A relatively lightweight dip into a number of aspects of mathematics and how they impact on our lives today. You don't need to remember much school maths to enjoy the book (but you do need an interest in it). Full of interesting facts and quirks - the best has to be a drill bit that drills square holes!
Locn. 469-70 the study found a strong correlation between a talent at reckoning and success in formal maths. The better one’s approximate number sense, it seems, the higher one’s chance of getting good grades.
Locn. 1496-1500 The Menger sponge is a brilliantly paradoxical object. As you continue the iterations of taking out smaller and smaller cubes the volume of the sponge gets smaller and smaller, eventually becoming invisible – as though the woodworm have eaten the whole lot. Yet each iteration of cube removal also makes the surface area of the sponge increase. By taking more and more iterations you can make the surface area larger than any area you want, meaning that as the number of iterations approaches infinity, the surface area of the sponge also approaches infinity.
Locn. 2633 Pi exhibits randomness non-randomly – which is fascinating, and weird.
Locn. 2686-88 One useful property of a Reuleaux triangle is that it can be rotated inside a square so that it touches all four sides of the square at all times. This property was exploited by Harry James Watts, an English engineer living in Pennsylvania, in 1914, when he designed one of the most bizarre tools in existence: a drill that can drill square holes.
Locn. 4560-63 The mathematical reason why the golden angle produces the best leaf arrangement around a stem is linked to the concept of irrational numbers, which are those numbers that cannot be expressed as fractions. If an angle is an irrational number, no matter how many times you turn it around a circle you will never get back to where you started. It may sound Orwellian, but some irrational numbers are more irrational than others. And no number is more irrational than the golden ratio.
Locn. 5480-82 Adolphe Quételet has good claim to being the world’s most influential Belgian. (The fact that this is not a competitive field in no way diminishes his achievements.) Locn. 5495 In Brussels in 1853 Quételet hosted the first international conference on statistics.
Locn. 5557 the quincunx. The word’s original meaning is the pattern of five dots on a die,
Monday, 28 February 2011
Saturday, 5 February 2011
Out of our Minds: Learning to be Creative (Mr. Ken Robinson)
Whilst at times the book tends to veer a little too far towards science & technology education bashing, especially in the early chapters, by the time you have read the whole book he does present a more balanced argument. His central thrust is that we need a more holistic view of education that encourages a love of learning right across the population and doesn't try and force everyone through a narrow academic route. My point would be that we do need some to follow the academic route (just as we have always done).
The book is more of an argument that we need to do something different rather than providing the solutions as to what we should be doing.
The chapters on culture and creativity and innovation within organisations definitely chimed with my personal experience.
Locn. 218-19 We won’t survive the future simply by doing better what we have done in the past. Raising standards is no good if they’re the wrong standards.
Locn. 346-47 Creative insights often occur by making connections between ideas or experiences that were previously unconnected.
Locn. 355-56 Creativity prospers best under particular conditions, especially where there is a flow of ideas between people who have different sorts of expertise. It requires an atmosphere where risk-taking and experimentation are encouraged rather than stifled.
Locn. 359-60 If ideas are discouraged or ignored, the creative impulse does one of two things. It deserts or subverts the organisation. Creativity can work for you or against you.
Locn. 530-31 The essential problem is that many governments and organisations seem to think that the best way to prepare for the future is to do better what we did in the past - just to do more of it and to a higher standard. The fact is we have to do something else.
Locn. 698-99 It has been estimated that each year something in the order of 10^17 microchips are being manufactured. This is roughly equivalent to the world population of ants.
Locn. 1080-81 In these circumstances, employers aim for exactly the same elite they would have taken on 20 years earlier : they just raise the bar and develop different techniques for selecting the people they want and add new criteria.
Locn. 1434-37 Theories develop in response to questions. And a question, as Susan Langer notes, can only be answered in a certain number of ways. For this reason the most important characteristic of an intellectual age is the questions it asks - the problems it identifies. It is this rather than the answers it provides that reveals its underlying view of the world.
Locn. 2110-15 To promote creativity it is essential to understand the main elements and phases of the creative process including: • the importance of the medium; • the need to be in control of the medium; • the need to play and take risks; and • the need for critical judgment.
Locn. 2418-21 So what’s involved in the process of being creative? 1 want to focus on three crucial features: • the importance of finding the right medium for your own creative strengths; • the necessity of being able to control the medium; and • the need for freedom to experiment and take risks.
