I feel like we are speaking past each other and I will try one last time. I am not disagreeing that there is difficult mathematics involved in railways, and I agree that tropical algebra will likely one day prove useful for ordinary railway officials and managers. But I doubt that will happen before 2030.
For railway folks, an analogy to tropical algebra is linear programming, which attempts to solve similar-looking problems with very different tools. Linear programming is much older and much better understood than tropical algebra, and is widely used in all sorts of areas, including railways. I believe it’s even taught in modern MBA programs. I would expect a middle-manager in railway scheduling to have familiarity with linear programming: being able to formulate a linearizable optimization problem as a formal linear program and at least having an idea of how to solve it (“put the parameters in Python, there’s this package” is a good answer).
The fact that linear programming is widely used and well-established is important: it is so widely used that Excel can solve certain linear programs. I am not aware of a single software package for computational tropical algebra, and if there are any they are certainly experimental. Unlike linear programming and convex optimization, tropical algebra is almost exclusively the realm of PhD mathematicians (along with handful of operations specialists).
So the question is: should we really expect middle-managers at railway companies to be familiar with tropical algebra for any reasons other than possible extracurricular interest? It seems to me the answer is no. It is like demanding that software architects be familiar with homotopy type theory - because see, look, this incredibly talented math PhD showed how you could use some topological theorems to prove interesting invariants about pointers in circle buffers. It’s very silly to insist your software architect waste so much of her time and precious neural resources on something so difficult and outside of her domain, and, at best, only conditionally useful.
For railway folks, an analogy to tropical algebra is linear programming, which attempts to solve similar-looking problems with very different tools. Linear programming is much older and much better understood than tropical algebra, and is widely used in all sorts of areas, including railways. I believe it’s even taught in modern MBA programs. I would expect a middle-manager in railway scheduling to have familiarity with linear programming: being able to formulate a linearizable optimization problem as a formal linear program and at least having an idea of how to solve it (“put the parameters in Python, there’s this package” is a good answer).
The fact that linear programming is widely used and well-established is important: it is so widely used that Excel can solve certain linear programs. I am not aware of a single software package for computational tropical algebra, and if there are any they are certainly experimental. Unlike linear programming and convex optimization, tropical algebra is almost exclusively the realm of PhD mathematicians (along with handful of operations specialists).
So the question is: should we really expect middle-managers at railway companies to be familiar with tropical algebra for any reasons other than possible extracurricular interest? It seems to me the answer is no. It is like demanding that software architects be familiar with homotopy type theory - because see, look, this incredibly talented math PhD showed how you could use some topological theorems to prove interesting invariants about pointers in circle buffers. It’s very silly to insist your software architect waste so much of her time and precious neural resources on something so difficult and outside of her domain, and, at best, only conditionally useful.