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Evan Buswell on Sun, 15 Mar 2009 08:36:43 -0400 (EDT) |
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Re: <nettime> Digital Humanities Manifesto |
> AND the operations defined in each system mirror each other. Isn't this redundant? Unless of course, the system is defined in such a way that it places limits on what operations are definable, which isn't the case with mathematical numbers, nor (theoretically) digitality. I'm pretty sure that's right, but I'd be interested to hear otherwise. Also: dichotomous (digital) states are not isomorphic with the natural numbers, they are isomorphic with binary numbers, i.e. the set [0, 1], not the set [0, 1, 2 ...]. To get the latter, you need to construct a system of mapping an arbitrary number to a *set* of digital states, of which many such systems exist and compete---see, e.g., endianness. To actually be isomorphic with the natural numbers, you would need an infinitely large set of states, effectively canceling the digital nature of the supposed device, as each state would be infinitely close to (in practice, indistinguishable from) another state. But then, when we actually deal with the natural numbers, as a whole, we deal more with natural numberness than with each discrete number. This is something a digital system is perfectly capable of representing. I guess it's less that (countable) numbers are isomorphic to digital states than (countable) numberness is isomorphic with digitality. But this is getting into pretty ill-defined territory. Evan Buswell # 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: nettime {AT} kein.org