I'm starting this post without knowing for sure that by the time I get to the pseudo-mathematical parts I'll have tracked down, installed and mastered the use of a proper formula typesetting tool. In other words, I am assuming a certain amount of calculated risk, on balance convinced that I will be able to overcome this challenge and deliver a desired result.
When I encounter a challenge (of any sort, not just typographic), what is it in my head that makes me think: "I can do this. Probably." -- ?
Do I literally calculate the odds of success? Only partly. And only if I have the benefit of some distance from the reality of the challenge, some breathing room, time to think, a level of abstraction. But mostly, I intuit the apparent likelihood of success/risk of failure and compare that fuzzy notion to some indefinable threshold, or risk-tolerance.
And yet, odds can be calculated or at least estimated; and statistically speaking that estimate can grow more precise with larger amounts of sample data on which to draw. So what does that mean? How do I reconcile the coexistence of risk as a gut sense of likely success vs risk as a quantitative expression of probability? When you put those two concepts side-by-side with each other, it seems like there might be an incongruity there.
As it turns out, this disconnect has been a topic of debate for several decades, and over the years a number of smart people of taken a stab at formalizing the relationship between risk - in the actuarial sense of the word - and uncertainty, which is the cognitive effect of not being confident of the outcome of a particular event. After Frank Knight identified this distinction in 1921, various disciplines have developed their own language for defining both risk and uncertainty.
From a straightforward engineering perspective, the Risk associated with a particular Event is specifically the product of the Probability of the Event and the Cost of the Event:
It turns out this represents one component of what game theorists call the Expected Value for a particular strategy. The generalized expression for Expected Value basically adds up all of the possible outcomes - both good and bad - that could result from taking a particular decision. Expressed as a sum, this looks something like:
In the field of stochastics, risk is uncertainty for which probability can be calculated or at least estimated:
Cognitive sciences say that uncertainty can be real or simply perceived:
So on the basis of those two definitions, and perhaps somewhat recklessly, I'm going to make a gross generalization. When an individual confronts a unique situation for which the outcome is uncertain, that uncertainty has two components: The part that's calculable and the part that's not. And...
... tying this back to what I talked about in the last post, we might say that the individual human processes the likely outcome of a challenging situation using two different types of reasoning: cognitive reasoning (to process the risk) and emotional/physiological reasoning (to process the uncertainty).