[PD] [OT] map vs territory (was Re: CVs)
Simon Wise
simonzwise at gmail.com
Mon May 23 13:54:06 CEST 2011
On 23/05/11 12:21, Chris McCormick wrote:
> My perspective is that in the case of e.g. sqrt(-1) the "territory" does not
> exist. There is merely the map that is inside our heads and that map can be
> used to correctly predict real and observable things that happen in reality.
> The things that happen in reality should not be mistake for actually being
> sqrt(-1) though. They are merely observations that are predicted correctly by
> the map most of the time.
>
> I don't think sqrt(-1) exists independently of the hardware (brains) to run
> it.
I think sqrt(-1) is in the same position as 3/4 here, both rational numbers and
complex numbers require an understanding of the language and the models that
define them to be understood, both have some very direct mappings to
measurements, distances and such. For example rational numbers can be mapped to
some of the lengths we can ask about, but they don't describe all the lengths
that we can think about, while complex numbers can be mapped in a very
straightforward and useful way to not just any distance along a line, but also
to any position within a plane, representing the distance and direction in 2
dimensions. They prove very useful in dealing with these quantities, and have as
much existence as any other number, once they are part of your vocabulary.
Simon
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