8/30/07

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

http://pascal.iseg.utl.pt/~ncrato/Math/Hamming.html

A question that I have been entertaining recently concerns the hypothetical limitations imposed upon us by our Faculty of Reasoning. Is it possible that Science with all of its utility result in a dogmatic viewpoint that blinds us to some alternative forms of knowledge?

Taking the Aristotelian viewpoint of the divinity of principles of logic makes me to believe that logical thinking and chains of reasoning are the closest link to reality. On the other hand, considering the evolutionary argument for the formation of principles of logic makes me to reconsider my seemingly rigid assumptions regarding the nature of the very reality we strive to make sense of via logical reasoning.

Hamming notes the way we perceive of the nature is directly affected by the kind of glasses we wear. So, does a purely logical interpretation and examination of natural events only empower us to have a better conception of reality or may it also limit us to glimpse what could lie beyond!

1 comment:

Anonymous said...

“The development of intelligence among early large mammals of the grasslands was due in great measure to the interaction between two ecologically synchronized groups of these animals, the hunting carnivores and the herbivores that they hunted. The interaction resulting from differences between predator and prey led to general improvement in brain functions; however, certain components of intelligence were improved far more than others. The kind of brain function favored by the interplay of increasingly smarter catchers and increasingly keener escapers is defined by attention- that aspect of mind carrying consciousness forward from one moment to the next. It ranges from a passive, free-floating awareness to a highly focused, active fixation. The range through these states is mediated by arousal system, a network of tracts converging from sensory systems to integrating centers in the brain stem. From the more relaxed to the more vigorous levels, sensitivity to novelty is increased. The organism is more awake, more vigilant; this increased vigilance results in the apprehension of ever more subtle signals as the organism becomes more sensitive to its surroundings. The processes of arousal and concentration give attention its direction. Arousal is at first general, with a flooding of impulses in the brain stem; then generally the activation is channeled. Thus begins concentration, the holding of consistent images. One meaning of intelligence is the way in which these images and other alertly searched information are used in the context of previous experience. Consciousness links past attention to the present and permits the integration of details with perceived ends and purposes. The elements of intelligence and consciousness come together marvelously to produce different styles in predator and prey. Herbivores and carnivores develop different kinds of attention related to escaping or chasing. Although in both kinds of animal, arousal stimulates the production of adrenaline and norepinephrine by the adrenal glands, the effect in herbivores is primarily fear, whereas in carnivores the effect is primarily aggression. For both, arousal attunes the animal to what is ahead. Perhaps it does not experience forethought as we know it, but the animal does experience something like it. The predator is searchingly aggressive, inner-directed, tuned by the nervous system and the adrenal hormones, but aware in a sense closer to human consciousness than, say, a hungry lizard's instinctive snap at a passing beetle. Using past events as a framework, the large mammal predator is working out a relationship between movement and food, sensitive to possibilities in cold trails and distant sounds. The herbivore prey is of a different mind. Its mood of wariness rather than searching and its attitude of general expectancy instead of anticipating are silk-thin veils of tranquility over an explosive endocrine system.”