> There is no positive difference between "discrete values or objects" > and some subset (possibly the entire set) of any countable infinite > set, including the set of natural numbers.
really? so there is no difference between an orange. and an orange section, each discrete and equal to one? you hold that a film and a scene, as arguably discrete objects are the same? there is a mereological problem of the construction of discreteness, i claim, in that the construction of what we see as discrete depends on our culture and the apparatuses we use. that we can construct discreteness from an assemblage of random objects, we can build a set, does not mean that we can always operate on this set as a discrete object and have the results recognized by anyone else. > Idealists may believe there is some essential difference, but that's a > question of metaphysics, and inconsequential. So "actually", "digital > things" are, in fact, "necessarily numbers". so you hold, there is no difference between the 'thing' and it's representation? >> while we think of digital computing as binary numbers, one can also >> thing of it as just a system of discrete signals, that may not need to >> map onto numbers. that you can represent things in numbers does not >> mean that the discrete object is a number, nor need it truly map to a >> number. there should be no necessary isomorphism, though, there usually >> is. > > There's an obvious necessary isomorphism: counting. Assign a different > number to each possible discrete signal. Since the signals are discrete, > it's always possible to count them. were it the case that counting was a universally stable practice and numeration were the same everywhere, I think you would have a point, but it isn't. There are variant ontologies behind different number systems and ways of counting that, in my mind, removes the necessity. not everyone in the world thinks that all discrete objects can be mapped into numbers and for some it is actually impossible to count some things you would claim that you can count. The anthropology of mathematics is an interesting field, but on looking at it a while, one realizes how narrowed and structured our models are. ---- Isomorphic is not the same thing as identical (see http://en.wikipedia.org/wiki/Isomorphism); Michael is being very careful with his choice of words. yes, i said it doesn't necessarily map, there is no necessary isomorphism between a thing and its numerical representation, though usually there is. The point where is not is when there is a mediating relationship in the discrete relationship itself. where there is a 'whole' that is actually 'parts'. you can still compute with the assumption of isomorphism, but your final result may not map from the representation to the actuallity. # distributed via <nettime>: no commercial use without permission # <nettime> is a moderated mailing list for net criticism, # collaborative text filtering and cultural politics of the nets # more info: http://mail.kein.org/mailman/listinfo/nettime-l # archive: http://www.nettime.org contact: [email protected]
