Quantum And Physics Infinite Divisibility - 1522 Words

Infinite divisibility has been a historically relevant theme in mathematics and philosophy. Before we had the tools to physically show the mathematical nature of the infinite, philosophers speculated on what happens when a space was divided into infinite parts. Parmenides and Zeno created theories, and paradoxes to prove that infinite divisibility was so significant that the universe is in a constant, unchanging state, and using that to show that motion cannot exist. Aristotle and other philosophers critiqued these ideas by defining various grammatical forms of the term infinity, in order to clarify what the paradoxes really mean and how it is best to talk about infinity. However, all three of them were proven wrong with the development†¦show more content†¦Achilles will then have to reach this new location. By the time Achilles reaches that location, the tortoise will have moved on to yet another location, and so on forever†¦ if we do believe that Achilles succeeds and that motion is possible, then we are victims of illusion, as Parmenides says we are.† (Dowden) This paradox assumes that space is infinitely divisible. Therefore, the premise of this argument is that between two distinct points, there an infinite number of points separating them. If that is the case, then one can never travel from one distinct point to the other because that would require an infinite number of tasks. This idea is seen again in the Dichotomy paradox: â€Å"Zeno argues that a runner will never reach a fixed goal along the racetrack. The reason is that the runner must first reach half the distance to the goal. But once he gets there, he must then cross half the remaining distance, then half of new remainder, and so on. If the goal is one meter away, the runner must cover a distance of 1/2 meter, then 1/4 meter, then 1/8 meter, and so on ad infinitum.† (Dowden). A regressive version of this paradox also exists: â€Å"the runner cannot even take a first st ep. For, any step may be divided conceptually into a first half and a second half. Before taking a full step, the runner must take a 1/2 step, but before that he must take a 1/4 step, but before that a 1/8 step, and so forth ad infinitum, so AchillesShow MoreRelated Does The Void Exist Essay836 Words   |  4 PagesLeucippus agrees with fact that the universe is one plenum. However, he believes that the universe is made up of an infinite amount of plena. These plena are invisible and when they come in contact with each other they react upon each other. This creates quot;Phenomenaquot; or one might say movement. This theory is parallel do modern quantum physics. The universe is made up of an infinite amount of atoms and compounds. We have chemical reactions when they come in contact. Therefore, matter is constantlyRead More The Limits of Science Essays3754 Words   |  16 Pagesreducible to notions that are commensurable to that body. This phenomenologically clarifies some of the m ost important discoveries in contemporary science. The Special Theory of Relativity shows the dependence of space and time on the accounting system. Quantum mechanics displays the limits of observation (Heisenberg) and logical indefiniteness by compelling the creation of a macropresentation of micro-objects and gets around logic (Feyerabend) through the principle of additionality. Experimental science