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Nov. 23, 2005 Let me start out my article with a disambiguation, since Wikipedia, which often has disambiguations, did not have one in this case. There are at least two continuum hypotheses, one from Mathematics and one from Mechanics. Here is Wikipedia’s statement of the mathematical case: “There is no set whose size is strictly between that of the integers and that of the real numbers.” Here is Cambridge University’s statement of the continuum hypothesis of mechanics: “The basis for much of classical mechanics is that the medium under consideration is a continuum. Crudely speaking, matter is taken to occupy every point of the space of interest, regardless of how closely we examine the material. Such a view is perfectly reasonable from a modeling point of view as long as the resultant mathematical model generates results which agree with experiment.” The latter continuum hypothesis is the one that I am interested in. This hypothesis states that in looking at steel, for example, I see continuous solid steel regardless of how many times I magnify it. There are no atoms, protons, neutrons or electrons involved. Nowadays, the term ‘classical mechanics’ may ring old-fashioned. This is the system of mechanics based on Newton’s laws and many subsequent developments. But even today, generally speaking, classical mechanics, divided into dynamics and statics, remains in use in the design of machines and structures. That it has since been demonstrated that, microscopically, steel and such materials are not really continua does not make a difference. Classical mechanics still works as well as it always did. In the design of gearwheels and girders, no consideration of the atomic structure of steel and other materials is made, anymore than relativistic dilatation of time and contraction of length are figured into the kinematic equations, say, of flight mechanics and robotics. This does not represent any kind of needless conservatism. Nor is it a slipshod approach by any means. Testing and design performed in accordance with the principles of classical mechanics yield results to virtually any degree of accuracy. Of course, nowadays the fine structure of metals and other materials is being studied too, and perhaps valuable insights will be gained, but basically it is the gross aspect of the behavior of materials that is the subject of interest, with such topics as tensile strength, yield point, strain, stress, elasticity, moment of inertia, velocity, acceleration, impulse, impact, force, work, energy, momentum and the like. One might read dozens of textbooks on these subjects and see hardly a mention of the atomic structure of the materials involved. Engineering manuals such as those published by AASHO, AREA, ANSI, ASTM, ASME and AISC, if I may be allowed not to spell out the lengthy names, hardly discuss the microscopic aspect. Obviously, the continuum hypothesis is the simplest explanation of the nature of things and agrees with common sense and even scientifically controlled experiments and measurements. It also agrees with Occam’s razor, for if I had asked Newton whether he accepted the continuum hypothesis or would subscribe to the idea that steel was really mostly wide open space with little particles rushing swiftly around to create the illusion of solidity, he probably would have chosen the former, opting to follow Occam’s Razor. So Occam’s Razor is not very dependable as a guide to the ultimate questions of physics and other sciences. It is merely a rule of thumb or a guideline. ------------ About the author Thomas Keyes: I have written two books: A SOJOURN IN ASIA (non-fiction) and A TALE OF UNG (fiction), neither published so far. I have studied languages for years and traveled extensively on five continents. Email: udikeyes@yahoo.com Tell a friend about this site! ------------ All articles are EXCLUSIVE to Useless-Knowledge.com and are not allowed to be posted on other websites. ARTICLE THIEVES WILL BE PROSECUTED! |
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