What's Optimal About Six Legs According to Physical Laws? In many respects the insects can be regarded as the most successful class of animals in evolutionary terms. And one of the most common features of insects is that they (mostly) all have six legs.
Not discounting other traits, is there something about six legs that has helped insects achieve this success?
Can we use physical laws to analyze and determine an optimality of having six legs - perhaps such as stability?
 A: I can think of two possible reasons: first, you can have half your legs up in the air at one time (as in walking - two on one side and one on the other, then change) and still be perfectly stable (3 legs = most stable, like a tripod); and second, if a predator chews off a leg on either side, you still have two legs (so you can still walk). I think those arguments are borderline biomechanical, rather than physical...
The first argument has some solid scientific backing - see for example http://web.neurobio.arizona.edu/gronenberg/nrsc581/powerpoint%20pdfs/cpg.pdf . It doesn't take a lot of brains to walk with six legs... I fact it can be done almost entirely with "local" neurons. That's a good thing when you don't have a lot of brains.
Quoting from https://answers.yahoo.com/question/index?qid=20090418111020AA75mgR :

Generalizing, insects walk with a metachronal gait and, with speed, a tripod gait - which involves a tripod stance - 2 legs on one side of the body and one on the other remain stationary while the other legs move forward, then the stationary legs walk as the others take a stance. In this way, walking involves maximum stability with a minimum of neural coordination. In fact, ganglia and other nerves and sensors located on each leg may contribute as much to the actual walking movement as the brain does. It's a very easy, stable and adaptable locomotory system which evolved from the basic arthropod body plan with 2 pairs of limbs on each body segment. 

A: 
Not discounting other traits, is there something about six legs that has helped insects achieve this success?

Spiders oftentimes have eight legs, mammals oftentimes have four. But centipedes have lots of legs, and millipedes have lots of legs. The reason mammals have four legs, and millipedes have lots and lots of legs isn't so much about optimality so much as that's how many legs their ancestors had.
The story of why people cut off the ends of the roast comes to mind. Great grandmother cut off the ends of the roast because a large roast wouldn't fit in the oven. The great grandchild follows this grand condition. Great grandmother did it because her oven was too small. The great grandchild's oven? It could easily accommodate a full-sized roast. Cutting off the ends of the roast is suboptimal.
Learning to cut off the ends of a roast because thats one's great grandmother did is a Lamarckian trait. Darwinian traits are even more strongly constrained. Spiders have eight legs because that's what ancestral spiders from hundreds of millions of years ago had. Insects have six legs because that's what ancestral insects from hundreds of millions of years ago had. Amphibians, reptiles, mammals, and birds have four appendages because that's what ancestral amphibians had hundreds of millions of years ago. Just as there's nothing optimal about cutting off the end of the roast now that the oven is bigger, there's nothing optimal about the number of limbs an animal has.
Oftentimes in evolution, the best answer for why some trait arose is that stuff happens, or rather, stuff happened.
