4 ms·

This is a really interesting topic and the article is nicely written. What bothers me, though, is the effort to link the mathematics to 'real-world' applicatio

This is a really interesting topic and the article is nicely written. What bothers me, though, is the effort to link the mathematics to 'real-world' applications. I agree that forest fires, disease outbreaks, and the spread of ideas might be good candidates for this sort of modelling. But I think you'd need an awful lot of solid evidence to back that up.

crazygringo 7y ago
Without the real-world applications a lot of this could seem dry and boring or irrelevant. Many years ago I went through teacher training, and one of the biggest things you learn is to always make material relevant to students by linking abstract concepts to real-world applications they actually care about. It is true that in writing an article like this, you need to be very careful with your wording to distinguish between things that "appear like", "are similar to", "suggest", or even "is a first-order approximation of", versus stating that this is the model of epidemiology, forest fires, etc. (which needs citations, etc.). But in this particular article, the examples seem fairly straightforward as first-order approximations -- curious what sentences you're specifically objecting to?
- soVeryTired 7y ago
  > curious what sentences you're specifically objecting to Lines like this: If we're simulating the spread of measles or an outbreak of wildfire, SIR is perfect. The author could have said "this kinda-sorta looks like it might be useful in simulating wildfire but I haven't checked", but of course that would be less convincing and less exciting. Which is fine as far as it goes. The problem is what happens when someone takes one of these models seriously without actually checking the details, or without being qualified to check them.
  - wDcBKgt66V8WDs 7y ago
    I think the author does a pretty good job of highlighting that there are imperfections and shortcomings while eliding over those details. They may have slipped up in some places such as your quote but I'm definitely not concerned of anyone taking any of this too seriously and extrapolating on it dangerously.
    - soVeryTired 7y ago
      > I'm definitely not concerned of anyone taking any of this too seriously and extrapolating on it dangerously. Not this particular article, no. But there's a whole genre of excited mathematical modelling literature where the author demonstrates a gee-whizz concept that looks like it could be really useful. The trouble is that once you start digging down into the specific details, they turn out to be really hard to get right, and at best you end up with a model that's brittle, for want of a better word. An example that I have in mind is the literature on power law distributions. A little bit of theory showed how power law distrbutions could arise via a process known as preferential attachment, and everyone got excited and suddenly people were spotting them everywhere. The literature on this topic is massive. The thing is, it turns out that it's quite hard to check that a given dataset follows a power law. This paper [0] showed that many of the claims were sloppy, and the researchers hadn't been careful with their statistics. The crux of what I'm saying is that establishing that a model fits well is hard, whether it's a diffusion model, a power law distribution, or anything else. If someone wants to claim that some mathematical widget can be used to model X, they'd better be able to back that claim up with a real demonstration and carefully laid-out details. Otherwise they're just waving their hands in the air. [0] http://www.cse.cuhk.edu.hk/~cslui/CMSC5734/Clauset_Shalizi_Newman_09.pdf http://www.cse.cuhk.edu.hk/~cslui/CMSC5734/Clauset_Shalizi_N...
  - dls2016 7y ago
    What happens when someone uses a hair dryer in the bathtub? As someone who spent a fair number of hours teaching mathematics to engineering students, exciting is what you want. What use is it to state the complex hypotheses of a theorem if the student cannot feel the result coming?
  - TeMPOraL 7y ago
    > The problem is what happens when someone takes one of these models seriously without actually checking the details, or without being qualified to check them. That's a problem with absolutely any kind of statement you can put on-line. There's only so much an author can do to prevent stupid from misreading them; the responsibility is not all on author here. > The author could have said "this kinda-sorta looks like it might be useful in simulating wildfire but I haven't checked" Why? Maybe they actually checked. I did, and keeping in mind that I'm not a medical scientist, it does seem that SIR model with modifications is widely used to study disease spread, and it also does look like a good first-order approximation for measles. It also does look like a good first-order approximation of wildfires. I actually did a thesis on using cellular automata for simulating indoor fires and used some of the same ideas presented here. SIR is essentially what I'd get if I ignored the details of heat convection, conduction and radiation - which at the scale of forest fire is something you can do (unlike my work, where modelling these details was kind of the entire point).
    - soVeryTired 7y ago
      > SIR is essentially what I'd get if I ignored the details of heat convection, conduction and radiation - which at the scale of forest fire is something you can do How do you know? To validate this sort of model surely you need to know an awful lot about statistical modelling and about forest fires. The main sort of insight this model would give you is that setting up clear spaces like roads through a forest would hinder the spread of fire. If you took the model literally, you might end up ignoring the fact that sparks can be carried by the wind to areas that are far away from the trees that are currently burning. > it does seem that SIR model with modifications is widely used to study disease spread Fair - there's a whole wikipedia page [0] about this sort of model. But like I'm saying, that page is big on theory and light on evidence. Those models are full of parameters like transmission rate that are not typically known until after the fact. The world is full of theorists writing down academic models that are, frankly, a little useless. What I would find more convincing is a writeup of how a big practitioner health organisation like the CDC or the WHO used one of these models to gain a new insight that they couldn't have found any other way. [0] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...
- wDcBKgt66V8WDs 7y ago
  I took calculus at the same time as advanced placement physics in highschool. Calc was taught dry and contextless, I wasn't doing well. Then we started learning calc in physics, and wowee it made so much more sense, would you believe my grades started going up in calc too. This article is a great example of that for diffusion I think.

