Anyway, with all that said, here are a bunch of thoughts on various topics related to the concept of genius.
Creativity and genius
What other people see as creativity, I believe, can be explained in other ways. I think that this creativity is a product of an understanding of the subject and an ability to relate and extend other ideas. Perhaps a new song can be created by understanding ideas such as the feelings that different notes and tempos and beats evoke, and the types of notes that sound good when hit together, and the patterns of notes that are common or rare. And maybe a new story can be created by understanding things that bring out emotion, extending real world concepts to something that may not exist, and taking your understanding of personalities, relating the imaginary concepts to real world concepts, and writing the events that would happen. As for a new math theory, it would most likely come from an understanding of base ideas, and then an extension of those base ideas, or an understanding of ideas that go beyond the base, and an ability to explain that understanding. Now, this understanding might not be something applied consciously. For the songs that I've made, I didn't specifically think about common and uncommon note patterns, but I think they did come into play, just not consciously.
Well then you might say that most people can't form that level of understanding of concepts and extend them and create new things, so call it creativity or call it understanding, it doesn't make a difference. But I don't know. People seem to think that creative thoughts just come out of nowhere, but I'm not sure that's the case. I think it's possible to become creative in a selective area through understanding.
More on understanding and extending concepts
What does it take to actually "understand" a concept? I believe that true understanding of a concept naturally allows for one to take the concept further. I think it goes beyond knowledge of the concept and an ability to apply it to an ability to answer the why's. The "Why does it work?" or "Why is it true?"
For example, consider multiplying numbers by hand. I mean, everyone understands that. First you have multiplication of 2 single digit numbers, and you can calculate that just by adding a number multiple times, or you probably just have it memorized from studying a multiplication table. Then if you multiply a 2 digit number by a 1 digit number, you can multiply the one's digit of the first by the second, and carry over and multiply the ten's digit by the second number. Well what if the first number has a lot of digits? That's obvious, right? You just do the same thing over and over. And then when the second number has 2 digits, you can multiply the one's digit in the second number by the first number, and then multiply the ten's digit by the first and put a 0 at the end and add. And what if the second number has a lot of digits? Well that's easy too, you just do the same thing.
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| In case you forgot how |
I'm sure most people know that. They would say they understand how to multiply two numbers together by hand. But can you say why you do it that way? Why does it work? Say you want to do 1234*8. It's the same as doing (1000 + 200 + 30 + 4)*8, which, due to the distributive property of multiplication, is the same as (1000*8)+(200*8)+(30*8)+(4*8). And then for something like 123*234 it's the same thing, just 123*(200+30+4). But you know what that means? It's not some concept that only applies to multiplying numbers by hand. It applies to anything that is distributive. So if you wanted to multiply two matrices, because matrix multiplication is distributive, you could apply the same property. Something like this:
Just like if you were multiplying, say, binary numbers, you could do it the same way. Or if you were doing some operation that wasn't multiplication but was also distributive, you could do it the same way.
When I attempt to understand a concept, I attempt to understand it at this level. When you are able to do that, the correct alternate applications and the extensions become much easier to see. When you don't understand the fundamentals behind a concept, you run the risk of trying to apply the concept to something that seems similar, but may work in a fundamentally different manner.
Sounding intelligent
Let's say someone gives you a table with the height and gender for some people, and then asks you what gender you think a new person is that wasn't in the table, based on their height. You could say, "I used a machine learning algorithm called the nearest neighbor algorithm, trained the system on the data provided, and then input the new instance into the system for classification," or you could say, "I found the person in the table that had the closest height to the new person and guessed that the new person was the same gender as that person." It's the same thing. I've never thought of the long and complicated explanations as important to solving problems or understanding concepts. In fact, sometimes I think that people focus too much on it, to the point where it makes it harder to truly understand concepts at a fundamental level. Really, the only area I think it even matters is in, well... communicating your ideas.
It's not that it's a bad thing. The terminology gives you a way to group things and state concisely concepts that could be rather complicated to state otherwise. It's just that it is easy to end up focusing more on having knowledge of these ideas and the related terminology rather than focusing on understanding the ideas.
Games that improve your mind
Ever heard of games such as Big Brain Academy or Brain Age? Or maybe sites like luminosity? All of these are trying to sell you on the idea that you can become smarter simply by playing some games. Man if that were the case, I'd be like some kind of super genius by now.
Small rant on luminosity: I only did the free stuff, but I have to question how they come up with the scoring on the games. For example, on the word bubbles game, they don't take into account how difficult the letters you start with are. You could get "zin" to start or you could get "res". And then, if there are no 4 letter words starting with the letters you're given, then the game fills up the 4 letter column and you can't get any points for 4 letter words, which means you lose 150 points off of the max possible score. If you get a really bad starting set, the best possible score you could get could be even worse than that. Basically, a 500 point performance with "xyl" or "vul" would be way better than a 500 point performance with, say, "sta". And I'm not sure about the areas they claim will be improved by playing the games. The lost in migration game says it will help you avoid distraction and increase work productivity, but this sounds to me like a case of trying to relate similar sounding concepts that may be fundamentally different. It may be true that you have to focus and concentrate to play the game, but it may also be the case that an inability to focus on work may be due to a lack of desire to do the work, rather than a poor ability to focus. In this case, even if you get better at focusing from the game, you probably wouldn't see the benefits elsewhere.
