Numbers are the product of ...

Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.
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 Gregory Bateson

Quotes from the same author

Whenever we pride ourselves upon finding a newer, stricter way of thought or exposition … we lose something of the ability to think new thoughts. And equally, of course, whenever we rebel against the sterile rigidity of formal thought and exposition and let our ideas run wild, we likewise lose. As I see it, the advances in scientific thought come from a combination of lose and strict thinking, and this combination is the most precious tool of science.
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 Gregory Bateson
What we mean by information - the elementary unit of information - is a difference which makes a difference, and it is able to make a difference because the neural pathways along which it travels and is continually transformed are themselves provided with energy. The pathways are ready to be triggered. We may even say that the question is already implicit in them.
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 Gregory Bateson
We do not know enough about how the present will lead into the future. We shall never be able to say, "Ha! My perception, my accounting for that series, will indeed cover its next and future components," or "Next time I meet with these phenomena, I shall be able to predict their total course.
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 Gregory Bateson
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
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 Gregory Bateson
Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next.
 See image
 Gregory Bateson