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You are going to read an extract from an article. Seven paragraphs have been removed from the extract. Choose from the paragraphs A-H the one which fits each gap (11-17). There is one extract paragraph which you do not need to use
As a mathematician with strong musical interests who grew up in a family of musicians, I have been asked about the connection between music and maths many times. And I have bad news: although there are some obvious similarities between mathematical and musical activity, there is (as yet) no compelling evidence for the kind of mysterious, almost magical connection that many people seem to believe in. I’m partly referring here to the ‘Mozart Effect’, the hypothesis that children who have heard music by Mozart are supposedly more intelligent, including at mathematics, than children from a control group
11.
Of course, this conclusion does not show that there is no interesting connection between mathematics and music. It was always a little implausible that lazily listening to a concerto would earn you extra marks on that maths test you are taking tomorrow, but what about learning to read music or spending hours practicing the piano? That takes genuine effort.
12.
Demonstrating a connection of this kind is not as easy as one might think. To begin with, there are plenty of innumerate musicians and tone-deaf mathematicians, so the best one could hope to demonstrate would be a significant positive correlation between the aptitudes at the two disciplines. And then on would face all the usual challenges of establishing a statistical connection.
13.
And yet, the belief that the two are interestingly related won’t go away without a fight. I cannot help observing that among the mathematicians I know, there do seem to be a surprising number who are very good indeed at the piano.
14.
Indeed, yes, we can. For a start, both mathematics and music deal with abstract structures, so if you become good at one, then it is plausible that you become good at something more general - handling abstract structures - that helps you with the other. If this is correct, then it would show a connection between mathematical and musical ability, but not the kind of obscure connection that people hope for.
15.
Of course, abstract structures are not confined to mathematics and music. If you are learning a foreign language then you need to understand its grammar and syntax, which are prime examples of abstract structures. And yet we don’t hear people asking about a mysterious connection between mathematical ability and linguistic ability.
16.
In an effort to dispel this air of contradiction, let me give one example of a general aptitude that is useful in both mathematics and music: the ability to solve problems of the “A is to B as C is to D” kind. These appears in intelligence tests (car is to garage as aircraft is to what?) but they are also absolutely central to both music and mathematics.
17.
I take the view that the general question of whether mathematical ability and musical ability are related is much less interesting than some similar but more specific questions. Are musicians more drawn to certain composers (Bach, for instance)? Are musical mathematicians more drawn to certain areas of mathematics? One can imagine many interesting surveys and experiments that could be done, but for now this is uncharted territory and all we can do is speculate.
A
I feel that it would be more like the straightforward link between ability at football and ability at cricket. To become better at one of those then you need to improve your finest and co-ordination. That makes you better at sport in general.
B
For example, identifying and controlling for other potentially influential factors is difficult, and as far as I know, there has been no truly convincing study of that type that has shown that musical ability enhances mathematical ability or vice versa.
C
The second phrase is a clear answer to the first. But one can be more precise about what this means. If you try to imagine any other second phrase, nothing seems ‘right’ in the way that Mozart’s chosen phrase does.
D
Could it be that the rewards for that time-consuming dedication spill over into other areas of intellectual life, and in particular into mathematics? Is there any evidence that people who have worked hard to become good at music are better at mathematics than people who are completely unmusical? And in the other direction, are mathematicians better than average at music?
E
My guess is that that is because the link exists but not the uncertainty; grammar feels mathematical. Music, by contrast, is strongly tied up with one’s emotions and can be enjoyed even by people who know very little about it. As such, it seems very different from mathematics, so any connection between the two is appealingly paradoxical.
F
It is not hard to see why such a theory would be taken seriously; we would all like to become better at mathematics without putting in any effort. But the conclusions of the original experiment have been grossly exaggerated. If you want your brain to work better, then not surprisingly, you have to put in some hard graft; there is no such thing as an intellectual perpetual-motion machine. Mozart CDs for babies, and toys that combine maths and music might help, but not much, and the effects are temporary.
G
I believe that there is a study waiting to be done on this: are mathematicians more drawn to this rather than to other instruments? Of the mathematicians I can think of who are superb instrumentalists, all but one are pianists. While we wait for scientific evidence to back up the anecdotal evidence, can we at least argue that it is plausible that there should be a connection?
H
Music is full of little puzzles like this. If you are good at them, then when you listen to a piece, expectations will constantly be set up in your mind. Of course, some of the best moments in music come when one’s expectations are confounded, but if you don’t have the expectations in the first place then you will miss out on the pleasure.
