Mental ability and common sense in an artificial society

Having equally valid premises pro and contra, what does a rational human being prefer? The answer is: nothing. We designed a test of this kind and applied it to an artificial society, characterized by a given level of mental ability. A stream of messages from media is supplemented by ongoing interpersonal communication. The result is that high ability leads to well-balanced opinions, while low ability produces extreme opinions. I. HOW WE DECIDE WHAT IS RIGHT OR WRONG We read newspapers and watch TV every day. There are many issues and many controversies. Since media are free, we can hear arguments from every possible side. How do we decide what is wrong or right? The first condition to accept a message is to understand it; messages that are too sophisticated are ignored. So it seems reasonable to assume that our understanding depends on our ability and our current knowledge. Here we show that the consequences of this statement are surprising and funny. To demonstrate this, we propose a computational model with two assumptions [1]. The first is that messages can be represented as points on a plane of a finite area, say, a square a × a. A consequence is that we can measure the distance between messages. The second assumption is that we can understand a message if it is not too far from what we already know. As a direct consequence of these two assumptions, we obtain a simple model of learning. In this model the mind is represented by an area around the messages understood by the mind's owner. Her/his ability is represented by a critical distance D c. A new message can be grasped if its distance to the closest previously understood message is shorter than D c. If this distance is longer, the message is ignored. Let us consider a new area of experience: differential calculus, traffic regulations, stock market, foreign policy or classic Latin grammar can serve as examples. Initially we know a small area on a square. Step by step, we expand our knowledge each time when a new message is found to be comprehensible. The speed at which the known area expands is determined by the parameter D c. If it is comparable with size a of the square, the mind understands everything after a few messages. However, if D c /a is small, initially most of the incoming messages are ignored, and …