Physicists From Greece

"Against the diseases of the mind, philosophy provides sufficient antidotes. The instruments which it employs for this purpose are the virtues; the root of which, whence all the rest proceed, is prudence. This virtue comprehends the whole art of living discreetly, justly, and honorably, and is, in fact, the same thing with wisdom. It instructs men to free their understandings from the clouds of prejudice; to exercise temperance and fortitude in the government of themselves: and to practice justice towards others. Although pleasure, or happiness, which is the end of living, be superior to virtue, which is only the means, it is every one's interest to practice all the virtues; for in a happy life, pleasure can never be separated from virtue."

"This happy state can only be obtained by a prudent care of the body, and a steady government of the mind. The diseases of the body are to be prevented by temperance, or cured by medicine, or rendered tolerable by patience."

"When pleasure is asserted to be the end of living, we are not then to understand that violent kind of delight or joy which arises from the gratification of the senses and passions, but merely that placid state of mind, which results from the absence of every cause of pain or uneasiness. Those pleasures, which arise from agitation, are not to be pursued as in themselves the end of living, but as means of arriving at that stable tranquility, in which true happiness consists. It is the office of reason to confine the pursuit of pleasure within the limits of nature, in order to the attainment of that happy state, in which the body is free from every kind of pain, and the mind from all perturbation. This state must not, however, be conceived to be perfect in proportion as it is inactive and torpid, but in proportion as all the functions of life are quietly and pleasantly performed. A happy life neither resembles a rapid torrent, nor a standing pool, but is like a gentle stream, that glides smoothly and silently along."

"There are two kinds of pleasure: one consisting in a state of rest, in which both body and mind are undisturbed by any kind of pain; the other arising from an agreeable agitation of the senses, producing a correspondent emotion in the soul. It is upon the former of these that the enjoyment of life chiefly depends. Happiness may therefore be said to consist in bodily ease, and mental tranquility."

"Pleasure, or pain, is not only good, or evil, in itself, but the measure of what is good or evil, in every object of desire or aversion; for the ultimate reason why we pursue one thing, and avoid another, is because we expect pleasure from the former, and apprehend pain from the latter. If we sometimes decline a present pleasure, it is not because we are averse to pleasure itself, but because we conceive, that in the present instance, it will be necessarily connected with a greater pain. In like manner, if we sometimes voluntarily submit to a present pain, it is because we judge that it is necessarily connected with a greater pleasure."

"The happiness which belongs to man, is that state in which he enjoys as many of the good things, and suffers as few of the evils incident to human nature as possible; passing his days in a smooth course of permanent tranquility. A wise man, though deprived of sight or hearing, may experience happiness in the enjoyment of the good things which yet remain; and when suffering torture, or laboring under some painful disease, can mitigate the anguish by patience, and can enjoy, in his afflictions, the consciousness of his own constancy."

"Since it is every man's interest to be happy through the whole of life, it is the wisdom of every one to employ philosophy in the search of felicity without delay; and there cannot be a greater folly, than to be always beginning to live."

"The end of living, or the ultimate good, which is to be sought for its own sake, according to the universal opinion of mankind, is happiness; yet men, for the most part, fail in the pursuit of this end, either because they do not form a right idea of the nature of happiness, or because they do not make use of proper means to attain it."

"Those who were best able to provide themselves with the means of security against their neighbors, being thus in possession of the surest guarantee, passed the most agreeable life in each other's society; and their enjoyment of the fullest intimacy was such that, if one of them died before his time, the survivors did not mourn his death as if it called for sympathy. (40)"

"Where without any change in circumstances the things held to be just by law are seen not to correspond with the concept of justice in actual practice, such laws are not really just; but wherever the laws have ceased to be advantageous because of a change in circumstances, in that case the laws were for that time just when they were advantageous for the mutual dealings of the citizens, and subsequently ceased to be just when they were no longer advantageous. (38)"

"Among the things held to be just by law, whatever is proved to be of advantage in men's dealings has the stamp of justice, whether or not it be the same for all; but if a man makes a law and it does not prove to be mutually advantageous, then this is no longer just. And if what is mutually advantageous varies and only for a time corresponds to our concept of justice, nevertheless for that time it is just for those who do not trouble themselves about empty words, but look simply at the facts. (37)"

"It is impossible for a man who secretly violates the terms of the agreement not to harm or be harmed to feel confident that he will remain undiscovered, even if he has already escaped ten thousand times; for until his death he is never sure that he will not be detected. (35)"

"Those animals which are incapable of making binding agreements with one another not to inflict nor suffer harm are without either justice or injustice; and likewise for those peoples who either could not or would not form binding agreements not to inflict nor suffer harm. (32)"

"Natural justice is a symbol or expression of usefulness, to prevent one person from harming or being harmed by another. (31)"

