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From: Gale <wmgale.domain.name.hidden>

Date: Mon, 01 Feb 1999 12:04:12 -0500

Gilles HENRI wrote:

*>
*

*> I just liked to remind you the old Greek paradox that demonstrates
*

*> rigorously that there cannot exist any sand heap:
*

*> Let N be the number of sand grains in the collection:
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*> if N=1, it is not a sand heap.
*

*> if you add a single grain to what is not a heap, you cannot transform it
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*> into a heap.
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*> So the proposition is logically demonstrated.
*

Very interesting way to put what I see as my agreeing with you...

The original observations were correct over the ranges given,

which where basically all high end, but not correct over the full range

of intelligence, memory, etc.

I guess for the Greek example you cite, one must *define* a sand heap

as a heap of >= N grains of sand. A heap must also be defined. Perhaps

a group of connected grains which either support at least one

other grain or are supported by at least one other grain.

Possibly the size can be made implicit by

requiring stability (against how much perturbation?) of the heap and

at least one supported grain. Four grains might then qualify... :)

Is there some reference for discussion of this paradox?

Bill Gale

Received on Mon Feb 01 1999 - 09:09:46 PST

Date: Mon, 01 Feb 1999 12:04:12 -0500

Gilles HENRI wrote:

Very interesting way to put what I see as my agreeing with you...

The original observations were correct over the ranges given,

which where basically all high end, but not correct over the full range

of intelligence, memory, etc.

I guess for the Greek example you cite, one must *define* a sand heap

as a heap of >= N grains of sand. A heap must also be defined. Perhaps

a group of connected grains which either support at least one

other grain or are supported by at least one other grain.

Possibly the size can be made implicit by

requiring stability (against how much perturbation?) of the heap and

at least one supported grain. Four grains might then qualify... :)

Is there some reference for discussion of this paradox?

Bill Gale

Received on Mon Feb 01 1999 - 09:09:46 PST

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