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November 19, 2010
Notes on Programming Neural Systems

Om Namo Shiva Nataraja
Cosmic Dancer
The Light of my Mind

The Limits of Information

I've always naively or intuitively thought that information had its basis in physical matter or energy; that it could not exist without energy. Information is an embedded attribute in physical energy. The ancient thinkers would call an exposition like this metaphysics or religion. But thinking like this is required to build a model.

As I've integrated my studies of entropy into my world view, I've personified it with a Hindu kind of mysticism. Entropy, which is the physical law of time ordered limitations, is also about the unending potential unfolding in Nature.

Placing constraints or limits on physical systems for doing abstract analysis helps us to learn about the system, but sometimes is not appropriate. For example, I think that the concept of infinity [1] or zero applied in certain instances to describe Nature may not be correct all the time. In certain cases in statistical mechancial theory, we cannot consider a system as a "close" system isolated from the rest of the world because the law breaks down in the more general cases [2]. In building models of our world, we necessarily have to put limitations on its behavior, but we need to try to understand these limitations carefully. Just as using the concept of infinity is a limitation, the process of breaking down a system by analysis is setting up a series of limiting conditions.

The measure of static information is a bit. But in real physical systems, no object remains at a constant level of information as function of time. The molecules and atoms are changing through radioactive decay for example. Nature is dynamic, and information is not static. Imagine extracting all the energy out of localized physical system. The movement in this system will approach zero. This system will get cold and rigid, and contain almost no information, but the law of entropy tries its hardest to prevents this extreme condition. Physical systems get very cold, but not as in taking the mathematical limit to zero.

The measure of instantaneous dynamic information is relative depending on the temporal resolution of the detector. The resolution of the detector is limited by the wave fields of physical matter expressed in the uncertainty relationship between energy and time. In this case there's a fundamental finite limit to the "smallness" of matter of which Planck's constant is an attribute. Unlike in theoretical mathematics there's no physically uncountable or infinite fields as in Cantor's set theory. The use of infinite limits in numerical equations are constructs of mathematics, and it sometimes blurs the real constraints imposed by Nature such as the limitations in processing information.

I think of the mind as an information generator. But it's capacity to create information is limited by the physical law of entropy. The brain's ability to create information is constrained by the dynamical flow of order. A good analogy to use is to compared the brain to a steam engine. The steam engine transfers the energy in coal to water to produce steam. The brain converts the energy in the food we eat and air we breath into synaptic waves of electro-chemical currents to produce thoughts.

The fundamental limitations in measuring physical variables can be channeled down into a formula which summarizes the uncertainty principle. With regards to information, this formula lies in the wave packet Fourier transformations used in describing waves.

1. There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination.

Rod Sterling's opening narration to season 1 of the TV series The Twilight Zone (1959).

2. I'm talking about the perspective on viewing the objects as a part of a larger whole, a Bohmian idea. It's confusing a first, but makes thinking of physical systems easier after awhile.