It was a nine minute read for me. Medium's estimates are always off and especially so when dealing with list-type posts.
Instead of relying on how long some website says something will take to read, it's usually a better idea to scroll through once just doing scanning at the high level to get an idea of length and then read it if you want to.
Agreed. It's as helpful as the other post on list of free online programming books. Needs more handholding to help people make the best use of the list.
This is the first link I found of this speech (it's called "Practical Thoughts about Practical Thought"), but its an application of combining mental models from many disciplines from the man himself:
Yep. Most of these models are thought-out explanations of how not-thought-out reasoning frequently goes very wrong. If you understand that this is a list of bugs in your initial gut reactions, you can recognize when and why you are about to make a mistake.
Nothing ground breaking here - I imagine most readers here already use most of the author's models - but this is a nice comprehensive list, which I have not seen before.
Does anyone have a pointer to a list of these lists? Would be interesting to know what models people use on a day-to-day basis, like usesthis.com for the brain.
I'd recommend it. I was grandfathered into the free plan but $11/year seems fair.
Regardless of what you settle on I'd look for the equivalent of http://www.packal.org/workflow/alfred-pinboard for whatever service and platform you use. Being able to instantly search through all fields of all items in your archive is pretty great and has changed the way I work.
Strictly no, though what's offered in part complements, in part substitutes, for critical thinking. Some of these are components of critical thinking (or describe), much isn't.
This is a set of both guidelines and heuristics, a set of patterns, if you will, which can be applied to situations or analyses. Some give you a fast route to a simple answer (Occam's Razor), some give pause before accepting what appear to be well-founded results (Simpson's Paradox -- I've encountered that before but had largely forgotten it). Some are simply shortcuts in estimation (order-of-magnitude, and log-based math -- multiplication and division become addition and subtraction).
I think these can be defended as mental models, even though the article doesn't do a good job of it.
We're familiar with inflation in the financial sense. But then there is also grade inflation. There is inflation of superlatives in our language, e.g. "great" and "awesome". Once we see a few examples we realise that inflation is a more general concept, and a useful one to use in explaining a lot of situations.
Same for peak oil, I think. Not sure about botnet.
Hmm.. the entry on inflation hasn't changed (doesn't say anything like what I said) but I see notes that mention grade inflation. I don't know whether that was there first time round.
Such cynical words, besides depriving the world of a much needed listicle, will also get us downvoted. Please don't offer such awkward comments which might cause people to pause and think. Now back to my facebook feed..
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.
Perhaps I need to explain my comment above "Upvote for Hysteresis", given the downvotes. It was a quick comment that might have come across as flippant, so I will explain:
I was first introduced to the concept of hysteresis as an EE undergrad.
As I went on to grad school, which was heavily economics-based, I took a course in system dynamics at mit [1]. In the intro class, the prof said: "system dynamics will change your mental model of the world" (and it did) [2]. As we went through the course, I realized that while many of the concepts in the course were econ-based, in reality were similar to my EE / mathematics concepts (capacitor=time delays, etc.) For me, systems dynamics showed me that concepts in one discipline could be applied to a completely different discipline with great effectiveness. In doing further economics work, I was immersed in many other mental models. My friends and I would use these economics-based mental models - many of which are in the OP article - to communicate in an efficient manner at school and when we were out on the town, almost like a shortcut way to speak and efficiently organize thoughts / explain a given situation.
By the time I re-entered the workforce, post-grad school - working in the venture world - I was regularly and subconsciously thinking/communicating in terms of these econ-models. But, a big aha happened when one day I heard one of the partners at my firm use the term "hysteresis", not to describe a hardware company we were looking at, but to describe a very specific management-related situation with one of the entrepreneurs we were speaking with. And I understood exactly what he meant by that term, as it applied to this management situation. Aha! It turned out that my EE world provided me with a whole toolbox of mental models - just like econ - that I can not only use to express myself, but also to be understood! (fair enough: this was the valley, where most people I dealt with were engineers). It was one of those moments when I realized what I had learnt many moons ago had direct applicability to what I was currently doing but in a completely different context.
Seeing "hysteresis" in the parent's post brought back memories to that realization and its backstory, thus my comment.
