A Quote by James Clerk Maxwell
All the mathematical sciences are founded on relations between physical laws and laws of numbers.
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All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.
Laws, in their most general signification, are the necessary relations arising from the nature of things. In this sense all beings have their laws: the Deity His laws, the material world its laws, the intelligences superior to man their laws, the beasts their laws, man his laws.
It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist.
While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics.
Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.
If God creates a world of particles and waves, dancing in obedience to mathematical and physical laws, who are we to say that he cannot make use of those laws to cover the surface of a small planet with living creatures?
Physical science enjoys the distinction of being the most fundamental of the experimental sciences, and its laws are obeyed universally, so far as is known, not merely by inanimate things, but also by living organisms, in their minutest parts, as single individuals, and also as whole communities. It results from this that, however complicated a series of phenomena may be and however many other sciences may enter into its complete presentation, the purely physical aspect, or the application of the known laws of matter and energy, can always be legitimately separated from the other aspects.
Does man's freedom consist in revolting against all laws? We say no, in so far as laws are natural, economic, and social laws, not authoritatively imposed but inherent in things, in relations, in situations, the natural development of which is expressed by those laws. We say YES if they are political and juridical laws, imposed upon men by men.
Of course you cannot free yourself from the laws of nature; but the laws of nervous systems are not the same as the physical laws.
We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?
Seurat and Signac mixed paintings with the dry and abstract laws of science. This approach, in my opinion, usually strays from the purpose of art in general. Because it means that one cannot expect from an artifact, that is created with mathematical laws, to establish an improbable and irrational relationship between the work and the viewer.
If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals.
It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method-I know not what.
Laws, it is said, are for the protection of the people. It's unfortunate that there are no statistics on the number of lives that are clobbered yearly as a result of laws: outmoded laws; laws that found their way onto the books as a result of ignorance, hysteria or political haymaking; antilife laws; biased laws; laws that pretend that reality is fixed and nature is definable; laws that deny people the right to refuse protection. A survey such as that could keep a dozen dull sociologists out of mischief for months.
In an information economy, entrepreneurs master the science of information in order to overcome the laws of the purely physical sciences. They can succeed because of the surprising power of the laws of information, which are conducive to human creativity. The central concept of information theory is a measure of freedom of choice. The principle of matter, on the other hand, is not liberty but limitation- it has weight and occupies space.
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