You nerds ready for a wall of text?
What's the difference between us and all other species that have ever lived? Language seems to be the unanimous answer, or rather the underlying computational operation that allows us to use language. I first learned about this from a few cognitive science courses I took in college, and it's sort of been a pet project of mine to keep up with the technical literature even to this day.
The parts of the brain responsible for language is almost certainly what separates us from the great apes , and if you go back roughly 60,000 years, other hominids.
Language is also not for communication, and did not evolve by natural selection. It's sounds very counter-intuitive but it seems to be the case. At least according to one theory of how the mind works that has gained traction by a few notable people. This idea that language is not for communication goes all the back to Aristotle. He argued it was simply an externalization of thought and the fact we communicate our thoughts is a secondary process. Decartes said more or less in the 17th century and Noam Chomsky in the modern period. Interestingly enough, in today's version language is not even the externalization of thought,
but rather a thought process in and of itself. Which would mean externalization (speaking) is the secondary process and communication a tertiary process. The evidence, at least from what I've read, seems to point in this direction.
We know homo-sapiens have been around for roughly 200,000 years plus or minus. And according to the archaeological evidence there was no improvement in our making of stone tools, weapons, and cultural artifacts from about 200,000 years ago up until about 60,000 years ago. (You can read about this in work by Ian Tattersall) Then something very special seems to have happened to our species around ~60,000 years ago. There's an explosion of new artifacts, tools, symbolic representations, and various cave drawings - this radical increase is sometimes called
The Great Leap Forward by paleontologists. This is also the same window of time when other similar species, like Neanderthal's, went extinct. Which means we lived along side them for at least 140,000 years then either wiped them all out or out-competed them for resources within ~10,000 years after getting this new property. So what was this amazing new property that allowed us to do all of this? Recursion. Or rather the operation that makes use of recursive thinking, called Merge. Merge is the ability to take two concepts already constructed in the mind, combine them to create a third concept, and to be able to keep doing this potentially infinitely. Those of you who took computer science courses probably remember recursive routines and how they work. You can read about it in this very influential paper from 2002 authored by Fitch, Hauser, and Chomsky:
http://psych.colorado.edu/~kimlab/hauser.chomsky.fitch.science2002.pdf
Merge in a nutshell:
This is the example that Chomsky famously uses. If you have the sentence:
Instinctively eagles that fly swim. We instantly all know we asking whether they can swim, not if they can fly. But it's not obvious why that is from a computational perspective, since fly is the closest verb. The reason is that
it is the closest verb when you construct the sentence using the Merge operation. Merge gives you a hierarchical structure where each concept can branch off another. And this branching process is potentially infinite because it is generated recursively. Which is why our brains, which are not infinitely large of course, can produce an infinite number of possible sentences.
But notice there was not a gradual increase in symbolic artifacts, it all seems to have happened instantaneously from a evolutionary point of view. Which means that this merge function cannot be the result of natural selection. The only other plausible explanation is that it is the result of some natural law that is not currently known. In the same way a crystal or snowflake forms, they both have very intricate and complex structures but didn't evolve. They are simply the result of natural laws interacting with each other. So at the level of brain circuitry there ought to be a snowflake in there somewhere that resulted from some biological or computational law of nature.
I could keep on going but I'll stop there.