[PD] [OT] map vs territory (was Re: CVs)

[Simon Wise]

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