According to legend, the first mathematical formulation of what we might today call a law of nature dates back to an Ionian named Pythagoras (ca. 580 BC-ca. 490 bc), famous for the theorem named after him: that the square of the hypotenuse (longest side) of a right triangle equals the sum of the squares of the other two sides. Pythagoras is said to have discovered the numerical relationship between the length of the strings used in musical instruments and the harmonic combinations of the sounds. In today's language we would describe that relationship by saying that the frequency—the number of vibrations per second—of a string vibrating under fixed tension is inversely proportional to the length of the string. From the practical point of view, this explains why bass guitars must have longer strings than ordinary guitars. Pythagoras probably did not it really discover this—he also did not discover the theorem that bears his name—but there is evidence that some relation between string length and pitch was known in his day If so, one could call that simple mathematical formula the first instance of what we now know as theoretical physics.

Apart from the Pythagorean law of strings, the only physical laws known correctly to the ancients were three laws detailed by Archimedes (ca. 287 BC-ca. 212 bc), by far the most eminent physicist of antiquity. In today's terminology, the law of the lever explains that small forces can lift large weights because the lever amplifies a force according to the ratio of the distances from the lever's fulcrum. The law of buoyancy states that any object immersed in a fluid will experience an upward force equal to the weight of the displaced fluid. And the law of reflection asserts that the angle between a beam of light and a mirror is equal to the angle between the mirror and the reflected beam. But Archimedes did not call them laws, nor did he explain them with reference to observation and measurement. Instead he treated them as if they were purely mathematical theorems, in an axiomatic system much like the one Euclid created for geometry.

As the Ionian influence spread, there appeared others who saw that the universe possesses an internal order, one that could be understood through observation and reason. Anaximander (ca. 6io BC-ca. 546 bc), a friend and possibly a student of Thales, argued that since human infants are helpless at birth, if the first human had somehow appeared on earth as an infant, it would not have survived. In what may have been humanity's first inkling of evolution, people, Anaximander reasoned, must therefore have evolved from other animals whose young are hardier. In Sicily, Empedocles (ca. 490 BC-ca. 430 bc) observed the use of an instrument called a clepsydra. Sometimes used as a ladle, it consisted of a sphere with an open neck and small holes in its bottom. When immersed in water it would fill, and if the open neck was then covered, the clepsydra could be lifted out without the water in it falling through the holes. Empedocles noticed that if you cover the neck before you immerse it, a clepsydra does not fill. He reasoned that something invisible must be preventing the water from entering the sphere through the holes—he had discovered the material substance we call air.

Around the same time Democritus (ca 460 BC-ca. 370 bc). from an Ionian colony in northern Greece, pondered what happened when you break or cut an object into pieces. He argued that you ought not to be able to continue the process indefinitely. Instead he postulated that everything, including all living beings. is made of fundamental particles that cannot be cut or broken into parts. He named these ultimate particles atoms, from the Greek adjective meaning "uncuttable." Democritus believed that every material phenomenon is a product of the collision of atoms. In his view, dubbed atomism, all atoms move around in space, and, unless disturbed, move forward indefinitely. Today that idea is called the law of inertia.

The revolutionary idea that we are but ordinary inhabitants of the universe, not special beings distinguished by existing at its center, was first championed by Aristarchus (ca. 310 BC-ca. 230 BC), one of the last of the Ionian scientists. Only one of his calculations survives, a complex geometric analysis of careful observations he made of the size of the earth's shadow on the moon during a lunar eclipse. He concluded from his data that the sun must be much larger than the earth. Perhaps inspired by the idea that tiny objects ought to orbit mammoth ones and not the other way around, he became the first person to argue that the earth is not the center of our planetary system, but rather that it and the other planets orbit the much larger sun. It is a small step from the realization that the earth is just another planet to the idea that our sun is nothing special either. Aristarchus suspected that this was the case and believed that the stars we see in the night sky are actually nothing more than distant suns.

The Ionians were but one of many schools of ancient Greek philosophy, each with different and often contradictory traditions. Unfortunately, the Ionians' view of nature—that it can be explained through general laws and reduced to a simple set of principles—exerted a powerful influence for only a few centuries. One reason is that Ionian theories often seemed to have no place for the notion of free will or purpose, or the concept that gods intervene in the workings of the world. These were startling omissions as profoundly unsettling to many Greek thinkers as they are to many people today. The philosopher Epicurus (341 BC-270 bc), for example, opposed atomism on the grounds that it is "better to follow the myths about the gods than to become a 'slave' to the destiny of natural philosophers." Aristotle too rejected the concept of atoms because he could not accept that human beings were composed of soulless, inanimate objects. The Ionian idea that the universe is not human-centered was a milestone in our understanding of the cosmos, but it was an idea that would b dropped and not picked up again, or commonly accepted, until Galileo, almost twenty centuries later.