Locn. 2481-83 They reach a stage where their creative ambitions have outrun their technical abilities. This is hardly surprising. Children don’t develop these abilities just by getting older, any more than they wake up on their 16th birthday to discover they can drive a car.
Locn. 2496-99 Creativity involves a dynamic interplay between generating ideas and making judgements about them. Getting the balance right is critical. Imaginative activity is the process of generating something original: providing an alternative to the conventional or routine. It’s a form of mental play that is essentially generative, in which we attempt to expand the possibilities of a situation, to look at it from a new perspective.
Locn. 2568-69 Creativity is not a separate faculty so much as an attitude: a willingness to reconsider what we take for granted.
Locn. 2602 Locn. 2602-4 Goleman describes this as emotional intelligence. Emotionally intelligent people are self-directed, self-starters, highly motivated and excellent communicators. As such they are likely to emerge at the top of organisations.
Locn. 2857-60 This is why ideas often come to mind without our thinking about them: why it’s often better to sleep on a problem or put it, as we say, to ‘the back of our minds’. There we can let the non-rational processes of thought mull it over and deliver a solution unbidden to us. Our best ideas may come to us when we’re not thinking about them.
Locn. 3114-15 We all live in two worlds: a world that exists whether or not we exist and a world that exists only because we exist, the world of our own thoughts, feelings and consciousness.
Locn. 3133-34 We are laced together in networks of knowledge. In large communities and organisations, these networks are highly complex. The creativity of a culture depends on how open these networks are and how easily we can access the knowledge of other people.
Locn. 3149-51 The store of human knowledge is now doubling every ten years and the rate of expansion is accelerating. One result is increasingly intensive specialisation in all disciplines: a tendency to know more and more about less and less.
Locn. 3158-61 As knowledge expands, greater specialisation is inevitable. The risk is that we lose sight of the larger picture, of how ideas connect and can inform each other. In these circumstances we need more than access to information and ideas: we need ways of engaging with them, of making connections, of seeing principles and of relating them to our own experiences and identities. This too has important implications for the culture of organisations.
Locn. 3298-3300 Cultural change is not a strictly logical process. New ideas take root not just because they are new or haven’t been thought of before. In fact this is often not the case. They take root when they do because they capture a mood. They appeal to the zeitgeist, the spirit of the times, the ghost in the social system,
Locn. 3334-36 The common-sense view is that human knowledge moves forward confidently on the basis of new theories building systematically on the old. This is not what happens at all. In practice, theories are as subject to social movements and fashions as the length of skirts or the cut of lapels.
Locn. 3358-59 • Creativity is not a purely personal process. Many creative processes draw from the ideas and stimulation of other people. Creativity flourishes in an atmosphere where original thinking and innovation are encouraged and stimulated.
Locn. 3360-62 If ideas are not encouraged, or when encouraged they are ignored, the creative impulse does one of two things. It goes out, or it goes maverick. It deserts the organisation or it subverts it. Creativity can work for you or against you.
• Creativity is a dynamic process and can involve many different areas of expertise. The exponential growth of knowledge has led to increasing levels of specialisation. In organisations, these often result in large numbers of separate departments and in the division of responsibilities to more and more specialist roles. But new ideas often come from the dialogue between different disciplines,
• Creativity is incremental. New ideas do not necessarily come from nowhere. They draw from the ideas and achievements of those that have gone before us or are working in different fields.
• Cultural change is not linear and smooth. It can be tumultuous, complex and drawn out. New ways of thinking do not simply replace the old at clear points in history.
• Cultural change is not strictly logical. Creativity and innovation should be seen as functions of all areas of activity and not only as confined to particular people or processes. The challenge is to promote processes of systemic innovation rather than of isolated specialist achievement.
Locn. 3431-32 Edward de Bono has developed a series of thinking tools including the Six Thinking Hats method and CORT, a suite of practical thinking techniques.
Locn. 3495-96 Everyone who works at our place has to work on at least two projects. In our organisation, we manage people’s commitment we don’t manage their time. In a research lab, time doesn’t mean anything.’
Locn. 3498-3500 Creativity relies on the flow of ideas. This happens best in an atmosphere where risk is encouraged, playfulness with ideas is accepted and where failure is not punished but seen as part of the process of success.
