an article called On Cherishing Talent is linked here. It is very interesting, and the writer speaks in a manner that suggests that there are "haves" and "have-nots" when it comes to (some) talent. Not all men are equal--metaphysically or morally.

http://www.theatlasphere.com/metablog/353.php

Edited by Victor Pross
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But this has not been demonstrated yet, I don’t know that it isn’t there or not. You have decided ahead of time and without any substantive argument that talent is not innate.

Surely you're aware of the onus of proof principle at least in name? Because you're flagrantly violating it.

There's piles and piles of evidence pointing to the fact that we are self-made in skills and abilities, and no evidence that it's inborn. The logical conclusion to draw is clear. I don't object to you wild speculations, but that's all they are. I do object to you saying that no one's made a substantive argument. It's your side that's made absolutely zero fact-based arguments.

Also, keep in mind: I am NOT saying that man is not “self-made”. Of course he is—in terms of ethical questions. I am speaking of aptitude, abilities, and talents—acquired or developed or innate. That’s what this thread is about. Ethical questions can apply to this topic, but it’s not what I’m addressing at the moment. So I don't understand the tone of reproach in your posts.

I thought I made it clear why I was incredulous. Indeed, the rest of your paragraph here makes me even more so.

Shayne

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Shayne,

Yes, of course I am aware of the onus-of-proof principle. But I have asserted no positive or negative position. I’m merely asking questions. It’s good to see you have “the truth” in your back pocket though.

I need to clarify something: I am NOT saying that people are not self-made in skills and abilities. But ALL of them? You set it up in such a way that suggests it’s all or nothing. Let’s change the direction for a moment: what does the word ‘aptitude’ suggest to you? What is your definition of that term?

Victor

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This is not a one-or-the-other situation! Human beings are not all physically or mentally identical! They just aren't!

Consider athletic talent, that's the easiest one to see.

It's always what you have and what you do with it.

There always seems to be this thing in some where they seem to completely deny physiological factors--trying to get away from the fact that humans are also animals, meaning all of them are minutely, at the minimum, different in one or more ways.

What you are given varies. What you do with it is up to you. How well you do at that, and how quickly you do that also depends, to some extent, on the physiological condition of the mind you were born with.

It's just not that easy. Or it's being made too hard... somewhere in there!

Or maybe we could talk about "proclivities" and how that impacts "talent." (?). I think sometimes people get a better grasp of the physiological terrain by considering what is there in terms of natural proclivities than "innate." Maybe.

Edited by Rich Engle
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For all of those who are interested in the question of talent, an article called On Cherishing Talent is linked here. It is very interesting, and the writer speaks in a manner that suggests that there are "haves" and "have-nots" when it comes to (some) talent. Not all men are equal--metaphysically or morally.

http://www.theatlasphere.com/metablog/353.php

He states, in that article "They were the work of geniuses, people so much more talented than us that we could never paint or write anything comparable to their achievements, no matter how hard we tried or how long we lived." Yet presents no evidence backing that claim. By what means did he come to know that no matter how hard any of us tried we could never accomplish the things these great people have? The scientific evidence suggests otherwise, it suggests that the harder you try and the more work you put toward something the greater your accomplishments and success are. None of that dimishes the recognition and admiration we give toward the great genuises of history, in fact it means more, I think, because it is congratulations and admiration based on thier individual contribution to their greatness, not some mystical greatness they had no control over. Aboslihing the 'natural talent' myth (which, again, the scientific evidence suggests has very little effect if any) simple means that people will again understand the magnitude of their own potential. Whether they hold themselves accountable to that is a matter up to them.

Research now shows that the lack of natural talent is irrelevant to great success. The secret? Painful and demanding practice and hard work

http://money.cnn.com/magazines/fortune/for...91794/index.htm

Of note “Scientific experts are producing remarkably consistent findings across a wide array of fields. Understand that talent doesn't mean intelligence, motivation or personality traits. It's an innate ability to do some specific activity especially well. British-based researchers Michael J. Howe, Jane W. Davidson and John A. Sluboda conclude in an extensive study, "The evidence we have surveyed ... does not support the [notion that] excelling is a consequence of possessing innate gifts."

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Another way to consider talent... Mozart talent and Beethoven talent.

If you look at Mozart manuscripts, they just flow along, very few corrections. Take a look!

If you look at Beethoven's, there's all kinds of toil, crossouts, corrections. You can practically feel the sweat.

Now, both were brilliant talents. Both worked hard to achieve. But, are those not two very different types of talent?

Different needs, different approach, very different end results, albeit results of genius.

*sigh* The nature/nurture thing is always such a pain in the ass...

Edited by Rich Engle
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Shayne and Michael Dickey,

May I ask why, if you think that anyone can become world-class great, you haven't become great at anything? If you're upset that people who believe in innate differences such as talent are just looking for a way to excuse laziness, what excuse do you prefer to use to explain why you haven't achieved greatness? Why have talented individuals become world-class creators and achievers by the time they were half your age, yet you're still just non-great-Shayne and non-great-Michael? Are you saying that you chose to be lazy, that you knowingly chose not to fully develop yourselves even though you're convinced that people with ordinary capacities can achieve genius-level greatness?

