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Mental Models I Find Repeatedly Useful

929 points| orph | 9 years ago |medium.com | reply

189 comments

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[+] mikekchar|9 years ago|reply
Interestingly, I find my favourite nitpick: Ockam's razor. The article quotes it as "The simplest solution is usually the correct one". This is a common misinterpretation of it and it's interesting that the quote links to the wikipedia page that has a better statement: "Among competing hypotheses, the one with the fewest assumptions should be selected."

The key problem is equating simplicity with correctness. This is usually disastrous. Once you feel that something is "correct" you stop looking for ways to falsify it. That's the exact opposite for what Occam's razor is used for.

Instead, if you have 2 competing hypotheses (two hypotheses for which the evidence supports both), you use the one with less assumptions. Partly because the one with less assumptions will be easier to work with and lead to models that are easier to understand. But mostly because less assumptions makes it easier to falsify.

Abusing this principle outside of the scientific method leads to all sorts of incredibly bad logic.

[+] abrichr|9 years ago|reply
Very interesting.

From [1]:

Famously, Karl Popper (1959) rejected the idea that theories are ever confirmed by evidence and that we are ever entitled to regard a theory as true, or probably true. Hence, Popper did not think simplicity could be legitimately regarded as an indicator of truth. Rather, he argued that simpler theories are to be valued because they are more falsifiable. Indeed, Popper thought that the simplicity of theories could be measured in terms of their falsifiability, since intuitively simpler theories have greater empirical content, placing more restriction on the ways the world can be, thus leading to a reduced ability to accommodate any future that we might discover. According to Popper, scientific progress consists not in the attainment of true theories, but in the elimination of false ones. Thus, the reason we should prefer more falsifiable theories is because such theories will be more quickly eliminated if they are in fact false. Hence, the practice of first considering the simplest theory consistent with the data provides a faster route to scientific progress. Importantly, for Popper, this meant that we should prefer simpler theories because they have a lower probability of being true, since, for any set of data, it is more likely that some complex theory (in Popper’s sense) will be able to accommodate it than a simpler theory.

Popper’s equation of simplicity with falsifiability suffers from some well-known objections and counter-examples, and these pose significant problems for his justificatory proposal (Section 3c). Another significant problem is that taking degree of falsifiability as a criterion for theory choice seems to lead to absurd consequences, since it encourages us to prefer absurdly specific scientific theories to those that have more general content. For instance, the hypothesis, “all emeralds are green until 11pm today when they will turn blue” should be judged as preferable to “all emeralds are green” because it is easier to falsify. It thus seems deeply implausible to say that selecting and testing such hypotheses first provides the fastest route to scientific progress.

[1] http://www.iep.utm.edu/simplici/#SSH4bi

[+] amasad|9 years ago|reply
One way to think about Occam's razor is from a probabilistic perspective. Consider the Conjunction Fallacy -- for any two events the probability of both events occurring together is less than or equal to the probability of either one occurring alone. Yet it often makes intuitive sense to people that the more specific conditions are more probable than the general one. (See examples in the wikipedia page: https://en.wikipedia.org/wiki/Conjunction_fallacy)

So the more assumptions you're adding to the hypotheses the more you're getting taxed on the likelihood of it being correct. Therefore it's more likely that the hypothesis with the fewer assumptions to be correct.

[+] omginternets|9 years ago|reply
Here's how I explain it to laypersons: "given two hypotheses, Ockam's razor tells you which one to test first"
[+] drzaiusapelord|9 years ago|reply
This is a good point. If you went with the "simplest" explanation then which one do you pick:

1. The patients humors are out of whack. The treatment is bloodletting.

2. The patient has a complex infection involving many physiological systems like immune system, foreign bacteria, gut flora, etc. The treatment is rest and administration of a lab engineered antibiotic for weeks.

Or:

1. The patient is possessed by a Djinn/Demon/spirit and needs an exorcism from a priest/shaman/imam.

2. The patient suffers from mental illness which is difficult to describe let alone treat. Treatment will be years, if not decades, of a mix of therapy, lifestyle changes, and medication.

Sadly, these attitudes still exist, even in the industrialized West. I often visit /r/paranormal because I have a thing for ghost stories and sometimes there's a posting about "possession" which is very clearly about a mentally ill person. When I point this out and ask why this person isn't getting proper care, I'm downvoted to -5 near instantly. Yes, that's right, the guy saying "This isn't a demon, this poor woman needs proper medical help," gets argued with like its the 13th century.