... moving randomly through space, like dust motes in a sunbeam, colliding, hooking together, forming complex structures, breaking apart again, in a ceaseless process of creation and destruction. There is no escape from this process. ... There is no master plan, no divine architect, no intelligent design.

All things, including the species to which you belong, have evolved over vast stretches of time. The evolution is random, though in the case of living organisms, it involves a principle of natural selection. That is, species that are suited to survive and to reproduce successfully, endure, at least for a time; those that are not so well suited, die off quickly. But nothing — from our own species, to the planet on which we live, to the sun that lights our day — lasts forever. Only the atoms are immortal ...

Salt water when it turns into vapour becomes sweet, and the vapour does not form salt water when it condenses again. This I know by experiment. The same thing is true in every case of the kind: wine and all fluids that evaporate and condense back into a liquid state become water. They all are water modified by a certain admixture, the nature of which determines their flavour.

Nature proceeds little by little from things lifeless to animal life in such a way that it is impossible to determine the exact line of demarcation, nor on which side thereof an intermediate form should lie. Thus, next after lifeless things comes the plant, and of plants one will differ from another as to its amount of apparent vitality; and, in a word, the whole genus of plants, whilst it is devoid of life as compared with an animal, is endowed with life as compared with other corporeal entities. Indeed, as we just remarked, there is observed in plants a continuous scale of ascent towards the animal. So, in the sea, there are certain objects concerning which one would be at a loss to determine whether they be animal or vegetable. For instance, certain of these objects are fairly rooted, and in several cases perish if detached.

When human life lay groveling in all men's sight, crushed to the earth under the dead weight of superstition whose grim features loured menacingly upon mortals from the four quarters of the sky, a man of Greece was first to raise mortal eyes in defiance, first to stand erect and brave the challenge.  Fables of the gods did not crush him, nor the lightning flash and the growling menace of the sky.  Rather, they quickened his manhood, so that he, first of all men, longed to smash the constraining locks of nature's doors.  The vital vigor of his mind prevailed.  He ventured far out beyond the flaming ramparts of the world and voyaged in mind throughout infinity.  Returning victorious, he proclaimed to us what can be and what cannot:  how a limit is fixed to the power of everything and an immovable frontier post.  Therefore superstition in its turn lies crushed beneath his feet, and we by his triumph are lifted level with the skies.

One thing that worries me is the fear that you may fancy yourself embarking on an impious course, setting your feet on the path of sin. Far from it. More often it is this very superstition that is the mother of sinful and impious deeds. Remember how at Aulis the altar of the Virgin Goddess was foully stained with the blood of Iphigineia by the leaders of the Greeks, the patterns of chivalry. The headband was bound about her virgin tresses and hung down evenly over both her cheeks. Suddenly, she caught sight of her father, standing sadly in front of the altar, the attendants beside him hiding the knife and her people bursting into tears when they saw her. Struck dumb with terror, she sank on her knees to the ground. Poor girl, at such a moment it did not help her that she had been first to give the name of father to a king. Raised by the hands of men, she was led trembling to the altar. Not for her the sacrament of marriage and the loud chant of Hymen. It was her fate in the very hour of marriage to fall a sinless victim to a sinful rite, slaughtered to her greater grief by a father's hand, so that a fleet might sail under happy auspices. Such are the heights of wickedness to which men are driven by superstition.

You yourself, if you surrender your judgment at any time to the blood-curdling declamations of the prophets, will want to desert our ranks.  Only think what phantoms they can  conjure up to overturn the tenor of your life and wreck your happiness with fear.  And not without cause.  For, if men saw that a term was set to their troubles, they would find strength in some way to withstand the hocus-pocus and intimidations of the prophets.  As it is, they have no power of resistance, because they are haunted by the fear of eternal punishment after death.  They know nothing of the nature of the spirit.  Is it born, or is it implanted in us at birth?  Does it perish with us, dissolved by death, or does it visit the murky depths and dreary sloughs of Hades?  Or is it transplanted by divine power into other creatures, as described in the poems of our own Ennius, who first gathered on the delectable slopes of Helicon an evergreen garland destined to win renown among the nations of Italy?  Ennius indeed in his immortal verses proclaims that there is also a Hell, which is peopled not by our actual spirits or bodies but only by shadowy images, ghastly pale.  It is from this realm that he pictures the ghost of Homer, of unfading memory, as appearing to him, shedding salt tears and revealing the nature of the universe.

