DouglasReay/GeniusKnol

Archived from [the knol], now that knols are being discontinued.

Genius

Educational perspectives on fostering intellectual accomplishment
Genius requires intelligence, learning and originality. Genius can only be fostered by fostering these three qualities.
Contents

    * What is genius?
    * Intelligence
    * Learning
    * Originality
    * Fostering Genius
    * Foster Intelligence.
    * Foster Learning.
    * Foster Originality

What is genius?

There are many words used to describe rare and superlative intellectual abilities and the people who possess them: prodigies, savants, polymaths, sages, lightning calculators, gifted, talented and genius. Some of these words are better defined than others. Where there is no commonly accepted definition, I will try to make clear how I intend to use the word. To start with, by way of example, let us consider the abilities of a sample of those almost universally accepted as being exceptional.

    * Linus Pauling - scientist, writer, political activist
    * John Stuart Mill - prodigy, polyglot, philosopher, economist and politician
    * John von Neumann - mathematician, scientist, economist
    * Johann Gauss - mathematician
    * Johann von Goethe - polymath, writer, theologian, scientist
    * William Whewell - polymath, scientist, theologian, historian, knowall
    * Isaac Newton - mathematician, scientist, theologian
    * Leonardo da Vinci - polymath, mathematician, scientist, artist, writer

Intelligence

All of these are exceptionally intelligent men; but exceptional intelligence does not, by itself, guarantee exceptional intellectual accomplishment, it is only a pre-requisite. These men had something more.

An initial glance at this list suggests that being a dead rich white European Christian male called John contributes highly towards people thinking of you as a genius; however this is a triply biased sample - firstly by the opportunities afforded different segments of the population in historic times, secondly by the currently prevailing views on what discoveries or other intellectual accomplishments are considered to be important, and thirdly by the views of the historians who chose what to record and pass on. For instance, the works of Hypatia, a pagan polymath who lived and taught in Egypt, have largely not been passed on - we know her mainly through what others wrote of her.

So what other qualities of mind or personality do they have in common?

There is no one subject they all excelled at (though many had an interest in maths and were good written communicators). Some were noted for their early educational achievements, but not all were considered prodigies when young. A few could perform amazing feats of memory or mental arithmetic. Some were persuasive social figures and some were shy eccentrics. Some were pushed by parents and others had to battle for learning against the odds. Some worked and excelled in diverse areas while others are well known only for their work within a single subject. A few, such as Whewell, had a reputation of knowing everything about everything, but most had interests outside their primary subject, even if they didn't have much time to spend achieving in those fields.

There are two qualities they do have in common, besides raw intelligence.

Learning

Without exception they all spent an immense amount of time using the skills related to their area of interest. [1] From studies of musical geniuses such as Mozart, Daniel Levitin has estimated that mastery of something takes a minimum 10,000 hours of effective practice [2]. Becoming a genius requires an intense internal motivation to spend the near obsessive hours of thinking and learning that are needed to master a subject; generally that motivation is passion (a compelling fascination for the subject) though it can be anything from religious to perfectionism. Ellen Winner calls this motivation the "rage to master" [3].

Originality

Originality requires both the honest creativity to look again at what is really there, from a novel point of view; and the dogged persistence to follow through on the insight, even when that means going against the crowd. There may be a certain amount of luck in finding an insight that will lead on to productive achievement. However those who study and build on the works of others (especially stuff that is new or from previously unrelated fields) maximise their chances. Some geniuses have one large new insight or technique, which they apply again and again. Others have a knack of finding new angles, and consider so many that their private journals are full of unpublished insights they never had time to follow up.

Genius, then, I shall define as being game-changing intellectual endeavour achieved by applying sustained effort to original insights afforded by superlative mastery of one or more subjects gained through outstanding intelligence and endless learning.

Fostering Genius

Genius cannot be created to order. The pre-requisite of intelligence has a large hereditary component [4]. And qualities of character are scarcely deterministic. However, if a particular child has the potential and inclination to be a genius, what can be done to help?

Many books and articles have been written on this subject. Two theorists are of note, because they put their theories into practice: László Polgár [5] and Boris Sidis [6]. Sidis raised his son, William, to be a mathematical prodigy. William Sidis, however, became a recluse early in life, and published most of his works anonymously. Polgár did not set out with a specific area in mind, but when his daughters showed an early interest in chess, applied his theories and ended up with three daughters all of Grandmaster level.

Here are the three things they advocate:

Foster Intelligence.

Actually there is little that can be done to increase the IQ of a child, beyond making sure they learn how to think effectively (eg metacognition) and exposing them to clarity of thought and precision of language [7]. However there is plenty to do to make sure their natural IQ is not decreased. Make sure the child has good nutrition, gets reasonable sleep and is not put under too much stress. Richard Feynman relates the following tale about his father [8]:

When I was still pretty young—I don't know how old exactly—I had a ball in a wagon I was pulling, and I noticed something, so I ran up to my father to say that "When I pull the wagon, the ball runs to the back, and when I am running with the wagon and stop, the ball runs to the front. Why?

How would you answer?

He said, "That, nobody knows." He said, "It's very general, though, it happens all the time to anything; anything that is moving tends to keep moving; anything standing still tries to maintain that condition. If you look close you will see the ball does not run to the back of the wagon where you start from standing still. It moves forward a bit too, but not as fast as the wagon. The back of the wagon catches up with the ball, which has trouble getting started moving. It's called inertia, that principle." I did run back to check, and sure enough, the ball didn't go backwards. He put the difference between what we know and what we call it very distinctly.