[+] danieltillett|9 years ago|reply
Ockam’s razor can’t tell you which theory is correct, just which one to use when you have more than one theory that accounts the data. It is purely a pragmatic way to rank competing theories.
[+] stared|9 years ago|reply
I find it interesting that now Ockham's razor moved from philosophy to applied statistics. That is, Bayesian statistics can quantify (a more complicated model which fits just as well has, or only slightly better, has lower likelihood) and in machine learning we use it in practice (to avoid overfitting, as too complex models may fit well to the training data, but be suboptimal for generalization).

See also BIC (Bayesian Information Criterium) for selecting models.

[+] scoot|9 years ago|reply
My conclusion on reading this discussion is that if a bunch of smart people can't agree on what Occam's razor is useful for, it isn't useful!
[+] barrystaes|9 years ago|reply
I'd say the thing with Occam's razor is that its easier to disprove a simpler answer with less assumptions, thus its easier to place more thrust in it if it does hold up to the same scrutiny as answers that have more assumptions and complexity.

Also, i like Hanlon’s Razor. "Never attribute to malice that which is adequately explained by stupidity." Generalizing here, but people _are_ stupid.

[+] kordless|9 years ago|reply
I wrote something on my white board this weekend that is similar in concept: forced efficiencies at random intervals. I hypothesize that systems which have the least moving parts are less likely to suffer "breakage" if the infrastructure on top of which they run is randomly reliable and/or stingy with resources. Also see Gates/Page's law: https://en.wikipedia.org/wiki/Wirth%27s_law
[+] cel1ne|9 years ago|reply
Actually the law is better translated as: "More things should not be used than are necessary."
[+] logicallee|9 years ago|reply
Genuine question: so why do physicists explore a theory that posits 11 dimensions, if the evidence at hand does not require 11 dimensions - i.e. if it is additional assumptions about the Universe beyond what has been collected. (This question refers to string theory.)
[+] kriro|9 years ago|reply
If you extend OR to theories you should select the one that has the least ad-hoc hypotheses (or the smallest set of auxiliary hypotheses in the Lakatos sense). In other words one could argue that theories get "worse" with more auxiliary hypotheses so from a scientific process point of view if you diligently falsify and force the creation of more auxiliary hypotheses you can weaken a theory enough for a (more elegant) alternative to take its place.
[+] unabst|9 years ago|reply
More specifically,

> two hypotheses for which the evidence supports both

If they are supported by the same evidence, then the truth that is being supported must be the same. The simplest hypothesis is therefore the smaller nutshell that captures that truth. The other one is bloated, and bloated information (what this is all about) punishes us with complexity and irrelevance.

Fundamentally, any theory is an abstraction of evidence. Ockham's razor is about the quality of said abstraction.

[+] pasbesoin|9 years ago|reply
In a sentence, "What is?" versus "What do I do?".

Occam's Razor is a useful -- but not fool-proof -- tool for the latter.

It says nothing definitive about the former. At best, it makes a very broad statistical generalization.

If it's actually statistical (measured), and not anecdotal.

[+] hderms|9 years ago|reply
Couldn't adding more assumptions also make it easier to falsify? Like if the assumptions obviously lead to inconsistencies or if the added assumption is required for the hypotheses and happens to be easier to test in isolation, then one could throwout the hypothesis while only checking a single assumption.
[+] blake8086|9 years ago|reply
I think a more accurate interpretation is "the simplest explanation is the likeliest". It follows as a consequence of Solomonoff induction.
[+] btilly|9 years ago|reply
Two adjustments that I would make.

Remove Metcalfe's law. It is a massive overestimate. See http://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf for the better n log(n) rule for valuing a network.

And I find Le Châtelier's principle generally applicable, and not just to Chemistry. It says that if you observe a system at equilibrium, and try to induce a change, forces will arise that push it back towards the original equilibrium. It is one thing to recognize this at work in a chemical reaction. It is quite another to be blindsided by it in an organization.

See http://bentilly.blogspot.com/2010/05/le-chateliers-principle... for my explanation of why this holds in general outside of chemistry.

[+] uola|9 years ago|reply
Ugh, maybe I'm the only one but I don't find this list useful. Not because it isn't interesting, but the implication that it will actually make you smarter. The problem today isn't information, it's knowledge. Even if you can correctly and fully understand all these models, something that could take years, you still most likely wouldn't be able to implement them, especially when they are in conflict with each other.