[1] this is a close enough comp for the Systems Dynamics course mentioned above - http://ocw.mit.edu/courses/sloan-school-of-management/15-871...
[2] An example is "stocks and flows", a way to view things as static or dynamic. This was used effectively in a cybersecurity market map / competitive analysis many years later.
This is more metaphysical than the basic technique. If I was going to exchange the hard drive in my laptop. I would visualize the entire process, noting the questions and problems as I completed each step.
* do I have the proper tools? Lookup special fasteners
* I will misplace the screws, a magnet or plastic cups would help
* It might be dirty inside, I need something to clean
* I might drop a screw inside, tweezers
* Could be dark, headlamp
* cable might not stay in place, tape
It might take 20-30 seconds to run through all the steps in ones mind, anticipating problems before they arise.
This is why my estimates are often really optimistic. For most tasks I can visualize the entire piece of work in just a few moments, but I forget to adjust for how long things actually take. I can picture having to do each piece of the task, but I forget that those tasks have to exist in real time, and that I will have to think and re-evaluate as I go.
I am getting better at it, but I have to be conscious of it, lest I estimate for superman by accident!
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.
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.
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.
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.
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.
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.
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.
I thoroughly enjoyed the book Inside The Box, which presents four mental models for creative problem solving. The core idea that creating rules can help creativity is a pattern toward which I think most technical people (including myself) feel averse, but actually can be beneficial when studied with an open mind.
> Frequency-dependent selection: fitness of a phenotype depends on its frequency relative to other phenotypes
> Evolutionarily stable strategy (ESS) is a strategy which, if adopted by a population in a given environment, cannot be invaded by any alternative strategy that is initially rare. It is relevant in game theory, behavioural ecology, and evolutionary psychology. Related to Nash Equilibrium and the Prisoners dilemma.
Economics
> Debasement (gold coins): lowering the intrinsic value by diluting it with an inferior metal.
It's an interesting list. Though I'm a bit baffled at why he has Power-law as a "1" (comes up frequently) and Heavy-tailed distribution as a "3" (rarely comes up). A power law is a heavy-tailed distribution!
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.
Take high school physics, where you assume that there is no resistance, cows are spherical, gravity is exactly the same everywhere, and so on. Assuming all that, you can make a much simpler model than when you don't.
But it is not about what theory is most likely. If two theories or models generate exactly the same predictions, they are equally true. Occam just says that in this case we should chose the simpler.
But if the theories produce different predictions, then it doesn't matter which one is simplest, the one which most closely match reality is the truest.
In practice we are often in situations where multiple hypothesis explain the data we observe but diverge from each other on data that we have not yet observed and it may be difficult to create the necessary situations to tell between them. In these cases we may still wish to choose a hypothesis to make predictions from.
There are an infinity of possible models to choose from, with most of those models containing no less information than the phenomenon they seek to model. Predictive power is what is important for models; a model that has enough dials to be adjusted to work with any new piece of data might be 'correct' but it is not useful. My favourite example of this is the fact that when the heliocentric model of the solar system was being developed, the geocentric model was providing much more accurate values for the positions of celestial bodies for a long time because it had had years of being tweaked to do so. Initially, it was the simplicity of the heliocentric model rather than its accuracy that was appealing.
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.
The second quoted paragraph seems to be attacking a strawman. I don't think it was suggested that we should add silly details to improve falsifiability, but rather remove them. Moreover, it seems like this is a way to choose between existing theories, rather than a way to mutate one theory into a better one.
It's pointing out that the equivalence of "simpler" with "more falsifiable" is not perfect. Nobody is suggesting that we just add silly details for the sake of increasing falsifiability, but suppose two research groups independently arrived at those competing theories. Should we choose the simpler one or the more falsifiable one?
A simpler explanation for valuing simplicity is that a simpler theory requires less storage/processing of the human brain. A more complex theory could explode in complexity so that all of its parts and ramifications wouldn't be easily learnable by a human.
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
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.
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.
Occam's razor, as stated by GP is not about correctness, but tractability. In fact, if you look at it probabilistically, the hypothesis founded on more assumptions is more likely to be correct:
Suppose you have a hypothesis, H, which is based on assumptions A1, A2, ..., Ak. This can be phrased logically as an implication:
So, appealing to the conjunction fallacy, assuming that we are adding more assumptions on top, rather than having a greater number of different assumptions, the probability of success actually goes up.
