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Gregory Bateson
Mind and Nature:
A Necessary Unity
Ch. II
Every Schoolboy Knows
9. Number is Different from Quantity
Numbers are the product of counting. Quantities are the product of measurement. This must mean 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.
Even when number and quantity are clearly discriminated, there is another concept that must be recognized and distinguished from both number and quantity. For this other concept, there is a sub-set of patterns whose members are the products of counting. Indeed, it is the smaller, and therefore commoner, numbers that are often not counted but recognized as patterns at a single glance. Card players do not stop to count the pips in the eight of spades and can even recognize the characteristic patterning of pips up to ‘ten’.
In other words, number is of the world of pattern, gestalt, and digital computation; quantity is of the world of analogic and probabilistic computation. (Bateson 59a.d, some emphasis mine)
Bateson illustrates with a bird experiment. There are birds that can distinguish number up to seven. The bird first flies to a cup. There is a limited number of pieces of meat in it. After it finishes, it may then fly to a plate with many more meat pieces than in the cup. But it is punished if it eats more plate pieces than were in the cup. Soon the bird learns to eat only as many plate pieces as were in the cup, and no more.
The question is if the bird computationally counted the plate meat-pieces, or used pattern recognition. The experimenter tried many tactics “to make it impossible for the jackdaw to create some sort of pattern or rhythm by which to recognize the number of the pieces of meat.” (60c) But despite these measures, we still might insist that “the taking of the meat from the cups becomes some sort of rhythmic dance and that this rhythm is in some way repeated when each bird takes the meat from the plate.” Nonetheless, the experiment does strongly suggest that the bird counts the meat. (60c)
Bateson, Gregory. Mind and Nature: A Necessary Unity.
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