There are many things in this world/levels of perspective that benefit from a non-mathematically rigorous analysis- up to and including the question "what is the benefit of rigorous mathematical analysis". That doesn't mean they don't have their own kind of rigor or that you should be able to understand them right away without any background knowledge. The attitude you have is shared by folks in the humanities who think that because they're experts in their field, they should be experts in everything, but luckily, human knowledge is broad and diverse, and there's no single master key.
So here's the operative difference: I can explain to a non-technical person what the Y-combinator gets you in terms of results. I could make a physicist or mathematician or mechanical engineer or even an analytic philosopher understand the significance, and then it's just a matter of notation.
And I really wish postmodernists would stop hiding behind the banner of "the humanities". Analytic philosophy, history, classics, religious studies, and art history are all capable of making meaningful and even true statements from time to time, and most of them can be made comprehensible to the typical person.
If you read the other comments on this thread, a number of people have clearly explained the significance of the theory.
As for the humanities thing, yes, I agree. Just as physicists can make many clear statements that resonate with people who don't even know math, there are many aspects of the humanities that are accessible and clear to people who have never studied theory. Your disdain for higher level theory would also make it difficult for you to enjoy certain texts by people like Aristotle, Kant, and Hegel, none of whom are "postmodernists".
I think you should apologize for making this post. There are a lot of important things that aren't mathematically rigorous but are nevertheless worth understanding.
If you're making grand opaque abstractions without applying some form of logical rigor, how can you be sure you're saying anything that's true and meaningful?
I agree that there are lots of things that are worth understanding but can't be expressed in rigorously logical terms. Things like the subjective experience of falling in love or laughing at a joke or the value of behaving toward others with compassion. Wovon man nicht sprechen kann, darüber muss man schweigen.
And yet, Wittgenstein goes on to write texts that are central pillars of contemporary theory. He also saw that laying out everything you can say in purely logical terms leaves a lot off the table.