I think it's a much better idea to study things like critical thinking, practical reasoning and operational leadership. Back in the day hacker values stated that you could ask for directions, but not for the answer. Because the process itself was as important as the answer. Not just for amusement, but because there might not be a right answer and the next time you're confronted with a similar problem you now have some experience of making those decisions.

A great deal of "stupidity" in technology these days seem to stem from schools that promote check box answers to complex problems and the popularity of these "laws" that make people so sure of themselves that it prevents them from proper reasoning.

[+] sitkack|9 years ago|reply
This is super useful, I have a similar list but it also includes techniques and ideas

  * Dimensionality Reducing Transforms
  * Hysteresis, Feedback
  * Transform, Op, Transform
  * Orthogonalization for things that are actually dependent
  * Ratios, remove units, make things dimensionless
A big one, that helps me immensely, is that when I need to do a big/risky/complex task, is to imagine myself doing with with sped up time. Instantly creates an outline and list of tools that one will need.
[+] rwallace|9 years ago|reply
Good list! A few suggested tweaks:

Veblen goods clearly exist, but the evidence for the existence of Giffen goods is much more suspect. (Did the poor really eat more bread because the price of bread rose, or because there was an across-the-board increase in the price of all kinds of food?)

The Precautionary Principle is not just dangerous or harmful, but guaranteed suicide; as things stand right now, we are all under a death sentence. It needs to be replaced by the Proactionary Principle, which recognizes that we need to keep making progress and putting on the brakes is something that needs to be justified by evidence.

Any list that has sections for both business and programming needs some entry for the very common fallacy that you can get more done by working more hours; in reality, you get less done in a sixty-hour week than a forty-hour one. (Maybe more in the first such week, but the balance goes negative after that.)

The distinction between fixed and growth mindset is well and good as far as it goes, but when we encourage the latter, we need to beware of the fallacious version that assumes we can conjure a market into existence by our own efforts. You can't become a movie star or an astronaut no matter how hard you try, not because you lack innate talent, but because the market for those jobs is much smaller than the number of people who want to do them.

[+] source99|9 years ago|reply
A technique I often use to test a theory is to change the inputs to be the maximum and minimum possible values and see if the model still holds true. I've found it to be incredibly useful in a few specific situations.
[+] taneq|9 years ago|reply
Or more generally, look for critical points in the model and see if it still holds. Max/min values (or odd combinations of max/min for different variables) are good candidates, as are zeroes, and anything which makes part of an equation go to zero.
[+] mistermann|9 years ago|reply
I've always thought this should be a very effective way to explain a point to someone, but in practice it rarely seems to work....maybe that saying applies, something about you can't use logic to change the mind of someone that didn't use logic to arrive at their conclusion.
[+] erikb|9 years ago|reply
Also a basic programmer skill. Check a normal value, limits, and if you find it some values that may lead to unexpected results like division by zero.
[+] Swannie|9 years ago|reply
Yeah, that's somewhat related to sensitivity analysis that's already in the list.

Though I think I'd agree that it's technically a different model, but related.

[+] erikb|9 years ago|reply
I think pg also wrote an essay about a mental model that I find interesting: When in doubt, it's probably not about you.

There are many events that we usually think are related to us, but actually aren't, like your boss or customer being angry is in most cases not about you but something else.

I have looked through a lot of pg's essays but didn't find it. He probably removed it just that I can't find it (/example).

If someone else finds it, please link.

[+] csallen|9 years ago|reply
I'm surprised he rates cost-benefit analyses as a 2 ("occasionally" used) rather than a 1 ("frequently" used). Making good decisions almost always requires taking a hard look at both the costs and the benefits. It cannot be overstated how often bad decisions are made because the parties involved simply neglected to factor in the costs (including opportunity costs).

I personally use cost-benefit analyses for every non-trivial decision in my life.

[+] delish|9 years ago|reply
Some commenters here are saying, "I already know this stuff." Indeed. I'd be curious if people could put out a list of "advanced" mental models. For example, Bayes' theorem is more advanced than Occam's razor.

What's clearly more advanced than Bayes' theorem, and as useful? ET Jaynes' flavor of probability theory? I'd posit the more advanced version of active listening as, "being able to perform a bunch of kinds of therapy--freudian, rogerian, family and systems etc." Of course I don't mean you go get a license for these things. I'm positing them as difficult, generally-applicable life skills. I'm not claiming these are good examples; I think HN can come up with better ones.

