The characteristic of the hour is that the commonplace mind, knowing itself to be commonplace, has the assurance to proclaim the rights of the commonplace and impose them wherever it will. - Jose Ortega y Gasset
Another article from "Thinks!", the Mensa Magazine, back around the middle of the 1980s. Ruth Lawrence was a mathematical prodigy, and this article argued against the status quo, the "Daily Mail" readers who said she should go through school at a normal pace, and lead a normal life. Interestingly, when I was teaching at Bideford Comprehensive, there were a small group of teachers there who thought that not enough was done in comprehensives to encourage the brightest pupils - they said there was a lot done for remedial learners, but brighter kids often got bored and lost interest because they were not stretched enough. This point of view had some support among other teachers.
In Praise of Excellence
A Personal Comment
There can be few people who have not heard of Ruth Lawrence. I have read the newspaper reports of her success in mathematics, and listened to the comments of people. The type of remarks I have heard are often strongly held, but lacking in critical thought. Nevertheless, I
believe that they are dangerous, because they are widespread, pervasive, and encourage the idea that such genius is, somehow, a perversion of the natural order.
The main argument made is of the following form: Ruth Lawrence has missed out on a normal childhood, and, as a result, she is a misfit. Linked with this is the notion that this will bring a psychological trauma in later life, because her intellect has advanced at the expense of her emotions. Despite denials, I cannot help feeling that the proponents of this view would like this to happen, and so be vindicated.
But this argument is badly flawed. It forgets that childhood, as a stage of life that all children pass through, is comparatively modern. You require a good deal of prosperity before you can afford to have such a period in life, which is why mass education only began after the industrial revolution. A feudal or slave economy has no place for idle hands among the lower orders.
Moreover, if we compare the curriculum of today's schools with those of the past, it might easily be argued that the intellect of today's child is advanced at the expense of its emotion. For so much more is packed into each subject than was present even fifty years ago. No one argues that this is detrimental. And why should we assume that this process has ceased in our time? Why should we be so arrogant as to assume that our education can provide a yardstick for all time, even the future? The great diversity in human culture throughout history and spread across the globe, with the multitude of different roles given to children, should make us very cautious of generalisations that are only too clearly linked to our own life and times.
The argument that Ruth Lawrence is likely to suffer sane psychological trauma at a later stage in her life, is based upon the fact that she deviates from the norm. In statistical terms, this is true; it is correct to say that she deviates from the norm, because she is above average. But it is not legitimate to assume from this that she is abnormal in a psychological sense. It is this false confusion of meaning which gives the argument its force, with the word "normal" being given emotive connotations for which there is no evidence.
Against Ruth's unique upbringing, the argument is that she would be happier, better adjusted to life, if she had gone through the general educational mill. In other words, she must be brought down to the level of other children, and forced to proceed at their pace, however frustrating that might be for her, and however much she might blame herself later for allowing others to squander so much precious time and talent. Would that not give rise to the possibility of psychological hurt? Has such a possibility ever been considered? The trouble with education today is a misplaced egalitarianism that prefers to reward failure than to praise excellence. Special help is given to those who find it difficult to learn, and they enjoy going at their own pace in classes of small size especially suited to that purpose. This is most praiseworthy, and I am in agreement with such a practice. But what of gifted children, of the calibre of Ruth? No such advantages are given to them. Instead, they are held back in much larger classes and waste time because the class proceeds more slowly, closer to the pace of the least clever member of that class than the brightest. Where is the praise of excellence here? It may be a good education for the average children, but it is likely to turn genius into mediocrity.
Perhaps those who would prefer such an education as this for Ruth, should listen to the prophetic words of Tocqueville (in 'Democracy in America"), and try to understand why her choice is legitimate:
"From hatred of privilege and from the embarrassment of choosing, all men are at last forced, whatever may be their standard, to pass the same ordeal; all are indiscriminately subjected to a multitude of petty preliminary exercises, in which their youth is wasted and their imagination quenched, so that they despair of ever fully attaining what is held out to them; and when at length they are in a condition to perform any extraordinary acts, the taste for such things has forsaken them."
Postscript:
Wikipedia notes that:
Ruth Elke Lawrence-Naimark (born 2 August 1971) is an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. Outside academia, she is best known for being a child prodigy in mathematics. At Oxford, her father continued to be actively involved in her education, accompanying her to all lectures and tutorials. Ruth completed her bachelor's degree in two years, instead of the normal three, and graduated in 1985 at the age of 13 with a starred first and special commendation. Attracting considerable press interest, she became the youngest British person to gain a first-class degree, and the youngest to graduate from the University of Oxford in modern times. Ruth followed her first degree with a second degree in physics in 1986 and a D.Phil in mathematics at Oxford in June 1989, at the age of 17. Her thesis title was Homology representations of braid groups and her thesis adviser was Sir Michael Atiyah. In 1998, Ruth married the Israeli mathematician Ari Naimark and changed her name to Ruth Lawrence-Naimark.[citation needed] The couple have four children, Yehuda Bezalel (born 2000), Esther Miriam (born 2001), Batsheva Simcha (born 2003) and Yehoshua Aharon (born 2006).
