For those who don't know, a heuristic can be loosely defined as, "a rule of thumb". Most of us use heuristics all the time, usually without realising it.
For example, if you want to catch a ball, there are 2 ways you could go about it. You could take the computational approach, which you might use for example if you wanted to program a robot to do this.You could calculate the speed and trajectory of the ball, perhaps factoring in gravity and wind speed, work out precisely where it was going to land, and then make sure your hand was in the right place. Or, you could take a heuristic approach. This would be something along the lines of, "the ball is getting bigger very quickly - I need to move my hand back a bit", and keep adjusting until it lands.
Heuristics are useful because most of us don't have enough information most of the time to make perfectly calculated decisions (or fast or precise enough brains to do so if we did), so we constantly have to make best guesses based on what we do know. Our ability to make such guesses correctly (or at least optimally) is constantly refined through experience. If it wasn't for heuristics we would all suffer from "analysis paralysis" - we would spend so long trying to work out how to do something, or even what to do, that we would never actually get around to doing anything at all! The trade off though, is that sometimes we get it badly wrong! This is where science comes in.
For thousands of years, people have taken a heuristic approach to all sorts of things and come to all kinds of wrong conclusions. For example, based on the information available to them at the time, people concluded that the Earth was at the centre of the Universe and that the world was flat. Science on the other hand, takes a much more stringent approach, and sometimes comes to conclusions that seem quite alien to our heuristic-oriented brains. For example, through a rigorous process of scientific investigation, we now know that most of what we call "matter" is actually made up of empty space (!) - populated by tiny particles bound together by electromagnetic forces, which cause them to arrange themselves in various formations that appear to us as solid, liquid or gas*.
For most of human history it seems, most people have believed in gods or in a God, but nowadays it seems, at least in certain corners of Western Civilisation, that this belief might be on the wane. The wave of scientific progress over the last couple of hundred years or so has overturned and/or thrown into question so many of our traditional assumptions and beliefs. It has also given us a much-heightened sense of confidence in our ultimate ability to solve all the fundamental problems and questions of the Universe. Science has taught us to be suspicious of our heuristic interpretations of reality and to distrust anything that cannot be rationally tested and proved. At the same time though, heuristics continue to be crucial to living our daily lives.
If you want to catch that ball for example, you're going to have to use a heuristic approach - you simply don't have sufficient knowledge or brain-processing-power to do otherwise. If you're considering a new job and want the best outcome for yourself and your family - you cannot work out what will happen in the future and will have to make the best guess you can with the information you have. If you ever want to be in a relationship with anyone, you're going to have to decide whether or not you can trust them - but there is no scientific or logical formula for this! Instead, based on the limited information you have, you are just going to have to decide whether or not to take the risk.
Faith is a heuristic approach to life, and it seems clear to me that in the past (and no doubt in the present) we have got some of it wrong. Faith needs to listen to science and to learn from it (although not necessarily from everything that is said by all of its practitioners!), but science also has a few things to learn from faith. Science will never be able to prove that there is no God, and good scientists - even those who are the most staunchly atheist - will usually admit to this when pushed. By the same token though, science will never be able to prove definitively that there is a God, if indeed He is omnipotent and does not wish to be "discovered" or "analysed" in this way.
For all its remarkable achievements, science is just a tool and remains limited in scope and application. There is so much in life and reality that we don't know, will never fully know, and could never fully analyse if we did. Therefore, although science can and does furnish us with valuable data to inform our decisison making process, most of the important things in life - including faith - must continue to be determined by heuristics.