Sorry for the mathematical nitpick here, but that seems to me like a strawman. You silently moved from the original question:
What is the probability that the hypothesis is correct?
To the very different question:
What is the probability that the implication "from the assumptions follows the hypothesis" is correct?
Moreover, this different question has a clear answer for every logically consistent theory: It is 1, because it is always true!
Why? Because that's exactly what the theory proves logically. The theory can't tell you whether A1, ..., Ak are all true in the real world, but it does tell you that _if_ these are true, H is also true.
So this is really a typical strawman argument (although maybe unintendedly): It is different from the original question, and it boils down to a trivial but misleading answer.
------------------
Going back to the original question, you'd have to compare the two hypotheses H1 and H2, where the set of assumptions of H1 are a strict subset of the assumptions of H2:
A1 & A2 & ... & Ak -> H1
A1 & A2 & ... & Ak & ... & An -> H2
But from here it is surprisingly hard to conclude "P(H1) > P(H2)", because we have implications and not equivalences. That is, H1 may be true even though the assumptions don't hold. It may be true for different reasons and derived from a different set of assumptions that turn out to be true. Same for H2. So we need to take into account the probabilities for H1 and H2 to be "true for different reasons", which we'll name Pd1 and Pd2:
To prove the probability variant of Occam's razor, we need to make the following additional meta-assumption: The probabilities that H1 and H2 are "true for different reasons" are very small, and moreover almost identical. So we have:
Pd1 = Pd2
But with that meta-assumption, we can finally prove the probability variant of Ocamm's razor, as we can now express P(H1) and P(H2):
You are right, they are different questions, but the straw man was not intentional, I thought the original phrasing was ambiguous enough that it could be interpreted in both ways ;)
In other words, it was unclear to me what the answer to the question "Are the assumptions part of the hypothesis?" was. If, as I did, we assume that "yes, they are" then I don't think it follows that the probabilities will both be `1`, because we do not have logical proofs for the claims, the implication could only be true in the model (they are not necessarily entailments).
The waters are muddied further still when the hypothesis itself is phrased as an implication.
EDIT
It also strikes me that for your line of reasoning to hold, it is not sufficient that Pd1 = Pd2 are small, but instead `Pd1 = 0 = Pd2`, in order to justify this line:
It's not "if these assumptions hold, the hypothesis is true". It's "for this hypothesis to be true, these assumptions must hold".
Suppose you have the hypothesis that Bruce Wayne is Superman. Then you see the two of them in the same room together. It's still possible that Bruce Wayne is Superman, but only if he has an identical twin. Your credence that Bruce Wayne is Superman should decrease accordingly.
Assumptions are the left-hand side of an implication, by definition. (And the right-hand side is called "conclusion".)
The relevant statement here is not "for this hypothesis to be true, these assumptions must hold".
It is: "for this hypothesis to be derived this way, these assumptions must hold".
There is always the possibility that a hypothesis can be proved in a different way from different assumptions.
Unless, of course, your theory not only proves "(A1 & A2 & ... & Ak) -> H" but "(A1 & A2 & ... & Ak) <-> H". That is, if your theory shows that your hypothesis does not only follow from the assumptions, but is equivalent to its assumptions. That's quite a rare case, though.
If you see Bruce Wayne and Superman in the same room, then "Bruce Wayne is Superman" can only be true if you assume something you didn't have to assume before. It means you should be less confident that Bruce Wayne is Superman.
I'm using the word "assumption" in a natural way. (Also in the way that it's used in Occam's razor.) If you have a definition that says I'm using it wrong, then your definition is silly.
This example is totally unclear to be. Although you declared a clear hypothesis in your very first comment, it is totally unclear what exactly your assumptions are that would lead to this hypothesis.
You can form a hypothesis without basing it on anything. You could for example randomly generate 1 billion sentences and then try to test if they are true.
This is not what is meant by "hypothesis" in Occam's razor, which is about hypotheses that are based on actual assumptions (and using these assumptions to pick a "best" hypothesis).
The initial hypothesis is only a starting point. When building a model where 'mice are smarter than humans' you need to account for all the evidence out there.* Compared to the model where 'humans are smarter than mice' it's vastly more complex or vastly less testable.
