Mathematics is often thought of as certain. It is a closed system, with strict rules that enables objective empirical verification by anyone of almost any age. Other animals can perform at least basic functions such as counting, adding and subtracting. In fact, if any species was unable to use at least basic mathematical functions they would simply not survive. They wouldn’t understand when they were being cheated or thriving and we know from research, they do understand those concepts.
I teach statistics. Many probably think of statistics like any other math class. That is a major error. Statistics does use mathematical operations. However, its intent is to use direct observations to infer and extrapolate parameters to unobserved hypothetical events.
Probability calculations are the simplest form. What are the odds of me rolling a six with a six sided unbiased die? What are the odds of me winning the lottery? These calculations are very simplistic, reliable, and verifiable - they are mathematically certain.
Unfortunately, even the basic principles of probability are misunderstood and misapplied constantly (even by statisticians). The intellectual statisticians would quickly point out that average people make errors regularly. There have been many studies and demonstrations of this. We are all familiar with what is called the Gambler’s fallacy, that red or heads is “due” after several previous occurrences of the opposite. However, I think that fallacy is a fallacy.
The Gambler’s fallacy simply misunderstands the constituents of reasoning. To a statistician it is obvious that the next roll or flip has the exact same probabilities as the previous, so that heads is equally likely as tails (do they really think gamblers don’t know this?). However, statisticians would also tell you that “in the long run” the occurrence of heads and tails should be equal. Because of the way research is done in this area, it appears the average person is unaware of both of these truisms. However, gamblers (and other animals) are keenly aware of both. When a gambler says red or heads is “due” they are reflecting awareness of the long run phenomena. Are they betting with certainty? No, they know they could be wrong; they know it is a gamble. Even a statistician would have to admit that after a long run of tails, the probability of heads becomes greater - if nearly incalculably so - than tails, if the distribution should be equal “in the long run”.
To intellectuals, rationality is equated with calculating probabilities, so they deride anyone stupid enough to play the lottery. The chances of winning are so small, it is irrational to waste money on such an activity. My first reaction to that is, try telling that to the winners. They had the exact same infinitesimal odds as everyone who lost, but now they can buy and sell you. This factor, the value of the outcomes, not the raw probabilities, is often discounted by intellectuals when defining pure reason.
Blaise Pascal, a 17th century mathematician, argued that "Reason's last step is the recognition that there are an infinite number of things which are beyond it." Pascal reasoned people should believe in God, not because the probability (pure cold reason) is high that God exists, but rather based on the costs and benefits of the alternatives. In his formulation there is only one condition that “wins”, so why not bet on that option, even if the probabilities are infinitesimally small.
Like the lottery gambler, the odds of winning may be low, but buying even one ticket drastically increases the odds from not playing at all, which is zero (and potentially horrifying). Those are not the odds of being right statistically, they are the odds of a desired versus feared outcome.
Now, the foregoing examples demonstrate how, in well understood games of chance, behavior is not guided simply by probability. Intellectuals may judge that as irrational, but research with human and animal behavior indicates otherwise. This may be because behavior outside of games of chance involves several more variables and real life consequences involving life and death. And in this real world arena is where intellectual emphasis on probability calculation as true rationality radically breaks down.
I will summarize two allegories I learned from reading Gerd Gigerenzer’s 1991 article, “How to Make Cognitive Illusions Disappear: Beyond ‘Heuristics and Biases’”. The first is a parent residing in a jungle, deciding where to send their child to play, knowing that over the last 100 years 10 children have died playing in the trees and only 1 child died playing in the river. Where should they send their child if yesterday a child was eaten by a crocodile in the river? If we believe reason is based solely on frequency probability the rational choice would still be the river. The probability is now just 2 in 100 years compared to 10 in 100 years for the trees. So, intellectuals that trust reason alone should send their offspring to the river. Natural selection at work. The second is a beggar that when offered money always takes a lower amount. This seems irrational. Yet, so many people come to offer him money just to see his irrationality, he still makes quite a sum. This is similar to economic markets of scale where margins are smaller but volume more than compensates.
There is a popular podcast based on a book called Freakonomics, by an economist and writer team, which I argue regularly makes a similar type of probability error. This error is very commonly committed by statisticians, economists, and other social and health scientists equating reason with simplistic frequency probability. The error occurs when the sample being measured is not representative of the population to which the findings are inferred. This happens when researchers have a simplistic or naïve understanding of the causal or correlational variables producing a specific outcome (which may be equally over-simplified).
An example from the Freakonomics book illustrates this point. In the author’s effort to show how stupid people are, they ask people if it is safer to send a child to play at a home with a pool or that has guns. They mock the irrationality of people saying it is safer to send kids to a pool home as being influenced by the fear of guns rather than the data which shows pools are much more lethal to children. While the data seem to support the duo, they have made a critical error that the parents of children rarely make. Parents likely take into account factors unique to their children that are not adequately represented in the statistics. For example, can their child swim, will they be supervised, how deep is the pool and how tall is their child, will there be floatation devices nearby, are the guns loaded or locked away, has their child been educated in proper gun safety, etc. etc.
This is just one error in their statistical reasoning of several I have pointed out from the book. They are by no means alone. Whether its calculating your probability of dying by lightning strike, shark, or in a car versus a plane, the “experts” are wrong. There are endless examples of humans and other animals behaving in ways that seem irrational, when measured by faulty statistical methods, but have obvious adaptive survival value. You can check out my YouTube channel for more examples: https://www.youtube.com/channel/UCldeKg5_-lbh46Xi7pZL1iw
So, what we have is a different operationalization of reason. Reason is not accurately calculating probability. No animal wins in survival simply from accurate probability calculation. The consequences of taking risk (when probability favors another action) are what really seem to matter. We are back to favoring Forest Gump’s “stupid is, as stupid does” formulation of intelligence rather than championing the intellect and “pure” reason.
In future newsletters I will highlight how designing realistic research is essential to a scientific understanding of behavior and reason. After all, research is a simulation. If it does not adequately represent reality, it is misleading, just as inferring results from a non-representative sample is misleading. Unfortunately, many of those designing research with humans or animals are more like Sheldon’s than Forest’s. They vastly over rely on their intellect rather than experience and so fail in simulating reality. I will also point to alternative ways of measuring behavior that positively correlate with reason.
Intellectual Failures - Probabilistic Reasoning