Mathematics as a native language

A couple of days ago, I was in a discussion in which I expressed one of my favourite views. This is that we should not be disturbed by our puzzlement at the meaning of quantum mechanics, or anything else of that nature. Explanations that try to picture the quantum world in the terms that are appropriate to our life in the macroscopic world are bound to be inadequate. The reality is in the mathematics, and the only thing to do is to start speaking mathematics as a native language.

I think my interlocutor agreed. But afterwards, I wondered whether there would be any reason why mathematics could not be a native language, in the way that French and German can be. Obviously, it is learnt later than other languages. The pattern of human development prevents its being a native language in the sense of the first language one learns. But that would not prevent its being a native language in the sense of a language in which one thinks, a language that is transparently meaningful. Likewise, someone who moves to a country with a different language, even as an adult, can go native, and take on his or her new language as a native language.

One possible difficulty would be that languages do not exist in isolation from the world. Just as one needs agency and a sense of agency in order to have a full sense of self, one needs to live in the world and navigate it, as well as living within a linguistic community, in order to know what words mean. Words need to latch on to the things with which one has dealings. This is not true of all words, but it needs to be true of at least some of them. How can this be true of mathematics?

The obvious answer is our starting-point. We live in the world that physics describes. Various mathematical statements can be interpreted to be about that world. So the terms and structures that are used latch on to the world. They could latch on to different things, but so could terms and sentences of a natural language. There is more scope for mathematical terms to latch on to something different than for terms of natural languages to do so. The mathematical terms are more neutral as between forms of life. Moreover, a given mathematical theory could latch on to any one of a set of isomorphic worlds, and the concept of isomorphism here underlines the neutrality as between forms of life. But this does not strike me as debarring us from seeing mathematical talk as latching on to the world in which we live.

The main problem would seem to be that the form in which the mathematical expression of quantum mechanics represents that world is utterly unlike the form in which the world is experienced by us. But even this does not strike me as a decisive objection to going native. As someone learns quantum mechanics, he or she learns how the quantum world gives rise to our everyday experience of medium-sized objects. The new picture of the world is linked to our experience through that understanding. Furthermore, the mathematical terms and methods that are used also have direct application in the world as it is experienced. We can come to understand them in that context, then apply them in the quantum context.

That leaves one last gap to close. Is anything lost when we transfer our understanding of mathematical terms and methods, acquired in the world as experienced, to our conception of the quantum world? I think it is not. At least, there is no loss that would debar us from taking on mathematics as a native language for the purpose of making sense of quantum mechanics.