Is lossless information transfer possible?

I have a hypothesis that, the only thing at which human beings are "superior" to other organisms is that we can transfer information without a loss to other human beings.

Don't forget our baldness, two legs, and broad nails. Highly superior.

Two relevant LW posts: One Two

Noiseless communication has not yet been demonstrated. There is some change (or, in information terms, loss) in even this communication.

The original citation seems to be this:

Stephenson, G. R. (1967). Cultural acquisition of a specific learned response among rhesus monkeys. In: Starek, D., Schneider, R., and Kuhn, H. J. (eds.), Progress in Primatology, Stuttgart: Fischer, pp. 279-288.

Can anyone find a PDF?

I think your hypothesis might be improved if you tried to better define (formalise) the concept of lossless information transfer. It is not obvious to me that losslessness is the best descpription of the difference between gorilla and human communication.

Also, you apparently generalise from one example and even that isn't particularly clear. As you describe it, the gorillas learn that trying to reach the banana causes hosing and they prefer not having the banana to being hosed. When the causal link between banana and hosing is broken, the gorillas still act like nothing has changed. But:

1. Your explanation by imperfect information transfer doesn't work. The gorillas clearly communicate the cause, since new gorillas know that it is eating the banana which is forbidden. It is not clear whether the effect is communicated since the new gorillas clearly know that they shouldn't eat the banana but needn't to know what happens if they break the rule unless they try to, which they presumably never do.
2. The observed evidence (and the assumed difference between gorillas and humans, about whom you seem to think that they would discover that banana doesn't correlate with hose anymore) can be explained in several ways that have nothing to do with information loss: perhaps the gorillas simply don't discover that banana does no more cause hosing. Or they are more hosing risk averse and once they discover that the banana might be associated with the unpleasant experience they avoid it even if they have reasons to think that the risk is relatively low.
3. Beware thoughts along the lines "there is one single thing which causes this important difference and we should only discover which it is". Why do you suppose that there is a single strict and simple principle that distinguishes humans from other animals?

Lossless information transfer between humans may be possible, but it's certainly not free with respect to work and time, and it's certainly not the default.

For instance: Whenever I want to communicate a thought or an idea, for instance verbally or on paper, I find that I must first apply some work-intensive, lossy compression which outputs bad English. The output invariably looks or sounds much worse in comparison to the uncompressed idea I have in my head. Throughput is abysmal. A few minutes of thinking can sometimes require a few hours of writing in order to be communicated with some lucidity. In order to restore some similarity to the uncompressed idea as it appears to me, I need to apply further work-intensive error correction, and repeatedly compare the revised output to my internal model.

"Lossless communication" doesn't quite seem to capture what is special about human communication. The difference is more about complexity of communication than losslessness. Being able to communicate using a fully recursive grammar is the key difference. I think that's the concept you're heading towards with "losslessness".

But which came first: being able to communicate using a fully recursive grammar, or participating in a viciously competitive political/social hierarchy and having the resulting selection pressure dramatically increase the size and complexity of our brains over what is, in geological terms, a ridiculously short period of time?

Yes, humans win over animals because we have language. We're the only species that acquires it automatically, and we have a big pile of adaptations that make language work better and that use language to support other functions. Why are we acting surprised about this?