vol III Development:
Chapter 3: Cybernetics
Table of contents
page 0: Introduction
Cybernetics is the study of control and communication. The transfinite computer network serves as a space in which to describe the observed Universe. In this chapter of the site we explore some of its general properties using cybernetic methods.
page 1: Control:
We may see the physical world as a lot of objects (particles) moving around space. All movement takes time, so the stage for physics is physcial spacetime. From a more abstract point of view, we can consider any sort of structure which can be used to assign addresses to particles to be a space. A movement in such an abstract space is simply modelled by a change of address. Cybernetics is the study of the dynamics of such abstract spaces.
page 2: Entropy:
We find that there are limits to the control of complex dynamic systems. One approach to understanding these limits is the 'principle of requisite variety' or requisite entropy. Entropy is a count of the number of states available to a system. The principle tells us that a system with few states cannot control a system with many states.
page 3: Communication
One of the most important abstract spaces is probability space. Shannon developed the mathematical theory of communication in probability space. The chances of messages being confused with one another depend on how close together they are in the 'message space'. By encoding messages into long sequences of symbols, the size of message space may be increased without limit, so that the probability of confusion and error may be made as small as we wish.
page 4: Creation
Deterministic processes like the execution of a Turing machine are not creative. In the past it had been thought that the Universe is deterministic, but the advent of quantum mechanics has made this position difficult to hold. We can reconcile the determinism of computers in a network with creativity by recognising that network (oracle) machines are subject to random interruptions which may introduce new processes that are not computable by an isolated machine.
page 5: Mathematics
All information is embodied physically, in our bodies, in books and buildings and the states of electronic and photonic systems. It is often convenient to ignore the physical realization of information and concentrate on the information itself as a purely formal entity. Logic and mathematics study the properties of formal systems which are not limited by physical embodiment. We can use arithmetic to study any discrete and identifiable objects, for instance, without caring whether they are peanuts or sheep.
page 6: Systems
We understand a system as a collection of discrete parts, capable of more or less independent existence, which work together to make something bigger than themselves. Each of us is a system made of trillions of trillions of stoms working together to create our lives. Cybernetics gives us formal insight into the possibilities and limitation of all sorts of systems,
page 7: The Transfinite Oscillator
Our own lives and our experience of the world show that system are created and annihilated. We are born, grow, reproduce and die. The transfinite oscillator is an abstract representation of this process, describing the increase and decrease of complexity that takes place between the simplest of fundamental particles and the complexity of the Universe as a whole.
page 8: Constraint
Many things are possible, but some are impossible. They cannot exist because their existence involves a contradiction, like black whiteness. Such contradictions define the boundaries of the possible Universe. In our creative Universe, many things, like heavier that air flight, which seems impossible at first sight, can often be realized by finding consistent ways to avoid inconsistencies
page 9: Evolution
Our scientific study of history shows us that the Universe started very simple and gradually became more complex. Many people find this impossible to understand without postulating a pre-existing creator. The principle of requisite variety suggests a similar conclusion, since simple systems cannot control complex systems. The theory of evolution provides a way to avoid this conclusion by demonstrating a consistent path from simplicity to complexity. The formal foundation for this path is Cantor's theorem, which demands the existence of the transfinite numbers