She was estranged from her father, but the problem there seems to be more to do with the way he was trying to be successful vicariously through her own achievements, rather than any psychological problems of her own. Contrary to the prophets of doom, she does not seem at all maladjusted and is happily married, and enjoys having children. Her father now helps with her proofreading.
On her own first child, she said: "There will not be any forcing, no attempt to try and push Yehuda faster than he wants to go. I, though, was always eager to learn more. I want Yehuda to develop in a natural way," she adds. "My husband and I will not do exactly as everybody else does when they bring up a child. But I don't want Yehuda to be 'different'. I want my child to be able to develop in a natural way. I suppose I might have liked my childhood to be different in some ways, but I do not want to judge my parents. And I do not envy them. I was not in their shoes. I very much appreciate the effort my father put in. I am enormously grateful for what he did for me. I can see now that being a parent is very difficult."
Currently, Ruth is still teaching courses on combinatorial knot theory, Lie groups, Khovanov theory, discrete mathematics and various courses on mathematics for physicists and engineers, at the Hebrew University in Jerusalem. Interestingly, despite her parents being very secular Jews, she has embraced her Jewish culture and heritage very strongly. A glance at her sight shows she is still producing solid mathematical work ; there's also a photo of her, with her name beneath in Hebrew. The area of mathematics she is working on is complex, and she suspects any applications in the real world will take 100 years to be manifest:
In 1997, the Independent commented on her and her work:
Knot theory is the broad term for the rarefied branch of maths Ruth is now studying and teaching at the University of Michigan in Ann Arbor, near Detroit. Broadly speaking, it is about, well, knots - their geometry and behaviour, the more complicated they get. But try to narrow it down and you will find yourself in a dense thicket of phrases like "partition functions of a topological quantum field theory".
Surely that's about as abstruse, and unapplicable to anything in real life, as they come? She systematically squashes the suggestion, citing the theory, developed at the beginning of this century, of infinite-dimensional complex spaces. Abstruse? Then, certainly. "But it led in the 1920s to the possibility of quantum theory; and that made it possible to understand the idea of energy levels of quantum objects. Which led, in time to the laser. "And even when lasers were invented, people were saying, 'What use is that?' Now, of course, it's everywhere, in compact disc players, laser printers... That's what maths is like: it has always shown itself to be useful in the end."
Another article from "Thinks!", the Mensa Magazine, back around the middle of the 1980s. Ruth Lawrence was a mathematical prodigy, and this article argued against the status quo, the "Daily Mail" readers who said she should go through school at a normal pace, and lead a normal life. Interestingly, when I was teaching at Bideford Comprehensive, there were a small group of teachers there who thought that not enough was done in comprehensives to encourage the brightest pupils - they said there was a lot done for remedial learners, but brighter kids often got bored and lost interest because they were not stretched enough. This point of view had some support among other teachers.
In Praise of Excellence
A Personal Comment
There can be few people who have not heard of Ruth Lawrence. I have read the newspaper reports of her success in mathematics, and listened to the comments of people. The type of remarks I have heard are often strongly held, but lacking in critical thought. Nevertheless, I
believe that they are dangerous, because they are widespread, pervasive, and encourage the idea that such genius is, somehow, a perversion of the natural order.
The main argument made is of the following form: Ruth Lawrence has missed out on a normal childhood, and, as a result, she is a misfit. Linked with this is the notion that this will bring a psychological trauma in later life, because her intellect has advanced at the expense of her emotions. Despite denials, I cannot help feeling that the proponents of this view would like this to happen, and so be vindicated.
But this argument is badly flawed. It forgets that childhood, as a stage of life that all children pass through, is comparatively modern. You require a good deal of prosperity before you can afford to have such a period in life, which is why mass education only began after the industrial revolution. A feudal or slave economy has no place for idle hands among the lower orders.
Moreover, if we compare the curriculum of today's schools with those of the past, it might easily be argued that the intellect of today's child is advanced at the expense of its emotion. For so much more is packed into each subject than was present even fifty years ago. No one argues that this is detrimental. And why should we assume that this process has ceased in our time? Why should we be so arrogant as to assume that our education can provide a yardstick for all time, even the future? The great diversity in human culture throughout history and spread across the globe, with the multitude of different roles given to children, should make us very cautious of generalisations that are only too clearly linked to our own life and times.
The argument that Ruth Lawrence is likely to suffer sane psychological trauma at a later stage in her life, is based upon the fact that she deviates from the norm. In statistical terms, this is true; it is correct to say that she deviates from the norm, because she is above average. But it is not legitimate to assume from this that she is abnormal in a psychological sense. It is this false confusion of meaning which gives the argument its force, with the word "normal" being given emotive connotations for which there is no evidence.