We formerly remarked, as a singular phaenomenon, that the animals in the southern provinces of the New Continent, are small in proportion to those in the warm regions of the Old. There is no comparison between the size of the elephant, the rhinoceros, the hippopotamus, the camelopard, the camel, the lion, the tiger, &c. and the tapir, the cabiai, the ant-eater, the lama, the puma, the jaguar, &c. which are the largest quadrupeds of the New World: The former are four, six, eight, and ten times larger than the [128] latter. Another observation brings additional strength to this general fact: All the animals which have been transported from Europe to America, as the horse, the as, the ox, the sheep, the goat, the hog, the dog, &c. have become smaller; and those which were not transported, but went thither spontaneously, those, in a word, which are common to both Continents, as the wolf, the fox, the stag, the roebuck, the elk, &c. are also considerably less than those of Europe.

In this New World, therefore, there is some combination of elements and other physical causes, something that opposes the amplification of animated Nature: There are obstacles to the development, and perhaps to the formation of large germs. Even those which, from the kindly influences of another climate, have acquired their complete form and expansion, shrink and diminish under a niggardly sky and an unprolific land, thinly peopled with wandering savages, who, instead of using this territory as a master, had no property or empire; and, having subjected neither the animals nor the elements, nor conquered the seas, nor directed the motions of rivers, nor cultivated the earth, held only the first rank among animated beings, and existed as a creature of no consideration in Nature, a kind of weak automaton, incapable of improving or seconding her intentions. She treated them rather like a stepmother than a parent, by refusing [129] them the invigorating sentiment of love, and the strong desire of multiplying their species. For, though the American savage be nearly of the same stature with men in polished societies; yet this is not a sufficient exception to the general contraction of animated Nature throughout the whole Continent. In the savage, the organs of generation are small and feeble. He has no hair, no bear, no ardour for the female. Though nimbler than the European, because more accustomed to running, his strength is not so great. His sensations are less acute; and yet he is more timid and cowardly. He has no vivacity, no activity of mind. The activity of his body is not so much an exercise or spontaneous motion, as a necessary action produced by want. Destroy his appetite for victuals and drink, and you will at once annihilate the active principle of all his movements: He remains in stupid repose, on his limbs or couch, for whole days. It is easy to discover the cause of the scattered life of savages, and of their estrangement from society. They have been refused the most precious spark of Nature’s fire: They have no ardour for women, and, of course, no love to mankind. Unacquainted with the most lively and most tender of all attachments, their other sensations of this nature are cold and languid. Their love to parents and children is extremely weak. The bonds of the most intimate of all societies, that of the same family, are feeble; and one family [130] has no attachment to another. Hence no union, no republic, no social state, can take place among them. The physical cause of love gives rise to the morality of their manners. Their heart is frozen, their society cold, and their empire cruel. They regard their females as servants destined to labour, or as beasts of burden, whom they load unmercifully with the produce of their hunting, and oblige, without pity or gratitude, to perform labours which often exceed their strength. They have few children, and pay little attention to them. Every thing must be referred to the first cause: They are indifferent, because they are weak; and this indifference to the sex is the original stain which disgraces Nature, prevents her from expanding, and, by destroying the germs of life, cuts the root of society.

Hence man makes no exception to what has been advanced. Nature, by denying him the faculty of love, has abused and contracted him more than any other animal. But, before examining the causes of this general effect, it must be allowed, that, if Nature has diminished all the quadrupeds in the New World, she seems to have cherished reptile and enlarged the insect tribes; for, though at Senegal there are longer serpents and larger lizards than in South America, yet the difference between these animals is not near so great as that which subsists between the quadrupeds. The largest serpent of Senegal is not double the size of the Cayenne [131] serpent. But the elephant is perhaps ten times the bulk of the tapir, which is the largest quadruped of South America. With regard, however, to insects, they are no where so large as in South America. The largest spiders, beetles, caterpillars, and butterflies, are found in Cayenne and other neighbouring provinces: Here almost all insects exceed those of the Old World, not in size only, but in richness of colouring, delicacy of shades, variety of forms, number of species, and the prodigious multiplication of individuals. The toads, the frogs, and other animals of this kind, are likewise very large in America. We shall take no notice of birds and fishes; because, as Nature has enabled them to pass from the one Continent to the other, it is hardly possible to distinguish those which are proper to each. But reptiles and insects, like the quadrupeds, are confined to their respective Continents.

   their weights and mine stand opposed: the latter being stated, not to produce a conclusion in favour of the American species, but to justify a suspension of opinion until we are better informed, and a suspicion in the mean time that there is no uniform difference in favour of either; which is all pretend.