The next thing is, if games like these are beneficial to your brain, wouldn't most games in general improve your brain? They all require focus, most of them require knowledge of certain things and an application of that knowledge, and they require certain technical skills and such. Some of the skills you need in a first person shooter are a constant awareness of your surroundings, knowledge of your weapons and their strengths and weaknesses, knowledge of your enemy's strengths and weaknesses, knowledge of efficient methods of getting from place to place, a plan of attack, and so on. To play any rhythm game well, you need constant focus, muscle memory, quick processing of and reaction to visual stimuli, etc. To play any fighting game well, you need to have your combos memorized, know your moves and their strengths and weaknesses, know your opponent's moves, learn how to counter strategies, learn your opponent's patterns of behavior and take advantage of them, etc. I fully believe that, if it's possible to improve your brain, then it's possible to do so simply by learning the skills to be successful in new video games. Now, I don't mean to say that that's the only way; you could probably accomplish the same thing by practicing to master any skill that requires you to be strong in an area where you were previously weak. It's just that I think that, in the wide variety of games that exist, there is such a variety in the skills they require that you could always find something new to learn in a new game or a new game genre, and in attempting to master something different and something new, perhaps you could become "smarter," in some sense.
The differences
You could call it a search to find the differences. If I am actually smarter than other people, then what is different about me that makes me able to understand more things or memorize things more efficiently? If someone is smarter than me, then what is different about them that makes them so?
This is certainly not something I can answer, especially not from my experiences. Perhaps it is just that the brains of some people were created in such a way that they work more efficiently than others. Could the difference be in memory? Is it an ability to understand concepts? To inherently understand the fundamental ideas behind concepts? If the major differences are known, then it's much easier to give advice to others on how they can improve. But I am definitely lacking in general knowledge of how others learn new things, and any answer I give could be a difference that is a result of personality, rather than intelligence...
Differences due to my personality
The biggest question mark I have is in the focus on a fundamental understanding of concepts. This is because, on one hand, it could be that, when you are more intelligent, you are more easily able understand the fundamental concepts behind ideas. On the other hand, it may just be that I focus on fundamentals because of my personality, and I just happen to be intelligent too, so I am able to take this focus and generate an amazing amount of success with it, not because it's the best approach, but because I am a very capable person, and it's the approach I chose. If I had to take a blind guess, I'd go with the latter. I could tell you all the benefits of this approach, just as most anyone can defend the views they strongly belief. However, I think that the amount of focus I put on learning things at a fundamental level is due to my personality. Perhaps an intelligent person will have some sense of the fundamental ideas behind higher concepts anyway, despite not putting the same amount of focus on them. But I think that plenty of very intelligent people would be more interested in sounding intelligent, creating more complex theories, developing something new and impressive rather than focusing on something simple and basic, and so on.
Ability driven by personality
I would hypothesize that intelligence is a measure of the brain's ability to function, and someone with high intelligence would in general solve problems, draw connections, understand concepts, and so on, more easily. Perhaps a strong memory is also a part of being intelligent, but I don't know. That brings back questions of "Can you be intelligent without a good memory?" and "Can you have a good memory without being particularly intelligent?" If I were forced to answer, I would probably say "Yes" and "Yes," under the reasoning that intelligence is a measure of problem solving and comprehension, but I could see either side.
Now, with this definition of intelligence, I would say that the way intelligence manifests itself is driven by personality and personal preferences. There are the obvious ways; for example, under this mindset, a musical genius is a genius who happens to enjoy creating music. With a higher level of intelligence, one would likely succeed in most pursuits, but these pursuits do not have to be the same. Ignoring any left brain and right brain theories, and any theories of multiple intelligence, an intelligent person will in general find a way to be successful in the areas they want to succeed in. But, even this level of success could be affected by personality, depending on the area. If your goal is to develop a strong understanding of general mathematics, then the effect of personality is less obvious (but may be very important still!). If your goal is to become a famous mathematician, then personality will play a much clearer role.
I would say the less obvious effects are in the ways one organizes their thoughts and their knowledge, with the easiest example I can come up with being that focus on basic ideas vs complex theories. It seems natural to expect that someone who doesn't want to make a mistake, someone who wants to have a guarantee that what they say is correct, someone who doesn't want to challenge the norm without this guarantee, will focus on basics. Focus on concepts from the ground up with a strong awareness of the chain of logic traveling through each step. Then, someone of the opposite personality might have a general idea of the basics, but focus on furthering ever more complex theories. If it is true that a difference like this exists due to personality differences, then I find it hard to believe that there wouldn't be more of these kinds of differences. Finally, if it is true that personality plays a significant role in the manifestation of intelligence, then the concept of what it means to be intelligent, and the expected behaviors of one who is intelligent, would likely vary with cultures. Identification of the habits and characteristics of geniuses from the observation of people from similar backgrounds or cultures might then mistakenly relate habits with intelligence when they are actually due to personality or a combination of personality and intelligence.
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