A math question. I know that math can only give us what we feed it. My question is about building the needed information that needs to be calculated, not missing any steps or at least approximating how far a missing piece if information will skew the answer.
Is this piece of building the equation still considered pure math or are other skills relied on here?Define “Pure math”. As an engineer I’d say figuring out “what needs to be calculated” is my job, and the math comes later. Math as applied to real world problems is often called “Applied math”. “Pure math” is basically inventing notation and proving stuff. But there is considerable overlap between math, science and engineering, and most actual mathematicians work on applied math.
That answered my question. I build archery primitive bows as a hobby. Over the years several PHD types have written papers on bow design using quite a bit of math. In some areas I noticed they kind of dropped the ball. Primarily when studying energy losses. Most likely because they lacked experience with actually building bows. My hobby is trying to do a better job of isolating these losses and better identifying how they affect a bow.
Sounds like engineering to me. Non-experts can get into a sort of “spherical cow” situation sometimes. Even though they’re experts at math or science, they’re not experts in the particular domain they are studying, and can ignore or abstract away some really important aspects of the problem because they don’t know any better. Grounding your results in experience is absolutely necessary.
An example is the terrible state of “Exercise science” these days. People with zero experience in making themselves stronger or coaching someone else into a significant strength improvement publish all these pointless studies about whether half-squats or quarter-squats are better for building leg strength over six weeks in a group of untrained college students. :smack: They have the right degree and wear lab coats though, so they must be correct.
That is a very good example and another area I have often questioned.
As an in-between answer… Take those “story problems” we used to get in school.
“A train leaves Denver at 8:00 a.m. going east at 40 mph…”
I would say that, yes, framing that question into an equation – “40 t - 800 = 0” – actually is “math.” It’s taking the information inherent in the “story” and putting it into standard notation. “Setting up the equation” is math.
But I also agree with DrCube that working up the original “story” in the first place is more engineering than math. The mathematician has nothing to do with starting the train, or why it was in Denver.