“ People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plussign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a windowpane merge; does one plus one make one? A cloud breaks up into two clouds more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy. ”
- Douglas R. Hofstadter- Copy
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“ Poised midway between the unvisualizable cosmic vastness of curved spacetime and the dubious shadowy flickerings of charged quanta, we human beings, more like rainbows and mirages than like raindrops or boulders, are unpredictable selfwriting poems vague, metaphorical, ambiguous, sometimes exceedingly beautiful. ”
- Douglas R. Hofstadter- Copy
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“ It turns out that an eerie type of chaos can lurk just behind a facade of order and yet, deep inside the chaos lurks an even eerier type of order. ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
- Douglas R. Hofstadter- Copy
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
- Douglas R. Hofstadter- Copy
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
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“ Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law. ”
- Douglas R. Hofstadter- Copy
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law. ”
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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“ Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law. ”
- Douglas R. Hofstadter- Copy
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
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“ All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally… ”
- Douglas R. Hofstadter- Copy
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“ Tortoise: But we must be careful in combining sentences. For instance, you'd grant that "Politicians lie" is true, wouldn't you? Achilles: Who could deny it? Tortoise: Good. Likewise, "Cast-iron sinks" is a valid utterance, isn't it? Achilles: Indubitably… ”
- Douglas R. Hofstadter- Copy
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