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A Game of Numbers


Starlord

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I have doubts whether, for 1 in particular, the concepts of "number" and "idea" are separable.  We know that nonhuman animals can count objects up to 4 or 5 or so, and sometimes beyond, and there are some recent papers that indicate some animals even have a grasp of zero.  Now those are different statements than saying they recognize 1 or 2 as being members of, e.g., the set of natural numbers; there are certainly human groups who have lacked that conceptual framework.  The ideas of fractions and irrational numbers are extensions on those less-than-universally-available concepts.  However, it is clear that the ideas of counting numbers have existed among humans for as long as any kind of enduring system of writing has existed; it is impressive how many samples of cuneiform, and how many of the translated cases of Linear B, involve what is basically accounting, keeping track of quantities of things.

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10 minutes ago, Cancer said:

 We know that nonhuman animals can count objects up to 4 or 5 or so, and sometimes beyond, and there are some recent papers that indicate some animals even have a grasp of zero.  

 

Mostly in my third-period class.

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5 hours ago, Cancer said:

I have doubts whether, for 1 in particular, the concepts of "number" and "idea" are separable.  We know that nonhuman animals can count objects up to 4 or 5 or so, and sometimes beyond, and there are some recent papers that indicate some animals even have a grasp of zero.  Now those are different statements than saying they recognize 1 or 2 as being members of, e.g., the set of natural numbers; there are certainly human groups who have lacked that conceptual framework.  The ideas of fractions and irrational numbers are extensions on those less-than-universally-available concepts.  However, it is clear that the ideas of counting numbers have existed among humans for as long as any kind of enduring system of writing has existed; it is impressive how many samples of cuneiform, and how many of the translated cases of Linear B, involve what is basically accounting, keeping track of quantities of things.

 

Cheers. Thanks for your comments. 

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