Regarding this business about names and words, I would tell you another story. 'We used to go up to the Catskill Mountains for vacations. In New York, you go the Catskill Mountains for vacations. The poor husbands had to go to work during the week, but they would come rushing out for weekends and stay with their families. On the weekends, my father would take me for walks in the woods. He often took me for walks, and we learned all about nature, and so an, in the process. But the other children, friends of mine also wanted to go, and tried to get my father to take them. He didn't want to, because he said I was more advanced. I'm not trying to tell you how to teach, because what my father was doing was with a class of just one student; if he had a class of more than one, he was incapable of doing it.

So we went alone for our walk in the woods. But mothers were very powerful in those day's as they are now, and they convinced the other fathers that they had to take their own sons out for walks in the woods. So all fathers took all sons out for walks in the woods one Sunday afternoon. The next day, Monday, we were playing in the fields and this boy said to me, "See that bird standing on the stump there? What's the name of it?"

I said, "I haven't got the slightest idea."

He said, 'It’s a brown-throated thrush. Your father doesn't teach you much about science."

I smiled to myself, because my father had already taught me that [the name] doesn't tell me anything about the bird. He taught me "See that bird? It's a brown-throated thrush, but in Germany it's called a halsenflugel, and in Chinese they call it a chung ling and even if you know all those names for it, you still know nothing about the bird—you only know something about people; what they call that bird. Now that thrush sings, and teaches its young to fly, and flies so many miles away during the summer across the country, and nobody knows how it finds its way," and so forth. There is a difference between the name of the thing and what goes on.

Foster Learning.

Provide a stimulating environment and opportunities to try a variety of intellectual areas. Encourage questioning and a joy in learning and practicing, by praise and by example. Make knowledge accessible so they have stuff to learn, whether through books, tuition, peers or activities. Expose the child to inspirational events and great people - let them aspire high. The following tale is recounted of how the Indian mathematician, Srinivasa Ramanujan, became inspired [9]:

While at school he came across a book entitled A Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr. The title of the book does not reflect its contents. It was a compilation of about 5000 equations in algebra, calculus, trigonometry and analytical geometry with abridged demonstrations of the propositions. Carr had compressed a huge mass of mathematics that was known in the late nineteenth century within two volumes. Ramanujan had the first one. It was certainly not a classic. But it had its positive features. According to Kanigel, “one strength of Carr’s book was a movement, a flow to the formulas seemingly laid down one after another in artless profusion that gave the book a sly seductive logic of its own.” This book had a great influence on Ramanujan’s career. However, the book itself was not very great. Thus Hardy wrote about the book: “He (Carr) is now completely forgotten, even in his college, except in so far as Ramanujan kept his name alive”. He further continued, “The book is not in any sense a great one, but Ramanujan made it famous and there is no doubt it influenced him (Ramanujan) profoundly”. We do not know how exactly Carr’s book influenced Ramanujan but it certainly gave him a direction. `It had ignited a burst of fiercely single-minded intellectual activity’. Carr did not provide elaborate demonstration or step by step proofs. He simply gave some hints to proceed in the right way. Ramanujan took it upon himself to solve all the problems in Carr’s Synopsis. And as E. H. Neville, an English mathematician, wrote : “In proving one formula, as he worked through Carr’s synopsis, he discovered many others, and he began the practice of compiling a notebook.” Between 1903 and 1914 he had three notebooks.

Foster Originality

Originality is the hardest of the three. If a child finds an area that they have a rage to master, get out of their way and keep others out of their way - find ways to let them spend the time learning that they want to. This is a balancing act between supportively exposing them to alternative viewpoints that may spark creativity and giving them the confidence they will need to persist in follow their own insights by letting them tackle challenging problems themselves. John Stuart Mill described his father's teaching methods thus [10]:

Such a mode of instruction was excellently calculated to form a thinker; but it required to be worked by a thinker, as close and vigorous as my father. The path was a thorny one, even to him, and I am sure it was so to me, notwithstanding the strong interest I took in the subject. He was often, and much beyond reason, provoked by my failures in cases where success could not have been expected; but in the main his method was right, and it succeeded. I do not believe that any scientific teaching ever was more thorough, or better fitted for training the faculties, than the mode in which logic and political economy were taught to me by my father. Striving, even in an exaggerated degree, to call forth the activity of my faculties, by making me find out everything for myself, he gave his explanations not before, but after, I had felt the full force of the difficulties; and not only gave me an accurate knowledge of these two great subjects, as far as they were then understood, but made me a thinker on both. I thought for myself almost from the first, and occasionally thought differently from him, though for a long time only on minor points, and making his opinion the ultimate standard. At a later period I even occasionally convinced him, and altered his opinion on some points of detail: which I state to his honour, not my own. It at once exemplifies his perfect candour, and the real worth of his method of teaching.

A pattern present in the lives of many great intellectual achievers is having a combination of periods of isolation (childhood illness, absent or dead parents, social ostracism) and periods of interaction (correspondence or study at a great seat of learning where they were exposed to or mentored by brilliant achievers from previous generations).

Not everyone has the potential to be a genius. But for those that do, there are things that can be done to improve the chances of that potential flowering: inspiration, challenge, support [11]; but above all, the time to learn [12].

References

   1. [Power law of practice]
   2. [Daniel Levitin]
   3. [Ellen Winner]
   4. [twin adoption studies]
   5. [László Polgár]
   6. [Boris Sidis]
   7. [Dual n-back]
   8. [Richard Feynman]
   9. [Srinivasa Ramanujan]
  10. [John Stuart Mill]
  11. [Advice from MENSA on how to raise gifted children to be happy]
  12. ["Outliers" by Malcolm Gladwell]

Feedback

[A Stroke of Genius: Striving for Greatness in All You Do], by R. W. Hamming
[Advice on gifted education], by Terry Tao

[more on William Whewell]

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