Abstract This paper explains that the solution to Stepran's infinitypuzzle is not so difficult and has nothing to do with infinity, although the calculus of this equation may in fact be infinite. The author underscores that the puzzle is not a puzzle at all and is not indicative of infinity but rather is purely an exercise in the limitations of physics. The paper agrees with Rucker's concept of infinity as simply a natural element of the universe or of being one of the basic functional elements of mathematical device. The author concludes that the useful concept of infinity is that it does naturally occupy points in both physical and mathematical space ,which truly cements it within the context of a tangible mathematical and physics principle rather than some far-off rationale construct created and identifiable only by mathematical theorists.
Table of Contents:
The Puzzle The Solution
Response Page to Postings
Discussion
From the Paper "Stepran's states that a person is tasked with turning a light switch off and on starting with on at 2 minutes and then in increments by half of the time remaining flipping the switch to the opposite position. On the surface the outcome appears as if it will be a simple persuasion of the ineluctable quality of time; that, time is unavoidable and all things must come to an end. Yet, as one begins the calculations it becomes apparent that the half increments are, apparently, infinite starting with two in terms of seconds: 120, 60, 30, 15, 7.5, 3.75, 1.875, .93, .46, .23, .117, .058, .029, ad infinitum, at least to the extent that a common calculator is capable of dividing."
Abstract This three page undergraduate paper examines an infinitypuzzle called 'Doing Business with the Devil'. The writer explains that resolving the puzzle requires accepting the interpretation that there may be many infinities. The writer discusses that if this is true, turning a light switch on and off at ever decreasing intervals and then determining whether the light would be on or off after two minutes would result in a conclusion that the light would be both on and off.
From the Paper "In discussing and analyzing the "Doing Business with the Devil" puzzle presented in the lecture, resolving the puzzle requires accepting the interpretation that there may be many infinities. If this is true, turning a light switch on and off at ever decreasing intervals and then determining whether the light would be on or off after two minutes would result in a conclusion that the light would be both on and off. From the point of view of Rucker, this is the only logical conclusion that can be made, "for the infinite regresses resulting from recursion" confirm that the infinite "is a real, rather than imagined, concept" (Rucker)."
Abstract The 'Doing Business with the Devil' puzzle presents us with a situation in which there are a finite number of one-dollar bills, and the writer is doing business with the Devil, who in this scenario is an avid bill collector. The Devil wants to buy the writer's one-dollar bill with the serial number of 001, and invites the writer to name the price. Some time later he returns and makes a similar offer for the 002 bill. A shorter time later he returns and wants the 003 bill.
From the Paper "The "Doing Business with the Devil" puzzle presents us with a situation in which there are a finite number of one-dollar bills, and I am doing business with the Devil, who in this scenario is an avid bill collector. The Devil wants to buy my one-dollar bill with the serial number of 001, and invites me to name my price. Some time later he returns and makes me a similar offer for the 002 bill. A shorter time later he returns and wants the 003 bill. This continues indefinitely, while I attempt to amass a fortune."
Abstract This paper describes the goals and objectives of a series of conferences between the Vatican and leading scientists on questions of Infinity. The paper examines the theological issues involved Infinity.
From the Paper "The Vatican has historically grappled with resolving the theological issues that are associated with new scientific discoveries. Recently the Vatican press office announced a new project on science and..."
Tags: Vatica, Roman Catholic CHurch, science, Infinity
Abstract This paper defines infinity and finite. The author describes how humans use cognitive processes to understand the finite with the infinite. The paper relates three types of infinity and how these can be broken down to understand infinity.'
From the Paper 'Is infinity real or is it imagined? How does a finite mind deal with the infinite? Consider the universe and how infinite it. Consider God and how infinite he is. Was there a universe before God? Did time even exist before the Creator? While these are infinite, but things people do are finite such as breathing. Considering whether infinite is real, it is important to look at time, space, and any intervals of these which can be divided or even subdivided and how infinite our minds are. It is important to understand how the finite is quite different than infinite.'
Abstract This paper discusses that crossword puzzles can be found in almost every newspaper in almost every country and in magazines and book dedicated solely to these puzzles. The author points out that crossword puzzles have inspired other gridded word games, like acrostic, cryptic and diagram-less puzzles, and board games, such as Scrabble. The paper relates that the predecessors of today's crossword puzzles is the 19th century British acrostic puzzle designed specifically for children, such as "Lewis Carroll's doublet puzzle". The author relates that the first known word square, called the Sator Square, was carved in stone and dates from the first century A.D. in Pompeii. The paper concludes that, although crossword puzzles provide a form of constructive entertainment during leisure hours, some people claim that puzzle solving is a human instinct.
From the Paper "Puzzles have been around since the beginning of history. "One of the earliest surviving manuscripts of human civilization is, as a matter of fact, a collection of mathematical puzzles", known as the Rhind Papyrus. In the ancient world, the first puzzles were in physical form, or labyrinths. According to Denasi (2002), "the biblical kings Solomon and Hiram were renewed for organizing riddle contests." The word 'puzzle' probably derives from the Middle English word poselet, meaning bewildered or confused. The crossword is the most common variety of word puzzle in the world, yet it is one of the few types of puzzles that do not have an ancient origin."
Tags: cryptic square times acrostics, mental exercises
Abstract This essay discusses whether infinity can be seen as a real entity. R. Rucker argues that it is quite possible that time may continue forever. Lakoff and Nunez argue that mathematics is the result of the human mind creating metaphors for phenomena it encounters.
