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Stepran's Infinity Puzzle, 2008.
This paper discuses Stepran's infinity puzzle as an excellent method to explore the character of infinity relative to tangible outcomes.
1,625 words (approx. 6.5 pages), 3 sources, MLA, $ 52.95
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Abstract
This paper explains that the solution to Stepran's infinity puzzle
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."
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Infinity and the Devil's Puzzle, 2005.
This paper discusses the idea of the 'Doing Business with the Devil' puzzle and looks at the concept of infinity.
675 words (approx. 2.7 pages), 2 sources, $ 26.95
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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."
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Conflicting Perceptions of Infinity, 2005.
This paper discusses the concept of infinity and provides an analysis of conflicting perceptions in this regard.
675 words (approx. 2.7 pages), 2 sources, $ 26.95
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Abstract
This three page undergraduate paper examines an infinity puzzle 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)."
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Infinity, 2005.
This paper discusses if infinity is real.
675 words (approx. 2.7 pages), 2 sources, $ 26.95
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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.'
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Vatican Congress on Infinity, 2005.
A discussion of a the Vatican's attitudes toward the question of Infinity.
1,150 words (approx. 4.6 pages), 12 sources, APA, $ 39.95
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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..."
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Infinity, 2002.
A philosophical discussion drawing on different opinions on whether infinity can be seen as a real entity.
1,150 words (approx. 4.6 pages), 2 sources, $ 44.95
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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.
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"One Two Three...Infinity", 2005.
A brief book review of "One Two Three...Infinity" by George Gamow.
985 words (approx. 3.9 pages), 3 sources, MLA, $ 34.95
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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..." "
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A False Puzzle, 2002.
An analysis of the debate ""Doing Business with Devil".
650 words (approx. 2.6 pages), 3 sources, $ 26.95
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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.
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"Infinity and the Mind", 2005.
A discussion about Rudy Rucker's book.
962 words (approx. 3.8 pages), 1 source, APA, $ 34.95
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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."
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A Pentangle, a Puzzle and Penance, 2006.
This paper explores the poem "Sir Gawain and the Green Knight" as well as the poet's use of language and symbolism in describing a warrior's shield.
2,361 words (approx. 9.4 pages), 10 sources, MLA, $ 72.95
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Abstract
This paper focuses specifically on the pentangle passage in the poem "Sir Gawain and the Green Knight," penned by an unknown poet. The writer of this paper delves into the symbolism and language in the passage while questioning the poet's reasons for going into such great detail about a mere marking on a warrior's shield. Geometrically the pentangle or pentagram corresponds to pentagonal symmetry, a common characteristic of organic nature as well as to the five senses which in the poem symbolically represent the five forms of matter. The writer describes in this paper how the pentangle passage provides the reader with adequate background, if well understood, to interpret the actions of Gawain and the other characters in the poem.
From the Paper
"By the end of the poem, Gawain has been fully tested, and has succeeded in upholding each of the Pentangle virtues, with the exception of one - honesty with his host. In this one sense, 'fidelity' as the translation of trawthe, does seem appropriate. However, if our other translators / expositors ideas are utilized, this particular virtue is not specifically named by the poet. It could easily be perceived to fall in with courtesy, or with fellowship. However, there seems to be little support for this, if we study the reaction of both the Green Knight, and his fellow knights at Camelot, to Gawain's grief that he succumbed to the temptation to spare his own life by using the gift from the Lady - the green girdle."
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"The Big Bow Mystery" - A Locked Room Puzzle., 2002.
An analysis of Israel Zangwill's mystery novel "The Big Bow Mystery".
1,650 words (approx. 6.6 pages), 1 source, $ 62.95
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Abstract
This paper dissects Israel Zangwill's mystery novel The Big Bow Mystery and analyzes it in terms of other mystery-novel standards: logical consistency, character evenness, and distraction (e.g. "red herrings"). It concludes that although the novel also functions as a critique of Victorian society, the novel itself has great worth as a mystery due to its supreme internal consistency, hard to achieve in the "locked room" subgenre.
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Crossword Puzzles, 2008.
This paper examines the nearly 100 year old history and popularity of the crossword puzzle.
955 words (approx. 3.8 pages), 3 sources, MLA, $ 33.95
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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."
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Games and Puzzles in Language, 2002.
This paper looks at the importance of games and puzzles in learning a new language.
1,400 words (approx. 5.6 pages), 5 sources, $ 53.95
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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.
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Godel and the "Theorem on Incompleteness", 2002.
Review of R. Rucker's discussion of the concept of infinity and how it relates to Godel's "Theorem on Incompleteness".
650 words (approx. 2.6 pages), 4 sources, $ 26.95
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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.
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Archimedes' Stomachion: A Perpetually Recombining Mystery, 2008.
A discussion of the geometric puzzle - Archimedes' Stomachion.
1,674 words (approx. 6.7 pages), 3 sources, APA, $ 54.95
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Abstract
This paper discusses all aspects of the ever complex geometric puzzle - Archimedes' Stomachion. It explains that the Stomachion is a collection of fourteen differently shaped geometrical objects, most self-evidently organizing to form a cube and for this reason, the object or set of objects is often also given the name Loculus of Archimedes, meaning Archimedes' Box. The paper points out that the object is one rife with mystery, from its historical obscurity to its continued rendering of insight and revelation, the Stomachion is an object that is increasingly yielding of questions as much as of answers. The paper also examines the Stomachion's history and its current relevance to mathematics and scientific culture. The paper concludes that there remains any number of aspects of this puzzle that are as yet uncovered and owing both to the condition of the parchment upon which Archimedes' original ideas are expressed and to the unfurling complexity of the puzzle, it remains uncertain what additional implications were either perceived or intended by Archimedes.
From the Paper
"Composing his ideas during the 2nd century BCE, Archimedes is not generally believed to have invented the puzzle in question so much as channeled its implications into a discourse on its mathematical suggestions, which have since proven increasingly extensive. Nothing of Archimedes' investigation here was spoken of for roughly 2000 years, with a parchment communicating through several centuries of mathematical discourse gradually becoming obscured under the oppressive thumb of religious revisionism. What is today known as the Archimedes palimpsest is a document beneath a document, with the former a descendent of Archimedes' preponderance on the subject of the riddle at hand. Its existence was unknown until 1907, when Danish philologist Johan Ludvig Heiberg discovered the forgery untouched by any interested parties for several hundred years in a monastery in Constantinople. (Wikipedia, 1) Using a magnifying glass in accordance with the technology available at the time, he could make out only small fractions of a text divulging the existences of the Stomachion, with only smatterings of information accessible regarding its meaning or purposes."
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