Locn. 3525-29 The processes of creativity can be stifled by a sense that innovation is unlikely to travel upwards through an organisation or that it won’t be welcomed if it emerges from the wrong places. It can be stifled by pressure from above to deliver the wrong sort of results over the wrong timescale: by demands for the wrong sort of accountability. In a practical sense, loosening hierarchies also means that those who run organisations should be accessible to those who work in them. They should encourage a flow of ideas and make it clear that ideas are welcomed and valued.
Locn. 3567-72 ‘Every single person in business needs to acquire the ability to change, the self-confidence to learn new things and the capacity for helicopter vision. The idea that we can win with brilliant scientists and technologists alone is absolute nonsense. It’s breadth of vision, the ability to understand all the influences at work, to flex between then and not be frightened of totally different experiences and viewpoints that holds the key. We need every single pressure from business at the moment to make clear that the specialist who cannot take the holistic view of the whole scene is no use at all.’ Sir John Harvey Jones
Locn. 3584-85 Productivity in a research laboratory means nothing. Creativity means everything, because most of what you do isn’t going to turn out how you thought it would.’
Locn. 3587 Organisations that make the most of
Locn. 3587-88 Organisations that make the most of their people find that their people make the most of them.
The book is more of an argument that we need to do something different rather than providing the solutions as to what we should be doing.
The chapters on culture and creativity and innovation within organisations definitely chimed with my personal experience.
Locn. 218-19 We won’t survive the future simply by doing better what we have done in the past. Raising standards is no good if they’re the wrong standards.
Locn. 346-47 Creative insights often occur by making connections between ideas or experiences that were previously unconnected.
Locn. 355-56 Creativity prospers best under particular conditions, especially where there is a flow of ideas between people who have different sorts of expertise. It requires an atmosphere where risk-taking and experimentation are encouraged rather than stifled.
Locn. 359-60 If ideas are discouraged or ignored, the creative impulse does one of two things. It deserts or subverts the organisation. Creativity can work for you or against you.
Locn. 530-31 The essential problem is that many governments and organisations seem to think that the best way to prepare for the future is to do better what we did in the past - just to do more of it and to a higher standard. The fact is we have to do something else.
Locn. 698-99 It has been estimated that each year something in the order of 10^17 microchips are being manufactured. This is roughly equivalent to the world population of ants.
Locn. 1080-81 In these circumstances, employers aim for exactly the same elite they would have taken on 20 years earlier : they just raise the bar and develop different techniques for selecting the people they want and add new criteria.
Locn. 1434-37 Theories develop in response to questions. And a question, as Susan Langer notes, can only be answered in a certain number of ways. For this reason the most important characteristic of an intellectual age is the questions it asks - the problems it identifies. It is this rather than the answers it provides that reveals its underlying view of the world.
Locn. 2110-15 To promote creativity it is essential to understand the main elements and phases of the creative process including: • the importance of the medium; • the need to be in control of the medium; • the need to play and take risks; and • the need for critical judgment.
Locn. 2418-21 So what’s involved in the process of being creative? 1 want to focus on three crucial features: • the importance of finding the right medium for your own creative strengths; • the necessity of being able to control the medium; and • the need for freedom to experiment and take risks.
Locn. 2481-83 They reach a stage where their creative ambitions have outrun their technical abilities. This is hardly surprising. Children don’t develop these abilities just by getting older, any more than they wake up on their 16th birthday to discover they can drive a car.
Locn. 2496-99 Creativity involves a dynamic interplay between generating ideas and making judgements about them. Getting the balance right is critical. Imaginative activity is the process of generating something original: providing an alternative to the conventional or routine. It’s a form of mental play that is essentially generative, in which we attempt to expand the possibilities of a situation, to look at it from a new perspective.
Locn. 2568-69 Creativity is not a separate faculty so much as an attitude: a willingness to reconsider what we take for granted.
Locn. 2602 Locn. 2602-4 Goleman describes this as emotional intelligence. Emotionally intelligent people are self-directed, self-starters, highly motivated and excellent communicators. As such they are likely to emerge at the top of organisations.
Locn. 2857-60 This is why ideas often come to mind without our thinking about them: why it’s often better to sleep on a problem or put it, as we say, to ‘the back of our minds’. There we can let the non-rational processes of thought mull it over and deliver a solution unbidden to us. Our best ideas may come to us when we’re not thinking about them.
