I agree, I've been thinking along these lines for a while too; thank you for phrasing it so clearly.
My current thinking led me to conclude that we don't have sufficiently good tools[0] for modelling O(n) problems with n > 2. Particularly when (what your simplification doesn't capture) there are feedback loops involved.
Take this O(2) problem: x causes more y, y causes more z, z causes less y but much more x. Or in a pictorial form:
You can't just think your way through that problem, you have to model it - estimate coefficients (even if qualitatively), account for assumptions, and simulate the dynamic behavior.
I argue that we lack both mental and technological tools to cope with this.
Speaking of global warming, a year ago I presented this problem: https://news.ycombinator.com/item?id=20480438 - "Will increase in coal exports of Poland increase Poland's CO₂ footprint?" Yes? No? How badly?
The question is at least this complicated:
Coal exports
^
| [provides Z coal to]
|
| [needs α*X = A kWh for coal]
Mining coal <---------------------\
| |
| [provides X coal to] |
v |
Coal power plants |
| | |
| | [γ*X = Y kWh burning coal] |
| v |
| Electricity --------------------/
|
| [burned coal into β*X = N kg of CO₂]
v
CO₂ emissions
(Presented this way it not only tells you that, ceteris paribus, it will, but roughly by how much and what are the parameters that can be tweaked to mitigate it.)
Why aren't we talking about climate change in these terms with general public? Why aren't feedback loops taught in school?
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[0] - Or, if they exist, they aren't sufficiently well known outside some think tanks or some random academic papers.
Your ascii art is much better than mine and I'm not going to attempt it, but I agree with everything that you've said except for
> I argue that we lack both mental and technological tools to cope with this.
I do think we have the tools to solve these issues. I do not think the mental tools are in the hands of the average person (likely not even in most of your above average people because the barrier to entry is exceedingly high and trying to model any problem like this is mentally exhausting and it thus never becomes second nature). Many of the subjects broached here aren't brought up until graduate studies in STEM fields, and even then not always. An O(aleph_n) problem is intractable but clearly O(10) isn't. We should be arguing about what order approximation is "good enough" but ignoring all the problems that arises is missing a lot of fundamental problem solving. Good for a first go, but you don't stop there. I think this comes down to people not understanding the iterative process. 0) Create an idea. 1) Check for validity. 2) Attack and tear it down. 3) If something remains, rebuild and goto 2 else goto 0. I find people stop at 1 on their own ideas but jump to 2 (and don't allow for 3) for others ideas.
> Why aren't feedback loops taught in school?
I think 3 other things should be discussed as well. Dynamic problems (people often reduce things to static and try to turn positive sum games into zero sum. We could say the TeMPOraL component), probabilistic problems, and most importantly: an optimal solution does not equate to everyone being happy (or really anyone). Or to quote Picard:
> It is possible to commit no mistakes and still lose. That is not a weakness. That is life.
The last part I think is extremely important but hard to teach.
(I should also mention that I do enjoy most of the comments you provide to HN)
> I think 3 other things should be discussed as well.
Strongly agreed with all three.
> Dynamic problems (people often reduce things to static and try to turn positive sum games into zero sum.
That's what I implicitly meant by talking (again and again) about feedback loops; problems with such loops are a subset of dynamic problems, and one very frequently seen in the world. But you've rightfully pointed out the superset. I think most people, like you say, try to turn everything into a static problem as soon as possible, so they can have a conclusive and time-invariant opinion on it. But it's not the proper way to think about the world[0]!
(I only disagree with the "try to turn positive sum games into zero sum"; zero-sum games also require perceiving the feedback loops involved. And then there are negative-sum games.)
> probabilistic problems
Yup. Basic probability is taught to schoolchildren, but as a toy (or just another math oddity) rather than a tool for perceiving the world.
(Thank you for the kind words :).)
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[0] - Unless your problem has a fixed point that you can point out.
> (I only disagree with the "try to turn positive sum games into zero sum"; zero-sum games also require perceiving the feedback loops involved. And then there are negative-sum games.)
