Intro. [Recording date: June 9, 2025.]
Russ Roberts: Today is June 9th, 2025, and my guest is mathematician and author Paulina Rowinska. Her book, which is our primary focus today, is Mapmatics: A Mathematician’s Guide to Navigating the World. Welcome to EconTalk, Paulina.
Paulina Rowinska: Thank you! I’m delighted to be here.
Russ Roberts: I must confess, I have a great affection for maps. I’ve always appreciated their variety and the stories they tell. While I’m not a collector, I used to keep a bunch of them when I had more physical space in my life, simply because I enjoyed their aesthetic and practical value. However, I want to clarify to our listeners that today’s discussion will transcend the conventional understanding of maps. Paulina, you suggest that a map means something much broader than the paper versions we used to unfold in our cars. It seems your book explores maps as representations of reality, touching on areas such as science, business, and medicine. Is that an accurate depiction?
Paulina Rowinska: Absolutely. My exploration revealed that maps encompass far more than I initially realized. They serve as various representations of reality, models that can be physical, digital, or conceptual. While paper maps are becoming less common, we now rely heavily on digital maps on our phones or specialized maps like tube maps, which can be vital for navigation, especially in complex urban environments.
Russ Roberts: Indeed, for our non-London listeners, a tube refers to the subway system in London.
Russ Roberts: Let’s dive into the traditional concept of maps—those old-school wall maps from our school days. You write, “Whenever we open a map, we hold in our hands the results of centuries of mathematical research.” This statement beautifully encapsulates the depth behind what we often take for granted. Can you discuss how mathematics was historically essential in the creation of maps, both in ancient and modern contexts?
Paulina Rowinska: Certainly. The crux of mapping lies in the challenge of representing a spherical Earth on flat surfaces. A fascinating mathematical theorem indicates that when we project a sphere onto a flat piece of paper, distortions occur—distances and angles can be skewed. This inherent distortion necessitates a careful approach in both map-making and interpretation.
Take the Mercator Projection, for instance, which remains one of the most widely used world maps. It magnifies areas near the poles, making Greenland appear massive compared to continents like Africa. This distortion, although mathematically sound, can warp our perception of the world.
To visualize this, imagine a transparent globe with continents illuminated by a light bulb, casting shadows onto a piece of paper. The placement of that paper dramatically alters the resulting map. Understanding these projections and their implications is crucial for accurately interpreting what we see.
Russ Roberts: If you’re planning a trip across Greenland, understanding the right map projection could significantly impact your preparations, from food supplies to clothing changes, depending on your chosen transport method.
That image of the globe casting a shadow is a striking metaphor for how maps represent reality.
How substantial is the difference in size between Greenland and Africa, in reality?
Paulina Rowinska: Greenland is indeed vast; it’s the world’s largest island. However, in reality, it’s about 14 times smaller than Africa, which is a staggering difference given how it appears on the Mercator map.
Russ Roberts: That’s an astonishing contrast.
Russ Roberts: Speaking of geographical representation, mapping coastlines presents its own set of challenges. Many people might assume that measuring a coastline is straightforward, yet you argue otherwise. Why is it that the coastline of England can vary in measurement?
Paulina Rowinska: It’s a common misconception. The measurement of a coastline is not a fixed number due to its natural irregularities. The length can change based on the measurement tool or method used. For instance, if you use a long stick to measure, you’ll miss many intricate details like bays and inlets. But if you switch to a shorter stick, you’ll capture more detail but still miss some. The shorter the measurement tool, the longer the perceived coastline becomes. This phenomenon highlights why there isn’t a definitive length for coastlines, unlike regular geometrical shapes where measurements converge.
Russ Roberts: It’s fascinating that even shared borders between countries can yield different measurements based on how each country decides to quantify them.
Paulina Rowinska: Yes, exactly! For example, when looking at the Portugal-Spain border, discrepancies arise because each country employs different methods to measure the same line. While one country might report a length of 1,214 kilometers, the other might claim it’s only 987 kilometers long. These differences are not mistakes; they arise from methodological variations.
Russ Roberts: It’s astonishing how subjective measurement can be.
Now, onto the topic of subway maps—what insights did you uncover regarding their design and functionality?
Paulina Rowinska: Initially, subway maps were straightforward, overlaying transportation lines onto geographical maps. However, as systems became more complex, this approach became cumbersome. Henry Beck, a draftsman, revolutionized the Tube map by prioritizing connections over geographical accuracy. The result was a topological map that simplified navigation by presenting straight lines and equal distances between stations, even if those distances were misleading. This design allowed users to focus on their journey rather than the convoluted geography of the city.
Russ Roberts: The power of simplification in mapping is evident here. A map must be useful, which often requires omitting certain details, or else it becomes too unwieldy to be practical.
Russ Roberts: Let’s transition to how mathematics plays a role in optimizing delivery routes, like those utilized by UPS. What challenges do delivery drivers face when determining efficient routes?
Paulina Rowinska: The challenge lies in the sheer number of possible routes. For instance, a driver with five stops has 120 potential ways to complete their journey, but this number grows astronomically as more stops are added. Given that every day presents different delivery needs, finding the optimal route quickly is essential for efficiency. Algorithms play a critical role in this process, allowing companies to determine routes that are “good enough” rather than perfect, thus saving time and resources while still maintaining effectiveness.
Russ Roberts: It’s important to strike a balance between optimal efficiency and practical execution, as the real world often demands flexibility.
Russ Roberts: Now, let’s talk about technology and its evolution in map-making—specifically, the rise of AI. Where do you see the intersection of artificial intelligence and mapping in the future?
Paulina Rowinska: AI is already transforming various fields, including map-making. However, I believe that while AI can assist in computations and data analysis, it cannot fully replace the human element of creativity and critical thinking. AI may streamline the process of proving mathematical theorems or generating maps, but human intuition will continue to play a vital role in determining relevance and context.
Russ Roberts: It’s an exciting time, indeed. As we wrap up, can you share your thoughts on how maps can guide us in our daily lives, particularly in the context of challenges like public health or urban planning?
Paulina Rowinska: Maps are crucial in many life-or-death situations, from tracking disease outbreaks to optimizing city services. I particularly enjoyed exploring geographic profiling in crime analysis, illustrating how mathematics can create safer communities. It’s clear that maps serve a fundamental purpose—helping us navigate not just the physical world but also the complexities of human society.
Russ Roberts: My guest today has been Paulina Rowinska, author of Mapmatics. Thank you for sharing your insights with us.
Paulina Rowinska: Thank you for having me!
