A Cultural Paradox:
Fun in Mathematics
Jeffrey
A. Zilahy
A Cultural Paradox:
Fun in Mathematics
J 2 the Z Publishing
Copyright © 11111011010 by Jeffrey A. Zilahy
All rights reserved.
E-Book Beta Version 1.0
Publisher Imprint: J 2 the Z Publishing
Printed in the United States of America.
Perfect Bound Paperback
ISBN
978-0-557-12264-6
Für Vierzig
Book Directory:
1. Introduction
2. Picking a Winner is as Easy as 1, 2, 3.
3. That's my Birthday!
4. Sizing up Infinity
5. I am a Liar
6. Gratuitous Mathematical Hype
7. LOL Math, Math LOL
8. In Addition to High School Geometry
9. Abstraction is for the Birds
10. NKS: Anti-Establishment as Establishment
11. 42% of Statistics are Made up
12. Undercover Mathematicians
13. I Will Never Use This
14. Gaussian Copula: $ Implications
15. A Proven Savant
16. History of the TOE and E8
17. One Heck of a Ratio
18. A Real Mathematical Hero
19. Casinos Heart Math
20. The Man who was Sure About Uncertainty
21. We Eat This Stuff Up
22. Do I Have a Question for you!
23. When Nothing is Something
24. Think Binary
25. Your Order Will Take Forever
26. When you Need Randomness in Life
27. e=mc^2 Redux
28. Quipu to Mathematica
29. Through the Eyes of Escher
30. Origami is Realized Geometry
31. Quantifying the Physical
32. Geometric Progression Sure Adds up
33. Nature = a + bi and Other Infinite Details
34. Mundane Implications of Time Dilation
35. Watch = Temporal Dimension Gauge
36. Modern Syntax Paradigms
37. Awesome Numb3rs
38. Some Sampling of Math Symbols
39. Computation of Consciousness
40. Auto-Didactic Ivy Leaguers
41. Zeno's Paradox in Time and Space
42. Needn't say Anymore
43. You can see the Past as it Were
44. Music: A Beautiful Triangulation
45. Mobius Strip: Assembly Required
46. e^(i*Pi) + 1 = 0 is Heavy Duty
47. Choice Words
48. Latest in Building Marvels
49. Your Eyes do not Tell the Whole Story
50. Internet Cred Worth Paying Attention to
51. A.I. Inflection Point
52. I Know Kung Fu
53. More Incompleteness
54. Alpha Behavior
55. Off on a Tangent
56. Quick Stream of Consciousness
57. This is Q.E.D.
Acknowledgements
Index
CH 1: Introduction or why did I write this?
So, as an unabashed science and technology aficionado, simply a love for discussing mathematics propelled me to formulate this book, mostly written over a few week span in late 2009, followed by several plodding months of refinement with the help of a few thoughtful people.
I have long appreciated the objective nature of science and been amazed at how much it has wrought for the inhabitants of this little rock we fondly call Earth. I seem to repeatedly find myself reminded of the pure chances of being born in this era and how awesome it is to be involved in science in such a time. I am of the belief that mathematics is the underlying "software" that powers the "hardware" that we live in, namely planet earth and of course the greater cosmos. It seems to me that there is a close relationship between the level of sophistication that a civilization possesses and the degree of mathematics that a civilization grasps. I would say that math is powerful, intriguing, and intensely relevant to all of our lives.
I think it is worth stressing that this is obviously not intended as an in-depth look at any of the subjects contained herein. Therefore, think of each chapter as a brief conversation on a topic and if you would like more detail; I encourage you to visit your local friend/bookstore/internet. This book is merely meant as a brief reflection on what I consider some of the most interesting and powerful ideas that swirl around in the mathematics community today. Really, this book represents my musings on early 21st century recreational math(s). There are countless other topics and areas of mathematics that can be addressed. The topics in this book are the ones that are simply on my radar right now and that are mostly tied into popular culture.
Naturally, this book is classified as Non-Fiction, and therefore all ideas are presumed to be fact, so while I have tried my best to be accurate, I must take responsibility for any subsequent errors found. It is also worth mentioning that this book was originally intended as a traditional book, and as such, this e-book version is missing a great deal of images and math symbols, consider Chapter 38 as an example of this difference. If you would like the full version, it can be purchased at lulu.com. Finally, I sincerely hope that these topics prove to be as interesting and surprising to you as they are to me. Thank you for reading.
CH 2: Picking a Winner is as Easy as 1, 2, 3.
Considering all the problems covered in this book, the Monty Hall Problem has to be one of the most strikingly confounding ones and therefore it is an apropos first topic for discussion. The Monty Hall problem is a great example of how mathematics can sometimes be counter-intuitive to common sense. It is so named for the game show host, Monty Hall, who actually featured this problem on a real live game show.
This problem deals with probabilities. The typical set up involves three doors. The contestant (i.e. you) is told that behind two of the doors are two undesirable prizes, let’s say a desktop computer running a 20th century operating system and with minimum RAM. Behind the third door is a really desirable prize, say the Nissan GT-R sports car. Monty starts by asking which door you believe the Nissan is behind. You say Door One, joking that there can be only one prize. He then surprises you by opening Door Two revealing a giant clunky outdated computer. The audience lets out a gasp as Monty turns to you and asks whether you would like to switch to Door Three.
Now the question to you is whether you would increase your odds of winning that prized car by switching from Door One to Door Three. Most people incorrectly assume that both Door One and Three have the same probabilities of revealing the car. In actual fact, switching from Door One to Three is a wise move. You go from having a 1/3 chance of finding the car in Door 1 to a 2/3 chance of finding the car with Door 3! Why, pray tell? Well, when you first were asked to pick a door, all three doors had the same chance of revealing the car. That means whichever door you chose, One, Two or Three, you have a guaranteed 1/3 chance of getting the right door. Now, when Monty opened the surprise door, Door Two, and eliminated that door as an option for containing the car, you now are contending with only two doors where you are guaranteed to find the car. But as we just said before, your door, number one, is a 1/3 probability of being the correct door. Now, since we know that there is a 100% chance of it being either Door One or Door Three, and since we also know that Door One represents 1/3 of that probability, then we know that now that we only have one other door, Door Three, the remaining 2/3 must belong entirely to Door Three. So essentially, by revealing Door Two, we increased the probability of finding the prize behind the door you did not choose, Door Three. Now, it is fair to say that this is a rather counter-intuitive result, wouldn’t you agree?