Mong các bạn có thể giúp mình giải chi tiết bài này ạ
. Mình làm sai nhiều quá mà không biết sai chỗ nào Cô mình cũng không nói chi tiết
Đây là đáp án do cô mình cung cấp
F-D-B-G-A-E-H
As a mathematician with strong musical interests who grew up in a family of musicians, I have been asked about the connection between music and maths many times. And I have bad news: although there are some obvious similarities between mathematical and musical activity, there is (as yet) no compelling evidence for the kind of mysterious, almost magical connection that many people seem to believe in. I’m partly referring here to the ‘Mozart Effect’, the hypothesis that children who have heard music by Mozart are supposedly more intelligent, including at mathematics, than children from a control group
11.
Of course, this conclusion does not show that there is no interesting connection between mathematics and music. It was always a little implausible that lazily listening to a concerto would earn you extra marks on that maths test you are taking tomorrow, but what about learning to read music or spending hours practicing the piano? That takes genuine effort.
12.
Demonstrating a connection of this kind is not as easy as one might think. To begin with, there are plenty of innumerate musicians and tone-deaf mathematicians, so the best one could hope to demonstrate would be a significant positive correlation between the aptitudes at the two disciplines. And then on would face all the usual challenges of establishing a statistical connection.
13.
And yet, the belief that the two are interestingly related won’t go away without a fight. I cannot help observing that among the mathematicians I know, there do seem to be a surprising number who are very good indeed at the piano.
14.
Indeed, yes, we can. For a start, both mathematics and music deal with abstract structures, so if you become good at one, then it is plausible that you become good at something more general - handling abstract structures - that helps you with the other. If this is correct, then it would show a connection between mathematical and musical ability, but not the kind of obscure connection that people hope for.
15.
Of course, abstract structures are not confined to mathematics and music. If you are learning a foreign language then you need to understand its grammar and syntax, which are prime examples of abstract structures. And yet we don’t hear people asking about a mysterious connection between mathematical ability and linguistic ability.
16.
In an effort to dispel this air of contradiction, let me give one example of a general aptitude that is useful in both mathematics and music: the ability to solve problems of the “A is to B as C is to D” kind. These appears in intelligence tests (car is to garage as aircraft is to what?) but they are also absolutely central to both music and mathematics.
17.
I take the view that the general question of whether mathematical ability and musical ability are related is much less interesting than some similar but more specific questions. Are musicians more drawn to certain composers (Bach, for instance)? Are musical mathematicians more drawn to certain areas of mathematics? One can imagine many interesting surveys and experiments that could be done, but for now this is uncharted territory and all we can do is speculate.
A
I feel that it would be more like the straightforward link between ability at football and ability at cricket. To become better at one of those then you need to improve your finest and co-ordination. That makes you better at sport in general.
B
For example, identifying and controlling for other potentially influential factors is difficult, and as far as I know, there has been no truly convincing study of that type that has shown that musical ability enhances mathematical ability or vice versa.
C
The second phrase is a clear answer to the first. But one can be more precise about what this means. If you try to imagine any other second phrase, nothing seems ‘right’ in the way that Mozart’s chosen phrase does.
D
Could it be that the rewards for that time-consuming dedication spill over into other areas of intellectual life, and in particular into mathematics? Is there any evidence that people who have worked hard to become good at music are better at mathematics than people who are completely unmusical? And in the other direction, are mathematicians better than average at music?
E
My guess is that that is because the link exists but not the uncertainty; grammar feels mathematical. Music, by contrast, is strongly tied up with one’s emotions and can be enjoyed even by people who know very little about it. As such, it seems very different from mathematics, so any connection between the two is appealingly paradoxical.
F
It is not hard to see why such a theory would be taken seriously; we would all like to become better at mathematics without putting in any effort. But the conclusions of the original experiment have been grossly exaggerated. If you want your brain to work better, then not surprisingly, you have to put in some hard graft; there is no such thing as an intellectual perpetual-motion machine. Mozart CDs for babies, and toys that combine maths and music might help, but not much, and the effects are temporary.
G
I believe that there is a study waiting to be done on this: are mathematicians more drawn to this rather than to other instruments? Of the mathematicians I can think of who are superb instrumentalists, all but one are pianists. While we wait for scientific evidence to back up the anecdotal evidence, can we at least argue that it is plausible that there should be a connection?
H
Music is full of little puzzles like this. If you are good at them, then when you listen to a piece, expectations will constantly be set up in your mind. Of course, some of the best moments in music come when one’s expectations are confounded, but if you don’t have the expectations in the first place then you will miss out on the pleasure.
Mong các bạn có thể giúp mình giải chi tiết bài này ạ
. Mình làm sai nhiều quá mà không biết sai chỗ nào Cô mình cũng không nói chi tiết Đây là đáp án do cô mình cung cấp
F-D-B-G-A-E-H
