Lately I've been imagining it along with the slowly boiling frog story and the crab-mentality too. As in some people can't tell we're headed to hell because it's coming so slowly, and some people will actively stop others from escaping hell or trying to fix the situation.
[0] So O(0) means x causes itself. O(1) is y causes x. O(n) is n causes y causes ... causes x. This is just a simplified framework and not meant to be taken too seriously.
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:
(++)
X<-------\
| (-) |
| ------Z
\ / ^
(+) v | (+)
Y-------/
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
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.
> 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)
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.
Jevons paradox is a great example of one which is both clear and counterintuitive: https://en.wikipedia.org/wiki/Jevons_paradox
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....