A Brief Introduction to Mathematics Related to Games

Our presentation was basically a brief introduction to mathematics related to games. It did not involve the actual theoretical explanations of games using mathematics but provided an insight as to how we may approach to explain games and look for gaming strategies using mathematics.

Throughout the presentation it was emphasized that we only need elementary mathematics to explain many gaming strategies, yet, obviously problem solving skills and mathematical thinking should be there to come up with insights so as to model the game. Concepts like abstraction, iteration and recursion used in mathematical modelling was introduced. Within the limited time frame problems related to knight tours, domination and independence in chessboards, tiling, spatial arrangements and etc. were discussed.

Abstraction is simply the process of discarding the unnecessary details of a physical problem and re-writing the physical problem in mathematical terms (i.e. equations, symbols, diagrams and etc.) This concept was introduced using the Guarini's Problem which is the oldest known chess board problem dating back to 1507 AD. It was observed that by abstraction we can transform the original problem in to a diagram from which the result to be proved was trivial. (You can find some interesting chessboard problems here.)

What is the minimum moves  required to switch
the position of the white and black knights ?  

Concept of abstraction was further applied to solve famous chessboard tiling problems making use of polyminoes. (i.e. Gomory's theorem and more) 3-D Constructions of cuboids were also a part of the exploration. Soma cubes was also briefly discussed.

7 Soma cubes and constructing a cube using them.

The concept of recursion was introduced using the towers of Hanoi problem. The solution provided at the presentation was a recursive one and it was emphasized that when dealing with games, recursive strategies are also important. 

Those who are interested can refer to these books where mathematics related to games are extensively discussed.

(This is the summary of what we discussed at our third session)

Interstellar Travel, Fiction or Future Reality

In many movies, TV series and science fictions, our descendants travel throughout the stars and galaxies as frequently as we travel around the earth by planes. In these stories the fly their space craft’s near the speed of light, or they might use Wormholes as a short cut. Sometimes they travel interstellar distances within few hours! Will the future advancement of science and technology allow all of this stuff to be happened? To answer all these questions we have to consider some modern understandings of physics.

As interstellar distances are measured in light years, to travel such distances within the lifetime of a person, it is essential to travel near the speed of light.(it is impossible to travel at or more than the speed of light as it violates the postulates of the theory of relativity). In order to achieve a speed of few percent of the speed of light an enormous amount of energy is needed. The energy that it would consume to speed up a ship that of the size of a space shuttle to a speed of 0.5c is nearly 1000 times the total annual energy use of the world today. Clearly it would need new types of energy sources in order to make the interstellar travel a reality.

Nuclear fusion would be a favorable source of energy. Although the technology today is not sufficient to carry out the fusion reactions in a controlled environment, we can keep hopes on the future technology to do so. Then faster space ships will not be a fiction.

Some scientists have proposed a way of achieving a speed that carries the ship to the nearest star within a century. That is by using nuclear explosions to ‘push’ the ship forward. Continuous nuclear explosions that take place behind the ship will generate a radiation pressure on the pusher plates at the back of the ship. In this case thousands of small nuclear bombs should be detonated, and the mass of the fuel will increase the mass of the ship making it harder to accelerate. One alternative is to reduce the mass of the fuel is to collect it from the interstellar medium. Although the density of the ISM is very low sufficiently large ‘scoop’ would be able to collect reasonable amount of Hydrogen as the nuclear fuel.

When focusing on completely theoretical methods that have being proposed to travel across the stars, wormholes have a special place among both scientists and writers. But it would be impossible to predict what will happen to the space ship or the crew, inside the wormhole, as the worm hole is a result of space-time discontinuity and the ship itself is a part of the space-time. 

In conclusion we can see although there are enormous obstacles to achieve interstellar travel, there is no reason to think it is impossible. If we continue to seek out the mysteries of the universe, one day our descendants will make journeys to the stars.

References: The Cosmic Perspective (Bennett,Donahue,Schneider,Voit)       

(This is the summary of what we discussed at our second session)

About us and our first meeting

First of all, let me introduce ourselves. We are a group of university students in Sri Lanka who have got together and decided to start a forum to discuss natural sciences and philosophy with the ultimate goal of contributing to the advancement of natural sciences and philosophy.

         

As students studying science, we are kind of lost in the sense where we are headed to in the filed of our interest. It is evident that continuous discussions, arguments and challenges are essential in advancing science and philosophy. However, nowadays we do not see such a trend amongst the undergraduates in Sri Lanka. Science students often discuss everything but science. This effort is to deviate from the current trend and create an arena to discuss ideas related to science and philosophy.

Three of us who meets almost everyday at lunch discussed this situation for about two to three months. After successful discussions we decided to ask the academic staff for help. With their encouragement we were able to call our first meeting.

Our Society and Its Subculture

In our meetings and discussions there are two ground rules. 

1. All things discussed must contribute to the advancement of natural science or philosophy.
2. All members can speak freely. (as long as what they speak fulfills our first ground rule)        

We get together every week to discuss a pre-proposed topic. One of us, proposes the topic. and the others, having done a background research on the topic, challenge or strengthen the points the presenter proposes. Further, we try to reach the shoulders of giants i.e. we discuss the history of sciences and philosophy and acknowledge the value of their contribution to their respective fields. 


(This is the summary of what we discussed at our first session)