Category: Maths

The Ethics of State Lotteries

January 28, 2015

Is it ethical for the government to run a lottery? Is the government profiting from people’s ignorance? If so is that unethical? What about how the lottery is advertised?

Is it unethical to take advantage of people’s mathematical ignorance? What about casinos?

“Government should not be in the business of exploiting the cognitive deficiencies of its citizens for monetary gain. Right? But state lotteries do just that.”

http://www.philosophyetc.net/2006/01/ethics-of-state-lotteries.html

https://philosophynow.org/issues/14/Lottery_or_Lootery

http://3quarksdaily.blogs.com/3quarksdaily/2006/01/the_moral_degen.html

http://www.nytimes.com/2007/10/07/business/07lotto.html?pagewanted=all&_r=0

A Natural Log: Our Innate Sense of Numbers is Logarithmic, Not Linear

January 27, 2015

“We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when ­di­vided) rather than their difference (when subtracted).”

http://www.scientificamerican.com/article/a-natural-log/

Do athletes really get “hot hands” when they’ve hit a few shots in a row?

January 27, 2015

Interesting research into whether making one basketball shot makes you any more likely to hit your next one. The first two links summarize the fallacy and the third one questions it. Interesting way of using math to help us know and understand something too large to keep track of or understand simply by our memory.

How does math help us understand the world around us? How do we reconcile mathematical knowledge that contradicts our intuitive knowledge?

http://www.huffingtonpost.com/art-markman-phd/having-a-hot-hand-increas_b_3721296.html

http://en.wikipedia.org/wiki/Hot-hand_fallacy

http://www.wsj.com/articles/SB10001424052702304071004579409071015745370

Mayan Number System

January 27, 2015

Mayan NumbersOur culture has a base 10 system and uses digits and place holders. We have been exposed to this system our whole lives and find it hard to imagine any other way. The truth is that our system is based on choices we have made rather than by some inherent quality of numbers or math. Different cultures have invented math and numbers in different ways. Take a look at the link below to get a sense of the Mayan system which was a base 20 system.

http://en.wikipedia.org/wiki/Maya_numerals

Here is a handout I made based on this topic:

Download Mayan Maths Handout

What Happens When You Can’t Count Past Four?

January 27, 2015

Interesting case of a tribe whose language doesn’t have any numbers past four. What effect would this have? Why would a language evolve this way?

“Two recent studies of Amazonian Indians reported in the journal Science, take a crucially different view. These studies, far from maintaining that number words are convenient, propose they are actually necessary.”

http://www.theguardian.com/education/2004/oct/21/research.highereducation1

Here is a handout I made based on this topic:

Download Cant Count Past Four

Numbers don’t lie…or can they? Interesting case of Illinois’s tax increase

January 27, 2015

In 2011, the state of Illinois increased its state income tax rate from 3% to 5%. One could communicate this by saying that people will be paying 2% more of their incomes to state taxes which doesn’t sound all that bad since Illinois increased its rate rate 2%. Or you could say that Illinois increased its state income tax by 66% which sounds catastrophic and is also correct because you’re changing what the number actually is referring to. Increasing from 3 to 5 is an increase of 66% (or 66.6% to be more accurate with a bar over the last 6 but I don’t know how to do that on a keyboard). People would react to the news differently depending on how you communicate even though both could be considered correct.

Here are two different sites reporting the story. Notice how the choice of language and numbers changes the feel of each story even though they are both reporting the same news.

http://www.cleveland.com/nation/index.ssf/2011/01/illinois_legislators_increase.html

http://www.foxnews.com/politics/2011/01/12/ill-lawmakers-pass-percent-income-tax-increase/

Using Math to make decisions about drafting NFL players

January 26, 2015

How can we use math to help us understand something in the real world? Here’s an interesting case of taking something hard to understand, the value of drafting football players, and using math to help quantify and interpret trends and outcomes that would otherwise be close to impossible to understand without math. Without some quantitative way, a lot of times, football people use intuition, sense perception, and memory to help them make decisions.

This is part of the larger trend of using data to understand information that used to be thought of as beyond the realm of mathematical analysis.

http://www.footballperspective.com/creating-a-nfl-draft-value-chart-part-i/