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

[Mathieu Bouchard]

On Mon, 23 May 2011, 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.

Claiming « sqrt(-1) is not in the territory » is an axiom. It's a 
definition. You are defining sqrt(-1) as meaning something that is not in 
the territory. The question is whether that's more useful than claiming 
that sqrt(-1) is a pattern that appears in the territory.

Same goes for any other number, actually. sqrt(-1) is not in a special 
situation here.

There are other ways to explain anything that uses complex numbers. In 
math that's called an Isomorphism, and there's a lot of abstract algebra 
that is about those equivalences. Especially the Representation Theory. It 
doesn't make sqrt(-1) any more virtual than any other numbers. If you go 
through enough algebra, you will see every number and every numeric 
operation has plenty of equivalences of any kind... that doesn't make them 
more virtual, that makes them more existent.

> Bryan and I took the other conversation off list so as not to bore 
> people. I would be quite happy to do that here as this is very OT!

Bryan took it to pd-ot where no-one ever writes. I had to subscribe to it 
in order to be able to reply. pd-list's volume is very much under its 
average, too. Bored people can hit the Delete key quite easily.

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