The Cat only grinned when it saw Alice. .....

'Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would like the name: however, it only grinned a little wider. 'Come, it's pleased so far,' thought Alice, and she went on. 'Would you tell me, please, which way I ought to go from here?'

[Alice speaks to Cheshire Cat] 'That depends a good deal on where you want to get to,' said the Cat.

'I don't much care where--' said Alice.

'Then it doesn't matter which way you go,' said the Cat.

'--so long as I get somewhere,' Alice added as an explanation.

'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.'

Alice felt that this could not be denied, so she tried another question. 'What sort of people live about here?'

'In that direction,' the Cat said, waving its right paw round, 'lives a Hatter: and in that direction,' waving the other paw, 'lives a March Hare. Visit either you like: they're both mad.'

        ---Lewis Carroll

Alice's Adventures in Wonderland, Chapter VI.
Illustrated version, printed and bound: The Complete Illustrated Lewis Carroll, Wordsworth Editions, 1991, with an Introduction by A. Woollcott, illustrations by J. Tenniel.
Online versions: searchable text; hypertext with Tenniel illustrations.
The quote used an an epigraph on p. xv in Operator Commutation Relations by Palle E. T. Jorgensen and Robert T. Moore, D. Reidel, Dordrecht / Boston / Lancaster, 1984, is an abridgement of the above passage.
Shortly after this passage, near the end of Chapter 6, is the memorable slow vanishing of the Cat, with its Schrödingerian associations. Designers of quantum computers may note that the Cat, in vanishing slowly, is complying with Alice's wish that the Cat "wouldn't keep appearing and vanishing so suddenly".

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