Friday, December 02, 2005

Memory and Intelligence

Our abstraction for a computational model is the Turing Machine (TM), which Kleene showed to be equivalent to his mathematical model. The TM model includes the notion of memory, in fact infinite memory. Let us first convince ourselves that infinite amount of data requires infinite storage space.

The memory in TM is an infinite tape of cells. One can write a single symbol from a finite set of alphabet on each cell. The collection of markings on a finite number of cells constitutes the encoding of the piece of data they represent.

Let us begin with the assumption that we have been able to encode an infinite amount of data on a finite number of cells. We may assume that the number of cells is a multiple of 2, or else we can simply add a few blank cells. We are going to split the tape in two equal parts. We may assume that the splitting does not occur inside an encoding. Otherwise we can add sufficient blanks to avoid that.

With these assumptions, let us split the finite tape into two equal parts. At least one of the two parts must contain an infinite amount of data recorded on it, for otherwise we must have started out with a finite amount of data. We take the half with infinite data on it for our next splitting. In a finite number of steps we will reach a single cell with infinite amount of data recorded on it. Since this is absurd, our assumption must be false (reductio ad absurdum).

Turing believed that TM is effectively equivalent to a human brain, at least with respect to computation. Computation requires data representation, and our finite brain can only have a finite amount of capacity for storage. Sumerians paved the way for increasing the capacity of our memory by writing on tablets.

History is our memory as species. We enter the whirlpool of Dante’s seven circles when a wicked captures the resources to take advantage of our vast historical data. So far, our intelligence has helped us avoid the seventh circle and retract.

Our brain’s computational mechanism starts out quite primitively. For instance, if a dog scares us at childhood, we simply generalize our unpleasant experience to all dogs. That is the most primitive form of inductive reasoning. From Piaget’s work it follows that for many of us the 12 years of schooling transforms our brain’s computational mechanisms so we can attend college without relying on our father’s bribery.

Our intellect is the totality of mechanisms of our brain for performing computations, symbolic manipulations and reasoning. Intelligence is the brain’s characteristic allowing the evolution of intellect. Thus, to become an intellect the entity must be intelligent. However, intelligence does not guaranty intellectual growth.

The computational mechanisms of Kleene’s model are mathematical notions, such as composition of functions. On the other hand, TM model comprises of mechanical actions such as reading and writing. Nevertheless, the two models are equivalent, and according to Turing’s belief the model is no less powerful than our intelligence.

The Church-Turing Thesis and its philosophical consequences are not the topic of this article. Here, we agree with the possibility of building a specific TM (like writing a program) that can learn. A machine has the ability to learn if it can evolve its reasoning mechanisms.

The idea of stored program was the first step towards endowing machines with intelligence. The next break through will come with the understanding of how a child’s reasoning mechanisms evolve while gaining more information.

The intelligence of a person growing up in a jungle is no less than one going to school in a modern city. Only the types of data that their brain manipulates are different. For instance, without exposure to mathematics brain does not evolve its abstract reasoning mechanisms.

With regard to our memory as species we only recall historical wounds and feuds, very much the same way that we retain our fear of a dog that scared us at childhood. The computational mechanisms acting upon the data stored in our historical memory are probably equivalent to that of a six-year-old’s. Turing might equate that to Kleene’s finite automaton, certainly not equivalent to TM.

Einstein was suspicious about the universe being infinite. However, he had no doubts about the cardinality of human stupidity. So, why is it that, when we are poor we think about the future of all children, but localize that view to our own children once we get rich? Did Piaget miss something about the evolution of our reasoning?

The most likely cause of our death seems to be stupidity. We are still killing one another for historical myth and fiction. When a socially stupid takes power in a third-world country, even in our days thousands are tortured to death. Saddam Hussein is only a few years older than I am.

The term social in this context refers to our scientific view of existence as species, the view that one acquires from a college of liberal arts. We have not grown up from the days of Attila except for building sophisticated computerized weapons.

Z++ is freely available from ZH Micro.