Mathematics

How people behave in a social network is somewhat mysterious, in the same way we can predict a presidential election with unprecedented accuracy but we can't predict how one person among the six percent of America that chooses a president will vote.

Decision-making often involves a confluence of opinions, decisions and behaviors of individuals influenced by their online networks, the same way they used to be shaped by their real-life networks.

A recent project set out to apply some math to help find some answers.


Ripple across social networks. Image credit: Laurel Papworth. Creative Commons

A young boy sits on the carpet, his feet disappearing into a giant pair of sweatpants he put on over his own clothes before loosely tying his ankles together.

He has taken the sweatpants off and is now trying to put them back on inside out without removing the ankle cuffs.

Yes, it can be done.



Holly Bernstein, who earned a PhD in mathematics at Washington University in St. Louis in 1999, watches him struggle for a bit and then says, “Remember the pants have more than one hole. You don’t necessarily have to put them back on the way you put them on in the first place.”

A desire to be part of the 'in crowd' could damage our ability to make the right decisions, according to a paper in the
journal Interface which claims that individuals have evolved to be overly influenced by their neighbors, rather than rely on their own instinct.

As a result, they believe, groups become less responsive to changes in their natural environment. So much for the wisdom of crowds.

When it comes to math, people mis-characterize themselves quite often. About 20 percent of the people who say they are bad at math score in the top half of tests while about 33 percent of people who say they are good at math score in the bottom half.

In the classical game theory match-up known as the Prisoner’s Dilemma, two prisoners kept isolated from each other are offered a deal: they can confess to a crime and if their accomplice remains silent the charges will be dropped in exchange for testimony against the other. If they both confess, they can both get early parole. If both remain silent, they get convicted of a lesser charge.

There is such a thing as 'too precise' when it comes to numbers. So what's appropriate? Erik Olsson, CC BY-NC-SA

By Jonathan Borwein (Jon), University of Newcastle and David H. Bailey, University of California, Davis


Kelly Abbott/Flickr, CC BY-NC

By Tim Trudgian, Australian National University

Consider a standard pizza box containing a standard circular pizza. How much more would you be willing to pay for a square pizza that filled the box?

The golden ratio is known as the divine proportion because it is found so often in nature. It has fascinated mathematicians since Euclid. A golden ratio is when the ratio of two numbers is the same as the ratio of their sum to the larger of the two quantities.


Credit: Wikipedia

Represented by the Greek letter phi (φ), its value is 1.61803399.

In a famous mathematical thought experiment, the goal is to make randomness deterministic by closed-form equation, so mathematicians tried to determine the path of a 'drunken sailor' staggering around a town. 

If there are street lamps, he will run into them, change his direction and keep moving until he gets out of the city. Logically, the time he spends in the area depends on the number of street lamps but the surprising answer is that the number of streetlamps are not the big factor.

Vaccines are medical technology and like all technology some of the production runs are misfires. Some shots fail due to "leakiness," lack of effectiveness on certain individuals in a population, or shorter duration of potency.