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October 27, 2010

Story-telling, statistics, and other grave insults

The New York Times (and the NYT Magazine) has been running a series of pieces about math, science and society written by John Allen Paulos, a mathematics professor at Temple University and author of several popular books. His latest piece caught my eye because it's a topic close to my heart: stories vs. statistics. That is, when we seek to explain something [1], do we use statistics and quantitative arguments using mainly numbers or do we use stories and narratives featuring actors, motivations and conscious decisions? [2] Here are a few good excerpts from Paulos's latest piece:

...there is a tension between stories and statistics, and one under-appreciated contrast between them is simply the mindset with which we approach them. In listening to stories we tend to suspend disbelief in order to be entertained, whereas in evaluating statistics we generally have an opposite inclination to suspend belief in order not to be beguiled. A drily named distinction from formal statistics is relevant: we’re said to commit a Type I error when we observe something that is not really there and a Type II error when we fail to observe something that is there. There is no way to always avoid both types, and we have different error thresholds in different endeavors, but the type of error people feel more comfortable may be telling.


I’ll close with perhaps the most fundamental tension between stories and statistics. The focus of stories is on individual people rather than averages, on motives rather than movements, on point of view rather than the view from nowhere, context rather than raw data. Moreover, stories are open-ended and metaphorical rather than determinate and literal.

It seems to me that for science, the correct emphasis should be on the statistics. That is, we should be more worried about observing something that is not really there. But as humans, statistics is often too dry and too abstract for us to understand intuitively, to generate that comfortable internal feeling of understanding. Thus, our peers often demand that we give not only the statistical explanation but also a narrative one. Sometimes, this can be tricky because the structure of the two modes of explanation are in fundamental opposition, for instance, if the narrative must include notions of randomness or stochasticity. In such a case, there is no reason for any particular outcome, only reasons for ensembles or patterns of outcomes. The idea that things can happen for no reason is highly counter intuitive [3], and yet in the statistical sciences (which is today essentially all sciences), this is often a critical part of the correct explanation [4]. For the social sciences, I think this is an especially difficult balance to strike because our intuition about how the world works is built up from our own individual-level experiences, while many of the phenomena we care about are patterns above that level, at the group or population levels [5].

This is not a new observation and it is not a tension exclusive to the social sciences. For instance, here is Stephen J. Gould (1941-2002), the eminent American paleontologist, speaking about the differences between microevolution and macroevolution (excerpted from Ken McNamara's "Evolutionary Trends"):

In Flatland, E.A. Abbot's (1884) classic science-fiction fable about realms of perception, a sphere from the world of three dimensions enters the plane of two-dimensional Flatland (where it is perceived as an expanding circle). In a notable scene, he lifts a Flatlander out of his own world and into the third dimension. Imagine the conceptual reorientation demanded by such an utterly new and higher-order view. I do not suggest that the move from organism to species could be nearly so radical, or so enlightening, but I do fear that we have missed much by over reliance on familiar surroundings.

An instructive analogy might be made, in conclusion, to our successful descent into the world of genes, with resulting insight about the importance of neutralism in evolutionary change. We are organisms and tend to see the world of selection and adaptation as expressed in the good design of wings, legs, and brains. But randomness may predominate in the world of genes--and we might interpret the universe very differently if our primary vantage point resided at this lower level. We might then see a world of largely independent items, drifting in and out by the luck of the draw--but with little islands dotted about here and there, where selection reins in tempo and embryology ties things together. What, then, is the different order of a world still larger than ourselves? If we missed the world of genic neutrality because we are too big, then what are we not seeing because we are too small? We are like genes in some larger world of change among species in the vastness of geological time. What are we missing in trying to read this world by the inappropriate scale of our small bodies and minuscule lifetimes?

To quote Howard T. Odum (1924-2002), the eminent American ecologist, on a similar theme: "To see these patterns which are bigger than ourselves, let us take a special view through the macroscope." Statistical explanations, and the weird and diffuse notions of causality that come with them, seem especially well suited to express in a comprehensible form what we see through this "macroscope" (and often what we see through microscopes). And increasingly, our understanding of many important phenomena, be they social network dynamics, terrorism and war, sustainability, macroeconomics, ecosystems, the world of microbes and viruses or cures for complex diseases like cancer, depend on us seeing clearly through some kind of macroscope to understand the statistical behavior of a population of potentially interacting elements.

