Recently, I had a conversation with a colleague which gradually led us to the topic of – is there a real world problem theoretical science aims to solve? The colleague said that theoretical science doesn’t address any real world problem and research (in the general sense) is the only thing it’s busy with. Despite the fact I agree with the statement that theoretical science is used to conduct research (though I’ll introduce an alternative term for this activity soon), I couldn’t agree with the colleague completely. I insisted that there is a real world problem all theoretical sciences are addressing. In the end, I was asked the question “What is the ‘real world problem’ that theoretical physics aims to solve?” My answer was “exploration and exploitation.” I’m not sure I managed to convince the colleague, but the topic seemed interesting for me, and I decided to express it as a blog post.
Those who have had a mathematical optimization course and have some insights into optimization algorithms, probably, have a hunch why I picked “exploration and exploitation” as the answer. Anyway, let me explain my idea in more detail.
I would like to introduce an example that can be found in many books about optimization theory which explains the so called gradient ascent or climb method. Imagine you are standing on a hilly landscape. Your goal is to climb to the highest hill, but it’s a dark night and all you have is a flashlight, so you can’t see further than a few feet in front of you. What would your strategy be? Most likely you would try to find the direction along which the elevation increases the most and go there. After a while you would look around again and find the direction in which you would move a bit further. You would continue this procedure until you reach a place from where you can only go down whichever direction you choose. At this point you could say you have reached the highest hill in the local area. This is what exploitation is about – you start from a random point and try to improve the position step-by-step. Easy!
The thing is, the highest hill in some area is not necessarily the highest hill on the landscape. Sometimes you need to go a little bit down first to reach a peak in the future. In other words, a chain of the locally best decisions does not necessarily lead to the best outcome. You don’t want to get stuck on a ten foot hill when Everest is nearby, and here exploration comes into play. Though some people can happily stay on a hill they have found, there are always “rangers” who thirst to know what lies beyond the border of the realm traced out by the flashlight. These guys are willing to go down the hill in the hope of finding a higher one. Don’t you think this process perfectly matches with what my colleague called “research?”
Now let’s extend this idea to the whole civilization. In the very beginning, mankind stood at some point in this highly bizarre world landscape. As an analogy, a higher hill on this landscape means a higher quality of life, e.g. more goods, better food, less routine work, etc. It’s obvious that many early discoveries such as fire and the wheel were made by accident. People moved in random directions and sometimes found these hills. We had to perform random small walks because we didn’t have a flashlight and weren’t brave enough to go in an unknown direction.
Back to the real world problem for theoretical physics. The real world problem that theoretical physics aims to solve can be called exploration (or research) and exploitation. Scholars explore the land of physics trying to find something that can be useful, whether in the present or in the future – points which look promising to start the climbing process from. They also draw maps of the visited places, so those who come after them can reach the frontier easily. I believe, each startup, lab, the whole civilization aims to solve the same problem in a certain sense.
Everything mankind does is trying to find “hills” on the real-world “surface” in which we can produce maximum value. At the same time, theoretical science supplies us with good starting points and educated guesses of the direction we should move from there – in other words serves us as a flashlight. The first is achieved with exploration and the second with exploitation.
Hope you don't get bored with this explanation :)