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Modeling cities as 'cellular' is a common mistake, well explored in A City is not a Tree by Christopher Alexander. http://en.bp.ntu.edu.tw/wp-content/uploads/2

Modeling cities as 'cellular' is a common mistake, well explored in A City is not a Tree by Christopher Alexander. http://en.bp.ntu.edu.tw/wp-content/uploads/2011/12/06-Alexander-A-city-is-not-a-tree.pdf http://en.bp.ntu.edu.tw/wp-content/uploads/2011/12/06-Alexan... tl;dr we tend to talk about cities in heirarchical, enclosed terms, as having "limits", "neighborhoods", "blocks", "plots", and so on. This can be modeled as a tree, in the maths and computer science sense. But it's more accurate to model these systems as semilattices. Thus a city isn't multicellular (the cells being the enclosed units of the tree model) nor super-cells (which sort of punts on the internal structure, while still enclosing the city in a sort of membrane which even a walled city doesn't resemble), but a thing distinctly itself.

siraben 5y ago
> But it's more accurate to model these systems as semilattices. That's the first time I've seen order theory used to describe hierarchical structures like a city. Continuing the analogy, what would the join of a nonempty finite subset of parts of a city be? Say the set was an apartment block, road and grocery store, would the join of all these concepts be the "local neighborhood" that makes up part of a town?
- rosetremiere 5y ago
  It feels to me this analogy is rather weak. Presumably, the point of semilattice (compared to tree) is that the hierarchy is not top-down but can have branches up and down. I'd say the algebraic structure of joins and meets is not really natural here… it's just some form of graph. Open to counter-arguments though!
  - nemetroid 5y ago
    Are you arguing that the model proposed by the essay does not describe a semilattice? Or that the model proposed does not describe cities well?
    - rosetremiere 5y ago
      I was (without any better argument than my intuition) arguing that the sentence “But it's more accurate to model these systems as semilattices.” sounds weak to me. I was not making a point on the article, but only on this specific idea. My feeling is that it's not really fruitful to describe "real life" phenomena in terms of abstract algebraic mathematical structures. It's more of a gut feeling than anything else, but I think there are two points that one can make here: * Generally, it's better to first observe a phenomenon, understand it, and try to find a good vocabulary for it, mathematical or otherwise, rather than take an out-of-the-box fancy sounding math concept and try to make it fit your phenomenon. * It seems as soon as you try to describe a phenomenon with an algebraic object, you'll soon get stuck trying to make sense of your functions/axioms: what's the meet? what's the join, is there a bottom element, etc. If you rather work with a more “geometric” notion (graphs, metric spaces,…) you don't have as many things to match, and you can focus on studying your objects. To be clear, I don't have any strong point here, it's mostly gut feeling/rumblings.
      - bsedlm 5y ago
        > My feeling is that it's not really fruitful to describe "real life" phenomena in terms of abstract algebraic mathematical structures I disagree, however I don't think you're enterily wrong. We just need a physical theory to bridge the abstract mathematics with the real world. as a starting point it occurs to me to wonder what does throwing a ball have to do with F = ma also, the whole point of math is to do everything with such a level of abstraction that you can apply the abstractions to many things.
paganel 5y ago
> we tend to talk about cities in heirarchical, enclosed terms, as having "limits", Which is funny in a way, because people involved in the city-making business (for lack of a better term) have tried to do just that (i.e. imposing city limits) for centuries (at least). The medieval city walls are a prime example of that, with anything that stood behind the walls treated as being part of the city and everything that was outside the walls seen as non-city, with non-city dwellers many times being required not to spend the night inside the city walls. More recently, just the other day I was reading a transcript from a Romanian Communist party meeting from the late 1980s where the Romanian dictator Ceausescu (I'm Romanian and live in Romania myself) was complaining that cities have been let to grow indefinitely and with impunity, without respecting the city limits that had been set in law. So you've got a late 20th communist dictator and Middle-Age burghers all trying to delay what I personally see as inevitable, i.e. the extension of the city by all means possible. A little OT, but imo slightly related to this, there was a urban theory that was regarding as "proper" cities only those places with clear limits, for example the European Middle-Age towns, while the places with no clear limits set (many of those places located in the present Middle-Eastern Countries or in Northern Africa) were most of the times seen as "bigger villages", not as proper cities/towns. That was kind of a orientalistic/colonizing way of looking at things which I think stood behind the late 19th-most of the 20th century effort to make those Middle-Eastern cities look like their Western counter-parts, i.e. with clear limits set and with a clearer and more easily readable road structure.
eternalban 5y ago
A semi-lattice structure does not preclude cells. The human body is not a tree. For those interested in mathematical approaches to architecture and spatial systems I recommend the research work and books of James Hillier and Julienne Hanson: Social Logic of Space, Hillier & Hanson https://www.cambridge.org/core/books/social-logic-of-space/6B0A078C79A74F0CC615ACD8B250A985 https://www.cambridge.org/core/books/social-logic-of-space/6...
- failwhaleshark 5y ago
  Butbutbut we have limbs, some people are true to their roots, and branch out. Okay, fine, I'll put the Texas Chainsaw Massacre implement down. Let's self out.