crazygringo 7y ago

Without the real-world applications a lot of this could seem dry and boring or irrelevant. Many years ago I went through teacher training, and one of the biggest things you learn is to always make material relevant to students by linking abstract concepts to real-world applications they actually care about. It is true that in writing an article like this, you need to be very careful with your wording to distinguish between things that "appear like", "are similar to", "suggest", or even "is a first-order approximation of", versus stating that this is the model of epidemiology, forest fires, etc. (which needs citations, etc.). But in this particular article, the examples seem fairly straightforward as first-order approximations -- curious what sentences you're specifically objecting to?

soVeryTired 7y ago
> curious what sentences you're specifically objecting to Lines like this: If we're simulating the spread of measles or an outbreak of wildfire, SIR is perfect. The author could have said "this kinda-sorta looks like it might be useful in simulating wildfire but I haven't checked", but of course that would be less convincing and less exciting. Which is fine as far as it goes. The problem is what happens when someone takes one of these models seriously without actually checking the details, or without being qualified to check them.
- wDcBKgt66V8WDs 7y ago
  I think the author does a pretty good job of highlighting that there are imperfections and shortcomings while eliding over those details. They may have slipped up in some places such as your quote but I'm definitely not concerned of anyone taking any of this too seriously and extrapolating on it dangerously.
  - soVeryTired 7y ago
    > I'm definitely not concerned of anyone taking any of this too seriously and extrapolating on it dangerously. Not this particular article, no. But there's a whole genre of excited mathematical modelling literature where the author demonstrates a gee-whizz concept that looks like it could be really useful. The trouble is that once you start digging down into the specific details, they turn out to be really hard to get right, and at best you end up with a model that's brittle, for want of a better word. An example that I have in mind is the literature on power law distributions. A little bit of theory showed how power law distrbutions could arise via a process known as preferential attachment, and everyone got excited and suddenly people were spotting them everywhere. The literature on this topic is massive. The thing is, it turns out that it's quite hard to check that a given dataset follows a power law. This paper [0] showed that many of the claims were sloppy, and the researchers hadn't been careful with their statistics. The crux of what I'm saying is that establishing that a model fits well is hard, whether it's a diffusion model, a power law distribution, or anything else. If someone wants to claim that some mathematical widget can be used to model X, they'd better be able to back that claim up with a real demonstration and carefully laid-out details. Otherwise they're just waving their hands in the air. [0] http://www.cse.cuhk.edu.hk/~cslui/CMSC5734/Clauset_Shalizi_Newman_09.pdf http://www.cse.cuhk.edu.hk/~cslui/CMSC5734/Clauset_Shalizi_N...
- dls2016 7y ago
  What happens when someone uses a hair dryer in the bathtub? As someone who spent a fair number of hours teaching mathematics to engineering students, exciting is what you want. What use is it to state the complex hypotheses of a theorem if the student cannot feel the result coming?
- TeMPOraL 7y ago
  > The problem is what happens when someone takes one of these models seriously without actually checking the details, or without being qualified to check them. That's a problem with absolutely any kind of statement you can put on-line. There's only so much an author can do to prevent stupid from misreading them; the responsibility is not all on author here. > The author could have said "this kinda-sorta looks like it might be useful in simulating wildfire but I haven't checked" Why? Maybe they actually checked. I did, and keeping in mind that I'm not a medical scientist, it does seem that SIR model with modifications is widely used to study disease spread, and it also does look like a good first-order approximation for measles. It also does look like a good first-order approximation of wildfires. I actually did a thesis on using cellular automata for simulating indoor fires and used some of the same ideas presented here. SIR is essentially what I'd get if I ignored the details of heat convection, conduction and radiation - which at the scale of forest fire is something you can do (unlike my work, where modelling these details was kind of the entire point).
  - soVeryTired 7y ago
    > SIR is essentially what I'd get if I ignored the details of heat convection, conduction and radiation - which at the scale of forest fire is something you can do How do you know? To validate this sort of model surely you need to know an awful lot about statistical modelling and about forest fires. The main sort of insight this model would give you is that setting up clear spaces like roads through a forest would hinder the spread of fire. If you took the model literally, you might end up ignoring the fact that sparks can be carried by the wind to areas that are far away from the trees that are currently burning. > it does seem that SIR model with modifications is widely used to study disease spread Fair - there's a whole wikipedia page [0] about this sort of model. But like I'm saying, that page is big on theory and light on evidence. Those models are full of parameters like transmission rate that are not typically known until after the fact. The world is full of theorists writing down academic models that are, frankly, a little useless. What I would find more convincing is a writeup of how a big practitioner health organisation like the CDC or the WHO used one of these models to gain a new insight that they couldn't have found any other way. [0] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...
wDcBKgt66V8WDs 7y ago
I took calculus at the same time as advanced placement physics in highschool. Calc was taught dry and contextless, I wasn't doing well. Then we started learning calc in physics, and wowee it made so much more sense, would you believe my grades started going up in calc too. This article is a great example of that for diffusion I think.