|
We all live in our own boxes, do we not?
Analytical solutions, in either close-form or open-form, are exact, even for complex problems. But they may not exit. Generations of mathematicians spent their whole lives search for such solutions. Despite the elegance of their works, the solutions they have found are tiny subset of problems present.
What do we do when we don't have the analytical solutions? Numerical methods are used. Following mathematical relationships among quantities, iterative algorithm is formulated to find out numerical values of the solution, point by point, starting from the initial and boundary conditions. Such numerical solutions are not exact. But with right methodology the error can approach zero, depending on number of iterations allowed. Such methods, although not exact, fit beautifully with computer, so they are widely used today. Before that, an office full of people are employed to crunch the numbers.
My high school friend Raymond was a brilliant mathematician, a real one. A beautiful mind behind he socially awkward appearance. He earned his post doctorate in pure maths before 30. I still remember the fear in the high school math teacher's eyes when Raymond raised his hand to ask question. He despised numerical analysis as it wasn't pure maths. Guess what his job is? He is top analyst with an internal financial firm in Tokyo, doing... Numerical analysis! He changed his mind after having wife and kids. He couldn't bear to see them being poor accompanying him in the search of perfect, exact, and elegant solutions in the endless ocean of mathematical symbols.
Back to the box of reality. Where the mass is removed from the hammer is important, if it is a rotating hammer. It is the moment of inertia that matters.
-TL
Sent from my SM-N960U using Tapatalk
|