We wave hand(s) to friends, fans, guests, neighbors, colleagues, & relatives with saying “Hi”, “See You”, “Bye”, “Good Bye”, “Meet you”, “Miss you” or “Take care” etc. Sometimes words can’t reach due to distance barrier but mere hand wave works. We feel better when we watch others waving their hands with dear words and smile on faces while confronting or going away. Why we’ve become so habitual of it? Why waving hands to make us & other feel better?
Hand wave has very basic purpose that makes us social by exhibiting disarmed and friendly state. By holding open palms with stretched fingers visible to others silently conveys "Feel safe from me! I'm not holding any arm or weapon". Waving hand isn't as formal like hand shake. Ritual of hand shake's like treaty of ensuring mutual disarmament and willingness to connect whereas hand wave goes beyond formality. It has become social and casual practice of showing off openness, friendliness and harmless intentions. More affectionate and intimate hand wave silently says "Don't forget me...", "I care for you..." or "Come again...".
It’s natural tendency to get attracted to thing that moves or flutters. In same context, hand wave becomes attention seeker while we say “Hey” or “Hello” aloud. It can convey “Do you see me?" or "I’m here.”. Other person may respond by waving hands reciprocating “Yes, I see you.” or "I'm coming to you."