A Stanford School of Engineering research team has developed a new mathematical model for how society becomes polarized, published in the March online edition Proceedings of the National Academy of Sciences. These models are similar to models that seek to predict the behavior of matter based on certain known modes of action, and they are always more difficult for human systems because humans are, inherently, unpredictable (that free will thing). However, they are not without benefit. Opinionaters, debaters, political pundits, anyone passionate about ideologies, can benefit from the insight.

As a Catholic trying to understand better ways to communicate with others, I see some ecumenical insights in this study. Catholicism is all about unity because our God is unity, three Divine Persons who are One God. But as we all know, people are divided. Ecumenism calls us all to engage with the world, whatever our belief, and move beyond our own spheres. Consider the models.

Model 1 – Homophily

The prevailing mathematical theory of social polarization goes like this: Like seeks like. People surround themselves with other people who share their opinions, thereby reinforcing those like opinions. Thus the name, homophily (loving the same).

The model also assumes that people within the polarized groups form opinions to minimize disagreement among like-minded peers, so that the opinions within the polarized group tend toward an averaging unity. People want to appear unified within their groups.

But does that hinder groups from uniting with outside groups? It would seem so.

The Stanford researchers, however, refute this model of homophily. Why? As one of the doctoral candidates and co-author of the paper put it, “You can’t create outliers by averaging.” Over a long enough time, they say, this model would predict that society as a whole, as more and more averaging occurs, would become unpolarized and united, monophilic. I don’t agree with this conclusion because mathematically or naturally, there’s no law that averaging within an outlier subgroup will ever be, or must ever be, extended to the entire population. Just because some molecules react with other ones, doesn’t mean the material world will someday be a mono-substance. But consider the other model anyway.

Model 2 – Biased Assimilation

The research team at Stanford uses another social science model called biased assimilation. This model assumes that what polarizes people is the way they form opinions. When presented with inconclusive evidence (for instance, studies about homosexual behavior, studies about contraception and abortion, studies about whether animals can think, etc.) people easily accept evidence that supports their already held opinion, and discredit anything that does not fit it. They, thus, tend to make more out of inconclusive evidence than they should. It seems counter-intuitive that two people could be presented with the same information, but become further divided in opinion, but the researchers say that is what happens.

Okay, I think we all can relate to that.

If you’ve debated online, you know how it happens. You provide a link to something that you just know will convince the opponent to have an epiphany, and it doesn’t work. Instead, you both talk past each other because you both are trying to further hold your opinions. Have I been guilty of this too? Probably, without even realizing it. At least being aware of the tendency will help to avoid it.

Biased assimilation shows us also why we need to be careful about media choices. Highly polarizing news sources intentionally seek out stories that will further polarize; it’s how they build their audience. Likewise, Internet targeting systems also place ads and news stories in our feeds based on computational preferences. It’s something to be aware of, especially the next time you read or hear a story that makes your blood boil. Try not to assimilate the information with bias, try to understand what the other person is saying.

Catholic Model – Four Concentric Circles

Here’s the thing. I generally find myself wondering after reading these studies why they needed math to figure this out. Isn’t this common sense? The Catholic Church has been pondering human nature for a long time, and rather than mathematical models, Pope Paul VI, for instance, uses an analogy in his 1964 encyclical on ecumenism, Ecclesiam Suam. He describes four concentric circles (96-115) that hold all mankind. Rather than viewing mankind as forming groups and subgroups that are either polarized or united, he describes mankind as one large circle, already united by God, one species.

The circle of mankind includes atheists, other religions, and other Christians — everyone. The next, smaller circle is that of all religions, united because they all seek God. The third inner circle is that of Christians, united because they believe in and love Christ. The fourth, innermost, smallest circle is that of Catholics. So instead of the seeing mankind as polarized by opinion into unmixable substances like oil and water, Catholics are asked to view mankind as one race already and to work from the inner unity we have as Catholics to reach out and draw others in.

So, there is some truth in the Homophily Model, and we ought to avoid seeing ourselves as isolated groups only uniting within. There is some truth in the Biased Assimilation Model, and we ought to be careful that our media sources do not cement extreme biases. However, no mathematical model can ever fully account for the inherent free will of humans. Any parent of a two-year-old or broker on Wall Street knows that. As much as we may benefit from the insight of the mathematical models, I still think the Catholic Church is ahead of the mathematicians on this issue. And I was careful not to assimilate them with bias.
 
 
Originally appeared at StacyTrasancos.com. Used with permission.
(Image credit: Free Math Worksheets)

Every year on March 14 fans of math gather to enjoy a slice of pie along with discussions about pi, or the ratio of a circle’s circumference to its diameter. Since the value of pi is approximately 3.14, pi day is held on March 14 (or 3/14) each year.

One objection to the Bible that pops up all over the Internet is the claim that the Bible teaches that Pi is actually three and not 3.14. In the first Book of Kings, Solomon selects Hiram to create a large, bronze basin of water for the new temple. 1 Kings 7:23 describes how Hiram “made the molten sea; it was round, ten cubits from brim to brim, and five cubits high, and a line of thirty cubits measured its circumference” (a cubit is about 18 inches in length).

The skeptic says this is mistaken, because if the diameter of the basin was ten cubits, then the circumference should be about 31.4 cubits, not thirty cubits. Steve Wells, the author of the Annotated Skeptics Bible, writes, "This verse implies that the value of pi is 3. (The actual value is approximately 3.14159)."

Of course, the Book of Kings is neither a mathematical textbook nor is it an architectural manual. The ancient writers would have had no qualms about referring to the circumference of Solomon’s basin as being 30 cubits in length even if it was actually 31 cubits in length. This is like how we might say a Boeing 747 jet airliner can hold 63,000 gallons of fuel even though technically it can hold 63,705 gallons of fuel.

Furthermore, we have to remember that the Bible is not trying to teach the value of pi; it’s just recording how a real object was created. Calculating the circumference of a circle in a math problem is easy, because the circle is composed of a line that technically has no width. In contrast, Solomon’s basin would have had thick sides in order to maintain its structural integrity. 1 Kings 7:26 says, “Its thickness was a handbreadth; and its brim was made like the brim of a cup, like the flower of a lily; it held two thousand baths.”

This means that the basin had a rim that was greater in circumference than the circumference of the basin’s main body (due to its ornate lilylike shape). According to 1 Kings 7:23, the basin was 10 cubits from “rim to rim,” which probably included the thick edge fashioned like a lily that was a “handbreadth” in width. This means that the diameter of the basin may have been closer to 9.6 cubits in order to allow for a rim that is about 3 inches wide (or a "handbreadth" in width). If it were, then the circumference of the basin below the ornate lily rim would have been 30 cubits in length, just like the Bible describes it.

Skeptics will always find what they consider to be errors in the Bible if they assume the Bible is some kind of divine encyclopedia written by God himself. But the books of the Bible have both a human and a divine author, which frees them from error but also imposes limits on what is taught (just as Christ was fully God but was still limited in his human nature). One such limitation includes rounding for simplicity.

In conclusion, a closer look at the passage shows that the skeptic's argument that the Bible teaches that pi equals three just doesn't add up.
 
 
Originally posted at Catholic Answers. Used with permission.
(Image credit: The Meta Picture)