I am not particularily familiar with the connotation of the term second-order-thinking, but to me it implies the somewhat mathematical meaning of it. The first order might be some value (e.g. a voltage) and the second order might be the rate with which that voltage changes and the third the rate with which this rate changes etc.

To me this implies that thinking on a higher order is somewhat about stepping back and viewing the construct from a meta position. E.g. instead of thinking about how to address an imidiate problem by applying a bandaid, one order higher would be to think about the root causes and deal with the root of the problem. Even one order higher would be to think about which culture or systems of thinking allow for the good solving of such problems etc.

It's simply about looking further down up the casual chain, not stopping at the initial cause-effect: thinking about the effects of effect themselves (and, in third order, the effects of the effects of the effects, and so on).

A simple example of failing to do so and only considering the first level cause-effect:

"The British government, concerned about the number of venomous cobras in Delhi, offered a bounty for every dead cobra. Initially, this was a successful strategy; large numbers of snakes were killed for the reward. Eventually, however, enterprising people began to breed cobras for the income. When the government became aware of this, the reward program was scrapped. When cobra breeders set their now-worthless snakes free, the wild cobra population further increased".

Here's another one:

Caribbean plantation owners were tired of their relentless war against field rats – the rodents were eating into their precious sugar cane crops. Come 1872, a chap called W.B. Espaut had an original idea: why not bring over a few Indian mongooses – those unpretentious mammals known as enthusiastic rat hunters? Espaut travelled to India, had some mongooses captured and brought them to Jamaica. The problem – it soon turned out – was that the mongooses did not just kill rats; they killed birds, ate eggs, insects, useful reptiles, even small deer fawns. True, the mongooses also hunted and killed lots of rats; but they did not kill them all. In fact, the rodents continued to multiply – and so did the mongooses. Worse, both rats and mongooses carry a disease called leptospirosis, which can be lethal to humans. To cut a long story short, rather than getting rid of one pest, the hapless Hawaiians ended up with two.

"Simpsons did it": https://www.youtube.com/watch?v=LuiK7jcC1fY i wonder at what point does game theory comes into play instead of second order thinking?

Great examples.

I believe we encounter second-order thinking in mundane day-to-day activities too which are generally categorized as 'instinct'; Say we drop the key under the table and we know before hand that we would hit our head if we get up under the table and so we crawl back(Or may be we've hit our head earlier and it becomes reinforcement learning?).

Then there are tasks which are totally dependent upon multi-order thinking like a game of chess (or) most other brain games.

I wonder if we could create a system to collect different second-order thinking decisions for different day-to-day activities to serve as a decision making tool powered by collective human knowledge?

Hawaiians? I thought the second story was set in Jamaica.

It is. I snipped some parts of the story to simplify it for the comment, and left out an important step:

The Jamaican example "grabbed the attention of Hawaiian sugar cane planters, who also suffered from the rats. Bringing mongooses to Hawaii as natural pest exterminators seemed such an elegant idea. "

Maybe this is actually the fourth-order effect.

No. It's "one and a half order" thinking, where you leave out half of the story, but the story still works for your brain.

'order' has many meanings in mathematics, and I'm not sure of the best metaphor that is actually called an order there, but when people talk colloquially about 'second order effects' etc. IME they mean something like a vertex v2 (doing something) in response to a change to v1, where there exists a vertex vj and edges (v1, vj) & (vj, v2) - and implicitly no edge (v1, v2). Higher 'orders' similarly extending the chain.

Or think chess - 'first order thinking' would make a move that merely escapes mate, or puts you in a position where another move immediately could be a great one; 'second order thinking' considers what the opponent will do from there (probably disallow the great move or threaten it back); etc.

IMHO, the figure of speech "n-th order" generally comes from Taylor series approximation, where n-th term is indeed expressed using n-th derivative. Also, if the series converges, the higher order terms will become smaller, thus the practice of approximating the reality up to n-th order term.

