Sunday, February 20, 2011

How many ants does it take...

...to solve the Towers of Hanoi? About 501 or less.

This study was conducted on Argentinian ants by a group of scientists that were using natural systems as a "source of inspiration for computer algorithms designed to solve optimisation problems". Before explaining the results obtained, let's look at the methods that the scientists used.

Two sets of experiments were conducted: Group tests and individual tests.

Group tests: 30 colonies containing 1000 workers and 2 queens, and 30 colonies containing 500 woekers and 1 queen were starved for 3 days.

Half of each of the colonies were given access into a 'maze' which was 1 m long and consisted of 64 idential hexagons aligned in a rhomboid. These were the 'pre-exposure trials'. The next set of ants were made to enter the made from one end. A food source was placed at the other end of the maze, and the scientists tried to observe how long it took the ants to figure out the shortest, or the 'optimal' path to the food, which happened to be the one along the edges. The surprising bit? The correct path was one in over 30,000.

Individual tests: 100 ants were starved for 3 days, and the ants were was put into the maze one at a time. The total distance the ants had to travel did not exceed 42 cm. After 8 minutes in the maze, the ant was taken out, and another was placed on the opposite end of the maze, to ensure that the pheromones from the first ant did not affect the behavior of the next one. 15 ants were tested in this way.

The results showed that other than the smaller (500 workers) colony, 93.3% of the times, the ants  not only found the optimal path, but did so in less than one hour. When the shortest path was blocked, 90 to 93.3% of the colonies with exposure were able to find the next shortest path, and 73.3 to 78.6% of the colonies without pre-exposure achieved this! Individual ants, as it turned out, walked much faster than ants in groups.

This experiment made me think what would happen if the same experiment was conducted on humans. I recently saw an NPR video that talks about how humans can never walk in a straight line if they're not aided by the sun, or other fixed points. Here's the link to that:

Now, this study isn't the same as the one done on the Argentinian ants, but would humans be able to solve the Towers of Hanoi as efficiently as ants did, if they can hardly walk in straight lines? Without antennae on our heads, I'd say probably not.


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