Re: Simple explanations. Was: what are the labs for?

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

Dewey, you are likely to start a philosophical thread here.

On Mon, 9 Feb 1998, Dewey Dykstra, Jr. wrote:

> Does the set of "simple" explanations not overlap the set of
> mathematical ones? 

Surely they must; but how populous is the intersection of these two sets?

> Is the set of "complicated" explanations more or less identical to the
> mathematical ones? 

"Complicated" isn't a useful descriptor. One who is fluent in mathematics
will find the mathematical treatments simpler, both practically and
conceptually. It's really difficult to construct a simple explanation
which actually works and has broad and general applicability. Usually you
hit upon the idea for the good simple explanations only *after* you've
thought it through with math. 

> In what sense is a mathematical explanation really an explanation? 

This one I really like. In my opinion there are no "explanations", only
different types of descriptions (models). If they appeal to us, and we are
fluent enough with them to get correct results and to account for all that
we observe, then we have a good feeling about them which we interpret as
meaning that we have achieved "understanding", and that the models have
"explained" something. We fool ourselves this way a lot. 

Someone once said that "The only models which work are the mathematical
ones."

> Just wondering...  
>
> Dewey

That's a good way to start. :-)

	-- Donald Simanek