A Gentle Introduction
What’s surprise got to do with it?
Isn’t it just…a second-hand emotion? Technically, a second-order emotion. According to some. But the common thinking these days is that humans aren’t endowed with useless feelings: every emotion has a specific purpose in the service of our survival. We, conscious beings, may be wasteful in our individual pursuits, but our bodies, honed over generations, are careful spenders. In the day to day, we speak of emotions as undesirable by-products of the human condition, setting a very low threshold for what is an acceptable degree of feeling. But in neuroscience, emotions provide a wealth of material to study and surprise is no exception. So what purpose does surprise serve?
Is surprise an emotion?
Surprise is, in functional terms, a feeling, associated with a cluster of physiological responses linked to the sympathetic nervous system. In the human then, we can agree that surprise is a visceral response, something we feel in spite of ourselves. As an emotion, surprise can be good or bad, depending on the person and the context. But stripped of its affective valence, it remains a signal in and of itself. And that signal simply reflects a deviation from the expected.
Without expectation, can we be surprised?
Surprise is born from expectation, a state that channels most1 of our decisions. We generally base our behavior on what we think we know. Of course, we cannot know everything because we are puny, and short-lived, and we’re always changing, and so is our environment. These unknowns incur unavoidable running costs associated with existence. And all these features essentially mean that, the matrix we live in is steeped in uncertainty, be it from a “faulty” perception in our senses, our brains, the inputs we receive, the noise in the environment or changes occurring in any of those systems.
To paraphrase Oughtred of Bebbanburgh2(and maybe challenge him a bit): uncertainty is all.
We make our way through life, testing and trying, guided by expectations that we often know are incomplete. In mathematical terms, expectations are probabilistic: there’s a high chance that we are right, but there’s always room for error. When we are confident in our expectations and the latter fail, we are surprised. The more confident we are in our expectations, the more we are surprised when they are not met.
Think about it. If you have no expectations, if any outcome is equally likely, as in the sex of an unborn child, you cannot be legitimately surprised, at least for one discrete pregnancy. Of course, you may be surprised at having 10 kids of the same sex. You have an expectation about one pregnancy (none) but that expectation translates to 50/50 as outcomes accumulate.
This is where surprise gets very interesting and distinguishes itself from most other feelings. Surprise is tied to probability, so you can quantify it without any special machinery. An average woman’s probability of bearing 10 girls in a row is 0.5^10 (or roughly a 0.1% chance). How surprised should you be at having 10 biological children of the same sex? Well you take the negative log of that probability, which gives you 10. Which is arguably meaningless without a benchmark. By comparison, if 10 pregnancies yield 5 girls and 5 boys, your surprise would be 1.
Surprise=−log (p(event))
Look at that, we went from feelings to logarithms in 5,6 paragraphs! The amount of surprise we computed comes from the field of Information Theory, an area of study based on a wonderful paper written by Claude Shannon in 19483. Now, Claude Shannon did not formally study humans, or their behavior or their brains, but signals, and signal processing and message reconstruction. His work looked at the minimal amount of information transmission required to reconstruct a transmitted message, because recipients have an expectation about a received message and therefore can infer missing bits. In the comparatively young field of cognitive computational neuroscience, we can bootstrap this elegant formula to both human behavior and brain activity.
Still…who cares?
Are we just getting fancy with surprise? After all, most people can simply tell us if they are surprised, and by how much. But what they generally can’t do is relay how surprised their brains are. A popular theoretical framework in the neurosciences is that of the probabilistic brain, or the brain as an inference machine. Briefly, it means the brain, by interacting with its environment, forms expectations about the latter. Repeated exchanges between the organism and the world teach the brain what to expect, forming a model that predicts events. These expectations come in the form of probabilities. When these expectations are violated, surprise emerges. In many circles, this is called a prediction error.
It’s the difference between what you thought and what came to be; the difference between observed and expected. That’s it. We can get fancier about it, the same way we might add Roquefort to a burger4: add lots of builder notation, parse times and so forth, but in the end, the crux of surprise is a simple difference. A subtraction. A – B.
The surprised brain
One reason why the quantification of surprise is still a topic of interest and debate for researchers in neuroscience and artificial intelligence is because, if your brain relies on expectations and probabilities to move you around your environment, it also knows how to deal with surprise. Surprise in the brain does not necessarily evoke that feeling we first spoke of. Our brains, or parts of them, can compute a surprise without your awareness, using those numbers to fine-tune its expectations and help you get around this shape-shifting world without your mind’s input.
1 There is also random lever pressing when you don’t know what to do. Or GUESSING. Also known in scientific circles as exploration.
2 Yes, it’s a very nerdy reference but it’s my blog so I write what I want. The line paraphrases what the main character in this series repeats : Wyrd bið ful aræd
3 Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3), 379-423.
4 Rest in peace, Spotted Pig.