[+] VLM|9 years ago|reply
Thinking being a flux of information, and EE telecom theory having discovered all kinds of laws about flow of information, its no surprised that those models apply pretty well to the engineering tradeoffs of general mental models of thinking or thinking about information in other contexts.

EE control theory class IS an entire senior year class on applying a model to something (a thermostat?) which isn't terribly hard, and then modeling and measuring its performance and finally optimizing the model which is pretty hard.

Shannons law explains how good ideas, noise/distraction/bad ideas, depth of concentration or maybe total volume of information, and rate of mistakes all interrelate and how changing one (or several) will affect the others in general.

There are some interesting tradeoffs in communication filter design (analog hardware or modeled in DSP) along the lines of you can freely trade smoothness in response (group delay, ripple, latency, monotonicity kinda), accuracy in response, and complexity/cost. These tradeoffs apply to everything in the world that processes things not just filter synthesis.

There is some kind of chaos theory "thing" where as feedback mechanisms become more complicated, oscillation becomes inevitable and unpredictable. Doesn't matter if we're talking about high gain amplifier design or world economic models.

This is aside from the general engineering mental models of a good engineer can freely exchange cost, reliability/safety, and performance. In fact it being enormously easier to exchange in those rather than expand, you can pretty much see thru transparent marketing that only mentions one or some factors. This applies to all of reality not mere structural engineering.

I think the optics people could say a lot about their seemingly endless stable of aberrations. There are so many effects and interactions its surprising anything optical works at all, much less works well. Optics is almost a meta law that everything interacts with everything and constants aren't.

[+] nhaliday|9 years ago|reply
I'm not sure about expanding on Bayes' theorem, but some other notions from ML/stats that would be good to know are overfitting/the bias-variance tradeoff and base rates.

One instance where I've seen the former applied to society is the idea of research benchmarks getting stale from "overfitting". Even when researchers do cross-validation, we might still expect our exploration of the space of ML models to be skewed towards models that perform unusually well on well-known benchmarks. This was described in http://www.deeplearningbook.org/ with reference to ImageNet (of course).

As for the latter, pretty much every time I've seen a discussion of statistics on social or old media, 90% of the participants seem unaware that base rates matter.

[+] agorabinary|9 years ago|reply
A nice metacognitive cheat sheet.

Missing a couple interrelated mental models I find very important:

- emergence: a process whereby larger entities, patterns, and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties

- decentralized system: a system in which lower level components operate on local information to accomplish global goals

- spontaneous order: the spontaneous emergence of order out of seeming chaos. The evolution of life on Earth, language, crystal structure, the Internet and a free market economy have all been proposed as examples of systems which evolved through spontaneous order.

[+] LeicesterCity|9 years ago|reply
Could someone give me a real example of somebody using mental models in a real world application? I just find the idea of learning and studying mental models to be distracting and confusing. Pardon my ignorance.
[+] scarecrowbob|9 years ago|reply
To be honest, I think that the process is something like:

I struggle with problems and eventually find a solution,

I encounter a name for a similar solution,

as I encounter new, similar problems, I begin to recognize "how the model works",

I forget about the model when I don't use it,

occasionally I come across a list like this one where it's fun becasue it validates the usefulness of the models I've already found and introduces me to new names for ones I already have encountered.

I don't feel that a list like this is super useful to me outside of that framework-- I wouldn't take it as a "study guide".

But I feel that framework has given me a lot of personal validation and pointers on how to better deal with problems I encounter.

[+] philip1209|9 years ago|reply
I mention it in a separate comment, but the book Inside The Box is co-authored by a psychology professor and a business consultant, and the book features many case studies of their primary mental models in business.
[+] corysama|9 years ago|reply
I mentioned elsewhere, the theme here is correcting common, default mental models that, without thinking through, lead many people to make a lot of mistakes. By recognizing the bugs in your default thought process, you can avoid many bad decisions that you would otherwise eventually regret.

Halons's Razor: A partner company just did something that makes life much more difficult for you and much easier for themselves. By all accounts it looks like they are only pretending to be "partners", but actually secretly trying to screw you over for their own gain. It's easy to get emotional and paranoid in this situation. If it's really true, you need to find a way to cut off the partnership quickly. That is serious business. But, it's more often better to default to the possibility that maybe they aren't actually fucking with you. Maybe they're just idiots. Maybe they got lazy. Maybe they didn't think through the consequences. Maybe you don't need to go into paranoid adversary mode, blindside your partners with suspicious reactions "out of no where" and fuck up a good partnership that in reality just needed better communication. Or, maybe they actually are out to get you. Just don't completely forget the more likely possibility that this is simply a mistake. It's very common that people do forget...

