The Moral of the Donut and Coffee Cup

(First published in Bali Advertise, August 3, 2005)

Topologically, a donut is equivalent to a coffee cup. – A mathematician’s observation

Normal people never confuse a morning donut with a cup of java. Mathematicians are not normal. They are seldom seen in the light of day before they are 30. They do funny things with numbers and squiggly lines. They are boring at parties and have bad haircuts. People don’t understand them and think only that mathematicians must be good at long division and their checkbooks must always balance when they remember to do them.

Topologists, a particularly odd species of mathematician, don’t bother with shape or distance. Their interest lies in sets of objects and the relationships between the objects and the objects of other sets. The only thing a topologist cares about a donut and a coffee cup (when thinking mathematically, not when having breakfast) is that they are solid and have holes through them – the donut hole and the hole in the coffee cup’s handle. It doesn’t matter that they don’t look anything alike; topologically, they can be considered an equivalent collection of “points” making up the solid part around a hole.

The mathematical assumptions of topology make it possible to treat a donut and a cup as the same thing. A change in the “standard” assumptions can also alter familiar rules. Mathematical assumptions can make a difference whether 2+2=4 or 2+2=0, for instance. It is only a matter of choosing the best system for a specific situation. Two plus two equals four is true in the system most often used, the agreed system of banks, accountants, and traffic cops.

If, however, I needed a mathematical system restricted to describing a flywheel moving in quarter turns, then I would choose the less familiar. Two quarter turns and the wheel has gone half way around; another two quarter turns and the wheel is back at the starting point. Thus, 2+2=0 models the flywheel’s movement, and nothing more complex is needed. As strange as the equation looks, it isn’t an abstract mathematical game – just don’t use it when figuring your bank balance.

Many mathematical systems would be less comprehensible. We don’t experience life as nuclear particles, for which the mathematics of quantum physics applies. Assumptions – mathematical, philosophical, and cultural -- make the difference in what is seen as odd and what is considered normal. This truth is often overlooked. It’s not the first thing that comes to mind when people confront something that doesn’t add up.

“He sees a coffee cup and a donut as the same thing? What are his assumptions?” isn’t the usual response. “Let me have some of what he’s smoking,” is more like it.

Differing assumptions are behind the culture shock all travelers and foreign residents have to deal with at one time or another. A bigger problem occurs when people who once shared a set of assumptions find that some members of the group have forsaken some of the assumptions or taken up others. It is an inevitable occurrence for a tribe or nation formed by the circumstances of a particular time and place. For a few generations, the original assumptions hold the grouping together. But as the descendants of the original group meet new challenges and face new dangers, the assumptions change. Some are dropped, others are added, and the subtractions and additions aren’t always accepted universally by the whole. Eventually, every intra-group conflict can be reduced to an argument over what the basic assumptions should be.

That’s America now, with people unable to agree on society’s fundamental axioms and every major news story, from the death of Terri Schiavo to the war in Iraq and Afghanistan and the nominations of Supreme Court judges, sending the American press and people into paroxysms of shrillness. Ostensibly, the debates are about a specific “crisis.” They are in reality another battle over the fundamental principles that are supposed to hold America together. And the problem isn’t restricted to America alone: within America, and between America and the countries of Western Europe, too, the assumptions have become so diffuse that they can support no coherent intellectual agreement. No one is getting the same answer for 2+2 anymore.

Some form of cultural topology could be the solution. A less rigid set of principles would allow some people to see an ideological donut and some a doctrinal coffee cup amid general acceptance that they are much the same thing. The only other eventual option is to start nuking any bastards – friends, enemies, countrymen, or foreigners -- who get any answer besides our four for our two plus two.

Copyright © 2005 Lee Roy LeRoi