siraben 5y ago

> But it's more accurate to model these systems as semilattices. That's the first time I've seen order theory used to describe hierarchical structures like a city. Continuing the analogy, what would the join of a nonempty finite subset of parts of a city be? Say the set was an apartment block, road and grocery store, would the join of all these concepts be the "local neighborhood" that makes up part of a town?

rosetremiere 5y ago
It feels to me this analogy is rather weak. Presumably, the point of semilattice (compared to tree) is that the hierarchy is not top-down but can have branches up and down. I'd say the algebraic structure of joins and meets is not really natural here… it's just some form of graph. Open to counter-arguments though!
- nemetroid 5y ago
  Are you arguing that the model proposed by the essay does not describe a semilattice? Or that the model proposed does not describe cities well?
  - rosetremiere 5y ago
    I was (without any better argument than my intuition) arguing that the sentence “But it's more accurate to model these systems as semilattices.” sounds weak to me. I was not making a point on the article, but only on this specific idea. My feeling is that it's not really fruitful to describe "real life" phenomena in terms of abstract algebraic mathematical structures. It's more of a gut feeling than anything else, but I think there are two points that one can make here: * Generally, it's better to first observe a phenomenon, understand it, and try to find a good vocabulary for it, mathematical or otherwise, rather than take an out-of-the-box fancy sounding math concept and try to make it fit your phenomenon. * It seems as soon as you try to describe a phenomenon with an algebraic object, you'll soon get stuck trying to make sense of your functions/axioms: what's the meet? what's the join, is there a bottom element, etc. If you rather work with a more “geometric” notion (graphs, metric spaces,…) you don't have as many things to match, and you can focus on studying your objects. To be clear, I don't have any strong point here, it's mostly gut feeling/rumblings.
    - bsedlm 5y ago
      > My feeling is that it's not really fruitful to describe "real life" phenomena in terms of abstract algebraic mathematical structures I disagree, however I don't think you're enterily wrong. We just need a physical theory to bridge the abstract mathematics with the real world. as a starting point it occurs to me to wonder what does throwing a ball have to do with F = ma also, the whole point of math is to do everything with such a level of abstraction that you can apply the abstractions to many things.

paganel 5y ago

> we tend to talk about cities in heirarchical, enclosed terms, as having "limits", Which is funny in a way, because people involved in the city-making business (for lack of a better term) have tried to do just that (i.e. imposing city limits) for centuries (at least). The medieval city walls are a prime example of that, with anything that stood behind the walls treated as being part of the city and everything that was outside the walls seen as non-city, with non-city dwellers many times being required not to spend the night inside the city walls. More recently, just the other day I was reading a transcript from a Romanian Communist party meeting from the late 1980s where the Romanian dictator Ceausescu (I'm Romanian and live in Romania myself) was complaining that cities have been let to grow indefinitely and with impunity, without respecting the city limits that had been set in law. So you've got a late 20th communist dictator and Middle-Age burghers all trying to delay what I personally see as inevitable, i.e. the extension of the city by all means possible. A little OT, but imo slightly related to this, there was a urban theory that was regarding as "proper" cities only those places with clear limits, for example the European Middle-Age towns, while the places with no clear limits set (many of those places located in the present Middle-Eastern Countries or in Northern Africa) were most of the times seen as "bigger villages", not as proper cities/towns. That was kind of a orientalistic/colonizing way of looking at things which I think stood behind the late 19th-most of the 20th century effort to make those Middle-Eastern cities look like their Western counter-parts, i.e. with clear limits set and with a clearer and more easily readable road structure.

eternalban 5y ago

A semi-lattice structure does not preclude cells. The human body is not a tree. For those interested in mathematical approaches to architecture and spatial systems I recommend the research work and books of James Hillier and Julienne Hanson: Social Logic of Space, Hillier & Hanson https://www.cambridge.org/core/books/social-logic-of-space/6B0A078C79A74F0CC615ACD8B250A985 https://www.cambridge.org/core/books/social-logic-of-space/6...

failwhaleshark 5y ago
Butbutbut we have limbs, some people are true to their roots, and branch out. Okay, fine, I'll put the Texas Chainsaw Massacre implement down. Let's self out.