"Of our desires some are natural and necessary, others are natural but not necessary; and others are neither natural nor necessary, but are due to groundless opinion. (29)"

"Of all the means which wisdom acquires to ensure happiness throughout the whole of life, by far the most important is friendship. (28)"

"If you reject absolutely any single sensation without stopping to discriminate with respect to that which awaits confirmation between matter of opinion and that which is already present, whether in sensation or in feelings or in any immediate perception of the mind, you will throw into confusion even the rest of your sensations by your groundless belief and so you will be rejecting the standard of truth altogether. If in your ideas based upon opinion you hastily affirm as true all that awaits confirmation as well as that which does not, you will not escape error, as you will be maintaining complete ambiguity whenever it is a case of judging between right and wrong opinion. (24)"

"We must consider both the ultimate end and all clear sensory evidence, to which we refer our opinions; for otherwise everything will be full of uncertainty and confusion. (22)"

"The flesh receives as unlimited the limits of pleasure; and to provide it requires unlimited time. But the mind, intellectually grasping what the end and limit of the flesh is, and banishing the terrors of the future, procures a complete and perfect life, and we have no longer any need of unlimited time. Nevertheless the mind does not shun pleasure, and even when circumstances make death imminent, the mind does not lack enjoyment of the best life. (20)"

"Ὁ δίκαιος ἀταρακτότατος, ὁ δ᾽ ἄδικος πλείστης ταραχῆς γέμων."

"Chance seldom interferes with the wise man; his greatest and highest interests have been, are, and will be, directed by reason throughout his whole life. (16)."

"The wealth required by nature is limited and is easy to procure; but the wealth required by vain ideals extends to infinity. (15)"

"It is impossible for someone to dispel his fears about the most important matters if he doesn't know the nature of the universe but still gives some credence to myths. So without the study of nature there is no enjoyment of pure pleasure. (12)"

"No pleasure is in itself evil, but the things which produce certain pleasures entail annoyances many times greater than the pleasures themselves. (8)"

"Οὐκ ἔστιν ἡδέως ζῆν ἄνευ τοῦ φρονίμως καὶ καλῶς καὶ δικαίως, οὐδὲ φρονίμως καὶ καλῶς καὶ δικαίως ἄνευ τοῦ ἡδέως. ὅτῳ δὲ τοῦτο μὴ ὑπάρχει ἐξ οὗ ζῆν φρονίμως, καὶ καλῶς καὶ δικαίως ὑπάρχει, οὐκ ἔστι τοῦτον ἡδέως ζῆν."

"A happy and eternal being has no trouble himself and brings no trouble upon any other being; hence he is exempt from movements of anger and partiality, for every such movement implies weakness. (1)"

"Self-sufficiency is the greatest of all wealth."

"He who is not satisfied with a little, is satisfied with nothing."

"τὸ φρικωδέστατον οὖν τῶν κακῶν ὁ θάνατος οὐθὲν πρὸς ἡμᾶς͵ ἐπειδήπερ ὅταν μὲν ἡμεῖς ὦμεν͵ ὁ θάνατος οὐ πάρεστιν͵ ὅταν δὲ ὁ θάνατος παρῇ͵ τόθ΄ ἡμεῖς οὐκ ἐσμέν."

"Let no one be slow to seek wisdom when he is young nor weary in the search of it when he has grown old. For no age is too early or too late for the health of the soul. And to say that the season for studying philosophy has not yet come, or that it is past and gone, is like saying that the season for happiness is not yet or that it is now no more. Therefore, both old and young alike ought to seek wisdom, the former in order that, as age comes over him, he may be young in good things because of the grace of what has been, and the latter in order that, while he is young, he may at the same time be old, because he has no fear of the things which are to come. So we must exercise ourselves in the things which bring happiness, since, if that be present, we have everything, and, if that be absent, all our actions are directed towards attaining it."

"Luxurious food and drinks, in no way protect you from harm. Wealth beyond what is natural, is no more use than an overflowing container. Real value is not generated by theaters, and baths, perfumes or ointments, but by philosophy."

"Δικαιοσύνης καρπὸς μέγιστος ἀταραξία."

"Μη φοβάσαι τον θεό, Μην ανησυχείτε για το θάνατο. Αυτό που είναι καλό είναι εύκολο να αποκτηθεί, και Αυτό που είναι τρομερό είναι εύκολο να υπομείνει."

"δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω. [Dôs moi pâ stô, kaì tàn gân kinásō.]"

"Tragically for all of us, he [Archimedes] was cut down by a Roman soldier because he refused to stop working. … If Archimedes hadn't been killed before his time, what could have he achieved? The industrial revolution could have happened two thousand years earlier. He might have kick-started the modern age."

