I don’t necessarily disagree with the gist of this post but there was one minor comment I found odd. It might just be my ignorance (I am not a transit person and have always been bad at algebraic geometry):
> Amtrak can and should fully replace its senior management with people who know how to run a modern intercity railroads, who are not Americans. But then middle management will still think it knows better and refuse to learn what a tropical algebra is or how it is significant for rail schedule planning.
Are transit middle-managers in Europe really applying tropical algebra to rail problems? My understanding is that the mathematical field of tropical algebra didn’t really exist until the 80s, and the research application to control theory is a 2010-era development. It strikes me as very strange to expect anyone who isn’t a PhD in math or operations research to even understand the algebraic geometry required, let alone apply it to a real problem.
But I suppose 30 years ago people would have said the same thing about linear programming. So maybe I am behind the times.
Per your quote they're lamenting the (apparent) refusal to learn what it is, not master it or how to apply it. This is a perennial management problem (well, a perennial organizational problem, but exacerbated when it's the managers). I've worked in offices that were absolutely convinced source code version control meant handing off a file or document to a person who kept the diffs and everything in sync, perhaps with their exclusive use of (often) some 80s or 90s version control system that no one else was allowed to directly access. I didn't need the managers to learn git (in the sense of being able to use it) but I did need them to learn that there were much better ways than the absolutely dysfunctional approaches they were preferring (due to familiarity).
Why would a rail manager learn (about) something that has no practical utility and requires a massive investment of effort (graduate mathematical training)?
> I didn't need the managers to learn git (in the sense of being able to use it) but...
The analogy states they don't need managers to learn the thing, just to have awareness of an alternative thing to the current thing. Implicit is a criticism of managers being didactic in specifying required tools/solutions, too often favoring "our way"/"the old way".
I had never heard of "tropical algebra" so I have no idea of its utility here. I'm only commenting on the distinction between learning about something and learning something.
The former enables you to direct your learning towards learning the thing itself when you realize it's applicable (JIT for learning) if that's your role. And if you're in a leadership position it helps you to recognize the insights those you are in charge of are bringing to you and their relative applicability, or to direct them towards a line of work that may be useful. (Of course, there's a level of incompetent awareness that often happens as well, and that's how SAFe shops are born.)
Let me be more direct. Tropical algebra is no of practical relevance to rail route planning. My understanding is that there's some highly speculative work in this direction, but nothing ready to be applied, or any indication this approach is more useful than standard methods. What you are seeing is someone who previously did pure mathematics wheel out a personal obsession and then (unwisely) chastise people for not caring about it.
Therefore, we should we should not care whether rail managers learn, or learn about, tropical algebra.
(Another observation: look at all the highly efficient European and Asian railways. As far as I can tell, algebraic geometry was used in the planning of exactly zero of them. American rail isn't going to be fixed by the application of high-powered mathematics.)
>What you are seeing is someone who previously did pure mathematics wheel out a personal obsession and then (unwisely) chastise people for not caring about it.
Hanlon's Razor suggests it's more likely that tropical algebra is just one of a relatively few examples of rail planning theory that the author is familiar with, not that he has a pernicious drive to promote the study.
As I understand it, it mostly is a transformation of expressions like:
Exp(vars, max(,), plus(,))
to give expressions like
Exp(vars, plus(,), times(,))
where solutions to the latter can give solutions to the former under some conditions. It seems plausible that some specialized versions could be explained to someone with a reasonably good understanding of high school math. New math doesn't have to be abstruse.
But all I know is I ran into a tropical algebra problem once and it was intractable.
Does there exist any evidence tropical algebra is used in practice, and is significantly better than older approaches to the problem? As far as I know, the answer is negative.
The symposium certainly sounds interesting. Looking at the talks, I am struck by the major separation between talks about tropical algebra and talks about railway optimization.
But the point of our comments is that this is a new research field, with very little proven application, and chastising railway middle managers for not following these deeply technical and somewhat esoteric developments is silly. It’s like getting on to a manger at Intel because they are unfamiliar with the architecture of photonic quantum computers.
There are financial incentives to solve scheduling issues in the UK. Trains must meet a schedule within time limits. Failure to maintain reliability at a regulatory 90.9% can mean the loss of the license to operate.
The UK interconnects with European networks via Eurostar, and the major hubs feed it. The tube runs trains every minute or two so connecting between these hubs, for example Waterloo to Kings Cross isn’t usually an issue. But arriving late at a hub can be very disruptive.
Middle managers, in europe generally, focused on targets don’t need to understand the math, but are in a competitive market that can require mathematicians to model and solve scheduling issues.
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.
My reading of the single mention of tropical algebra in the article wasn't that its use is another example of established European rail superiority -- though I think the text is ambiguous.
> Worse, this is a nationwide problem. Amtrak can and should fully replace its senior management with people who know how to run a modern intercity railroads, who are not Americans. But then middle management will still think it knows better and refuse to learn what a tropical algebra is or how it is significant for rail schedule planning. They do not know how to learn, and they do not recognize that it’s a problem. This percolates down to planners and line workers, and I don’t think Americans are ready for a conversation about full workforce replacement at underperforming agencies.
Rather the thesis is more like like:
- upper management don't know how to learn the major established lessons from Europe (one might call this strategy)
- middle management don't know how to learn about new (not yet standard anywhere) refinements that augment the existing system (one might call this tactics)
You may be right that it's just an unsupported and false claim, not a hypothetical, and probably if the wind changes direction and I read it again, I'd agree with you on the author's meaning. Nevertheless, I find the "need to learn to learn strategy and tactics" argument plausible.
I'm hoping we can replace all middle management with AI, that just reports green/yellow/red, relays messages, whatever.
I'm tired of being called the expert yet somehow reporting to someone that is many levels below me in knowledge. Why exactly do you need to know this if you're not going to be able to influence the direction? Why are leaders not required to be better than who they lead in whatever it is they do (in order to have foresight)? I don't know but here's to hoping it will be automated in some future.
You're right. There are a lot of good complaints about the American rail system, but the fact that tropical geometry isn't being used to plan routes isn't one of them.
I am really sorry to be so pedantic about this and if you don’t know that’s completely understandable: are you sure those firms are actually using tropical algebra for this? I am sure that there are many firms that handle the mathematical/computational headaches that come about in transit planning, I am just skeptical that any of these headaches involve questions of tropical varieties.
My point was that the specific field is very cutting edge, and my understanding is that any 2021 application of tropical algebra to a real transit network would be a high-risk speculative research project, not a well-tested optimization methodology.
My familiarity with tropical geometry is mostly conversational :) and entirely on the pure math side. The basic definitions use obviously lend themselves to optimization problems (and I think the field is in many ways an algebraic generalization of classical variational calculus) but I don’t really know of anything specific.
> Amtrak can and should fully replace its senior management with people who know how to run a modern intercity railroads, who are not Americans. But then middle management will still think it knows better and refuse to learn what a tropical algebra is or how it is significant for rail schedule planning.
Are transit middle-managers in Europe really applying tropical algebra to rail problems? My understanding is that the mathematical field of tropical algebra didn’t really exist until the 80s, and the research application to control theory is a 2010-era development. It strikes me as very strange to expect anyone who isn’t a PhD in math or operations research to even understand the algebraic geometry required, let alone apply it to a real problem.
But I suppose 30 years ago people would have said the same thing about linear programming. So maybe I am behind the times.