Jim on Sat, 14 Mar 2009 20:11:12 -0400 (EDT)

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Re: <nettime> Digital Humanities Manifesto

What exactly do we mean by isomorphism? There is the mathematical
definition of isomorphism where two systems are isomorphic if and only
if there is one-to-one correspondence between the objects in each
system AND the operations defined in each system mirror each other.
The natural numbers are not just the sequence denoted by the decimal
numerals 0,1,2,3,4,.... They are that plus the operations of addition,
subtraction, multiplication and division along with the relationships
of less than, greater than, and equals. Just because a collection of
things can be numbered doesn't make that collection isomorphic to
numbers in the strict mathematical sense.

Furthermore although we may speak of binary and decimal numbers there
are, strictly speaking, just numbers which have binary or decimal
representations and these representations are strings of characters.
So there are, strictly speaking, binary numerals but not binary
numbers. When we learned our arithmetic in grade school we learned
algorithms for operating on strings of decimal digits.

Am I misunderstanding something?

Flick Harrison wrote:

> I think the main problem I have in this discussion is that I can't
> say that a lightswitch is isomorphic with numbers. Nor is a telegraph
> button.

On Mar 10, 2009, at 3:05 PM, inimino wrote:

> Isomorphism is not equality.

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