5. How Did Human Beings Acquire the Ability to do Math?

TL;DR

There is no math gene, and no single ability that some people inherit and others lack. Mathematical thinking grew out of the same mental roots as language, because both depend on the capacity to build complex mental models of things not physically present. A stone-age brain, shaped long before formal math existed, repurposed this capacity to invent numbers and geometry.

Transcript

Stanford University okay so for today's um final uh session we as usual two lectures one is dealing with sort of mathematical cognition and how the brain got to be able to do mathematics at least a story that we can tell that we think is moderately plausible or I think is plausible um and then I'll finish with a sort of a grand finale by talking ab... Read More

Key Insights

• There is no math gene, according to Keith Devlin, because natural selection places a capacity into the shared gene pool for everyone to greater or lesser degrees rather than gifting it to a select few individuals.
• Mathematics is evolutionarily recent, with formal mathematics roughly two thousand years old and numbers invented around ten thousand years ago, far too recent for major structural changes in the brain to have occurred.
• The human brain is essentially a stone-age brain doing modern work, meaning the capacities used for mathematics must have existed latently, serving other purposes, for many hundreds of thousands of years before math emerged.
• The brain is the most expensive organ in the body, making up about two percent of body mass while consuming about twenty percent of the body's energy, so its evolutionary payoff had to be enormous to justify that cost.
• Mathematical thinking likely shares the same mental roots as language, since both require constructing complex mental models of things in the future, the past, or elsewhere, rather than simple present-tense communication.
• Language is not fundamentally about basic communication, because a small vocabulary and gestures handle local needs; full grammatical language becomes necessary only to express complex thoughts, plans, and models of the world.
• Mathematical cognition treats mathematics as a way of thinking, a thought process, rather than as a product or set of techniques you apply to problems, which is a meaningful distinction in research and application.
• Cooking food may have fueled brain growth, per recent research Devlin cites, because cooking releases much more usable energy from food, helping support the metabolically costly expansion of the human brain.

Questions & Answers

Q: Is there really no such thing as a math gene?

Keith Devlin argues firmly that there is no math gene. He reasons from how natural selection works: when something enters the human gene pool, it is present for everybody to greater or lesser degrees, not handed to a select few. The ability to do mathematics is a genuine capacity that somehow got into the human gene pool, meaning it is broadly available across large groups of people rather than a rare inherited talent that some students happen to lack.

Q: How did the human brain acquire the ability to do mathematics?

Devlin explains that because mathematics is evolutionarily recent, the brain could not have developed dedicated new structures for it. Instead, the capacities needed for mathematics must have existed in the brain latently, doing other things, for many hundreds of thousands of years. Our essentially stone-age brain repurposed pre-existing mental abilities. He suspected from the start that these abilities were bound up with language, and eventually built a thesis that mathematics emerged from the same mental roots that gave us language.

Q: Why is mathematics considered evolutionarily recent?

Devlin points out that formal mathematics is roughly two thousand years old, numbers were invented around ten thousand years ago, and counting with notches goes back at most tens of thousands of years. These spans are far too recent for any major structural changes in the brain or body to have evolved specifically for math. So mathematics is something a very old brain does with modern content, which is exactly what makes its origin puzzling and interesting.

Q: What is the connection between mathematics and language?

Devlin suspected mathematics came out of the same mental roots as language because both are equally puzzling and both require constructing complex mental models. He notes language is not truly needed for simple local communication, where gestures and a few words suffice. Full grammatical language becomes necessary only to talk about the future, the past, distant places, and to form plans and complex thoughts. Since complex thoughts resemble mathematical models, language and mathematics appear to share a common cognitive origin.

Q: Why is the human brain so costly in evolutionary terms?

The brain is the most expensive organ in the body, making up about two percent of body mass yet consuming about twenty percent of the body's energy. Humans are also born without a fully grown brain, requiring many years and extensive parental care to reach maturity. By these measures the brain looks like an evolutionary non-starter, so it must confer huge advantages to justify its enormous energy demands and the long, vulnerable period of immaturity it imposes.

Q: What role did cooking play in the growth of the human brain?

Devlin cites recent research, published in the National Academy's proceedings, supporting a long-standing thesis that cooking enabled the brain to grow. When humans cook their food, they extract much more usable energy from it, and that additional energy helped fuel the growth of the metabolically expensive brain. This idea addresses how our ancestors could afford such a large, energy-hungry organ, which in turn made possible the later development of capacities like mathematics.

Q: What is mathematical cognition as a field of study?

Mathematical cognition is the study of mathematics as a way of thinking rather than as a product you apply. Devlin describes how his book, along with works by Stanislas Dehaene and by George Lakoff and Rafael Nunez, appeared around the same time and helped cement this field. The approach treats mathematics as a thought process. Devlin notes his own later applied research focused on applying mathematical thinking rather than applying mathematics, which he considers a significant distinction.

