“Never be anyone’s hope, be their faith. They are like proof and belief. Hopes aren’t meant to last, but faiths last forever.”
So, lets begin the argument of which is stronger. Why is the collision between science and religion so intense (especially from the 1600s)? One requires proof and one is based on belief. One demands events to be repeatable, verifiable and measurable, the other requires only that you believe. One promises you materialistic advancements, one gives you character refinement, way of living (at least for complete religions quite unlike Christianity or Buddhism), spiritual basis, etc. Of course, your faith in God is only meaningful if you believe and don’t want proof of existence. You may ask God to show you how He creates from nothing, but that is not proof for your faith in Him, it is just out of interest.
One of the greatest problems with proof is that you cannot disprove anything unless you exhaust all possibilities. Second law of thermodynamics cannot be proven because it is ‘negative’. Same goes for some parts of theory of relativity. But if you believe them to be true, you won’t be searching for counter-examples. Similarly, proofs walk a very fine distance from being proven wrong.
Consider parsing, their are two general methods, top-down and bottom-up. In top-down parsing, one of the most well understood method is LL(k) parsing. In bottom-up parsing, LR(k) parsing is the strongest (generally! :) ). LL parsing is more restrictive, LR parsing imposes minimal constraints on the parser. Therefore, LR parsers recognize a larger class of grammars than LL parsers.
Turning to personal examples, I watched many class-mates having mounds of different (actually indifferent) certifications. They always told me that everyone cared about how much certifications you had, but I had faith in myself that I will be able to prove myself without such supports, which turned out to be true. An expectation I would never have to nerve to fulfil if I had hoped to get a good professional position.
I don’t believe in panspermia, unless I have seen proof. I believe in creation of everything by a Higher being. If you follow the logical conclusion, you will appreciate the proof that Adam and Eve lie at the top of human hierarchy and they must have been created specially. But again, if you believe in panspermia, this proof should not shift your opinion. And, I must add, we are only humans because we have the ability to leap beyond logic which boils down to believing and not wanting proof as not everything can be proven even by science.
You can always clearly see the difference among the people who hope and who have faith in their goals. Those who hope rarely achieve, those having faith often twist the circumstances to their benefit.