For many years I have been modeling neural networks and biological systems. And when teaching my university students to simulate the biological world using a computer, we kept encountering the same obstacle: boundary conditions. This is a concept in physics, and it is the most unpredictable variable when solving any problem. Using the "bagel principle", I was able to open up the game field so you could play on the «other side» of the board, with no boundaries or limitations. We transformed the 3D shape of a bagel into a 2D playing field.
Back then I was an employee at the St. Petersburg State University, and I authored a book called "Mathematics Biology". At this incredible point of my life, I was finally able to devote myself fully to my hobby: my game called CTOR. Then, in 1988, I created the first and simplest version of the game. It did not allow for team play and had no clock, but the game field was already unlimited. The first 100 thousand copies sold out in Russia in six months. It was such an immense success that the popular journal "Science and Life" removed their “School of Go” column and replaced it with “School of CTOR”.
The game involves the three basic concepts of physics: space, time and matter. The elements of the game:animals, fish, and abstract chips represent matter. The unique playing field is the space. And finally, time determines the length of each turn.
The goal of the system is to achieve equilibrium: the entire field is occupied, and those who put down the most pieces win.
We created a mathematical formula for determining how many changes occur on the field each turn. These changes include a chip being placed, moved, or «taken» by the opponent. Computer modeling allowed us to measure each turn’s «power of complexity».
In other games, for example, in chess, complexity only increases by two units each turn. If more complicated physical processes occur on the field, like in our game, the complexity can be increased by 3-5 units. This increases the number of possible combinations for the next move by a whole order of magnitude. There is no computer powerful enough to calculate the possible number of changes and the logic behind them…
The left brain and the right brain
This discovery was named the "power of complexity", and it is related to how our brain works. If the amount of changes is fairly small, and a lot of time is given for each move, we can use the left brain to calculate the next move logically, without haste. On the contrary, if there are a lot of changes, and the time limit is short, like 10 seconds per turn, we are forced to turn to the right half of our brain, because the left one cannot cope with these conditions.
This was important to us when creating new rule sets for the game. Here in Canada, for the first time in the game’s history, we have created a set of rules where the left brain could play against the right one. It may sound strange, but it has been proven in practice. Moreover, the turn limits allow you to configure which brain half is currently playing and which is training: the right one or the left one...