Originally posted by twhiteheadSo you imply that although I DID make a "theory BUT my "theory" is NOT a "scientific theory" but rather is ONLY a "mathematical theory".
I personally see science as a study of the natural world (with study of humans still falling withing the 'natural world'. You are studying mathematics not nature. So you are using scientific methods to study maths. I don't think I would call your theories 'scientific theories' as it might cause confusion.
I would suggest sticking to normal maths terminology.
Originally posted by twhiteheadwhat you are saying seems to be hinted at with;
I believe the correct term for your not yet rigorously proved ideas is 'conjecture':
Originally posted by humyI would say yes.
My observation of that input-output pattern of my computer simulations of random sampling of a hypothetical probability distribution CAN be completely validly called "empirical evidence" in the strictly SCIENTIFIC sense of the term.
Originally posted by twhiteheadSo to update that, that should be;
I would say yes.
[b]HOWEVER, despite that, it is NOT true that the unproven conjectures I make from such observation can be validly called a "SCIENTIFIC theory";
Here I would say it is a matter of convention, not a true or false thing. We are, after all, talking about a definition here.
they are "conjectures", NOT scientific theories. ...[text shortened]... fic findings of simpler systems. Overall, there is much overlap between science and mathematics.[/b]
Originally posted by humyTo explore this a bit further, there is a whole domain of mathematics dealing with the Cartesian plane. Now one could investigate a Cartesian plane using a computer simulation, and come up with various conjectures and possibly prove some of them mathematically. But the Cartesian plane is a logical construct not a real world object, so I wouldn't call any of that science.
So what a completely valid mathematical theorem says is NOT a "scientific fact" but is still "mathematical fact".