Boxing Pythagoras

Philosophy from the mind of a fighter

Archive for the tag “mathematics”

On the Irrationality of the Square Root of 2

Consider a triangle with two legs of equal length which meet at a right angle. What is the proportion of the length of the Hypotenuse to the length of one Leg?

Radical2

 

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Drunvalo Melchizedek is Bad at Math

I decided to go through The Ancient Secret of the Flower of Life with a fine-toothed comb in order to determine the veracity of the mathematical claims which Drunvalo Melchizedek makes in his most well known work. This post represents my review of every single mathematical claim which I could find in ASoFoL Volume 1. For a book which is purported to be focused primarily on geometry, I found surprisingly little mathematical information. Out of its 225 pages of material, only 32 pages mentioned any mathematical principles. Nearly 86% of the pages in this book have absolutely nothing to do with mathematics or geometry.

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On really, really, stupidly large numbers

When I was a kid and I got into an argument, inevitably it would devolve into a “Yuh-huh!” followed by a retort of “Nuh-uh!” After that, my brilliant counter argument would be “Yuh-huh, yuh-huh!” which was usually followed by “Nuh-uh, nuh-uh, nuh-uh!” It wouldn’t take us long to realize that repeating this, ad nauseum, would become irritating even to ourselves, so we soon came up with the idea of multiplying our answers: “Yuh-huh times ten!” would be followed by “Nuh-uh times a thousand!” But soon, we would reach the extent of big numbers that we could name. Most kids were familiar with “million,” “billion,” and even “trillion,” but numbers bigger than that often eluded us. Usually, after that, kids would either use nonsense words like “bajillion” or else they’d go back to repetition with “million million million.” However, occasionally, there were those few of us clever enough to learn about the bigger numbers. We’d learn “quadrillion” through “nonillion,” but the prefixes after that quickly became too confusing for little kid brains. Then we learned about a googol, 10^{100}, or (as we knew it) “a one followed by a hundred zeroes.” This number seemed insanely large, but remained easy (and fun!) for kids to say. Soon after learning about a googol, we would learn about the number googolplex, 10^{10^{100}} or “a one followed by a googol zeroes.” This number was so large, most of us couldn’t truly comprehend it, but since it was easy to say, we kept on using it.

I’m an adult, now, and even though my style of persuasive argument has become just a bit more sophisticated than it once was, I still find myself fascinated with really, really large numbers. Today, I want to talk about one of my favorites, called Graham’s number. It is so ridiculously, stupidly large, that a googolplex is only negligibly larger than 1, when compared to Graham’s number. The number was invented by Robert Graham in the late 70’s to represent the largest possible solution (or “upper bound,” in math speak) to a particular mathematics problem. I’d love to just tell you what Graham’s number is, but there’s a problem. You see, Graham’s number is so large that the usual mathematical operations with which people are familiar are entirely inadequate to describe it. A billion can be easily explained as “a thousand times a thousand times a thousand,” and a googolplex can be understood as “10 to the 10 to the 100th power;” but Graham’s number is so inordinately big that even nesting exponents is fairly useless in describing it. So, I’ll begin our journey, today, by talking about Knuth’s up-arrow notation.

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Alexandria: The Most Important City in History

In 332 BCE, Alexander the Great’s incredible military campaign advanced on Egypt. As his armies moved in, the people there regarded Alexander as a savior, hailing him as the Son of the Most High God, and declaring him Master of the Universe. The young conqueror quickly fell in love with the country, and in the following year, he founded a new capital city: Alexandria-by-Egypt. From its very inception, Alexandria was created to be one of the most important cities in the world. Its ports became a prominent trade destination, in the Mediterranean, and its culture flourished and prospered from a mix of disparate peoples, religions, and philosophies, even at its onset. The Lighthouse of Alexandria was an incredible and beautiful building, standing over 400 feet tall, regarded as one of the Seven Wonders of the Ancient World. But, without a doubt, the most incredible and amazingly important feature of Alexandria was the Museum.

The Museum of Alexandria became, almost immediately, the center of knowledge in the ancient world. It was not a museum, in the modern sense, but rather more like a modern research university. Students went there to learn all they could about the sciences of the day, while the teachers and academics received state salaries to simply do research and increase the knowledge of Mankind. The Museum boasted an incredible library, one which would quickly become the largest collection of books in the Ancient World. A tradition was developed, in the city, whereby foreign visitors would allow any books which they brought with them to be copied, so that the Library’s stocks would continue to increase. Vast amounts of knowledge were developed and stored in Alexandria.

The Museum was destined to make Alexandria-by-Egypt the most important city in the history of the world. An inordinately large amount of our modern knowledge of mathematics and science is owed directly to men educated or employed by this institution. What follows are brief descriptions of just 16 such scholars.

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Mathematics: Natural or Supernatural?

Yet again, Dr. William Lane Craig’s weekly Reasonable Faith podcast discusses a topic with which I am keenly interested. Unfortunately (and unlike last week), I once again find myself in a state of disagreement with the famous apologist. Dr. Craig’s discussion, this week, is entitled “God and Math,” and centers around a claim that mathematics is “unreasonably” effective. WLC builds his argument off of an article published in 1960 by a physicist named Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Having mentioned the Wigner quote, Dr. Craig attempts to show that the mathematical foundation which underlies all of the natural sciences is not, itself, natural. He intimates that mathematics is a supernatural construct by which a deity composed the cosmos.

William Lane Craig does not understand mathematics.

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