Morris Kline

Mathematics and the Physical World

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nesehudenhas quoted3 years ago
where ignorance is bliss, ’Tis folly to be wise.
—THOMAS GRAY
nesehudenhas quoted3 years ago
To say that zero is a number means that we can operate with zero much as we operate with any other number. Thus, 5 + 0 = 5 but 5 + nothing is a meaningless expression and yields nothing.
nesehudenhas quoted3 years ago
Number is a concept of the mind, no doubt suggested by physical objects but independent of them.
nesehudenhas quoted3 years ago
The senses are limited. The eye sees only a small range of light waves and is easily deceived as to sizes and locations of objects. The ear hears only a limited range of sound waves. The sense of touch can reach only to objects accessible to the hand and is not a precise sense at that. On the other hand, man’s reason can encompass distances, sizes, sounds, and temperatures beyond the range of the senses. More than that, reason can contemplate phenomena which transcend the senses and even the imagination
nesehudenhas quoted3 years ago
every abstraction that even the greatest mathematician has introduced is ultimately derived from and is therefore understandable in terms of intuitively meaningful objects or phenomena.
nesehudenhas quoted3 years ago
Mathematics is a multistage Roman candle. It is packed with physical gunpowder and set alight by the fire of human minds. It then shoots off in a direction somewhat determined by human thought but not necessarily exactly in the direction planned. Then the candle flares up and successive flashes of light reveal aspects of the physical world not readily illuminated from man’s earthbound station. Each successive thrust of the candle into space is followed by flares from higher and higher altitudes that reveal more and more of the constitution of our universe.
nesehudenhas quoted3 years ago
This is the germ of the great Greek discovery, perhaps the greatest discovery man has ever made. Reasoning can produce knowledge that not only covers a multitude of cases in one swoop but may produce physically meaningful information that is entirely unforeseen.
nesehudenhas quoted3 years ago
It is true that many people pass their whole lives without being bothered at all by such questions. These people are content with shelter, food, sex, and a few material pleasures. But others are not content to live only on a physical level. They have minds that are aware of the pervasive natural mysteries and are as obsessed to resolve them as any businessman may be to acquire wealth.
fopajuwovohas quoted3 years ago
zero is a number means that we can operate with zero much as we operate with any other number
fopajuwovohas quoted3 years ago
when numbers arise in physical situations, one must abstract the quantitative facts, perform the appropriate mathematical operations, and then interpret the mathematical answer.
fopajuwovohas quoted3 years ago
Number is a concept of the mind, no doubt suggested by physical objects but independent of them
fopajuwovohas quoted3 years ago
part of the secret of mathematical power lies in its use of abstract concepts. By this means we free our minds from burdensome and irrelevant detail and are thereby able to accomplish more
fopajuwovohas quoted3 years ago
The mental processes that may lead to the correct insight are indeed as difficult to describe as is the creative process in art, literature, or music
fopajuwovohas quoted3 years ago
The senses are limited. The eye sees only a small range of light waves and is easily deceived as to sizes and locations of objects. The ear hears only a limited range of sound waves. The sense of touch can reach only to objects accessible to the hand and is not a precise sense at that. On the other hand, man’s reason can encompass distances, sizes, sounds, and temperatures beyond the range of the senses. More than that, reason can contemplate phenomena which transcend the senses and even the imagination
fopajuwovohas quoted3 years ago
every abstraction that even the greatest mathematician has introduced is ultimately derived from and is therefore understandable in terms of intuitively meaningful objects or phenomena
fopajuwovohas quoted3 years ago
It is true that many people pass their whole lives without being bothered at all by such questions. These people are content with shelter, food, sex, and a few material pleasures. But others are not content to live only on a physical level. They have minds that are aware of the pervasive natural mysteries and are as obsessed to resolve them as any businessman may be to acquire wealth.
fopajuwovohas quoted3 years ago
Reasoning can produce knowledge that not only covers a multitude of cases in one swoop but may produce physically meaningful information that is entirely unforeseen.
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