Abstract This paper discusses how language teachers are discovering, too, that incorporating word games and puzzles into their second-language instruction helps the student absorb the necessary information in a manner that is both fun and challenging.
Abstract This essay will look at this debate in the context of the puzzle, "Doing Business with Devil," and will explore the debate through the points of view of R. Rucker's Infinity and the Mind and G. Lakoff and R. Nunez's Where Mathematics Comes From.
Abstract R. Rucker helps us better understand Godel's "Theorem on Incompleteness" by discussing infinity and whether it can be seen as a real entity. In his view, infinity can be seen as a tangible reality. He argues that it is quite possible that time may actually continue forever - and that is precisely what infinity is. Rucker also sees the possibility of the potential infinite divisibility of space into smaller and smaller pieces.
Abstract This paper presents two differing conceptions of infinity and how they apply to a single thought experiment. The author points out that the first viewpoint is that of Rucker who believes that infinity is as real as any other mathematical concept and is essentially a Platonist viewpoint. The paper relates that the other conception is that of Lakoff and Nunez who believe that infinity is an abstract metaphor whose use should be employed when it is useful, but which is not real.
From the Paper "In "Doing Business with the Devil", we are presented with an interesting intellectual dilemma that has a few things to do with our discussion of the infinite. At first glance (and even second and third glances) the puzzle seems nearly nonsensical. The words make sense, but the point is elusive. In the puzzle, an individual is dealing with the Devil in a situation with an infinite number of one-dollar bills, which the Devil just happens to collect."
Abstract Author Rudy Rucker has a way of explaining science and mathematics so that even the 'technology challenged' can usually get a grip on it. This paper shows that in his book, "Infinity and the Mind", Rucker explains "physical infinities" in a way that makes it simple for the layman to comprehend.
From the Paper "Dante, Nicolas of Cusa, Bruno and Giordano all believed in the infinitude of space, and isn't it a fascinating note in science that Bruno was traveling around Europe and teaching his doctrine of the universe in the late 1580s? By mentioning Bruno's travels and lectures (and his dialogue of 1584, "On the Infinite Universe and Worlds"), Rucker helps readers understand that the theories that are out there on infinity are not only old, but still up for debate."
Abstract What is existence? This essay categorizes existence, with reference to the conceptions of reality made by Aristotle and Sartre. The paper asks if existence of something unknowable is possible? Is metaphysics a legitimate enterprise based on an authentic order to the world? The paer shows that existence is to be examined as whole and all encompassing, and that reality and non-reality are necessary components for experience.
From the Paper "When we consider our experience, and the "place" in which it occupies, many questions come to mind. What is this experience? Is what I experience all that exists? Do things out there exist? Why does this exist? And so on. It is my contention that all of these questions, and many others of a similar nature are all related in a fundamental way to the question of infinity. Naturally enough, when we think of infinity, we think of it pertaining to something, as a property of something. It is this question of whether a thing is finite or infinite that comes before all others, even whether it has the "property" of existence. This is due to the fact that finity and infinity define two possible values of existence. Finite existences have a subset of properties that establish its nature. Infinite existences, or possible existences, also have another subset of properties that establish its nature. It is my further contention that infinity represents an ultimate logical impossibility in the establishment of existence, and threatens the "wholeness" that establishes a reality. With that in mind, we can rule out the subset of properties associated with infinite existences, as they turn out to be the very properties of non-existence, which, as I will show, if a fundamental aspect to a reality itself. In short, this essay will systematize reality from non-reality, existence from non-existence using the notion of absolute finitude as a touchstone."
Abstract This paper looks at Gamow's book and how the storytelling format with which the author and mathematics instructor, George Gamow, approaches his subject and grabs the interest of the reader goes far beyond math, science, physics, and mere numbers placed in esoteric formulae.
From the Paper "Gamow did indeed "strive" during his life and career - and in One Two Three...Infinity - to "emphasize" the importance of science and technology. He also strove to In his original Preface, written in 1947 at the time the book was first published, Gamow acknowledges that he did not "attempt to tell the whole story" of modern science; he also shows his ability to understand and be modest when he writes (vi) that he has restricted himself to "a general account of physical facts and events in the world of planets, stars, and nebulae..." "
Abstract This paper provides a clear explanation of Blaise Pascal's "Wager for Sceptics." It explores, in depth, its merits and its flaws and focuses on the flaws in Pascal's reasoning that resulted in it not achieving his stated goal. This paper demonstrates that, ultimately, the arguments against the "Wager for Skeptics" all stem from the incomprehensible nature of infinity, a notion that lies at the heart of Pascal's work.
From the Paper "Emanating from his mathematical background, comes Blaise Pascal's Wager - a line of reasoning designed to lure people into the Christian faith. Pascal is acutely aware of human nature, and so bases his campaign around the reader's self-interests, rather than actual theological proofs. The Wager's basic proposition is that if a person believes in the Christian God, there is a chance of them gaining infinite reward. Conversely, if a person does not believe in God, they have no chance of gaining the reward which is on offer. This is a deceptively simple choice: one that immediately appears both enticing and convincing. However, our initial arousal begins to subside just as quickly when we realise that there are major flaws in Pascal's reasoning. Pascal attempts ardently, though unconvincingly, to quash some of the objections that might be proposed. The argument itself, however, if taken as convincing, leads to some unexpected outcomes - ones that do not align with those that Pascal intended. Ultimately, the Wager does not succeed in providing a compelling reason for believing in Pascal's God over any other form of belief."
