[munificent]

Sure, but the probabilities are numbers too. Which is again sort of acknowledging the need to fit quantum mechanics into a numeric framework.

Imagine you were studying ice cream flavors. You might design a study like, "We'll ask a lot of people and the flavor that the most people prefer is the best." In other words, the metaprocess you use to design your experiment itself tacitly assumes you need a numeric result. The presumption of comparison and quantifying frames the questions you even think to ask.

But you can imagine an alternate culture that when studying ice cream flavors doesn't even ask questions with numeric answers. It could be, "We'll ask a lot of people to try flavors and write poems about the experience."

We wouldn't even call this "science". Because there is a hidden border around even the term that affects how we are able to evolve the scientific process.

[klyrs]

Funny thing about quantum mechanics... we use numbers to describe probabilities and functions to describe probability distributions. But the mathematical models we use are incomplete (and, looking at neutron decay, incompatible) so can we really conclude that numbers are the right abstraction?

And no, not poems. Elements of finite groups are not numbers, but they crop up in physics frequently. Topologies are not numbers, but they're also significant in physics.