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 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)."

Tags:infinity, and, perception

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."

Tags:limitations, solution, natural, continuum, switch

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.'

Tags:infinite, finite, mathematics

Abstract
This paper focuses on Stepran's puzzle, explaining that this puzzle provides an excellent method to explore the character of infinity relative to tangible outcomes. The paper asserts that 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.

Tags:equation, mathematics, switch

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
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."

Tags:infinity, devil, rucker

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..." "

Tags:maths, physics

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."

Tags:Aristotle, Plato, philosophy, universe

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.

Tags:godel, theorem, incompleteness