I have recently been lucky to relocate from Yale to Center for Theoretical Study in Prague, Czech Republic. The institute brings together philosophers, mathematicians, physicists, sociologists, economists, biologists and others; it is similar to Santa Fe Institute or Princeton Institute for Advanced Study, and its aim is to stimulate interdisciplinary approaches to science, encouraging new ways of interaction and cooperation between disciplines.
The institute hosts the toughest kind of seminar that I have seen; it is called Thursday seminar. Guest speaker has one hour to present, but the audience reserves the right interrupt him at any time. And people do it a lot – sometimes the speaker doesn't even get beyond the first half, and his/her basic assumptions and premises are already in ruins. Follows another hour of discussion where what remains is disintegrated and buried under monologues from the audience. The guest is then brought to a pub, filled up with heavy Czech food and beer (yes, we drink beers for lunch), and subjected to another round of academic inspection.
Apart from the Thursday seminars, irregular lunches, and occasional random encounters in the coffee corner, we all meet again on Monday seminars where we contemplate a common unifying theme. Since we are in a center for theoretical study, the theme is anything but applied.
This year's theme is “Process vs. event”.
When I joined, the Monday seminar series had already been in progress, and after I'd figured out what's up, I immediately got my usual but deceptive feeling that “I've got it right and they are all confused” (blame it to my youth), and I could feel the rising urge to come out with my most beloved heavy caliber: statistics. Here is how I very briefly presented it:
Statistics clearly distinguishes models (theories, hypotheses), which is what we think, and data, which is what we see. Models are the processes, or the ideas in Platonic sense, further classifiable to stochastic or deterministic. Data are the events, sometimes also called outcomes of the processes. Statistics tells the story about how the data came to be by making statements about the P(model|data), or P(data|model). That's it.
The following discussion was passionate, direct, with hard edges and egos smoking hot. After few minutes I lost track about the fate of what remained of my own contribution, or if anybody actually cared, but I'd learned that some people are definitely less confused than I initially thought.
Here are some notable ideas:
Philosopher Alexandr Matoušek noted that seeing is a peculiar term – our mind can see an idea (model, theory) more clearly than the actual event (data). This somehow resonates with my recent realization that theory is not necessarily a way of knowing how the world is, but it is rather the way of looking at the world (I have this from Marquet et al.'s recent piece in Bioscience). I need to explore these connections more.
Alexandr Matoušek and mathematician Petr Kůrka also pointed to the problem that, ultimately, we will have to deal with stochastic processes in the light of the problem of free will (and the problem of whether it exists). This is a key unresolved issue, and it can generate some intense discussions in the future.
Novelist and philosopher Michal Ajvaz presented an attempt to outline the dichotomy between processes vs. events using dimensions (time, space, horizontal, vertical) and scale. To unify this view with the statistical view will be a major and important undertaking, and I am really curious to see what comes out of it.
Paleoecologist Petr Pokorný pointed to the potential connection between rarity of an event and its significance (I think that there is no such connection). He also brought up the butterfly effect story, which turned out to be thought-provoking, but it also generated considerable misunderstanding. I reckon that this story can serve as a particularly useful illustration of our ideas, if interpreted carefully.
Sociologist Zdeněk Konopásek reminded me that quantitative science, and especially statistics, can generate substantial suspicion among some social scientists – for them, statistics potentially reduces complex stories to mere counting, without the understanding of what's really going on. I tend to defend statistics. First, no matter how deep an understanding, it is worthless if it's not formalized and communicated, and statistics (and mathematics) is a formal way to represent and communicate understanding. Second, statistics enables to separate general principles from anecdote, and while anecdotes can be entertaining, they are hard to build on. Finally, modern statistics is not only inductive and reductionist – it can also relate an individual observation to an existing model, and investigate probability (likelihood) of this observation, given the model; this guarantees the possibility for a single unusual observation to shoot down the whole model.
Mathematician Marie Větrovcová brought me to the notion of complex conditional processes in which models are conditional on the data, parts of the models are conditional on other parts of the model, but data are never conditional on other data. I'd like to explore this idea in a more formal way.
The seminar left me excited and in a state of intellectual discomfort, which I guess is a good sign.