Thursday, October 29, 2009

Matchbox Maths Games

There is a great article here on Matches on India. No really read it.
In fact, 97% of rural households purchase matches on a monthly basis. Matches are a unique product because of their high, constant demand and low price point.Their ubiquitous presence provides fascinating insights into India's rural distribution networks, and offer potential ways to inform and interact with India's relatively untouched market.

The article then suggests using the matchboxes to spread public health messages
What if that space was used to relay information? Imagine the possibilities of spreading new health/educational information or advertising to 97% of rural families on a monthly basis. Simple pictorial designs would pique interest and accommodate India's vast differences in literacy rates and languages. Awareness of important topics such as the installation of chimneys to reduce smoke inhalation or cleaning and covering water containers to prevent stomach ailments could be spread to households across India, and potentially save lives

I would recommend selling the glamor of flushing toilets and chimneys and such rather than nagging in your images. But i do not know enough about rural Indians and their diseases to advise on what health images to provide them. There are some interesting studies on what does kill these people here.

However what if all you put on the boxes was games? Many people have a ludic philosophy of life. You see a love of games in maths nerds in particular. This love of games I believe adds a cognitive richness that aids intellectual development.

There is a great book called "everything bad is good for you". That claims the increase in IQ in recent decades is due to increased complexity in our culture. I have not studied the Flynn effect enough to be sure it is not caused by nutrition or even to be sure it is important. But I will assume it is and that intellectual challenges improve general cognitive abilities. I will go further out on a limb and claim that such improvements in cognitive abilities would aid rural Indians. Never having been a rural Indian this really is a big assumption.

So what intellectual challenges could fit on a matchbox and be read by an illiterate farmer? How about puzzles and games?

There are some face meltingly brilliant match puzzles here(pdf). Other then puzzles there are games like NIM, dots and boxes, chomp and loads of others you can play with matches. I would imagine if a brand of matches has a game on it that keeps the kids from bothering you this would be a popular feature.

So can you think of some way to explain a puzzle or the rules of a game on a matchbox without using text? Do you think it really could be useful to put mathematical games and puzzles on matchboxes?

Wednesday, October 28, 2009

A work sceduling problem

I saw this problem recently
A city authority is considering placing a toll booth on its new bridge. The beginning
times for the shifts are 8am, noon, 4pm, 8pm, midnight and 4am. A collector
beginning a shift at one of the above times works for the next 8 hours.
The following staffing levels during each of the 24-hour periods have been estimated

Hour.................... Minimum Collectors Needed
8am - Noon.............. . 5
Noon – 4pm ................6
4pm – 8pm .................10
8pm - Midnight........... .7
Midnight – 4am ...........4
4am – 8am .................6

Find the minimum number of collectors that need to be hired to begin the 8 hour shifts
at each of the six times.

A GLPK program to calculate this is

var x1 >= 0, integer;
var x2 >= 0, integer;
var x3 >= 0, integer;
var x4 >= 0, integer;
var x5 >= 0, integer;
var x6 >= 0, integer;
/* objective function */
minimize z: x1+x2+x3+x4+x5+x6;

/* Constraints */
s.t. ctr1:x1 + x6 >= 5;
s.t. ctr2:x1+x2>= 6;
s.t. ctr3:x2+x3>= 10;
s.t. ctr4:x3+x4>= 7;
s.t. ctr5:x4+x5>= 4;
s.t. ctr6:x5+x6>= 6;

The answer is 19 and no one starts working at 8am.
This is a simplified version of the program described here. Not a major revelation or anything but always find these puzzle solving programs cool.

Sunday, October 18, 2009

Prediction with game theory

I am going to this talk on Thursday so I am reading the book Predictioneer by Bruce Bueno De Mesquita. He has a ted talk video on his prediction ideas.

The use of game theory in forecasting seems based on the axiom that people are rational. The problem is they are not, here is a list of the different ways they are not. If you know how they are going to be irrational you can alter your models to take this into account. However if you fail to do this you will end up with less accurate models.

In chapter 2 the book claims people are rational and particularly that we are transitive in our preferences. "to be rational.. their preferences must not go in circles. For instance if I like chocolate ice cream better then vanilla and vanilla better then strawberry i presumably like chocolate ice cream better than strawberry." So no rock paper scissors can exist in human preferences.

The problem is they do. There is loads of evidence that people can have intransitive preferences. For example May showed in 1952 that people can have intransitive preferences for wealth, looks and intelligence in a partner. So how can you have a mathematical system modeling the world where one of your axioms is false?

While on the subject of intransitive never play dice with Warren Buffet. There are loads of stories of how he tries to con people with a set of intransitive dice. Edward Thorpe for example. Or Bill Gates as described in Bill Gates Speaks: Insight from the World's Greatest Entrepreneur By Janet Lowe

Buffet once attempted to win a game of dice with Bill Gates using intransitive dice. "Buffet suggested each would choose one dice and discard the other two. They would bet on who would roll the highest number most often. Buffet offered to let Gates pick first. This suggestion instantly aroused Gates curiosity. He asked to examine the dice after which he demanded buffet choose first."

Friday, October 16, 2009

Boy in Balloon, did the balloon have enough lift?

I love this story, it reminds me of the time myself and my dad nearly burned down the house. We made a tinfoil hot air balloon with a gas camping cooker to power it. The cooker was tipped onto the lino and the melting began. It was my mums fault for leaving us alone in the house together. In general I love these homemade balloon stories, like Larry Walters across California.

Could we have told in advance it was a haox? "Few had raised the issue of whether such a balloon could even lift off with a 50-pound kid inside, and then float the way it did"

So how big was the balloon? "Authorities said the silver balloon, 20-feet long and 5-feet high, at times reached 7,000 feet above the ground while adrift. It was found more than 90 minutes later in a field near Colorado Springs."

Then it would have a diameter of 6 meters and a height of 1.5m high. Taking the balloon as a cylinder then according to here would give it a volume of 42.5 cubic meters.

Gross Lift (Helium) = Volume (cubic meters)*1.05kg
So 42.5 * 1.05=44.625 kg lift.

Now that seems just within the bounds of possibility as the kid weights about 20 kilos and the balloon itself should be light. But could the balloon have gotten to a height of 2000 meters? There are all sorts of tables for these I might work it out later

Another site gives "Helium provides about 9.8 newtons of lift per cubic meter, at sea level and room temperature. That's enough to lift 1kg". So 20 kilos would require 20 meters squared to lift it. Same result as before.

Thanks to the best program on Television we know how many balloons it takes to lift a small child.
"It would require such a large number of balloons (3,500) to lift an average four-year-old girl of 44 pounds (20 kg) just a few feet off the ground that there is no way the myth could have happened unintentionally."

Update: Wired have an article here about how people should have realised the balloon was empty. Their estimation of the carrying capacity of the balloon is similar to mine. they point out that the balloon does not move like it has a heavy weight hanging from the bottom of it.