"To Infinity and Beyond!" is Buzz Lightyear's famous catchphrase in the Toy Story films and the standard definition is Without limits, limitless, sky's the limit but, hidden in this phrase is a deeper philosophical meaning. Dr. Kent A. Bessey wrote about how the German mathematician Georg Cantor published papers that explained the aspects of infinity and was set on figuring out as much as he could about the limits of infinity. With his tenacity it led Cantor to discover a realm of infinity that no other mathematician was able to discover. Bessy states that Cantor discovered, “a remarkable realm where half of a pie is as large as the whole infinity comes in all different sizes, and miracles become mathematically plausible.” Cantor would come
In other words, maybe Descartes could think up the idea of infinity, because he is
For this project we chose to interview a current professor of mathematics, Dr. Chris Ahrendt. Dr. Ahrendt is one of our former professors and teaches at the University of Wisconsin- Eau Claire. As students we were impressed by his overall knowledge and enthusiasm for mathematics. This lead us to inquire into the source of his excitement and his experience in the field of mathematics.
Pi is an irrational number that represents the ratio of a circle’s circumference to its diameter. In the Mile of Pi, Numberphile printed out the first million digits of Pi in a continuous long piece of paper, which stretched for over a mile. They printed out pi and rolled it out for one mile to show that there are cycles of repeating sequences within pi and that every number does not appear evenly. Brady Haran also presents some interesting things that could be found along the way. He points out the Feynman Point which has the number 9 repeated six times. He also pointed out the point where Akira Haraguchi (known for memorizing the most digits of pi) memorized up to. When they reached the end of the mile long paper, the last digit was 1 in
Also, the starships would not even arrive at their destination in time, or at least in time corresponding to the movies. According to Wookieepedia, the Star Wars Universe is a hundred thousand light years in diameter. A light-year is a distance that light travels in one year, so if a person moves at the speed of light from one end of the galaxy, that person will arrive at the other end in one hundred thousand years. However, in the movies, it takes shorter than a hundred thousand years to get from one side to another, so this is clearly not what is happening, and will also not work. Another way that “making the jump to hyperspace” would be possible if you travel through a wormhole.
By using geometry to evade irrational numbers, a mathematical crisis had been covered. Although Greeks could not tolerate irrational numbers, they accepted “irrational geometric quantities such as the diagonal of the unit square” (Lecture 8. Eudoxus, Avoided a Fundamental Conflict), or square root
In “Where is Here?” by Joyce Carol Oates, the visitor demonstrates the idea of infinity. Many elements lead me to believe this idea of infinity. For example, in the passage, the drawing, house and characters all show a conception of infinity.
Once again, numbers have surprised me with their surprisingly complex simplicity. In this passage of Taming the Infinite: The story of mathematics from numbers to chaos theory, the author writes about a vast array of topics, including number theory, prime numbers, calculus, many mathematicians, among many others.
He was highly respected in the field of mathematics and much of his early work as a professor was spent studying number theory. Cantor is known as the first mathematician to understand infinity. Infinity in and of itself is not a number. It means something that goes on forever with no end. It is the idea of being endless and going on forever. The idea of infinity never ends because you can always add one. Cantor’s work suggests that there are different kinds of infinity and some infinities are bigger than others. If we attempt to list all natural numbers, or all decimals, or fractions, we discover that it is impossible to list all the numbers that lie between. For example, on a number line from zero to one, if you attempted to list all the different sets of numbers in whatever form (i.e. fractions, decimals, etc.), you could not list them all. It is impossible. Cantor was ridiculed for attempting to place precision on the idea of infinity by all of his contemporaries because it was such a complex topic. He was ridiculed so heavily that he eventually was diagnosed with a mental illness and died having made no known contribution at the time. The concept of infinity in the Cantor set became so small that it came to be known as the Cantor Dust that is referred to in The Number Devil: A Mathematical Adventure. The idea is that in order to create Cantor Dust, you start with a line segment and divide it into
Descartes mentioned that Archimedes had a saying where he could shift the entire earth given he just found one certain and “immovable” point. Descartes also share a similar belief with Archimedes where he too can achieve unimaginable things given that he can be certain of just one thing.
It is impossible to think about the Star Wars Expanded Universe without the medium that formed the meat on its bones, the novel. The Star Wars Expanded Universe consists of hundreds of them. When looked at from a distance, quite daunting! But picking a novel to start with at random is often a rewarding experience. You can quickly find yourself wanting to know more about the characters and places within, whether you were just introduced to them or you were familiar with them from the movies.
The world of comic books has long been home to heroes and heroines. So it was little surprise that Marvel took the Star Wars Universe into the comic book world with great enthusiasm all the way back in the 1970's. They would later be followed by Dark Horse Comics when the Expanded Universe really reached its stride. The heroes of the movies were quickly joined by those from the novels as well as new creations for the medium.
1989, the year Marty McFly went Back to the Future to 2015 and gave us a glimpse of what technology held for us. Well, here we are in 2015 and some predictions were right, others not so much. With these new technologies came consequences, consequences that even Doc Brown could not predict. Technological advances have obvious benefits, for example better security devices to keep people safe or medical advances that prolong lives and combat illness; however, these technologies can also have what is referred to as unintended consequences, those less obvious outcomes that cannot be seen during the initial onset of a technological advance such as creating power struggles and unduly influencing society. It is those consequences that appear after
The implications of infinity (co) are actualiy not that old. The Greeks were some of the first mathematicians recorded to have imagined the concept of infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of infinity. Many claim that infinity is not a number. This is true, but it does have a value. So, infinity may be used in mathematical equations as the greatest possible value. i The value of infinity Infinity (00) is the greatest possibleivalue that can exist. However, there are different infinities that, by logic, are greater than other forms of itself. Here is one example: to the set of ait Naturai numbers Z43, 2, 3, 4,...}, there are an infinite amount of members. This is usualiy noted by Ko, which is the cardinality of the set of alt natural numbers,
Mathematics has contributed to the alteration of technology over many years. The most noticeable mathematical technology is the evolution of the abacus to the many variations of the calculator. Some people argue that the changes in technology have been for the better while others argue they have been for the worse. While this paper does not address specifically technology, this paper rather addresses influential persons in philosophy to the field of mathematics. In order to understand the impact of mathematics, this paper will delve into the three philosophers of the past who have contributed to this academic. In this paper, I will cover the views of three philosophers of mathematics encompassing their
Dr. Montessori said that man is provided with an innate power "The Mathematical Mind". She takes this term of the French mathematic, physic and philosopher Blass Pascal (1623-1662), who was the first to say that the human mind naturally has the characteristic of being mathematical and if you think for a minute we see that all progress man has developed is because the human mind has a propensity for accuracy, order