When I came home for Christmas after my first term as a PhD student, I went to meet some friends at the pub clutching a printout of my first research result: a map that I had made - me! - showing the distribution of mass in a distant cluster of galaxies. I excitedly told my friends about how this was one of the most massive objects in the Universe, and that we could infer where all the mass in it was by measuring the gravitational pull that it exerted on the light from objects - other galaxies - that were in the background. The map showed that this cluster, like many others being studied at the time, was a lot more massive than it looked: I had mapped out huge quantities of Dark Matter, that we knew had to be there despite not being able to see it directly. “That’s cool,” said Chris. “What’s Dark Matter?”
Usually when I tell this story, the joke is that astrophysics is easy - it’s not rocket science! There’s so much that we don’t know, you can just ask the simple question and you’re already at the frontier of knowledge. But there’s another point to it. It’s amazing that we can infer the existence, presence, and distribution of Dark Matter, without knowing anything about what it is.
The process of inference that I started learning about during my PhD still captivates me now. It essentially involves combining two sets of beliefs, in order to improve our understanding of the natural world through a model which we use to represent it. These beliefs are quantified mathematically (as probabilities), but we can understand them just fine without equations. First we need to write down what we believe about our model before even thinking about its implications. These are our “prior” beliefs. Then we need to make some assumptions and figure out what our model would predict in the way of observations. This second set of beliefs gives us a way of calculating how likely any particular example of our model would be, given the data that we plan to get and the assumptions we made. When we actually do make some observations, the data act (in the math) to update our prior beliefs into a set of “posterior” beliefs - and we have learned something about our model. In my case, I learned that the mass that I had assumed to be in the cluster was far more spread out than expected, and there was much more of it than expected.
I don’t know whether you think about your beliefs in terms of probability distributions, but after 16 years of living with them, I find that it’s the only way I can. For me, beliefs are hypotheses to be tested, that get stronger or weaker when they are updated, under various assumptions, by new data. Thinking in these terms seems to be good for me, especially when I feel strong opinions starting to form!
Data is worshipped by scientists. We shape its worth by carefully building expensive instruments, that yield it to us in vast arrays of precious numbers to be archived for endless re-use, and which provide us with a connection to the physical reality that generated them. But the interpretation of our data, and the context for them that our priors provide, are both subjective. We cannot do inference without making assumptions. Certainly, as we collect more and more data, our beliefs get stronger and stronger, we can make our model more and more detailed, and it seems more and more real, more and more like “objective truth.” But it’s interesting that even when the data are very good, our understanding is still in terms of our model, defined by its assumptions. This subjective aspect to inference makes many of my colleagues uneasy. The working solution seems to be to do science in communities, and be continually comparing inferences obtained under different assumptions, with different models, using different datasets, until a well-tested and coherent picture emerges. It’s hard to learn about the Universe on your own!
Still, many of my colleagues hold, as an article of faith, the existence of an underlying truth about how the Universe works, to be discovered by scientists (preferably themselves). To a large extent, it doesn’t matter whether they are right about this or not. The models that we make to represent the Universe do a fantastically good job of predicting its behavior, enabling humans to do things that our ancestors never even dreamed of. We put faith in our models that make sense of the things we can see, and are rewarded with visions of things we didn’t even know existed.