Why Do I Need to Understand Math?
Mathematical ability and human social evolution.
Posted May 04, 2018
It’s a standard conversation between math students and teachers all around the world:
Student: “Why do I need to know this stuff anyway?”
Teacher: “Because it will show up on the SAT and you need it to get into college!” (lame!)
Student: “How in the world will this information ever be practical in my future?”
Teacher: “If you end up going into particle physics, you may use some formulas from Calculus III at some point in your work.” (still lame!)
Student: “How will this stuff every help me at all?”
Teacher: “It helps build general critical thinking abilities - I think I learned that in a continuing education class one time …” (yes, still lame!)
OK, so there is the setup. Why are we the mathematical ape? Look, the human mind is capable of all kinds of amazing feats. Across our history, we have solved the question of our own origins, figured out how to communicate with other humans across the globe in real time, and we have sent people to the moon. While we are not all geniuses, humans are pretty smart when you get down to it.
From an evolutionary perspective, it is always useful to dig deeper when trying to understand some basic aspect of what it means to be human.
Highly advanced intellectual abilities, such as the ability to do advanced mathematics, pose a particular challenge to evolutionists who study people because such abilities are clearly found across our entire species (in various degrees across individuals). Mathematical abilities are species-typical, in other words. And this fact, of course, begs the question of why?
Why Are Humans Good at Math?
Math is a basic part of educational systems across the globe. In the US, it is considered foundational, with students between Kindergarten and graduate school being required to demonstrate various mathematical proficiency. And students in the US are considered to be lagging behind students in many other countries!
So if you look at the educational systems of so many societies across the globe, you see that math is highly valued.
From an evolutionary perspective, features of an organism that become typical across a species often have clear adaptive value. That is, such features usually play a clear role in facilitating survival and/or reproduction. Well how does the ability to solve a one-way analysis of variance problem by hand help with survival or reproduction? How does a deep understanding of matrix algebra get you a date? How does the ability to determine the details of an advanced algebraic function help you live another day? What is adaptive about human mathematical abilities? Where did these abilities come from?!
Reciprocal Altruism and Human Mathematical Abilities
As is the case with many features of our evolved psychology, our efforts to understand the origins of our mathematical abilities are not perfect. We have to use a combination of evolutionary logic and solid research on the topic to make headway.
But here is a starting point. In 1985, Robert Trivers published the now-classic book Social Evolution. This book elaborates on many of his ideas related to the evolution of social behaviors across the animal kingdom. In this book, he explores the implications of his theory of reciprocal altruism (Trivers, 1971). This theory on the nature of altruism essentially argues that altruistic behavior between non-kin members can evolve in a species under certain conditions (such as in a species that has individuals who can recognize each other and in a species in which individuals live in stable social groups for long periods of time). Reciprocal altruism, in brief, is the tendency to help someone else with the implicit expectation of being helped in return in the future. This seemingly simple idea has proven very powerful in explaining a wide variety of instances of helping behavior across various classes of animals.
To the point at hand, consider this passage by Trivers (1985) which speaks to the possible evolutionary function of mathematics in humans:
Because human altruism may span long periods of time, and because thousands of exchanges may take place that involve many different goods and many different cost/benefit ratios, the problem of computing the relevant totals, detecting imbalances, and deciding whether they are due to chance or to small-scale teaching is a difficult one.
In essence, Trivers paints humans as the reciprocal-altruistic ape sine qua non, in talking about thousands of exchanges that take place between individual humans with one another across a lifespan. Think about that. Now think about how many people exist in your world with whom you have regular exchanges. Your family members, your friends, your co-workers, the folks in your volunteer organization, the people at your church, friends on Facebook, your neighbors, and more.
The fact of being human carries with it many relationships that each have many exchanges across time.
In a species such as ours, it is important to not be exploited. That is, it is easy to get cheated out of all kinds of goods. If you don’t watch out, you can easily find yourself giving a lot to others and getting very little in return.
Consider the following examples:
- You happily drive your neighbor to the airport. Three weeks later, after doing nothing to help you out in the meanwhile, your neighbor asks you to, again, drive her to the airport, taking five hours of your weekend to help with this request. Hmm …
- You gladly buy items to help celebrate a colleague’s birthday at work. Cake, plates, napkins, balloons, etc.. Two weeks later, another colleague has a birthday coming up. A senior colleague suggests that you’d be great to put together a little celebration for this other colleague as well. Hmm ....
- You and your spouse go out with a couple with whom you are friendly. You decided to be kind and get the entire check at the end of dinner. A few weeks later, you all go out again. The waitress happens to give you the check at the end of the meal. Neither member of the other couple flinches. Looks like it is on you again. Hmm …
In a species such as ours, where social exchanges between a broad array of individuals happen with regularity, we need to be able to keep track of things! We need to be able to count. We need to be able store mathematical information. We need to be able to assign weights to different actions. We need to be able to think about these calculations taking all kinds of short and long-term costs and benefits into account. We need to be able to compute probabilities regarding what is likely to happen in the future. In short, we need math!
Maybe math didn’t evolve so that we can do well on the SAT. Maybe it didn’t evolve because it somehow helps with honing generic critical-thinking skills. Maybe mathematical abilities emerged in humans because we are a species that is deeply immersed in relationships that are characterized by all of the features of reciprocal altruism. Maybe mathematical abilities characterize humans today because our ancestors who were good at making these kinds of calculations were less likely than were other ancestors to make smart decisions in social contexts and end up as winners in the game of reciprocal altruism in life.
One of the things I love about evolutionary psychology is that work in this area often leads to novel predictions that are highly testable. Here are some testable predictions based on this idea of human mathematical abilities as rooted in the deep nature of reciprocal altruism in our species:
- People who score relatively high on mathematical aptitude will be less likely to be victims of cheaters in social interactions.
- People who score relatively high on mathematical aptitude will show optimized levels of altruistic behaviors in social interactions with others.
- Across a sample of regular adults, the ability to accurately make calculations when content is framed in terms of social exchanges should be better than the ability to make those same calculations when the content is not framed as relevant to social exchanges.*
Why does math matter? I say that math teachers who are regularly faced with this eternally annoying question think outside the box and look to our evolutionary heritage. As Trivers (1971) famously demonstrated nearly 50 years ago, reciprocal altruism is one of the most powerful forces in social evolution across a broad array of species—including humans. If you are not able to do the math in terms of who all might help you versus who all might exploit you, you’re in trouble. Mathematical abilities, then, may well have evolved partly to help our ancestors solve these important questions regarding social exchanges.
* This prediction is similar to the predictions made in classic research on social cognition conducted by Leda Cosmides and John Tooby
Cosmides, L. & Tooby, J. (1992). Cognitive adaptations for social exchange. In J. Barkow, L. Cosmides, & J. Tooby (Eds.), The adapted mind: Evolutionary psychology and the generation of culture. New York: Oxford University Press.
Trivers, R. L. (1971). The evolution of reciprocal altruism. Quarterly Review of Biology, 46, 35–57.
Trivers, R. (1985). Social evolution. Menlo Park, CA: Benjamin/Cummings.