Cultural Rituals and Mathematics

Cultural anthropologists teach us that there exists an interplay between all of our cultural rituals and our philosophies and values. By observing our rituals we can deduce that American thinking is dualistic and zero-sum. Dualistic means that there are always two opposing sides. Zero-sum means that for every gain there is a loss. Here we propose two variations in the game of volleyball to remove the dualistic and zero-sum characteristics.

Written: 1999

Formatted: January 2010


Triple Volley Ball - mixed teams version

As shown in the diagram, there are three teams, and three sections. However each team is split between two sections mixing them with members of the other teams.

Thus in each section there will be members of competing teams with uncommon goals. They must find some way to cooperate for their common good. The rules will be similar to regular volley ball, except that the score goes to the team that does not have a member in the section that lost the volley. In this arrangement, we eliminate dualism in a very simple way, we have three teams play at once. We simulate real life by creating situations where players must cooperate with others who have opposing goals. Like real life, "being on the same team" becomes a poorly defined concept.


By analogy, think of your work situation. Can you always tell if your manager is on the same team, or has the same goals? What about your vendors, or customers? Is it not in your own best interest to cooperate with them anyway?

triple ball map

Viewing from the top: the dividing lines represent the nets, each colored dot represents a player from one of three teams represented by three colors

Triple Volley Ball - Two ball version

In this arrangement, there are three teams each in their own section. This again is a minor change from dualism. However, in this arrangement the game will be played with two balls being volleyed at the same time. Points are scored every time a team successfully volleys two balls at the same time. The goal is no longer to force the other team to fail, it is now to take advantage of success (two balls being volleyed) when it comes your way.

The zero-sum mentality has been eliminated. Forcing the other team to fail creates no intrinsic advantages for your team. Spiking is no longer a strategy for success, since stopping the volley scores no points.


Again, think of work. Do you do better by accomplishing your own goals, or by forcing your competitor to fail?

triple ball map

Viewing from the top: the nets create three sections with teams each in their own section

Related Pages at this site:

Outside Links


The Math, the Anthropology, and the Philosophy

American culture depends on dualistic thinking. Our thinking is dualistic in that we persist into defining things into two opposing groups: corporations vs. unions, men vs. women, republican vs. democrat, plaintiff vs. defendant, empowered vs. oppressed, our team vs. your team. We may recall the song from the '70s that declared, "I've seen the world from BOTH sides now ...."

Similarly, our rituals are primarily zero-sum; there must be one winner and one loser, for every gain there is a loss. For our team to win your team must lose. For the defendant to win the plaintiff must lose. For the poor to have more the rich must be taxed. For a Republican to win a Democrat must lose. -Two sides, no in between, no other options!

Dualistic thinking is very limiting, and zero-sum methods are unsustainable. These modes of thinking are not good for problem-solving We must find new ways of thinking to face the challenges of the future. To do this we must reflect our changed thinking in our cultural rituals.

Various other cultures have rituals that are not based in winning. Some cultures have rituals that are based in finding balance or developing cooperation. Our culture has few of these. There are only a few sports that are not dualistic and zero-sum. In mountain climbing everyone who makes to the top and down again wins. Some do it faster, some do it with less, some along new routes, but everyone who makes it wins.



Return to: