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

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