I recently read Peter Watts' short story "The Things" and was blown away. It's based on the 1982 John Carpenter film "The Thing," but told from the perspective of the alien. What I loved about Watts' story was his ability to step inside the mind of an intelligent being radically different from a human. The prose is philosophical, but not in an intellectual or academic way—more in the sense of being a phenomenological description of an extraterrestrial's experience of the world, which has the effect of de-familiarizing the world and making the reader see it from a completely different perspective:

The world spoke to itself, in the same way I do when my communications are simple enough to convey without somatic fusion. Even as dog I could pick up the basic signature morphemes—this offshoot was Windows, that one was Bennings, the two who'd left in their flying machine for parts unknown were Copper and MacReady—and I marveled that these bits and pieces stayed isolated one from another, held the same shapes for so long, that the labeling of individual aliquots of biomass actually served a useful purpose.

I'm looking for more like this.

I'm less interested in fantastical worlds, alien cultures, etc and more in what it would be like to think and experience and act as something whose intelligence developed via a totally different evolutionary path from homo sapiens. A story from the perspective of an octopus, a nanobot swarm, Cthulu, a superintelligent plant that lacks all five human senses but has its own distinct modes of perception... the weirder and more alien the better!

One of the only other pieces of media I know of that's given me this same impression is the film Under the Skin. I know that film is based on a novel by Michael Faber, but from what I've read of it, it seems much more anthropomorphized of a perspective than the movie.

Jorge Luis Borges' story "Tlön, Uqbar, Orbis Tertius" similarly gave me the same feeling of encountering a radically alien way of thinking—he describes a culture that believes in an extreme form of philosophical idealism, seeing the world "not as a concurrence of objects in space, but as a heterogeneous series of independent acts," with a family of languages that lacks nouns, so that a statement like "the moon rose above the water" becomes "upward behind the onstreaming it mooned." This language/worldview even effects how the world gets carved up perceptually and descriptively:

The literature of this hemisphere (like Meinong's subsistent world) abounds in ideal objects, which are convoked and dissolved in a moment, according to poetic needs. At times they are determined by mere simultaneity. There are objects composed of two terms, one of visual and another of auditory character: the color of the rising sun and the faraway cry of a bird. There are objects of many terms: the sun and the water on a swimmer's chest, the vague tremulous rose color we see with our eyes closed, the sensation of being carried along by a river and also by sleep. These second-degree objects can be combined with others; through the use of certain abbreviations, the process is practically infinite. There are famous poems made up of one enormous word. This word forms a poetic object created by the author. The fact that no one believes in the reality of nouns paradoxically causes their number to be unending.

The story is told from the perspective of a scholar studying this culture, and so lacks the full first person embodiment of that way of seeing that I'm looking for, though Borges does try to dig deeply into what thinking, experiencing, and communicating would be like as a member of this culture.

Which is to say I'd also be interested in any examples of radically alien intelligence that don't take a first person view, so long as they really go in depth in attempting to describe an alternate form of cognition or being-in-the-world. I already have a decent to-read list in that department: I just picked up Watts' Blindsight, have been curious about Embassytown, Children of Time, and Fire Upon the Deep, and have been working my way through Stanislaw Lem's bibliography for a while now, having just finished Eden.