J

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Another way to consider talent... Mozart talent and Beethoven talent.

If you look at Mozart manuscripts, they just flow along, very few corrections. Take a look!

If you look at Beethoven's, there's all kinds of toil, crossouts, corrections. You can practically feel the sweat.

Now, both were brilliant talents. Both worked hard to achieve. But, are those not two very different types of talent?

Different needs, different approach, very different end results, albeit results of genius.

*sigh* The nature/nurture thing is always such a pain in the ass...

Speaking as an ex-musician I can tell you that 1) Beethoveen's music did have more complexity than Mozart's music 2) Music is a creative process and while it is mathematical in one respect there are plenty of instances where arbitrary descisions are necessary. For example, should this cadence end at double time or should the tempo increase or should we use this harmony instead, etc etc etc, depending on what you want to convey from the piece you're creating, revisions can be made as often as the musician feels is needed until his product is at what he wants it to be. But there is no such thing as an objective measurement over what kind of innate talent Beethoveen or Mozart had, otherwise perhaps you can explain to me how one can objectively say a C major harmony at cadence number 4, bar number 3, be better than an E minor harmony? (There is no difference it's just arbitrary so long as those harmonies conform to music theor). Each had their own psyches and desire for perfection at play here, and fullfilling their own happiness in creating a musical piece they like plays a huge part.

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I'm a musician/songwriter...

To clarify, I wasn't making a qualitative judgment of one over the other, no way!! Not those two, for sure!

I was trying to point out the different means to the end(s), both beautiful and brilliant.

On the other hand, surely there are some things past opinion...

For instance, one of my teachers was American composer Frederick Koch. Fred wrote a lot of stuff, and it's very good. Fred's the real deal. But, and I know Fred would agree, he ain't no Beethoven or Mozart.

Tricky business, indeed!

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Shayne and Michael Dickey,

May I ask why, if you think that anyone can become world-class great, you haven't become great at anything? If you're upset that people who believe in innate differences such as talent are just looking for a way to excuse laziness, what excuse do you prefer to use to explain why you haven't achieved greatness? Why have talented individuals become world-class creators and achievers by the time they were half your age, yet you're still just non-great-Shayne and non-great-Michael? Are you saying that you chose to be lazy, that you knowingly chose not to fully develop yourselves even though you're convinced that people with ordinary capacities can achieve genius-level greatness?

Not knowing Michael, I would not presume that he wasn't great. I don't know what he does outside of this forum. Why would you? And even if he wasn't great, I wouldn't presume to know his personal history, which would be the only way to understand what a given individual ended up achieving and why. So why would you? I'd guess it's the same kind of habits of presumption that make you assume that talent has such a great role.

Shayne

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Victor I'm not going to get into who said what here. Plenty of people here are alleging that talent is inborn. I'm answering your question by pointing out that there is no evidence for that claim, and that there is tons of evidence that what people refer to by "talent" is really just hard work. In the face of no evidence for one conclusion and piles of it for the other, I have to wonder at the motives for someone who is "merely asking questions."

I like your sarcasm about having "truth" in my "back pocket". Poetic.

You suggest that I claim that nature has no role to play. Well I already said otherwise when I talked about capacities. So you're missing my point. You ask about "aptitude". It probably means for me the same thing it means for you. The difference is, I regard a person's aptitude is plastic, as open to change by them. If they had no aptitude for math, they could have if they applied themselves. You regard aptitude as fixed.

There is a sense here in which you just can't speak for someone else. If someone claims to have really tried and just can't do it because they don't have the inborn capacity, well what can you say. I can't prove they didn't try even if I wanted to. I can recognize that it's an easy excuse, and tell the person that it may be a self-fulfilling prophecy. But it's their business not mine. If you guys want to think that you have these inborn limits, OK. I think it's a bad idea to think of yourself that way, but it's your life.

What I do know is that all my experience with my own mind and body points to adaptability. WIth regard to the mind, this is particularly so after studying Objectivism; places I was "stuck" before for various errors I was making opened up to me. E.g., if you believe that God reveals important truths, it's easy to claim that some guy came up with a particular mathematical result from being "inspired" rather than doing the necessary work to figure out how you could do it with your own mind.

I have a few anecdotes I'll share. Once I started to realize the right method of inducing truth in mathematics, I went back to some areas that were always a mystery to me as to how the guy came up with it. Information theory was one area that I validated for myself. What I figured was that what they were showing us was actually backwards from the way the original guy must have discovered it. They gave us the results first and showed us how to apply them; in truth it was the applications that Shannon used, inductively, to get the results. Another was the Pythagorean theorem. I'd never seen a proof of this, they always just gave us the formula (better teachers will prove it but not all). One weekend I sat down for a few hours and figured out the geometrical method of proving this. It started with recognizing that the squares can be related to areas, and then working from that mostly experimentally to figure out if there's a convenient geometrical representation of the equation. Things like this made me realize that "genius" is probably largely a measure of effort unencumbered by bad premises, and in any case, it's better to regard the universe as knowable and open to you than not.

Shayne

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