Against Ruth's unique upbringing, the argument is that she would be happier, better adjusted to life, if she had gone through the general educational mill. In other words, she must be brought down to the level of other children, and forced to proceed at their pace, however frustrating that might be for her, and however much she might blame herself later for allowing others to squander so much precious time and talent. Would that not give rise to the possibility of psychological hurt? Has such a possibility ever been considered? The trouble with education today is a misplaced egalitarianism that prefers to reward failure than to praise excellence. Special help is given to those who find it difficult to learn, and they enjoy going at their own pace in classes of small size especially suited to that purpose. This is most praiseworthy, and I am in agreement with such a practice. But what of gifted children, of the calibre of Ruth? No such advantages are given to them. Instead, they are held back in much larger classes and waste time because the class proceeds more slowly, closer to the pace of the least clever member of that class than the brightest. Where is the praise of excellence here? It may be a good education for the average children, but it is likely to turn genius into mediocrity.
Perhaps those who would prefer such an education as this for Ruth, should listen to the prophetic words of Tocqueville (in 'Democracy in America"), and try to understand why her choice is legitimate:
"From hatred of privilege and from the embarrassment of choosing, all men are at last forced, whatever may be their standard, to pass the same ordeal; all are indiscriminately subjected to a multitude of petty preliminary exercises, in which their youth is wasted and their imagination quenched, so that they despair of ever fully attaining what is held out to them; and when at length they are in a condition to perform any extraordinary acts, the taste for such things has forsaken them."
Postscript:
Wikipedia notes that:
Ruth Elke Lawrence-Naimark (born 2 August 1971) is an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. Outside academia, she is best known for being a child prodigy in mathematics. At Oxford, her father continued to be actively involved in her education, accompanying her to all lectures and tutorials. Ruth completed her bachelor's degree in two years, instead of the normal three, and graduated in 1985 at the age of 13 with a starred first and special commendation. Attracting considerable press interest, she became the youngest British person to gain a first-class degree, and the youngest to graduate from the University of Oxford in modern times. Ruth followed her first degree with a second degree in physics in 1986 and a D.Phil in mathematics at Oxford in June 1989, at the age of 17. Her thesis title was Homology representations of braid groups and her thesis adviser was Sir Michael Atiyah. In 1998, Ruth married the Israeli mathematician Ari Naimark and changed her name to Ruth Lawrence-Naimark.[citation needed] The couple have four children, Yehuda Bezalel (born 2000), Esther Miriam (born 2001), Batsheva Simcha (born 2003) and Yehoshua Aharon (born 2006).
She was estranged from her father, but the problem there seems to be more to do with the way he was trying to be successful vicariously through her own achievements, rather than any psychological problems of her own. Contrary to the prophets of doom, she does not seem at all maladjusted and is happily married, and enjoys having children. Her father now helps with her proofreading.
On her own first child, she said: "There will not be any forcing, no attempt to try and push Yehuda faster than he wants to go. I, though, was always eager to learn more. I want Yehuda to develop in a natural way," she adds. "My husband and I will not do exactly as everybody else does when they bring up a child. But I don't want Yehuda to be 'different'. I want my child to be able to develop in a natural way. I suppose I might have liked my childhood to be different in some ways, but I do not want to judge my parents. And I do not envy them. I was not in their shoes. I very much appreciate the effort my father put in. I am enormously grateful for what he did for me. I can see now that being a parent is very difficult."
Currently, Ruth is still teaching courses on combinatorial knot theory, Lie groups, Khovanov theory, discrete mathematics and various courses on mathematics for physicists and engineers, at the Hebrew University in Jerusalem. Interestingly, despite her parents being very secular Jews, she has embraced her Jewish culture and heritage very strongly. A glance at her sight shows she is still producing solid mathematical work ; there's also a photo of her, with her name beneath in Hebrew. The area of mathematics she is working on is complex, and she suspects any applications in the real world will take 100 years to be manifest:
In 1997, the Independent commented on her and her work:
Knot theory is the broad term for the rarefied branch of maths Ruth is now studying and teaching at the University of Michigan in Ann Arbor, near Detroit. Broadly speaking, it is about, well, knots - their geometry and behaviour, the more complicated they get. But try to narrow it down and you will find yourself in a dense thicket of phrases like "partition functions of a topological quantum field theory".
Surely that's about as abstruse, and unapplicable to anything in real life, as they come? She systematically squashes the suggestion, citing the theory, developed at the beginning of this century, of infinite-dimensional complex spaces. Abstruse? Then, certainly. "But it led in the 1920s to the possibility of quantum theory; and that made it possible to understand the idea of energy levels of quantum objects. Which led, in time to the laser. "And even when lasers were invented, people were saying, 'What use is that?' Now, of course, it's everywhere, in compact disc players, laser printers... That's what maths is like: it has always shown itself to be useful in the end."
Links:
http://www.ma.huji.ac.il/~ruthel/ - Ruth's Website
http://www.independent.co.uk/news/uk/home-news/child-prodigy-ruth-tells-why-shes-all-tied-up-in-knots-1273133.html
http://www.ma.huji.ac.il/~ruthel/ - Ruth's Website
http://www.independent.co.uk/news/uk/home-news/child-prodigy-ruth-tells-why-shes-all-tied-up-in-knots-1273133.html
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1 comment:
I remember Ruth Lawrence being interviewed by Terry Wogan at the height of her fame, and serenely riding over his rather crass attempts to manoeuvre her into looking like a geek or freak. She seemed level headed and quietly charming to me.
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