* I have heard this defined as hypothetical baggage or implicit baggage. ie. if CO2 is not increasing temperature then why not?
Okay, it sounds like what you call assumptions, I would call "data". Or "background data" or something.
If I think Bruce Wayne is Superman, I might base that on the fact that they're both physically very fit; that one would need to be very rich in order to have the kind of technology that is indistinguishable from alien powers; that Bruce Wayne's parents were murdered, and this could conceivably draw him to a life of fighting crime, which is a thing Superman does.
That sort of thing leads me to form the hypothesis: "Bruce Wayne is Superman".
But that sort of thing isn't what Occam's razor is about. It's about things that we haven't observed to be true, but which would need to be true for the hypothesis to hold. You should prefer a hypothesis that requires fewer such things.
If I see Bruce Wayne and Superman in the same room, then in order for Bruce Wayne to be Superman, he must have an identical twin. I haven't observed him to have one, but that's what the hypothesis requires. Accordingly, my confidence in the hypothesis decreases.
At least in the terminology I'm used to, of mathematical proof, an assumption is a part of the context under which a thing is proven. So having more assumptions weakens the claim (and there is an associated weakening rule [1]).
In other words, the claim "Assuming Q, I prove P" does not mean (to me) that Q must hold in order for P to hold, but rather that one way to show that P is true is to show that Q is true.
In the search for a cure for head ache, some guy took aspirin and did a magic rite, and he was cured; another guy just took aspirin and he was cured. Both account can be reproduced, and so far have worked. Therefore when doing analysis you can ignore the bit about magic, while it may be relevant in some mystical sense (the spirits are more happy if you do it, whatever), it is unnecessary to explain the cure from head ache.
I took a class in College where the Professor revolved the class around Occam's razor. Every quiz we would have a word limit associated with each question. It was honestly a quite difficult exercise to concise your answer and remove unnecessary information.
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.
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.
> 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.
It is easy to do in many cases. Take the following two theories:
Rocks falls downwards since masses attracts each other.
Rocks falls downwards due to invisible ghosts making masses attract each other.
Both of these theories have the same amount of evidence supporting them, but one is strictly simpler than the other. If one theory isn't a simple reduction of the other then Occam's razor doesn't apply, but in those cases it is usually possible to make experiments which disproves one of them.
Less is not arbitrary. Be it fewer assumptions, variables, bits, rules... And these are all abstractions. Abstractions can be counted, so all simple really means is fewer abstractions. Theories tend to refine themselves because ultimately we arrive at one word, and with new evidence, even words will adapt. What was gravity yesterday is graviton today.
Occams razor does not ask that you accept the simplest explanation. It asks that one take into account as many, and only as many factors as necessary to explain a phenom. It does not promote fallacy or lessen rigour. It is a "loose leash but a tight chain"
As originally defined, it stated: Entities should not be multiplied without necessity(Entia non sunt multiplicanda praeter necessitatem).
Bertrand Russel held the principle in high regard. This quote from Newton encapsulates its application: "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." and simplified for scientists in this form: ""when you have two competing theories that make exactly the same predictions, the simpler one is the better" http://math.ucr.edu/home/baez/physics/General/occam.html
using occam's razor i reject your conclusion because you are assuming that there are a bunch of smart people engaging in discussion.
this is an extraneous assumption in your theory. and thus, in humorously recursive fashion, i have used occam's razor to disprove your conclusion about occam's razor not being useful. needless to say , a theory with fewer assumptions about this discussion doesn't assume that the people having it are smart. (i'm not saying they are stupid!!! ...how about the default non assumption that they are merely average )
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.)
Well first you have to come up with at-least two theories that _both_ explain the phenomenon. Then you apply the principle to choose one that's "simpler".
You cant do a 'premature' optimization and not even attempt to piece together a theory that sounds complex, when maybe that is currently the only theory that explains the phenomenon.
I'm not a quantum physicist so take this with a grain of salt, but my favourite analogy is heliocentric vs geocentric orbits: http://i.imgur.com/AReqgfP.gif
The collection of data can have assumptions built in that you are unaware of. If you aren't thinking about the earth moving when measuring the orbits of the other planets the data shows that the orbits are pretty crazy.
