The Webster definition fails to qualify the term FIRST TIME. Everything an infant or a species 'discovers' is a first time. This does not render the process of discovery nor what has been discovered unique or novel in any manner that can objectively be identified as any different from the unlimited number of things it has yet to discover, does it really?
If you are a parent, you will have observed the baby's *discovery* of its hand and fingers, for the first time. I watched my daughter for days as she was experimenting with this extraordinary discovery.
I did not claim an exclusive nature to *discovery*. The point was that everything we know is ultimately a discovery, even if we weren't looking for it. We discovered that DDT does not just kill insects, but also that DDT has the unintended consequence of softening the eggshells of birds which feed on *treated* insects.
For sentient minds there is always a *first time* discovery. Ask any cosmologist, they all say that when a new equation yields consistent results, they all say that it brings a feeling of discovery. When we analyze and experiment with the *new* information and its properties, it is science; when we use it for practical purposes it's technology.
Language is a conceptual tool with more gaps and flaws than your average cracked sieve. This is only the tiniest one. Only the language we call math has more and bigger gaps in understanding.
I disagree, the
mathematical function is invariable, we just have not yet discovered all the mathematical functions. But I am confident that the as yet unknown mathematical functions will be discovered *for the first time* in the future, often accidentally.
p.s. As English is my second language, I go by definitions from recognized reliable sources, such as Webster.
Definition is the purview of philosophy, an area of learning both older and more flawed than science and math. All but a select few definitions are self-referential. Identify what those are, as I have, and you will gain an understanding of how little we really have to reason with.
According to Tegmark, there are a near infinite number of mathematical events, but the underlying mathematics are relatively simple.
As I understand it, if an equation yields a result of infinity, the equation is flawed. It's a scientific no-no..
Question: Does a self-referential equation not always yield an answer of infinity?