Asking questions for science and defining problems for engineering 2. Developing and using models 3. Planning and carrying out investigations 4. Analyzing and interpreting data 5.
Development of Dynamics; XXV. A glance at ancient physics Although at the time of Christ's birth Hellenic science had produced nearly all its masterpieces, it was still to give to the world Ptolemy's astronomythe way for which had been paved for more than a century by the works of Hipparchus. The revelations of Greek thought on the nature of the exterior world ended with the "Almagest", which appeared about A.
Those of its works that escaped the fires kindled by Mohammedan warriors were subjected to the barren interpretations of Mussulman commentators and like parched seed, awaited the time when Latin Christianity would furnish a favourable soil in which they could once more flourish and bring forth fruit.
Hence it is that the time when Ptolemy put the finishing touches to his "Great Mathematical Syntax of Astronomy" seems the most opportune in which to study the field of ancient physics.
An impassable frontier separated this field into two regions in which different laws prevailed.
From the moon's orbit to the sphere enclosing the world, extended the region of beings exempt from generation, change, and death, of perfect, divine beings, and these were the star-sphere and the stars themselves.
Inside the lunar orbit lay the region of generation and corruption, where the four elements and the mixed bodies generated by their mutual combinations were subject to perpetual change.
The science of the stars was dominated by a principle formulated by Plato and the Pythagoreansaccording to which all the phenomena presented to us by the heavenly bodies must be accounted for by combinations of circular and uniform motions. Moreover, Plato declared that these circular motions were reducible to the rotation of solid globes all limited by spherical surfaces concentric with the World and the Earth, and some of these homocentric spheres carried fixed or wandering stars.
Eudoxus of Cnidus, Calippus, and Aristotle vied with one another in striving to advance this theory of homocentric spheres, its fundamental hypothesis being incorporated in Aristotle's "Physics" and "Metaphysics".
However, the astronomy of homocentric spheres could not explain all celestial phenomena, a considerable number of which showed that the wandering stars did not always remain at an equal distance from the Earth. The astronomy of the "Almagest" explained all astronomical phenomena with a precision which for a long time seemed satisfactory, accounting for them by combinations of circular motions; but, of the circles described, some were eccentric to the World, whilst others were epicyclic circles, the centres of which described deferent circles concentric with or eccentric to the World; moreover, the motion on the deferent was no longer uniform, seeming so only when viewed from the centre of the equant.
Briefly, in order to construct a kinematical arrangement by means of which phenomena could be accurately represented, the astronomers whose work Ptolemy completed had to set at naught the properties ascribed to the celestial substance by Aristotle's "Physics", and between this "Physics" and the astronomy of eccentrics and epicycles there ensued a violent struggle which lasted until the middle of the sixteenth century.
In Ptolemy's time the physics of celestial motion was far more advanced than the physics of sublunary bodies, as, in this science of beings subject to generation and corruption, only two chapters had reached any degree of perfection, namely, those on optics called perspective and statics.
The law of reflection was known as early as the time of Euclid, about B. Dioptrics, being more difficult, was developed less rapidly. Ptolemy already knew that the angle of refraction is not proportional to the angle of incidence, and in order to determine the ratio between the two he undertook experiments the results of which were remarkably exact.
Statics reached a fuller development than optics. The "Mechanical Questions" ascribed to Aristotle were a first attempt to organize that scienceand they contained a kind of outline of the principle of virtual velocities, destined to justify the law of the equilibrium of the lever; besides, they embody the happy idea of referring to the lever theory the theory of all simple machines.
An elaboration, in which Euclid seems to have had some part, brought statics to the stage of development in which it was found by Archimedes about B.
It will here suffice to mention the works of genius in which the great Syracusan treated the equilibrium of the weights suspended from the two arms of a lever, the search for the centre of gravity, and the equilibrium of liquids and floating bodies. The treatises of Archimedes were too scholarly to be widely read by the mechanicians who succeeded this geometrician; these men preferred easier and more practical writings as, for instance, those on the lines of Aristotle's "Mechanical Questions".
Various treatises by Heron of Alexandria have preserved for us the type of these decadent works. Science and early Christian scholars Shortly after the death of Ptolemy, Christian science took root at Alexandria with Origen aboutand a fragment of his "Commentaries on Genesis", preserved by Eusebiusshows us that the author was familiar with the latest astronomical discoveries, especially the precession of the equinoxes.
However, the writings in which the Fathers of the Church comment upon the work of the six days of Creation, notably the commentaries of St.
Ambroseborrow but little from Hellenic physics; in fact, their tone would seem to indicate distrust in the teachings of Greek sciencethis distrust being engendered by two prejudices: The debates raised by this question gave St.
Augustine an opportunity to lay down wise exegetical rules, and he recommended Christians not to put forth lightly, as articles of faithpropositions contradicted by physical science based upon careful experiments. Isidore of Seville d.
His "Etymologies" and "De natura rerum" are merely compilations of fragments borrowed from all the pagan and Christian authors with whom he was acquainted.
Influenced by the various treatises already mentioned, Guillaume of Conches or and the unknown author of "De mundi constitutione liber", which, by the way, has been falsely attributed to Bedeset forth a planetary theory making Venus and Mercury satellites of the sun, but Eriugena went still further and made the sun also the centre of the orbits of Mars and Jupiter.
Had he but extended this hypothesis to Saturn, he would have merited the title of precursor of Tycho Brahe. A glance at Arabian physics The authors of whom we have heretofore spoken had only been acquainted with Greek science through the medium of Latin tradition, but the time came when it was to be much more completely revealed to the Christians of the West through the medium of Mussulman tradition.
There is no Arabian science. The wise men of Mohammedanism were always the more or less faithful disciples of the Greeks, but were themselves destitute of all originality.Natural sciences in theological work - The scientific image of the world and its implications for theology when reading biblical Revelation.
André Neves is a leading figure in geometric analysis with important contributions ranging from the Yamabe problem to geometric flows. Jointly with Fernando Marques, he transformed the field by introducing new ideas and techniques that led to the solution of several open problems which were.
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software.
Under the umbrella of social networks are many different types of graphs. Acquaintanceship and friendship graphs describe whether people know each other.
By analogy with macroscopic devices, feasible molecular machines presumably include manipulators able to wield a variety of tools. Thermal vibrations in typical structures are a modest fraction of interatomic distances; thus, such tools can be positioned with atomic precision.
Formal Analysis. Formal analysis is a specific type of visual description. Unlike ekphrasis, it is not meant to evoke the work in the reader’s mind. Physics is the most fundamental and all-inclusive of the sciences, and has had a profound effect on all scientific development.
In fact, physics is the present-day equivalent of what used to be called natural philosophy, from which most of our modern sciences yunusemremert.comts of many fields find themselves studying physics because of the basic role it plays in all phenomena.