Locn. 3114-15 We all live in two worlds: a world that exists whether or not we exist and a world that exists only because we exist, the world of our own thoughts, feelings and consciousness.
Locn. 3133-34 We are laced together in networks of knowledge. In large communities and organisations, these networks are highly complex. The creativity of a culture depends on how open these networks are and how easily we can access the knowledge of other people.
Locn. 3149-51 The store of human knowledge is now doubling every ten years and the rate of expansion is accelerating. One result is increasingly intensive specialisation in all disciplines: a tendency to know more and more about less and less.
Locn. 3158-61 As knowledge expands, greater specialisation is inevitable. The risk is that we lose sight of the larger picture, of how ideas connect and can inform each other. In these circumstances we need more than access to information and ideas: we need ways of engaging with them, of making connections, of seeing principles and of relating them to our own experiences and identities. This too has important implications for the culture of organisations.
Locn. 3298-3300 Cultural change is not a strictly logical process. New ideas take root not just because they are new or haven’t been thought of before. In fact this is often not the case. They take root when they do because they capture a mood. They appeal to the zeitgeist, the spirit of the times, the ghost in the social system,
Locn. 3334-36 The common-sense view is that human knowledge moves forward confidently on the basis of new theories building systematically on the old. This is not what happens at all. In practice, theories are as subject to social movements and fashions as the length of skirts or the cut of lapels.
Locn. 3358-59 • Creativity is not a purely personal process. Many creative processes draw from the ideas and stimulation of other people. Creativity flourishes in an atmosphere where original thinking and innovation are encouraged and stimulated.
Locn. 3360-62 If ideas are not encouraged, or when encouraged they are ignored, the creative impulse does one of two things. It goes out, or it goes maverick. It deserts the organisation or it subverts it. Creativity can work for you or against you.
• Creativity is a dynamic process and can involve many different areas of expertise. The exponential growth of knowledge has led to increasing levels of specialisation. In organisations, these often result in large numbers of separate departments and in the division of responsibilities to more and more specialist roles. But new ideas often come from the dialogue between different disciplines,
• Creativity is incremental. New ideas do not necessarily come from nowhere. They draw from the ideas and achievements of those that have gone before us or are working in different fields.
• Cultural change is not linear and smooth. It can be tumultuous, complex and drawn out. New ways of thinking do not simply replace the old at clear points in history.
• Cultural change is not strictly logical. Creativity and innovation should be seen as functions of all areas of activity and not only as confined to particular people or processes. The challenge is to promote processes of systemic innovation rather than of isolated specialist achievement.
Locn. 3431-32 Edward de Bono has developed a series of thinking tools including the Six Thinking Hats method and CORT, a suite of practical thinking techniques.
Locn. 3495-96 Everyone who works at our place has to work on at least two projects. In our organisation, we manage people’s commitment we don’t manage their time. In a research lab, time doesn’t mean anything.’
Locn. 3498-3500 Creativity relies on the flow of ideas. This happens best in an atmosphere where risk is encouraged, playfulness with ideas is accepted and where failure is not punished but seen as part of the process of success.
Locn. 3525-29 The processes of creativity can be stifled by a sense that innovation is unlikely to travel upwards through an organisation or that it won’t be welcomed if it emerges from the wrong places. It can be stifled by pressure from above to deliver the wrong sort of results over the wrong timescale: by demands for the wrong sort of accountability. In a practical sense, loosening hierarchies also means that those who run organisations should be accessible to those who work in them. They should encourage a flow of ideas and make it clear that ideas are welcomed and valued.
Locn. 3567-72 ‘Every single person in business needs to acquire the ability to change, the self-confidence to learn new things and the capacity for helicopter vision. The idea that we can win with brilliant scientists and technologists alone is absolute nonsense. It’s breadth of vision, the ability to understand all the influences at work, to flex between then and not be frightened of totally different experiences and viewpoints that holds the key. We need every single pressure from business at the moment to make clear that the specialist who cannot take the holistic view of the whole scene is no use at all.’ Sir John Harvey Jones
Locn. 3584-85 Productivity in a research laboratory means nothing. Creativity means everything, because most of what you do isn’t going to turn out how you thought it would.’
Locn. 3587 Organisations that make the most of
Locn. 3587-88 Organisations that make the most of their people find that their people make the most of them.
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