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Mathematics is a language unto itself, and some concepts are more difficult to map to natural language than others. Even if you had a much broader English vocab
by robbedpeter 5y ago
Mathematics is a language unto itself, and some concepts are more difficult to map to natural language than others. Even if you had a much broader English vocabulary, with unique words assigned to every currently known mathematical abstraction, the intuitive sense in which we speak and read and understand will clash with the behavior and features of mathematical symbols.
Natural language maps onto an embodied experience designed by evolution. Math transcends what our brains are built to expect and predict. Infinities, exponentials, quantum entanglement, and an infinite array of other very real things simply exist outside what we are capable of understanding intuitively, without some special conjunction of neural wiring, training, or happenstance.
The nature of infinities might seem like navel gazing, but it helps us understand the features of different types of numbers, and those are the building blocks of proofs. Knowing to which infinity class a number belongs might help inform the optimization of real world engineering of chips or data storage, or drug design algorithms, and so on. It could eventually be part of figuring out practical quantum computers, solving p vs np, or maybe just a piece of a better factorization algorithm that improves cryptography.