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Thursday, July 31, 2014

Throwback Fact of the Week - Newcomb's Paradox - 7/31/14

Newcomb's Paradox

Newcomb's Paradox is a thought experiment devised by William Newcomb in 1960.

The problem has taken on various forms over the years but the general idea(s) remain in place.

Before you are two boxes: one transparent (box 1) that always contains $1,000 and one opaque (box 2) which either contains $1,000,000 or $0. An entity, often called the Predictor, is exceptionally good at predicting people's actions, the Predictor is almost never wrong. The Predictor explains that you have two choices: take what is in both boxes, or take only what is in the opaque box, box 2. 

There is a twist; the Predictor has made a prediction about what you will decide. If the prediction is that you will take both boxes, then $0 will have been placed in the opaque box. If the prediction is that you will take only the opaque box, then $1,000,000 will have been placed inside of it. By the time the game begins, the prediction has already been made and the contents of box 2 already determined. 

Which box do you choose? 

In a 1969 article, philosopher Robert Nozick noted that  "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."

To this day there is much disagreement on the best strategy.

Thursday, July 24, 2014

Throwback Fact of the Week - The Rhind Papyrus - 7/24/14

The Rhind Papyrus

The Rhind Papyrus (pictured below) is an important document from ancient Egypt that contains a bountiful amount of information on ancient Egyptian mathematics. It is dated to be from the year 1650 B.C. The scroll is named after Alexander Rhind, a Scottish lawyer and Egyptologist. Alexander Rhind came across the famous scroll in 1858 when visiting a market in Luxor, Egypt. The scroll was originally discovered in a tomb in Thebes, on the bank of the Nile river. 

Rhind Papyrus, picture credit: Paul James Cowie

The scroll was copied by the scribe, Ahmes, around 1650 B.C. and contains the earliest known symbols for mathematical operations. Other content of the Rhind Papyrus includes problems involving fractions, arithmetic progressions, algebra and geometry (particularly areas and volumes). 

Ahmes wrote that the scroll gives an "accurate reckoning for inquiring into things, and the knowledge of all things, mysteries...all secrets."

Friday, July 18, 2014

Summer, Sigma, Savings

As you (hopefully) know, here at the Center of Math, we publish only free and affordable, high-quality math resources. Worldwide digital textbooks offer more for less and our print textbook prices are hard to beat. (Did you know with Worldwide Calculus you could ace your college calc classes for less than $30?!) It gets better. While supplies last this summer, the Center is selling overstocked copies at up to 90% off the list price. In some cases you'll pay only for shipping!

This is a perfect opportunity for those of you who have yet to try Worldwide Textbooks.

Take a look at some of the heavily discounted titles available in the Center of Math Store:

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Click here to get your PRINT: Matrices, Vectors, and 3D Math for $19.95+shipping.

DO the math. DON'T overpay. #dothemath

Thursday, July 17, 2014

Throwback Fact of the Week - Seven Bridges of Königsberg - 7/17/14

Seven Bridges of Königsberg Problem

Königsberg was a city in Prussia, situated on the Pregel river. This river flowed through the town and created two large islands. These islands were connected to the mainland by 7 bridges, as depicted in the image below. 

Königsberg Bridges, image credit: Bogdan Giuşcă
The problem asked if it was possible to take a walk through town and cross over each bridge once and only once. Try it for yourself using the image above!

The answer to the question turns out to be "no" and a proof of this was published by Leonhard Euler in 1735. Euler's work laid the foundations of Graph Theory. Euler let each individual landmass represent a "vertex" (4 in all) and each bridge an "edge" (7 in all). The order of a vertex is the number of edges at that vertex. Euler showed that a graph such as this is only traversible if there are at most two vertices of odd order.

All four of the vertices in the Königsberg Bridge problem have odd order, and thus it is not possible to walk through town and cross each bridge only once. 

Wednesday, July 16, 2014

Fun Fact for Rainy Days

Over here at the Center of Math, we've had a few rainy days breaking up our sunny afternoons. While we spend more time indoors, here's a short video we found to help those that have to get through the rain! Well, maybe an umbrella might help more... 

 Check out our YouTube channel for more fun videos and all of your mathematical needs!

Friday, July 11, 2014

Want to Know the Secret of Life? It's Math!

Ever wonder what distinguishes life from death? According to physicist, Max Tegmark, math is what defines everything. The Massachusetts Institute of Technology professor argues that consciousness consists of nothing more than mathematical patterns and that nothing but changes in atom arrangement differentiate life from death. You can watch it right here!

This video was recorded during his talk at TEDxCambridge last month. Check out the other speakers and performers here!

Thursday, July 10, 2014

Throwback Fact of the Week - Fermat's Last Theorem - 7/10/14

 "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." - Pierre de Fermat, 1637

Stated formally,  x^n+y^n=z^n,  where x, y, z, and n are non-zero integers has no solutions for n > 2.

This equation, known famously as Fermat's Last Theorem, would remain unproven for over 350 years. Building off centuries of work by mathematicians, the theorem was finally proven by Andrew Wiles in 1994.

Tuesday, July 8, 2014

Can Math Predict the Future... Of the World Cup?

Today is the first game of the World Cup Semi-finals! Unfortunately, this time around we don't have Paul the Octopus to help us know who the victors will be, but Microsoft has us covered! Cortana, the intelligent personal assistant for Windows devices, has used Microsoft's Bing search engine to correctly predict the outcome of every elimination round match of this year's World Cup. Using algorithms and machine learning models, Bing has correctly predicted not only World Cup games but also picked contestants of voting shows. Here's more information on what it is and how it was designed.

Want to see the predictions for the Semi-finals? Let's see if Master Chief was right in going with Cortana over an octopus. Check it out here!