An essential distinction exists between two stages in the process of advancing our knowledge of the laws of physical phenomena; the first stage consists in observing the relations of phenomena, whether of such as occur in the ordinary course of nature, or of such as are artificially produced in experimental investigations, and in expressing the relations so observed by propositions called formal laws. The second stage consists in reducing the formal laws of an entire class of phenomena to the form of a science; that is to say, in discovering the most simple system of principles, from which all the formal laws of the class of phenomena can be deduced as consequences.

All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon. But then we must call in Geometry and Arithmetics, to our Assistance, unless we are willing to content ourselves with natural History and conjectural Philosophy. For, as many causes concur in the production of compound effects, we are liable to mistake the predominant cause, unless we can measure the quantity and the effect produced, compare them with, and distinguish them from, each other, to find out the adequate cause of each single effect, and what must be the result of their joint action.

The aim of research is the discovery of the equations which subsist between the elements of phenomena.

It is surely a pure delight to know, how and by what processes this earth is clothed with verdure and life, how the clouds, mists and rain are formed, what causes all the changes of this terrestrial system of things, and by what divine laws order is preserved amidst apparent confusion. It is a sublime occupation to investigate the cause of the tempest and the volcano, and to point out their use in the economy of things, — to bring the lightning from the clouds and make it subservient to our experiments, — to produce as it were a microcosm in the laboratory of art, and to measure and weigh those invisible atoms, which, by their motions and changes according to laws impressed upon them by the Divine Intelligence, constitute the universe of things. The true chemical philosopher sees good in all the diversified forms of the external world. Whilst he investigates the operations of infinite power guided by infinite wisdom, all low prejudices, all mean superstitions disappear from his mind. He sees man an atom amidst atoms fixed upon a point in space; and yet modifying the laws that are around him by understanding them; and gaining, as it were, a kind of dominion over time, and an empire in material space, and exerting on a scale infinitely small a power seeming a sort of shadow or reflection of a creative energy, and which entitles him to the distinction of being made in the image of God and animated by a spark of the divine mind. Whilst chemical pursuits exalt the understanding, they do not depress the imagination or weaken genuine feelings; whilst they give the mind habits of accuracy, by obliging it to attend to facts, they likewise extend its analogies; and, though conversant with the minute forms of things, they have for their ultimate end the great and magnificent objects of nature. They regard the formation of a crystal, the structure of a pebble, the nature of a clay or earth; and they apply to the causes of the diversity of our mountain chains, the appearances of the winds, thunder-storms, meteors, the earthquake, the volcano, and all those phenomena which offer the most striking images to the poet and the painter. They keep alive that inextinguishable thirst after knowledge, which is one of the greatest charactics of our nature; — for every discovery opens a new field for investigation of facts, shows us the imperfection of our theories. It has justly been said, that the greater the circle of light, the greater the boundary of darkness by which it is surrounded.

The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory.

The first essential in chemistry is that you should perform practical work and conduct experiments, for he who performs not practical work nor makes experiments will never attain to the least degree of mastery. But you, O my son, do experiment's so that you may acquire knowledge. Scientists delight not in abundance of material; they rejoice only in the excellence of their experimental methods.

It can scarcely be denied that the fundamental phenomena which first led mankind into chemical inquiries are those of combustion. But, as we have just seen, minimized beings would be unable to produce fire at will, except by certain chemical reactions, and would have little opportunity of examining its nature. They might occasionally witness forest fires, volcanic eruptions, etc.; but such grand and catastrophic phenomena, though serving to reveal to our supposed Lilliputians the existence of combustion, would be ill suited for quiet investigation into its conditions and products. Moreover, considering the impossibility they would experience of pouring water from one test tube to another, the ordinary operations of analytical chemistry and of all manipulations depending on the use of the pneumatic trough would remain forever a sealed book.

This is the key of modern science and is the beginning of the true understanding of nature. This idea. That to look at the things, to record the details, and to hope that in the information thus obtained, may lie a clue to one or another of a possible theoretical interpretation.

Science proceeds by abstracting what is essential from the accidental details of matter and process.

The diligent investigator of natural phenomena can give the causes of all natural effects... by the rules and roots and foundations given from the power of geometry.

Classical science in its diverse disciplines, be it chemistry, biology, psychology or the social sciences, tried to isolate the elements of the observed universe - chemical compounds and enzymes, cells, elementary sensations, freely competing individuals, what not -- expecting that, by putting them together again, conceptually or experimentally, the whole or system - cell, mind, society - would result and be intelligible. Now we have learned that for an understanding not only the elements but their interrelations as well are required: say, the interplay of enzymes in a cell, of many mental processes conscious and unconscious, the structure and dynamics of social systems and the like.

We must never forget that it is principles, not phenomena, — laws not insulated independent facts, — which are the objects of inquiry to the natural philosopher. As truth is single, and consistent with itself, a principle may be as completely and as plainly elucidated by the most familiar and simple fact, as by the most imposing and uncommon phenomenon. The colours which glitter on a soapbubble are the immediate consequence of a principle the most important, from the variety of phenomena it explains, and the most beautiful, from its simplicity and compendious neatness, in the whole science of optics. If the nature of periodical colours can be made intelligible by the contemplation of such a trivial object, from that moment it becomes a noble instrument in the eye of correct judgment; and to blow a large, regular, and durable soap-bubble may become the serious and praise-worthy endeavour of a sage, while children stand round and scoff, or children of a larger growth hold up their hands in astonishment at such waste of time and trouble. To the natural philosopher there is no natural object unimportant or trifling. From the least of nature's works he may learn the greatest lessons. The fall of an apple to the ground may raise his thoughts to the laws which govern the revolutions of the planets in their orbits; or the situation of a pebble may afford him evidence of the state of the globe he inhabits, myriads of ages ago, before his species became its denizens. And this, is, in fact, one of the great sources of delight which the study of natural science imparts to its votaries. A mind which has once imbibed a taste for scientific inquiry, and has learnt the habit of applying its principles readily to the cases which occur, has within itself an inexhaustible source of pure and exciting contemplations. One would think that Shakspeare had such a mind in view when he describes a contemplative man as finding

The first step in developing a science of any kind of phenomena is to develop and refine instruments that allow one to observe and possibly experiment with the phenomena under investigation. The only instrument we have that enables us to observe mental phenomena directly is the mind itself. But since the time of Aristotle, the West has made little, if any, progress in developing means of refining the mind so that it can be used as a reliable instrument for observing mental events. And… there continues to be considerable resistance against developing any such empirical science even today.

It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which give us the key to the understanding of the phenomena of Nature.