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To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the cheshire cat. to the physicist it is an indispensable characteristic. it would be going too far to say that to the physicist the cat is merely incidental to the grin. physics is concerned with interrelatedness such as the interrelatedness of cats and grins. in this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.
-Arthur Eddington
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To The Pure Geometer The Radius Of

Arthur Eddington
To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the cheshire cat. to the physicist it is an indispensable characteristic. it would be going too far to say that to the physicist the cat is merely incidental to the grin. physics is concerned with interrelatedness such as the interrelatedness of cats and grins. in this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.
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Cat Math Would Be

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Oh cat, i'd say, or pray: be-ootiful cat! delicious cat! exquisite cat! satiny cat! cat like a soft owl, cat with paws like moths, jewelled cat, miraculous cat! cat, cat, cat, cat.
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It is easy to understand why the cat has eclipsed the dog as modern america's favorite pet. people like pets to possess the same qualities they do. cats are irresponsible and recognize no authority, yet are completely dependent on others for their material needs. cats cannot be made to do anything useful. cats are mean for the fun of it. in fact, cats possess so many of the same qualities as people that it is often hard to tell the people and the cats apart.
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You encountered a misery near the end of the day and it took a while to gauge its full extent. some miseries had sharp curvature and could be negotiated readily. others had almost no curvature and you knew you'd be spending hours turning the corner. great whopping-big planet-sized miseries.
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So is not mathematical analysis then not just a vain game of the mind? to the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.
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To do any important work in physics a very good mathematical ability and aptitude are required. some work in applications can be done without this, but it will not be very inspired. if you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? you cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
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With cats, some say, one rule is true: don’t speak till you are spoken to. myself, i do not hold with that — i say, you should ad-dress a cat. but always keep in mind that he resents familiarity. i bow, and taking off my hat, ad-dress him in this form: o cat! but if he is the cat next door, whom i have often met before (he comes to see me in my flat) i greet him with an oopsa cat! i think i've heard them call him james — but we've not got so far as names.
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