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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 an

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.

Jtsummers 5y ago
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).
- spekcular 5y ago
  Why would a rail manager learn (about) something that has no practical utility and requires a massive investment of effort (graduate mathematical training)?
  - Jtsummers 5y ago
    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.)
    - spekcular 5y ago
      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.)
      - resonantjacket5 5y ago
        I thought it was used for the railway timetables
        spekcular 5y ago
        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.
- proc0 5y ago
  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.
spekcular 5y ago
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.
bollu 5y ago
Do you have any recommendations to learn about how tropical geometry is used for control theory?
- nicklecompte 5y ago
  I haven’t read it but I would guess this is a good place to start: https://arxiv.org/abs/1408.0313 https://arxiv.org/abs/1408.0313 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.
akvadrako 5y ago
The managers building railways and deciding on schedules hire firms to build these models. I shared a co-working space with a guy who did this for a few years.
- nicklecompte 5y ago
  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.

Jtsummers 5y ago

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).

spekcular 5y ago
Why would a rail manager learn (about) something that has no practical utility and requires a massive investment of effort (graduate mathematical training)?
- Jtsummers 5y ago
  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.)
  - spekcular 5y ago
    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.)
    - resonantjacket5 5y ago
      I thought it was used for the railway timetables
      - spekcular 5y ago
        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.
proc0 5y ago
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.

spekcular 5y ago

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.

bollu 5y ago

Do you have any recommendations to learn about how tropical geometry is used for control theory?

nicklecompte 5y ago
I haven’t read it but I would guess this is a good place to start: https://arxiv.org/abs/1408.0313 https://arxiv.org/abs/1408.0313 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.

akvadrako 5y ago

The managers building railways and deciding on schedules hire firms to build these models. I shared a co-working space with a guy who did this for a few years.

nicklecompte 5y ago
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.