Also, it's often practical to ignore 2nd order and higher terms, because then you have a linear function - something really easy to work with. Therefore, "2nd order effects" have effectively become synonymous to "non-linear effects".

I really doubt this is where "nth order" comes from colloquially.

There are many examples in physics, for example: https://physics.stackexchange.com/questions/310875/second-or...

Yes, but physics is not colloquial. Most people are unfamiliar with physics.

This is what I've always assumed as well. The feeling of "things that usually don't matter but may explode (if it turns out the series doesn't converge)" seems to fit the expression pretty well.

Higher order functions have nothing to do with derivatives however.

However, regular types do: "The Derivative of a Regular Type is its Type of One-Hole Contexts"

[0] http://strictlypositive.org/diff.pdf

E = mc^2 is a notable example.

I think it’s simply order of events. If you do N, N+1 will happen

That's what I described - v1 leads to vj, which leads to v2.

I think it roughly amounts to “thinking through the implications of the implications”.

I think that's 3rd order, actually.

Why does this remind me of Abbot and Costello?

https://youtu.be/sShMA85pv8M?t=64

"If x, then y" is one implication, so that's first-order reasoning.

"If y, then z" is second-order reasoning.

Wouldn't "if x, then y because z" be second order?

As I see it, z is a different type than x and y. It’s the causal arrow linking x to y. The existence of a second causal arrow would make it second-order.

In a way, I think you and your parent are both right. The missing link is that the analogy is based on multivariate series. First order deals with each variable in isolation. X1, X2, X3, . . . Second order contains interaction terms like X1 x X2 (The X1^2 can be thought of as a self interaction.) Third order would consider interactions between three variables and so on.

I’m not sure if this a false etymology, but it’s how I’ve always understood the term and I’ve met others who understand it this way as well.

I think the origin may be from linear regression with polynomial terms, which is very common in the medical sciences and social sciences. Terms like X1 x X2 are called interaction terms in that context and coefficients are often treated as quantifying the impact of a term on the result. Strictly speaking, the analogy would then be with any multivariate polynomial approximation, not just Taylor series.

The best, simple, metaphor I can think of is playing out a chess game in your head. As in, you make a move, and see how the scenario changes, and predict the opponents moves. In chess, it's just 2D and one opponent or agent. In the real world you need to weigh many possible agents, estimate their motivations, and predict their responses. This way you can visualize the cascading effects of a decision.

You are stepping back and looking how your decision consequences will impact the network of causes and consequences that exists on the real world.

Root cause analysis is a different thing.

Which often involves second order effects.

A -> (caused) B

C -> D

When B and D occur (within a window) -> Error

It is that connection between B and D that needs to be discovered.

The connotation of the term second-order refers to systems-thinking principles.

In the causal graph of entities interacting in a system, considering one element of the system, second-order thinking corresponds to considering effects on neighbors of that element which are caused by changes to that element itself.

Math isn't characterized by unmeasurable magic phrases

Higher order thinking is a trap phrase for people who want to sound deep by filling in details on the fly from their imaginations in the clothing of science

Nothing evidence based supports any of this

You’re mixing up derivatives (rate of change) and approximation (order).

I don't know if this is quite the model the article describes, but I say this is at least a similar and equally useful model.

You are on the right track. Second order means second derivative. So, if we are predicting future positions, using acceleration in addition to velocity will always be better. Second order is much more difficult because in more than one dimension you have to consider how every pair interacts.

I think people just interpret "future" very differently. For some "future" does include your second and third paragraph, since it is also a potential causality down the line. For others, it's only first paragraph example. Future for some is a branching tree, for others just a linked list.

I popped in to say much same. But the statistician in me thinks about it such that 2nd order thinking and longer term impacts often coincide due to the time it may take 2nd order impacts to play out. But in some systems, 2nd order impacts happen on short timeframes. So I’d describe it as a correlation between 2nd order and long term thinking.

