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Imagine if we forced people to think only in valid math. It would make proofs by contradiction impossible to even imagine. Alternatively think of computer pro
by ajuc 2y ago
Imagine if we forced people to think only in valid math.
It would make proofs by contradiction impossible to even imagine.
Alternatively think of computer programming. Imagine your editor forces your code to be compilable at every keystroke. It would suck (who used paredit knows the struggle ;) ).
So it's perfectly possible that making "invalid" results expressable in the language your model uses might be beneficial.
- gklitz 2y agoProofs by contradictions are still expressed in valid math. Invalid math is when you start giving answers like “1.3(4æ87+^%<[{“, that is completely disregarding syntactical and consistency rules of the language you are using to express yourself in.
- ajuc 2y agoI guess there's several levels of invalid, I was thinking of "3/0" or "sqrt(-1)" level of invalid. Maybe it was a bad analogy. Still - going from one to another valid expression is often faster if you can go through invalid expressions.
- gklitz 2y ago> going from one to another valid expression is often faster if you can go through invalid expressions. I still don’t think you really comprehend what an invalid expression is in this case. Ñ¥æd huiåp xiip ææææOP. It won’t make anything “faster” to “go through” these, as expressed extremely cleanly and fast in the last statement expressed in invalid English. Invalid expressions doesn’t mean “this mathematical expression expresses an inconsistency” like 3/0, it means “this expression isn’t a mathematical expression because it doesn’t follow the basic rules for the language” like “$/(!!@?3.3.3”