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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
by atoav 4y ago
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.
- omginternets 4y agoI think it roughly amounts to “thinking through the implications of the implications”.
- drewcoo 4y agoI think that's 3rd order, actually. Why does this remind me of Abbot and Costello? https://youtu.be/sShMA85pv8M?t=64 https://youtu.be/sShMA85pv8M?t=64
- omginternets 4y ago"If x, then y" is one implication, so that's first-order reasoning. "If y, then z" is second-order reasoning.
- Akronymus 4y agoWouldn't "if x, then y because z" be second order?
- omginternets 4y agoAs 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.
- hervature 4y agoYou 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.
- OJFord 4y ago'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.
- js8 4y agoIMHO, 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".
- thrown_22 4y agoHigher order functions have nothing to do with derivatives however.
- earleybird 4y agoHowever, regular types do: "The Derivative of a Regular Type is its Type of One-Hole Contexts" [0] http://strictlypositive.org/diff.pdf http://strictlypositive.org/diff.pdf
- sanderjd 4y agoI really doubt this is where "nth order" comes from colloquially.
- JohnHaugeland 4y agoMath 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
- steppi 4y agoIn 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.
- marcosdumay 4y agoYou 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.
- nerpderp82 4y agoWhich 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.
- coldtea 4y agoIt'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.
- Brian_K_White 4y agoI 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.
- agitator 4y agoThe 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.
- pkrumins 4y agoYou’re mixing up derivatives (rate of change) and approximation (order).
- uoaei 4y agoThe 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.