In 1991, Laura-Ann Petitto filmed deaf babies raised with sign language. At the age when other infants say 'bababa', they produced repetitive hand movements with the structure of signs: genuine manual babbling. So babbling isn't about the mouth. It's the brain rehearsing the rhythm of a language, whatever form that language takes.
In Kuşköy, a mountain village in northern Turkey, people talk across valleys by whistling Turkish. A 2015 study showed that whistled Turkish draws on both hemispheres fairly evenly, whereas spoken Turkish relies mostly on the left. The physical form of the signal, it turns out, matters to the brain.
Speech has no gaps between words. In 1996, researchers played 8-month-old babies a continuous stream of made-up syllables for just two minutes. The infants picked out the 'words' by tracking which syllables tend to follow one another. That's probability calculation, done without a calculator or any visible effort.