Work on Bridges-2 shows the approach can help explain persistence of some cultural practices as well as how culture changes over time

Do human culture and practices evolve in a predictable way over time? A team from Carnegie Mellon University and the Santa Fe Institute used a mathematical approach that compared data from 407 world religions as if they existed on a “landscape” where functional patterns of worship and belief are found at local “peaks,” possibly separated from each other by wide and hard-to-cross “valleys.” Their work on PSC’s Bridges-2 system showed that the approach can explain how some religions persist, others change, and still others die out, offering a new tool for understanding how human traditions develop and diverge.


How do human culture and beliefs change through time?
Starting in the 20th Century, scientists studying biological evolution used new mathematical tools to sketch out a kind of landscape that described how some species evolve into other species. Certain body plans, for example, sit in a kind of local “peak” of evolution — once there, an animal’s form is so useful and successful that it tends to persist. One example of these would be the shape of a dolphin versus the similar shape of dinosaur-era reptiles, ichthyosaurs. Others include the body plan of a wolf, paralleled by the thylacine, or Tasmanian “tiger;” and that of the modern bat, which looks something like the flying, extinct pterosaur reptiles.
The evolutionary landscape approach described paths of natural selection as crossing into low-lying valleys and climbing higher up to the peaks. For example, a particular species may not develop into another, more stable form, because a valley-like barrier lies between them. The mathematics behind this way of explaining evolution proved stunningly effective at understanding species and how they change.

“[Variation and selection] is an idea that comes out of biology in the early 20th Century. Biologists started thinking about evolution in more mathematical ways … The thing people started to talk about was called ‘landscapes’ … It’s also a visual metaphor, thinking about how short-sighted rules can still climb to an evolutionary ‘peak.’ You see a further peak out in the distance, and you ask, ‘How do I get from here to there?” – Simon DeDeo, CMU

Predoctoral fellow Victor Møller Poulsen, working with Professor Simon DeDeo’s team at Carnegie Mellon University’s Department of Social and Decision Sciences, wanted to know whether he could apply that successful mathematical approach to the question of how human culture changes and evolves over time — in other words, cultural landscapes. To test this approach against data concerning worldwide religious beliefs, Poulsen, now at the Santa Fe Institute in New Mexico, turned to PSC’s National Science Foundation-funded Bridges-2 supercomputer.


The scientists collected data from 407 religions across the globe. But the data had problems: First, a lot more is known about some of these religions than others. Also, the data didn’t equally sample different parts of the world. Vast amounts of historical literature documented the three largest modern religious traditions — Christianity, Hinduism, and Islam. But others, many of which were important in world history, are today known only by fragmentary sources and archaeological findings. The history of religion in Europe is well documented; we know far less about religious history in Africa. Incomplete knowledge of some religions and of religion in different places in the world posed the risk of biasing the results toward what we know and are familiar with today.

To pierce this uneven veil, the researchers would need to apply mathematical tools that corrected for incomplete and biased data. Such a framework existed, in the form of Bayesian logic. This approach focuses on how the relationship between factors can depend on many other factors. For example, whether a given religion practices small-scale or large-scale rituals, or both, could depend on whether that religion was sponsored by the political state, among other factors. By focusing on many relationships at once, the CMU team’s unrestricted Boltzmann machine could tease out missing factors and what their values would likely be.

The real challenge with this approach would be computational. Being rigorous about what they did and didn’t know would mean exploring a huge number of different possibilities in the computer. The limited data meant many blank spots that needed to be filled, and so even more possibilities to be calculated. These computations increased exponentially, meaning that every new unknown would double the number of calculations. Bridges-2 and its many powerful nodes made the computation possible.

“There’s a trade-off here. By being rigorous as to how we treat missing data, by being rigorous about how we handle finite data, we get an exponentially increasing computational demand … if we simulate histories of religions evolving, we can see if our algorithm can infer the known data correctly. Bridges-2 gave us this ability.” – Simon DeDeo, CMU

The results shed light on how religious beliefs come about and develop. State-endorsed religions and their practices, not surprisingly, experienced stability. Evangelical religions, non-state-sponsored religions, and mystery religions each had their own kind of stability — existing on a kind of “floodplain” that offers stability but also ability to change easily. They were more likely to persist, but also more likely to evolve into related but diverging traditions. More extreme traditions, such as those that involved human sacrifice, were not stable and didn’t persist over time. The scientists reported their findings in the Jan. 31, 2023, issue of the journal Entropy.

The new report represents only the beginning of studying human beliefs and practices with the cultural landscape approach. Poulsen and DeDeo would like to use it to learn more about world religions, particularly those for which we have minimal information. Did members of a particular prehistoric religion believe in a God? Did that God care whether they were good people, such as in Christianity or Islam, or not, as in ancient Greek religion? Can stable religious practices predicted by the team’s work but not present in the 407 religions they studied actually exist, somewhere, at some time, but aren’t seen today because of landscape barriers that prevented people from “getting there from here?” And how can the CMU investigators apply their work to other cultural and political practices? Future work will address these and other questions.