Nature
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# A Slimy, Brainless Amoeba Just Found A Completely Unexpected Solution To A College-Level Math Problem

Unless you’ve studied math to a pretty high level, you probably haven’t heard of the Traveling Salesman Problem. That’s a shame because it’s one of the finest examples available to the question we’ve all asked at some point – “when will I ever need math in the real world?”

The Traveling Salesman Problem goes like this: Given a list of cities you have to visit, what is the shortest possible route you can take that gets you to every city and back home again?

Students who are assigned the problem in school or college often receive a simple version, planning a journey between, say, four cities. That’s not too hard; there are only three possible routes you can take.

But if we double that number to eight cities, there are over 2,500 possible routes we can take – and all of them need to be checked if we want to be sure we’ve got the shortest one. It’s an NP-hard problem, which means that as we add cities to the list, the amount of time – and pain inflicted on students who are assigned the problem – increases exponentially.

Well, now those students get to feel even worse. It turns out the problem is so easy, a single amoeba can do it.

A new study published this week in Royal Society Open Science has shown that a plasmodium, or “true slime mold” amoeba, is able to find near-optimal solutions to the Traveling Salesman Problem in linear time – meaning that adding more cities does not result in a huge increase in the amount of time our slimy friend takes to find an answer.

The researchers placed the amoeboid academic in a petri dish containing agar – one of the microbe’s favorite snacks. To try to get at as much of the agar as possible, the amoeba would try to expand into the 64 narrow channels surrounding it, which had been labeled as the “cities” on the salesman’s route.

But there was a catch. True slime mold amoebas hate light, so in order to guide the mini mathematician towards a solution, the researchers used a neural network model to illuminate certain channels. This meant they could stop the amoeba from visiting the same “city” twice, or direct it to the closer option of two it was visiting simultaneously.

At the moment, the single-celled scholar is no match for computers in terms of speed, but the method it uses to solve the problem is completely unexpected. Instead of processing feedback sequentially, it tackles the problem all at once, exploring the solution space with its amorphous, gel-filled body – a new and bafflingly reliable approach that the researchers think may hold the key to future analog computers.

“How the amoeba maintains the quality of the approximate solution, that is, the short route length, remains a mystery,” explained lead researcher Masashi Aono in a statement. “Each of these branches is oscillating its volume with some temporal 'memory' on illuminated experiences. Groups of the branches perform synchronization and desynchronization for sharing information even though they are spatially distant.”