This is an often snipe I make to people talking about economics (I do agree with the lack of mention of negative sum games, but they also tend to be less common, at least in what people are about). Like the whole point of the economic game is to create new value where it didn't previously exist (tangent).
> Yup. Basic probability is taught to schoolchildren, but as a toy (or just another math oddity) rather than a tool for perceiving the world.
I think this is where we get a lot of "I'm not good at math" and "what is it useful for" discussion. Ironically everyone hates word problems, but at the heart of it that's what it is about.
Great point. Those problems are really hard to reason about, partly because without specific knowledge of the coefficients, all you can expect a well-reasoned person to conclude is that "it can go either way". And even knowing the data, most practical problems in this category would take either computer modeling or simplifying assumptions to really draw conclusions about.
Worse, someone motivated to shape the story one way or the other can create a just-so story where they emphasize only one feedback path or the other, depending on what conclusion they want their audience to draw.
I think the best antidote, although by no means a cure, is to teach clear and specific examples early on so that everyone at least can have a mental category for this class of problem, if not the tools to work through them.
There's a danger of bad reasoning being involved, but I argue that "well-reasoned people" and just-so stories are problems either way. But I think that attaching a specific model to a problem grounds the conversation in reality.
Taking the carbon exports example I pasted, the model presented structurally tells you that carbon footprint is going to grow with exports. We can haggle about "how much", but - under this model - not about "whether". You can tweak the parameters to mitigate impact, you can extend the model with extra components and tweak those to cancel out the impact (and that automatically generates you reasonable solution candidates!). Or, you can flat out say that the model doesn't simplify the reality correctly, and propose an alternative one, and we can then discuss the new model.
The good thing is, at every point in the above considerations you're dealing with models and reality and somewhat strict reasoning, instead of endlessly bickering about whether A causes B or the other way around, or whether arguing A causes B is a slippery slope, or whatnot.
I strongly agree with teaching examples, both real (serious) ones and toy ones, to teach this kind of thinking.
Jevons paradox is indeed great to dig into and I suppose offer some sort of counterexample to what I'm talking about. The nature of the phenomenon is in a feedback loop, and whether it'll go good or bad depends on the parameters (the increased use can reduce the value of the intervention, cancel it out, or even make it worse than doing nothing). But from what I hear, people sometimes pick one of the possible outcomes and use it as thought stopper (e.g. "we shouldn't do X because obviously Jevons paradox will make things worse!").
> [0] - Or, if they exist, they aren't sufficiently well known outside some think tanks or some random academic papers.
Are you familiar with Judea Pearl's work regarding graphical analysis of causal problems? If not, he'd probably interest you. While he mostly falls in the category of "random academic papers" (and academic books), but he has also co-authored a very readable (and enjoyable) popular science book. A review of that book is here: http://bostonreview.net/science-nature/tim-maudlin-why-world. And a more technical overview of his graphical approach is here: https://www.timlrx.com/2018/08/09/applications-of-dags-in-ca....
My current thinking led me to conclude that we don't have sufficiently good tools[0] for modelling O(n) problems with n > 2. Particularly when (what your simplification doesn't capture) there are feedback loops involved.
Take this O(2) problem: x causes more y, y causes more z, z causes less y but much more x. Or in a pictorial form:
You can't just think your way through that problem, you have to model it - estimate coefficients (even if qualitatively), account for assumptions, and simulate the dynamic behavior.I argue that we lack both mental and technological tools to cope with this.
Speaking of global warming, a year ago I presented this problem: https://news.ycombinator.com/item?id=20480438 - "Will increase in coal exports of Poland increase Poland's CO₂ footprint?" Yes? No? How badly?
The question is at least this complicated:
(Presented this way it not only tells you that, ceteris paribus, it will, but roughly by how much and what are the parameters that can be tweaked to mitigate it.)Why aren't we talking about climate change in these terms with general public? Why aren't feedback loops taught in school?
--
[0] - Or, if they exist, they aren't sufficiently well known outside some think tanks or some random academic papers.