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Occams principle is seen as a corner-stone of modern science, are there any examples where its opposite is shown to be useful?

Occams razor states that given a choice between differing explanations one should always choose the simplest. Of course this begs the question as to what one could mean by simplest.

I'm interested in situations in which the opposite principle has been found correct. That the more complex explanation wins out.

A possible example could be: There is life only on this planet and it is carbon-based as opposed to there are many kinds of life on many planets and they are not neccessarily carbon-based.

Given that choice the simplest seems to be the first, whereas I think the second, the more complex explanation is likely to be correct.