Q: How did Devlin approach investigating the origins of mathematical ability?

Devlin used a standard scientific strategy of divide and conquer. Rather than treating mathematics as one broad subject, he split the problem into smaller sub-questions. He framed four guiding questions: how the human brain acquired this ability, when it acquired it in evolutionary terms, what else was going on at that time, and what evolutionary advantage the ability conferred. Breaking the large puzzle into these manageable pieces let him examine each aspect separately and build toward a coherent thesis.

Summary

In this video, the professor discusses the evolution of mathematical thinking in the human brain. He shares his own research and findings from other experts in the field to explain how the brain acquired the capacity for mathematics and how it has developed over time. The professor argues that mathematics is a way of thinking and that it evolved from our ability to handle abstraction and reason about relationships. He also draws parallels between mathematics and soap operas to emphasize the importance of relationships in mathematical thinking.

Questions & Answers

Q: What was the main question the professor wanted to answer?

The main question the professor wanted to answer was how the brain acquired the ability to do mathematics, considering that mathematics is a relatively recent development compared to the age of the human brain.

Q: How did the professor approach answering the main question?

The professor approached answering the main question by dividing mathematics into basic constituent capacities and explaining how each of these capacities evolved and what survival value they offered. He then explored the relationship between these capacities and the development of mathematical thinking.

Q: What are the basic capacities that contribute to mathematical thinking?

The basic capacities that contribute to mathematical thinking, according to the professor, include number sense, numerical ability, spatial reasoning ability, causal reasoning ability, algorithmic ability, abstraction ability, logical reasoning ability, and relational reasoning ability.

Q: How do numbers and language relate to each other?

Numbers and language are closely related. Research has shown that numbers are linguistic constructs and they are tied to language. Bilingual individuals are faster at arithmetic in the language they learned it in, which implies that numbers and language are interconnected in the brain.

Q: What is the role of abstraction in mathematical thinking?

Abstraction plays a crucial role in mathematical thinking. The ability to handle abstraction allows us to construct and reason about abstract mathematical models. Mathematical thinking is essentially the process of reasoning with these abstract models of numbers, shapes, and other mathematical entities.

Q: How are mathematical relationships similar to relationships in soap operas?

Mathematical relationships and relationships in soap operas share similarities in that they both involve understanding and reasoning about connections between different objects or entities. In soap operas, the relationships are based on human emotions and interactions, while in mathematics, the relationships are based on properties, equalities, and other mathematical concepts.

Q: Why does the professor compare watching a soap opera to doing mathematics?

The professor compares watching a soap opera to doing mathematics to highlight the difference in perceived complexity and ease between the two activities. While soap operas may appear more complex and intricate with their many characters and relationships, mathematics requires abstract reasoning and mental manipulation of mathematical concepts, which can be more challenging.

Q: What is the main conclusion of the professor's research?

The main conclusion of the professor's research is that mathematical thinking is not something separate or distinct from other cognitive abilities in the brain. Instead, it utilizes existing capacities such as language and reasoning about relationships in novel and abstract ways. Mathematics is a way of thinking that emerged as society became more complex and required the ability to reason about abstract concepts.

Q: What is the significance of gossip in relation to human relationships?

Gossip plays a significant role in human relationships as it helps to maintain and strengthen social bonds. It serves as a form of communication that allows individuals to exchange information about others and understand social dynamics. Gossip is considered important enough to occupy a large portion of our language use and is seen as the "oil" and "glue" that smooths and fuses relationships between individuals.

Q: How does the professor explain the evolution of mathematical thinking?

The professor explains the evolution of mathematical thinking by proposing that the brain already had latent capacities for mathematical thinking, but it required a trigger to bring them into use. As society became more complex, the need for mathematics arose, and individuals began to interpret and reason about the world using mathematical models. This transformation was facilitated by the brain's ability to handle abstraction and reason about relationships.

Summary & Key Takeaways

• Keith Devlin closes his Stanford Continuing Studies course by asking how the human brain acquired the ability to do mathematics. Because math is evolutionarily recent, the underlying capacity must have existed in the brain for a very long time, serving other functions before math appeared.

• Devlin's central message, drawn from his year-2000 book, is that there is no math gene. Natural selection distributes a genuine capacity across the whole gene pool, so the ability to do mathematics is something broadly available to people rather than a rare inherited talent.

• He argues mathematics grew from the same mental roots as language. Both demand complex mental models of things not present, and building such complex thoughts closely resembles building mathematical models, suggesting math and language emerged from one shared cognitive foundation in our ancestors.