Swinging of arms

Why do we swing our arms when we walk? Like the others have said, it's probably to keep balance. Try running, and you'll be swinging your arms like crazy. If you try to run without swinging your arms, I believe you are more likely to topple over since you're not balanced. Notice that when you step with your left foot, your right arm tends to swing up and when you step with your right foot, your left arm swings up. That convinces me that you do it for balance.Also, you made a point about babies being quadrupedal before being bipedal. If you observe a baby, as well as any other quadrupedal animal, its right forelimb and left hindlimb are synchronized in motion, just like its left forelimb and right hindlimb.

But isn't walking simply a slower version of runnning? Except for the fact that when we walk, we stay in contact with the ground more, there's not much of a difference, except in speed. And we might not swing our arms as much, because we don't need to be as balanced for walking than running.

So what? Just because the body carries itself differently when walking as opposed to running, it doesn't mean that balance is not required for walking. Obviously when you're running, you have to propel yourself forward and it is likely that different muscles work differently to do that, but in terms of balance, you need your arms swinging in both walking and running.