'Beauty is truth, truth beauty,—that is allThese lines came to mind after the mathematical equation eiπ + 1 = 0, which came to mind as I was reading the BBC News article "Can 10,000 hours of practice make you an expert?"
Ye know on earth, and all ye need to know.'
In "Can 10,000 hours of practice make you an expert?", Ben Carter presents the opposing sides in the psychology debate about whether an exceptional performance in a sport, in playing music or in other fields requires innate talent or whether 10,000 hours of practice over a ten year period is enough (2014). Some experts think that the right sort of practice is sufficient to guarantee excellence, but others think that at least some fields also require talent to begin with.
And that wonderful eπi + 1 = 0 in my title? It's Euler's identity. I thought of it when I read an example near the end of Carter's article, where one of the arguing experts, Malcolm Gladwell, explains that someone who think mathematical equations and theorems are beautiful will be highly self-motivated to spend a lot of time working on mathematics at home, and that practice will make them improve far more quickly than students who do not find mathematics beautiful. I was one of those people who loved mathematics in high school, and one of the highlights of my school career was working through the proof of Euler's amazing and truly beautiful equation, along with many other mathematical truths, which unlike almost everything else we known, is also 100% certain. This was the link with the Keats poem, which I also studied and enjoyed in high school. Even though his topic is an ancient Greek urn, I'm not sure that Keats had anything like a2 + b2 = c2 in mind as he was writing. Then again, maybe he did - perhaps this is an idea worth exploring a bit more. Although the AEP program doesn't teach mathematics, an important component, and one tested in such tests as TEOFL, is critical thinking, for which mathematics is excellent practice, and in Quest, Hartmann regularly has exercises on critical thinking skills.
However, what I really liked about Carter's article is that it emphasis the importance of practice, especially of deliberate practice. If you want to excel at something, you need to practice. Tiger Woods practices golf constantly. Great pianists practice daily. And this practice has to be the right sort: deliberate and challenging. Similarly, excellence in reading and writing the academic version of English, or any other version of English, or any other language, requires regular practice that challenges you to do a little better than you did last week. And that is very relevant to our class: if the reading and writing practice we do is easy, if it doesn't challenge you, it's probably not helping you very much. I hope this class helps you a lot. And that the material is not only challenging, but also interests you.
And I'm always happy to welcome disagreement. Academics argue all the time: it's how progress is made. Without discussion of opposing ideas, without questioning and testing old ways of thinking, errors cannot be corrected and knowledge cannot be discovered, although this is also one area where mathematics is spectacularly different to most other fields of knowledge that we might study. In physics, Galileo proved Aristotle and his followers wrong about almost almost everything, and in turn Newton, proved moved us forward beyond Galileo, only to be replaced in his turn by Einstein. In biology, our knowledge is even less certain than in physics, whilst the social sciences such as history, economics, literature, political science and my own area, philosophy, are are even more full of argument. But at least philosophy also includes as a major branch logic, which is the fairly solid foundation of mathematics. I think that like the ancient Greeks and others, it was the absolute, perfect certainty of mathematics that attracted me to it: I also loved physics, and other sciences, but in mathematics, we could prove things and the proofs are true forever, and beautiful.
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Reference
Keats, J. (1919). Ode on a Grecian urn. In A. Quiller-Couch (ed.). The Oxford Book of English Verse: 1250 - 1900. Oxford: Oxford University Press. Retrieved from http://www.bartleby.com/101/625.html (Originally published 1819).
I think the innate talent is very helpful. It may help to reach our goals easier. However, I believe that we can become successful if we try hard and don't give up. Many people succeeded when they had tried very hard for a long time such as Thomas Edison.
ReplyDeleteI'm a person who don't have any talent. When I start learning figure skating, my coach told me that if I want to become a professtional figure skater, I need to have an innate talent. When I heard that, I felt sad. However, deeply I still believe that I can become a successful figure skater if I pratice hard. Now, I look back and see how far I have come in this sport for very short time, I'm really proud of myself. I will definitely continue practicing skating hard with hope and patience.
I really hate when I read article like you need to have the innate talent. It discourages me.
In,
DeleteIn his article, Carter's main example of someone who wants to excel at golfing seems to me to support your idea: the golfer is about half way through the 10,000 hours of deliberate practice he's aiming at, and his golfing is much better. It will be interesting to see how he is after he's put in a lot more practice. But even he's not another Tiger Woods, his golfing will be much better, and he was sure he had no innate talent for golf.
I'm sort of in the middle. I think some natural ability is necessary, but most human beings have that. Stick with the ice skating you are passionate about: whatever the end result, you are already achieving something of value and worth to yourself.
Dear...Peter
ReplyDeleteSince, I first met you, I already knew you were born to be a teacher!
I was amazed how much you are passionate about mathematics and sciences, and i admired the idea about sufficiency practice can guarantee excellence that what I've been trying to do for improving my English.
However, there are some of your ideas that I'm not sure, I've learned from my experiences and my mistakes so i'd say sometimes it's better to never ask "why", something it's better to not be translated.
In Psychology, we're not expected to ask "why" when we are talking with people.
Just let it be beautiful, just the way it is (but i totally understand your idea and what are you talking about.! I'd just like to share my idea)
Thank you Yao.
DeleteI agree with your idea that we don't always want to ask "why?" It's probably not the best strategy for a chat with a friend, or a mother. And if you are doing research in pyschology, or working with someone seeking help, you probably don't want to follow my teaching habits.
But in an academic context, we are expected to support our opinions, and explain our ideas. And to question ideas - both our own and those of others. (Is my sentence without a main verb OK?)
And blogging is a good way to test out ideas in a more tentative way, which is probably one reason that many classes at western universities now encourage, or require, students to blog on the ideas in class. For example, Michael Sandel's class in moral philosophy at Harvard, a very famous class, also has an active blog for students to compare ideas, to argue for and against positions and to refine their understanding of the ideas covered in his lectures. If you would like some more challenging listening practice, Sandel's Harvard lectures are online at http://www.youtube.com/playlist?list=PL30C13C91CFFEFEA6&feature=plcp
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