Could you use large colonies of ants to solve difficult math problems for you?

Question

I’m thinking of how ants find the shortest, easiest path from nest to food source and use it. What if you separated an ant’s nest and their only food source with a complicated 2 dimensional glass maze. You know, one with millions of possible paths, and all the “easy” options turn out to be duds. Would the ants as they proceed thru the maze on a daily basis, making millions of ant-trips over millions of ant-hours and miles, finally settle on the route that was the shortest, by sheer statistical enumeration. Because if they could, then you could use them to solve many intractable problems in maths like the “travelling salesmen” problem.


The idea is to use ants like an analog computer version of a supercomputer. Each ant's journey, provided it did more than just follow the leader, must add some data to the ants' knowledge of the best way there. Has such an experiment ever been done? Coz it should be. You would be using nature as a ready-built computer to solve your probs for you.

Answer 1

the traveling salesman problem involves visiting a series of "cities" with varying distances and travel times. To Solve the traveling Salesman problem, you need to find the most efficient way to visit all the cities, and then return to your starting point. these problems are of Order n!, which means they become incredibly difficult very quickly.

However, since the ants would only go to and from the food source, with little to no required stops in between, it wouldn't work for solving the TSP.

It does make a potentially good argument for a shortest path problem, though. There does exist one starting point, one ending point, and a series of possible paths, each with varying "costs" to taking them. What i see you saying is making a maze with lots of twisty hoses to increase the travel times between various points and seeing what path the ants settle on.

However, there already exist many algorithms for solving these types of problems. For example, I took a combinatorial Optimization class in college, and we learned about the Ford-Bellman Algorithm, which has a run time of Order nm.

The ant solution would work, but a computer could churn through the algorithm a lot faster than the ants could find a way to get to the food in the first place.

Answer 2

Even though it is said that "two heads are better than one" I doubt that consulting with a hoard of ants will do much to improve your math score.

A tutor might be a better course of action.

Sounds like someone is trying to get a federal grant to study eusocial insects.

Answer 3

If you could teach them to say" yes" or" no" you could do it, a bit slow though.
The concept is fascinating.

Answer 4

Somebody's read too many Discworld novels...

Answer 5

Go on with your badself eddo!