Question: Consider our world at 18-19 centuries. Our civilization knows how to print books, build steam machines, we have made first experiments on electricity. And one day the [Mad God Sheogorath](http://elderscrolls.wikia.com/wiki/Sheogorath) is emerged. He can bend the reality by his will. 

For example, he can violate the principles of conservation of energy - build Perpetuum Mobile just to irritate scientists. 

He can convert Darwin back into the monkey just to help him prove his theory. 

He can make forgery of dinosaur skeletons, so we have found caterpillar riding tankosaurus instead of diplodocus.

He can resurrect people.
And, do a lot of things we are not aware.

So, in potential he can spoil every scientific acquired experiments result in a way, that is hard to see. 

So, the question is: is scientific method still possible in this world?

UPD: after 20 years Sheogorath have just vanished. Can we undo his trickery and restore science methods?

Answer: 
**It very much depends on your god's sense of humour.**

If he's decided for example that [da red wunz go fasta](https://en.wikipedia.org/wiki/Ork_%28Warhammer_40,000%29) and anything blue can fly then you've pretty much had it. All the rules that you come up with are going to be wrong.

If his logic has an internal consistency and lasting effect even after he's gone, messing with the fossil records etc, then the damage is done and you can never get a right and proper answer. If there's no consistency and he's just randomly poking experiments and giggling then it's all about spotting and excluding the results that don't fit.

If on the other hand, the red ones continue to go faster even after he's gone and you can ignore aerodynamic lift and just paint it blue instead, perhaps the scientific method remains valid. You just won't get the answers that maybe you did before he came along.
As a writer and reader, if I'm dealing with a being with what we might call "godlike powers", they still have to operate within a larger reality. For example in your setup, Sheogorath builds a tiny "Perpetual Motion Machine" but is actually cheating because in some mysterious god power way, it is perfectly converting a few molecules of MysteriousInvisibleSubstance to Energy at the nano-level. Maybe there's even enough MysteriousInvisibleSubstance to last a thousand years and it's really really hard to detect. MysteriousInvisibleSubstance can also alter visible reality so that Darwin is now stuck in what appears to be a monkey body. Sheogorath can also in some odd way travel in time and use his nifty MysteriousInvisibleSubstance powered MatterReasssembler to screw with the fossils just to screw with the human's of the future's heads. Then Sheogorath disappears. 

Until the sentients are clever enough to figure out how to detect and then use MysteriousInvisibleSubstance at the molecular level, no "laws of reality" in that fictional world disturbed. That said, for the WorldBuilding exercise to be any fun to read, etc. When the sentients or others of Sheogorath's species figure out what he's been up to and how, Sheogorath is going to be in BIG BIG trouble, right?