"According to legend, nothing could get between him [Archimedes] and his work, and sometimes he would even forget to eat. Ideas would come to him at any moment, and he would scribble them on any available surface. Famously, he was in the bath when he discovered the laws of buoyancy, leading him to run naked through the streets shouting "Eureka!" … Eureka means "I have found it," and it could be argued that Archimedes found out more than anyone else before or since."

"Archimedes was a brilliant inventor and a mathematician. He says to the people around him, "Don't just live in the lap of the gods. Don't be dominated by Mother Nature. You, as a man, can take control of your own destiny.""

"εὕρηκα [heúrēka]"

"Archimedes was the earliest thinker to develop the apparatus of an infinite series with a finite limit ...starting on the conceptual path toward calculus. Of the giants on whose shoulders Isaac Newton would eventually perch, Archimedes was the first."

"Using his masterful understanding of mechanics, equilibrium, and the principles of the lever, he weighed in his mind solids or figures whose volumes or areas he was attempting to find against ones he already knew. After determining in this way the answer...he found it much easier to prove geometrically... Consequently The Method starts with a number of statements on centers of gravity and only then proceeds to the geometrical propositions and their proofs. ...[He] essentially introduced the concept of a thought experiment into rigorous research. ...[He] freed mathematics from the somewhat artificial chains that Euclid and Plato had put on it. ...He did not hesitate to explore and exploit the connections between the abstract mathematical objects (the Platonic forms) and physical reality (actual solids and flat objects) to advance his mathematics."

"Almost all modern translations of Archimedes’ works stem from a single Greek manuscript that was copied from an earlier original at Constantinople in the ninth or tenth century, was translated into Latin in the thirteenth century, and eventually disappeared without a trace in the sixteenth century."

"In Euclidean geometry the infinitely small was rejected and in the classical treatises of Archimedes we have the finest example of mathematical rigour in antiquity. Notwithstanding, in the discovery method we find him manipulating line and surface indivisibles skilfully, imaginatively and non-rigorously"

"The estimations, which occur in the summing of infinite series and in limiting operations, the "epsilontics", as the calculation with an arbitrarily small ε is sometimes called, were for Archimedes an open book. In this respect, his thinking is entirely modern."

"To conceive of a parabolic segment or of a triangle as the sum of infinitely many line segments, is closely akin to the idea of Leibniz, who thought of the integral \int y~dx as the sum of infinitely many terms y~dx. But, in contrast to Leibniz, Archimedes is fully aware that this conception is... incorrect and that the derivation should be supplemented by a rigorous proof."

"Modern mathematics was born with Archimedes and died with him for all of two thousand years. It came to life again with Descartes and Newton."

"There is here, as in all great Greek mathematical masterpieces, no hint as to the kind of analysis by which the results were first arrived at; for it is clear that they were not discovered by the steps which led up to them in the finished treatise. If the geometrical treatises had stood alone, Archimedes might seem, as Wallis said, "as it were of set purpose to have covered up the traces of his investigations, as if he has grudged posterity the secret of his method of inquiry, while he wished to extort from them assent to his results.""

"The treatises are, without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader."

"In these days an infinite number of chemical tests would be available. But then Archimedes had to think... afresh. The solution flashed upon him as he lay in his bath. He jumped up and ran through the streets to the palace, shouting Eureka! Eureka! (I have found it! ...) This day... ought to be celebrated as the birthday of mathematical physics; the science came of age when Newton sat in his orchard. Archimedes... had made a great discovery. He saw that a body when immersed in water is pressed upwards by the surrounding water with a resultant force equal to the weight of the water it displaces. ...Hence if W lb. be the [known] weight of the crown, as weighed in air, and w lb. be the [unknown] weight of the water which it displaces when completely immersed, W - w [from which (knowing W) the weight w of the equal volume of water can be derived,] would be the extra upward force necessary to sustain the crown as it hung in the water. [Alternatively, the weight of water, equaling the volume of the crown, and overflowing a tub, could be weighed directly.] Now, this upward force can easily be obtained by weighing the body as it hangs in the water [Fig. 3]...But \frac{w}{W} ...is the same for any lump of metal of the same material: it is now called the ... Archimedes had only to take a lump of indisputably pure gold and find its specific gravity by the same process. ...[N]ot only is it the first precise example of the application of mathematical ideas to physics, but also... a perfect and simple example of what must be the method and spirit of the science for all time. The discovery of the theory of specific gravity marks a genius of the first rank."

"Some of the later Greeks, such as Archimedes, had just views on the elementary phenomena of and optics. Indeed, Archimedes, who combined a genius for mathematics with physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics."

"Archimedes originally solved the problem of finding the solid content of a sphere before that of finding its surface, and he inferred the result of the latter problem from that of the former. ...another illustration of the fact that the order of propositions in the treatises of the Greek geometers as finally elaborated does not necessarily follow the order of discovery."