This is a good analogy .. many of the comments in this thread that are confusing 2nd order thinking with long term thinking are clearly just thinking of iterating 1st order thinking along the time line.

The problem I have with exploring neighbouring causal links is that when overdone it can lead to analysis paralysis.

I often get stuck simulating too many different branches in possible futures and casual links to the point of slowing down my present capabilities.

My GF calls it overthinking, and not in a good way.

Perhaps I just need a bigger brain with more processing power.

I’ve seen the analysis paralysis happen as well, but I think the key is to also assign likelihoods/severities upside downside to the analysis, you can usually quickly triage what to focus on from there (or as I often find the nice you’ve bounded the range of likely outcomes, pick the one one that fits your risk tolerance (e.g. do I take the train for an almost guaranteed 3hr trip, or do I try and outsmart the traffic and either be right and have a 2hr trip, or be wrong and have a 4hr trip)

This. I've received consistent feedback (from mentor, from family, etc) to do less second-order analysis. It can be very productive in some specific scenarios, especially when I used to do initial architecture; but these days, it's a complete analysis paralysis. Moving from technological architecture to people leadership / client relationship management, second order thinking brings up so many pros and cons for each action, with insufficient data to weigh the balancing.

I've taken to using a sort of internal version of "disagree and commit" - I have the little mental debate with myself, arrive at an ambiguous juncture, then pick an option (at random if necessary) and go all-in on it. If it turns out I was wrong there's usually still time to course-correct.

Delaying or not making a decision is a choice itself, one that is almost always inferior to the options you're stuck between.

Yep, fail fast is often going to have a superior resolution time than time spent in deep analysis.

Plus you get more experience making decisions, more experience making quick decisions, and more problem-solving experience that way.

I agree. I believe it is not that second-order thinking is unhelpful, but rather that it is only useful when applied wisely. The challenge is knowing when and how to apply it, and of course having the tool kit necessary to do this kind of thinking.

Leveled thinking is common in competitive games, for obvious reasons. There's no better illustration of what you're talking about than the poison scene in Princess Bride:

https://www.youtube.com/watch?v=rMz7JBRbmNo

The way I've heard most competitive gamers talk about the line between leveling and tail-chasing is to play at level 2:

Level 1: The obvious strategy

Level 2: Strategy that beats the obvious strategy <-- Default to this level

Level 3: Strategy that beats level 1

The problem is, if you're playing in a competitive environment, everyone knows about leveling, so you may actually gain more edge by picking a strategy randomly. I've heard competitive Magic player Huey Jensen would make random plays when he was behind on the chance he could throw his opponent off and trap them in leveling second-guessing.

I think it requires balance. Seems to me like the more you can consider the better decision you can reach, but there is a point where thinking more is negative value, and you must decide.

“The instant of decision is madness”

-Kierkegaard

You can use a mind mapping tool and limit your expansion radius. I've had some success with that.

or the opposite - in ML terms more brain will likely just introduce overfitting - while less brain makes way for some neat generalization that is quick and works just good enough ;)

In SRE roles I've been in it's often second-order issues that plague software. In many ways, things boil down to process and what value/principles each process delivers and operates on. Misalignment in that space can be causal to a great number of things. Explaining second-order issues tends to be difficult as well, mainly because due to their nature there's often incomplete data to work with, so solving them is often piece-meal.

I wonder whether this is an example that in part also might cause us to question the utility of second/nth-order thinking? Because the more distant causal links are also estimated with more and more uncertainty (and necessarily so, insofar as uncertainty compounds across causal links), to the point where it becomes hard to weigh highly uncertain distant consequences against relatively certain near consequences?

It boils down to "actions have consequences," some of which may be unfavorable. And those consequences have other possible consequences. It grows exponentially. So you need to figure out how to anticipate these consequences.

I would expect a Venn diagram of 1st order thinking vs unintended consequences, to have more overlap than a 2nd order thinking vs unintended consequences.