On 1/19/2014 4:18 PM, LizR wrote:
On 20 January 2014 10:39, meekerdb <[email protected] <mailto:[email protected]>>
wrote:
On 1/19/2014 1:26 PM, LizR wrote:
On 20 January 2014 08:56, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 1/18/2014 7:38 PM, LizR wrote:
Or it could be because we, denizens of this physics/universe,
invent them.
Why would that make it effective, though? After all we also invented
fairy
tales, and conspiracy theories, and religion, and...)
And those fairy tales were effective too - up to a point. "Don't sleep
near
the swamp because the night demons will make you sick.", probably saved
a lot
of people from malaria.
Fairy tales and religion "work", in this sense (when they do - there's a
lot of
nonsense invented by humans, too!) because they encode knowledge about the
world.
So why does maths work? If it encodes knowledge about the world, where does
that
information come from?
It doesn't encode knowledge about the world. It encodes relations between
sentence,
i.e. axioms=>theorems. With suitable interpretation we can use it to model
the world
(and evolution hardwired this to some degree): One apple and one orange
makes two
fruit. Two tennis players and two basketball players make four players -
oops, one
of the tennis players is also a basketball player, so it's only three players.
Interpretation is essential.
Why does it model the world (apparently to quite a lot of decimal places) if it's only
relations between sentences?
The modeling of the world is in our interpretation of it, a mapping from the observable
world into mathematics, manipulation and inference, and the interpretation of the result
as applying to the observable world. If it works to a lot of decimal places it means
we've created a good model and the relations between sentences must correspond to some
relation in the world.
Brent
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