How is faith different when applied to science then when it is applied to religion?
If faith is defined as placing greater confidence in something than what evidence suggests, then it's hard to see where faith can be a good thing at all?
In this respect, I would say Buddha's analysis of uselessness of such faith is right on target.
Canki Sutta: With Canki
----------------------------------------------------------------------------------------------------------------------------------------
"There are five things that can turn out in two ways in the here-&-now. Which five?
Conviction,
liking,
unbroken tradition,
reasoning by analogy, &
an agreement through pondering views. These are the five things that can turn out in two ways in the here-&-now.
Now some things are firmly held in conviction and yet vain, empty, & false.Some things are not firmly held in conviction, and yet they are genuine, factual, & unmistaken.
If a person has conviction, his statement, 'This is my conviction,' safeguards the truth. But he doesn't yet come to the definite conclusion that 'Only this is true; anything else is worthless.' To this extent, Bharadvaja, there is the safeguarding of the truth. To this extent one safeguards the truth. I describe this as the safeguarding of the truth. But it is not yet an awakening to the truth.
Similarly the other five.
...
However,
But to what extent is there an awakening to the truth? To what extent does one awaken to the truth?
When, on observing that the monk is purified with regard to qualities based on delusion (etc.), he places conviction in him. With the arising of conviction, he visits him & grows close to him. Growing close to him, he lends ear. Lending ear, he hears the Dhamma. Hearing the Dhamma, he remembers it.
Remembering it, he
penetrates the meaning of those dhammas. Penetrating the meaning, he
comes to an agreement through pondering those dhammas. There being an agreement through pondering those dhammas, desire arises. With the arising of desire, he becomes willing.
Willing, he contemplates (lit: "weighs," "compares"). Contemplating, he makes an exertion
. Exerting himself, he both realizes the ultimate meaning of the truth with his body and sees by penetrating it with discernment.
"To this extent, Bharadvaja, there is an awakening to the truth. To this extent one awakens to the truth. I describe this as an awakening to the truth.
But it is not yet the final attainment of the truth.
"The cultivation, development, & pursuit of those very same qualities: to this extent, Bharadvaja, there is the final attainment of the truth. To this extent one finally attains the truth. I describe this as the final attainment of the truth."
--------------------------------------------------------------------------------------------------------------------------------------
Thus faith or conviction is simply the beginning point of any field of discipline, secular or religious, it is a state of mind one needs to be receptive to the knowledge and experiences of that field. But if one, after sufficient time of practice in that field, is still talking in terms of faith or conviction, then there is something seriously wrong with either the mode of learning or the field itself.