11 Jul '17 08:025 edits

All this actually happened MANY times in my actual real-life research;

I made a computer program for simulating the random sampling of a hypothetical and newly-defined new type of probability distribution.

After I inputting many thousands of combinations of input values into the program and running the simulations to see what the corresponding output would be, I observe a pattern between input and the output.

Question 1;

can that observation of that input-output pattern of those computer simulations be completely validly called "empirical evidence" in the strictly SCIENTIFIC sense of the term?

I then work out a maths equation E that fully describes that pattern and make the assumption that that equation E is always correct.

I then test E for yet many more combinations of input values in yet more simulations and find that the way those combinations of input values correspond to the resulting output also conforms to E.

I conclude via induction that E is PROBABLY always true BUT I don't, at least not yet, have a mathematical/deductive proof that it is true and don't currently know of any purely DEDUCTIVE-logic reason why it SHOULD always be true so cannot (yet) be absolutely rationally sure.

Question 2;

Can that assumption and conclusion that E is PROBABLY always true be completely validly called a "SCIENTIFIC theory"?

Is E a "theory" and/or a "SCIENTIFIC theory"?

If the answer to question 2 is "yes";

Question 3;

What if I suddenly were to accidentally stumble across a valid mathematical proof that E must always be true?

Can E still be called a "theory" and/or a "SCIENTIFIC theory" but now is a PROVEN one (and is now also call a 'theorem' but that isn't part of my question) ?

I made a computer program for simulating the random sampling of a hypothetical and newly-defined new type of probability distribution.

After I inputting many thousands of combinations of input values into the program and running the simulations to see what the corresponding output would be, I observe a pattern between input and the output.

Question 1;

can that observation of that input-output pattern of those computer simulations be completely validly called "empirical evidence" in the strictly SCIENTIFIC sense of the term?

I then work out a maths equation E that fully describes that pattern and make the assumption that that equation E is always correct.

I then test E for yet many more combinations of input values in yet more simulations and find that the way those combinations of input values correspond to the resulting output also conforms to E.

I conclude via induction that E is PROBABLY always true BUT I don't, at least not yet, have a mathematical/deductive proof that it is true and don't currently know of any purely DEDUCTIVE-logic reason why it SHOULD always be true so cannot (yet) be absolutely rationally sure.

Question 2;

Can that assumption and conclusion that E is PROBABLY always true be completely validly called a "SCIENTIFIC theory"?

Is E a "theory" and/or a "SCIENTIFIC theory"?

If the answer to question 2 is "yes";

Question 3;

What if I suddenly were to accidentally stumble across a valid mathematical proof that E must always be true?

Can E still be called a "theory" and/or a "SCIENTIFIC theory" but now is a PROVEN one (and is now also call a 'theorem' but that isn't part of my question) ?