Seeing clearly, however, depends on finding new and better ways to build our intuition about the general principles that take inherent randomness or contingency at the individual level and produce complex patterns and regularities at the macroscopic or population level. That is, to help us understand the many counter-intuitive statistical mechanisms that shape our complex world, we need better ways of connecting statistics with stories.

27 October 2010: This piece is also being featured on Nature's Soapbox Science blog.


[1] Actually, even defining what we mean by "explain" is a devilishly tricky problem. Invariably, different fields of scientific research have (slightly) different definitions of what "explain" means. In some cases, a statistical explanation is sufficient, in others it must be deterministic, while in still others, even if it is derived using statistical tools, it must be rephrased in a narrative format in order to provide "intuition". I'm particularly intrigued by the difference between the way people in machine learning define a good model and the way people in the natural sciences define it. The difference appears, to my eye, to be different emphases on the importance of intuitiveness or "interpretability"; it's currently deemphasized in machine learning while the opposite is true in the natural sciences. Fortunately, a growing number of machine learners are interested in building interpretable models, and I expect great things for science to come out of this trend.

In some areas of quantitative science, "story telling" is a grave insult, leveled whenever a scientist veers too far from statistical modes of explanation ("science") toward narrative modes ("just so stories"). While sometimes a justified complaint, I think completely deemphasizing narratives can undermine scientific progress. Human intuition is currently our only way to generate truly novel ideas, hypotheses, models and principles. Until we can teach machines to generate truly novel scientific hypotheses from leaps of intuition, narratives, supported by appropriate quantitative evidence, will remain a crucial part of science.

[2] Another fascinating aspect of the interaction between these two modes of explanation is that one seems to be increasingly invading the other: narratives, at least in the media and other kinds of popular discourse, increasing ape the strong explanatory language of science. For instance, I wonder when Time Magazine started using formulaic titles for its issues like "How X happens and why it matters" and "How X affects Y", which dominate its covers today. There are a few individual writers who are amazingly good at this form of narrative, with Malcolm Gladwell being the one that leaps most readily to my mind. His writing is fundamentally in a narrative style, stories about individuals or groups or specific examples, but the language he uses is largely scientific, speaking in terms of general principles and notions of causality. I can also think of scientists who import narrative discourse into their scientific writing to great effect. Doing so well can make scientific writing less boring and less opaque, but if it becomes more important than the science itself, it can lead to "pathological science".

[3] Which is perhaps why the common belief that "everything happens for a reason" persists so strongly in popular culture.

[4] It cannot, of course, be the entire explanation. For instance, the notion among Creationists that natural selection is equivalent to "randomness" is completely false; randomness is a crucial component of way natural selection constructs complex structures (without the randomness, natural selection could not work) but the selection itself (what lives versus what dies) is highly non-random and that is what makes it such a powerful process.

What makes statistical explanations interesting is that many of the details are irrelevant, i.e., generated by randomness, but the general structure, the broad brush-strokes of the phenomena are crucially highly non-random. The chief difficulty of this mode of investigation is in correctly separating these two parts of some phenomena, and many arguments in the scientific literature can be understood as a disagreement about the particular separation being proposed. Some arguments, however, are more fundamental, being about the very notion that some phenomena are partly random rather than completely deterministic.

[5] Another source of tension on this question comes from our ambiguous understanding of the relationship between our perception and experience of free will and the observation of strong statistical regularities among groups or populations of individuals. This too is a very old question. It tormented Rev. Thomas Malthus (1766-1834), the great English demographer, in his efforts to understand how demographic statistics like birth rates could be so regular despite the highly contingent nature of any particular individual's life. Malthus's struggles later inspired Ludwig Boltzmann (1844-1906), the famous Austrian physicist, to use a statistical approach to model the behavior of gas particles in a box. (Boltzmann had previously been using a deterministic approach to model every particle individually, but found it too complicated.) This contributed to the birth of statistical physics, one of the three major branches of modern physics and arguably the branch most relevant to understanding the statistical behavior of populations of humans or genes.

posted October 27, 2010 07:15 AM in Scientifically Speaking | permalink