Zero Sum: It's easy to default to a "If they are getting richer, someone else is getting poorer" mindset. A significant number of businessy people have a "In order for me to win, YOU MUST LOSE" mindset. From both directions, this cuts off the greatly preferable win-win outcome. Recognizing this flaw in default thinking can lead you to an even better outcome for yourself than the "you defeating someone" outcome. You can instead find a way for both of of you come out ahead of the "individual victor" outcome.

Streisand Effect: You just fucked up majorly in a way that isn't obviously your fault. There are two different ways that you can try to improve your situation that will likely backfire very badly. 1) You can pretend nothing happened and hope it goes away. That is very easy. But, when the truth becomes clear, you won't just be a fuck-up, you'll be a lying bastard betrayer fuck-up, unworthy of trust or respect. 2) Even worse: You could try to shift the blame to someone else. Doing this will mostly serve to bring focus on the problem that you yourself caused. So now, even more people become strikingly aware that you are a lying bastard betrayer fuck-up who back-stabs innocent people for your own benefit. In the end, if you had simply admitted the problem and discussed how you were trying to solve it, most people would have been OK with your fuck up. But, by trying to hide it, you only made it much worse.

Framing: Sometimes mechanically analyzing a complicated situation is difficult for a human. It's easier to fall back on prior, similar references. Unfortunately, that tendency can be hijacked and abused in situations where you don't actually have much in the way of prior references. By presenting brief, false, set-up situations, an adversary can plant invented prior references into your decision process. If you are not aware enough to dismiss those plants, you will likely make a very poor value judgement. The adversary might not be a person, but instead simply a situation.

And so on...

[+] agentgt|9 years ago|reply
I still think Social Psychology was one of the most useful classes I ever took in college. Sure some if it is probably dated by now but the cognitive biases theories really helped me further in life.

I remember telling some class mates to take the class and they assumed it was for an easy A and not for how useful the class would be (and I went to a GaTech a long time ago and well the social sciences were just not respected like engineering disciplines at the time).

[+] adamnemecek|9 years ago|reply
To the development section, I would add the concept of computational context/state, caching, and queue/event loop.

This HN comment summarizes it pretty nicely "everything in an OS is either a cache or a queue" https://news.ycombinator.com/item?id=11655472

Also Overton window

[+] karmacondon|9 years ago|reply
I have a similar list of useful concepts. My goal so far this year was to expose myself to those concepts as often as possible. I made an app for my phone that displays the concept of the day on my home screen (right now it's the rhetorical concept of periodic sentences). I also made images for each of the concepts that I use as my chromecast backdrop. I've seen each of them dozens of times by now, mostly unconsciously.

So far, mixed results. I would like to say that I think of "Bayes Theorem" at the perfect time because I wrote it on a list, but that never happens. I guess I've benefitted from thinking about these concepts more, but that's almost impossible to measure. A list of 100 useful mental models has limited value if you can't hold all of them in memory at once and retrieve them at the right time. I'm still trying to come up with a solution for this. Unfortunately I think this might be a fundamental limitation of human learning.

[+] Double_Cast|9 years ago|reply
> What am I missing?

In planning a strategy, I've found it helpful to consider Win Conditions. It forces me to think backwards from the goal, construct a dependency tree, and consider resource allocation. I first heard about it from videogames but I've also seen it in math, engineering, logistics, recipes, etc. I also pattern-match it the insight that solved the Problem Of Points [0] which motivated Probability Theory. If it were on the curated list, I'd expected to find it under "models" next to cost-benefit analysis.

[0] https://en.wikipedia.org/wiki/Problem_of_points#Pascal_and_F...

[+] frankus|9 years ago|reply
Great list, although I prefer the term "thought technology" (as coined by John Roderick) to "mental model".
[+] ternaryoperator|9 years ago|reply
His definition of a "strawman" is incomplete. It's not simply misrepresenting someone's argument, it's misrepresenting it specifically by analogizing it falsely to something similar that is easier to attack. The example he links to is a rather exaggerated strawman. I think most people would favor the strawman explanation in Wikipedia[1]

[1] https://en.wikipedia.org/wiki/Straw_man

[+] k__|9 years ago|reply
The wrong assumption about Ockams Razor is probably the cause of so many people re-inventing the wheel.

"I don't need this big framework, I can do with much less!"