Science as Observation and Experiment a. He asks the reader to carefully observe an eyeball, say that of an ox, from which a portion of the rear has been removed with sufficient care to leave the eyeball fluid untouched. The portion removed is covered with a thin piece of paper.
Differential geometry The German mathematician Carl Friedrich Gauss —in connection with practical problems of surveying and geodesy, initiated the field of differential geometry. Using differential calculushe characterized the intrinsic properties of curves and surfaces. For instance, he showed that the intrinsic curvature of a cylinder is the same as that of a plane, as can be seen by cutting a cylinder along its axis and flattening, but not the same as that of a spherewhich cannot be flattened without distortion.
Instead, they discovered that consistent non-Euclidean geometries exist. Topology Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing.
The continuous development of topology dates fromwhen the Dutch mathematician L. Brouwer — introduced methods generally applicable to the topic.
History of geometry The earliest known unambiguous examples of written records—dating from Egypt and Mesopotamia about bce—demonstrate that ancient peoples had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers.
It concludes with a brief discussion of extensions to non-Euclidean and multidimensional geometries in the modern age.
Similarly, eagerness to know the volumes of solid figures derived from the need to evaluate tribute, store oil and grain, and build dams and pyramids. Even the three abstruse geometrical problems of ancient times—to double a cube, trisect an angle, and square a circle, all of which will be discussed later—probably arose from practical matters, from religious ritual, timekeeping, and construction, respectively, in pre-Greek societies of the Mediterranean.
And the main subject of later Greek geometry, the theory of conic sectionsowed its general importance, and perhaps also its origin, to its application to optics and astronomy.
While many ancient individuals, known and unknown, contributed to the subject, none equaled the impact of Euclid and his Elements of geometry, a book now 2, years old and the object of as much painful and painstaking study as the Bible.
Much less is known about Euclidhowever, than about Moses. Euclid wrote not only on geometry but also on astronomy and optics and perhaps also on mechanics and music. Only the Elements, which was extensively copied and translated, has survived intact. What is known about Greek geometry before him comes primarily from bits quoted by Plato and Aristotle and by later mathematicians and commentators.
Among other precious items they preserved are some results and the general approach of Pythagoras c. The Pythagoreans convinced themselves that all things are, or owe their relationships to, numbers.
The doctrine gave mathematics supreme importance in the investigation and understanding of the world. Plato developed a similar view, and philosophers influenced by Pythagoras or Plato often wrote ecstatically about geometry as the key to the interpretation of the universe. Thus ancient geometry gained an association with the sublime to complement its earthy origins and its reputation as the exemplar of precise reasoning.
Finding the right angle Ancient builders and surveyors needed to be able to construct right angles in the field on demand. One way that they could have employed a rope to construct right triangles was to mark a looped rope with knots so that, when held at the knots and pulled tight, the rope must form a right triangle.The Science of Freedom: An Intriguing Perspective, Questioning Determinism Through Philosophy, Cognitive Neuroscience & Quantum physics (Popular Science) - Kindle edition by Michael Abraham.
Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading The Science of Freedom: An Intriguing Perspective.
Descartes’ Discourse on the Method (Part IV) Descartes’ Discourse on the Method In Descartes’ Discourse on the Method, Descartes tries to explain his existence by the science of reasoning. His research led him to traveling to many countries around the world to observe how other cultures lived.
Thus, Descartes’ claim that there are two methods of demonstration amounts to the claim that there is a method for proving things and a method for explaining things, an interpretation which is reinforced by Descartes’ insistence that synthesis follows analysis (AT.
VII. ; CSM. 2: ). Descartes therefore devises the method of doubt for this purpose — a method to help “set aside” preconceived opinions. Method of Doubt Descartes opens the First Meditation asserting the need “to demolish everything completely and start again right from the foundations” (AT ).
Descartes' Error: Emotion, Reason, and the Human Brain is a book by neurologist António Damásio, in part a treatment of the mind/body dualism question.
Damásio presents the "somatic marker hypothesis", a proposed mechanism by which emotions guide (or bias) behavior and decision-making, and positing that rationality requires emotional input. Contemporary Metaphilosophy. What is philosophy? What is philosophy for? How should philosophy be done?
These are metaphilosophical questions, metaphilosophy being the study of the nature of philosophy.