5 ms·

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.
- gregsq 5y ago
  It’s a research field in the UK at least. For the UK’s extensive rail network. https://www.birmingham.ac.uk/research/railway/index.aspx https://www.birmingham.ac.uk/research/railway/index.aspx Edit: Further symposium on this subject. https://www.birmingham.ac.uk/schools/mathematics/news-and-events/events/2018/tropical-mathematics-optimisation-railways.aspx https://www.birmingham.ac.uk/schools/mathematics/news-and-ev...
  - nicklecompte 5y ago
    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.
    - gregsq 5y ago
      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. https://golem.ph.utexas.edu/category/2018/05/tropical_mathematics_and_optim.html https://golem.ph.utexas.edu/category/2018/05/tropical_mathem... https://www.independent.co.uk/news/uk/home-news/late-network-rail-breaches-licence-6279260.html https://www.independent.co.uk/news/uk/home-news/late-network...
      - nicklecompte 5y ago
        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.
- dundarious 5y ago
  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.

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.

gregsq 5y ago
It’s a research field in the UK at least. For the UK’s extensive rail network. https://www.birmingham.ac.uk/research/railway/index.aspx https://www.birmingham.ac.uk/research/railway/index.aspx Edit: Further symposium on this subject. https://www.birmingham.ac.uk/schools/mathematics/news-and-events/events/2018/tropical-mathematics-optimisation-railways.aspx https://www.birmingham.ac.uk/schools/mathematics/news-and-ev...
- nicklecompte 5y ago
  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.
  - gregsq 5y ago
    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. https://golem.ph.utexas.edu/category/2018/05/tropical_mathematics_and_optim.html https://golem.ph.utexas.edu/category/2018/05/tropical_mathem... https://www.independent.co.uk/news/uk/home-news/late-network-rail-breaches-licence-6279260.html https://www.independent.co.uk/news/uk/home-news/late-network...
    - nicklecompte 5y ago
      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.
dundarious 5y ago
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.