Charles Babbage, one of the father of computers, once wrote:
I will yet venture to predict that a time will arrive, when the accumulating labour which arises from the arithmetical applications of mathematical formulae, acting as a constantly retarding force, shall ultimately impede the useful progress of the science, unless this or some equivalent method is devised for relieving it from the overwhelming incumbrance of numerical detail.
He meant that one day his computer -- at that time seen as a costly and useless device -- would be not just useful but required to make further economic progress. He was right in all but one respect: he thought that day was in the future. In fact, he was already living in it. Scientific and economic progress have always been limited by the available computational power -- but until quite recently, the level of power available never changed, so the limit was imperceptible.
Now that computing power routinely grows by orders of magnitude, it is easier for us to grasp the idea that we are limited by available computation -- it would be nice to decode genes faster, fold proteins quicker, make more accurate weather predictions. We understand these things will get better, in the same way that Babbage could grasp that calculating logarithmic tables (the primary purpose of computation in the 1850s) would someday be quicker.
What is more difficult for us to grasp is that we are still horribly limited by our lack of computational power. We cannot see how limited until those limitations are lifted. Take, as the shadow of an example, the way that one can browse live online maps from one's phone and already scarcely remember how one got by before that ability. In the future, ubiquitous and mind-bendingly powerful computation will make these tasks seem as divorced from utility and convenience as grinding gears to create logarithmic tables seems now.
Human beings are bad at predicting phase changes. We can predict iteration but not invention, so we write stories about giant spaceships that have wired telephone lines. You have no idea how amazing the future is really going to be.