Likewise when we measure at the quantum level things seem pretty crazy, things in two places at once, etc. Saying "Once something is small enough it can behave completely differently from what we observe at larger scales" is a pretty big assumption.
String theory trades some assumptions for others to rationalize some of the 'crazy behaviour' at small scales.
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.
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.
I meant this as an informal rule, i.e. the "spirit" of the law. I think your suggestion is fairly close, in effect, as you can consider assumptions to imply greater resources (namely in validating them).
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.
Fewer assumptions = special cases and exceptions stand out more and are harder to integrate without altering the theory beyond recognition. More assumptions = more moving parts.
Because the idea is that the theory will be tweaked anyway. Nothing's gonna be perfect on the first try.
So, a question back at you. Let's suppose an ontology of technological mechanisms. That is, describing technologies by how they operate. I've kicked some ideas around and come up with:
1. Process-knowledge. Arts and practical stuff, say, agriculture, construction, boatbuilding, sailing, etc.
Besides its original meaning (repeated uninvited bombardment with information packages) I can think of only one alternative use of the pattern: games.
For example, rocket / grenade / arrow spam in TF2, or Lucio / Hanzo / Symmetra projectile spam in Overwatch. In this context, spamming is just firing in the general direction of the enemy, hoping that some of the rounds will hit.
Maybe this generalizes to repeated application of some cheap technique that has a low probability of success, where the low chances of success are compensated by the low amount of effort per 'shot' required -- but I can't think of any more examples.
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.
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.
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.
That might be because you're trying to use it to argue politics, where it's less applicable; hard cases often make bad law, and you can easily end up with a straw man. It works better in science and engineering.
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.
One problem with cost-benefit analyses are the unknown-unknowns. Just because you have a cost-benefit model, it doesn't mean the model reflects the reality of your situation. There is a very real risk that much time is spent considering eventualities that can never occur, while ignoring all of the things that are actually happening.
Along with the reference to Arrow's Impossibility Theorem, I'd want a reference to the fact that voting can be done in ways other than ranking, e.g. approval or score voting.
198 comments
[ 3.1 ms ] story [ 252 ms ] threadAll the information, easier to read quickly.
Instead of relying on how long some website says something will take to read, it's usually a better idea to scroll through once just doing scanning at the high level to get an idea of length and then read it if you want to.
http://mungerisms.blogspot.com/2010/04/charlie-munger-turnin...
Regardless of what you settle on I'd look for the equivalent of http://www.packal.org/workflow/alfred-pinboard for whatever service and platform you use. Being able to instantly search through all fields of all items in your archive is pretty great and has changed the way I work.
This is a set of both guidelines and heuristics, a set of patterns, if you will, which can be applied to situations or analyses. Some give you a fast route to a simple answer (Occam's Razor), some give pause before accepting what appear to be well-founded results (Simpson's Paradox -- I've encountered that before but had largely forgotten it). Some are simply shortcuts in estimation (order-of-magnitude, and log-based math -- multiplication and division become addition and subtraction).
Critical thinking has varying definitions, but I'd generally describe it as more structured and procedural than what's offered by @wegge. See: https://en.m.wikipedia.org/wiki/Critical_thinking
We're familiar with inflation in the financial sense. But then there is also grade inflation. There is inflation of superlatives in our language, e.g. "great" and "awesome". Once we see a few examples we realise that inflation is a more general concept, and a useful one to use in explaining a lot of situations.
Same for peak oil, I think. Not sure about botnet.
I was first introduced to the concept of hysteresis as an EE undergrad.
As I went on to grad school, which was heavily economics-based, I took a course in system dynamics at mit [1]. In the intro class, the prof said: "system dynamics will change your mental model of the world" (and it did) [2]. As we went through the course, I realized that while many of the concepts in the course were econ-based, in reality were similar to my EE / mathematics concepts (capacitor=time delays, etc.) For me, systems dynamics showed me that concepts in one discipline could be applied to a completely different discipline with great effectiveness. In doing further economics work, I was immersed in many other mental models. My friends and I would use these economics-based mental models - many of which are in the OP article - to communicate in an efficient manner at school and when we were out on the town, almost like a shortcut way to speak and efficiently organize thoughts / explain a given situation.
By the time I re-entered the workforce, post-grad school - working in the venture world - I was regularly and subconsciously thinking/communicating in terms of these econ-models. But, a big aha happened when one day I heard one of the partners at my firm use the term "hysteresis", not to describe a hardware company we were looking at, but to describe a very specific management-related situation with one of the entrepreneurs we were speaking with. And I understood exactly what he meant by that term, as it applied to this management situation. Aha! It turned out that my EE world provided me with a whole toolbox of mental models - just like econ - that I can not only use to express myself, but also to be understood! (fair enough: this was the valley, where most people I dealt with were engineers). It was one of those moments when I realized what I had learnt many moons ago had direct applicability to what I was currently doing but in a completely different context.
Seeing "hysteresis" in the parent's post brought back memories to that realization and its backstory, thus my comment.
[1] this is a close enough comp for the Systems Dynamics course mentioned above - http://ocw.mit.edu/courses/sloan-school-of-management/15-871... [2] An example is "stocks and flows", a way to view things as static or dynamic. This was used effectively in a cybersecurity market map / competitive analysis many years later.
I am getting better at it, but I have to be conscious of it, lest I estimate for superman by accident!
One of them is using the efficient market hypothesis (true enough for this application) to avoid being taken in by a real estate broker.
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.
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...
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.
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.
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.
Evolution
> Frequency-dependent selection: fitness of a phenotype depends on its frequency relative to other phenotypes
> Evolutionarily stable strategy (ESS) is a strategy which, if adopted by a population in a given environment, cannot be invaded by any alternative strategy that is initially rare. It is relevant in game theory, behavioural ecology, and evolutionary psychology. Related to Nash Equilibrium and the Prisoners dilemma.
Economics
> Debasement (gold coins): lowering the intrinsic value by diluting it with an inferior metal.
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.
But if the theories produce different predictions, then it doesn't matter which one is simplest, the one which most closely match reality is the truest.
There are an infinity of possible models to choose from, with most of those models containing no less information than the phenomenon they seek to model. Predictive power is what is important for models; a model that has enough dials to be adjusted to work with any new piece of data might be 'correct' but it is not useful. My favourite example of this is the fact that when the heliocentric model of the solar system was being developed, the geocentric model was providing much more accurate values for the positions of celestial bodies for a long time because it had had years of being tweaked to do so. Initially, it was the simplicity of the heliocentric model rather than its accuracy that was appealing.
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
http://exo-blog.blogspot.com/2007/09/what-intel-giveth-micro...
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.
Suppose you have a hypothesis, H, which is based on assumptions A1, A2, ..., Ak. This can be phrased logically as an implication:
Decomposing the implication, we get: Then So, appealing to the conjunction fallacy, assuming that we are adding more assumptions on top, rather than having a greater number of different assumptions, the probability of success actually goes up.Why? Because that's exactly what the theory proves logically. The theory can't tell you whether A1, ..., Ak are all true in the real world, but it does tell you that _if_ these are true, H is also true.
So this is really a typical strawman argument (although maybe unintendedly): It is different from the original question, and it boils down to a trivial but misleading answer.
------------------
Going back to the original question, you'd have to compare the two hypotheses H1 and H2, where the set of assumptions of H1 are a strict subset of the assumptions of H2:
It is clear that: But from here it is surprisingly hard to conclude "P(H1) > P(H2)", because we have implications and not equivalences. That is, H1 may be true even though the assumptions don't hold. It may be true for different reasons and derived from a different set of assumptions that turn out to be true. Same for H2. So we need to take into account the probabilities for H1 and H2 to be "true for different reasons", which we'll name Pd1 and Pd2: To prove the probability variant of Occam's razor, we need to make the following additional meta-assumption: The probabilities that H1 and H2 are "true for different reasons" are very small, and moreover almost identical. So we have: But with that meta-assumption, we can finally prove the probability variant of Ocamm's razor, as we can now express P(H1) and P(H2): In short:In other words, it was unclear to me what the answer to the question "Are the assumptions part of the hypothesis?" was. If, as I did, we assume that "yes, they are" then I don't think it follows that the probabilities will both be `1`, because we do not have logical proofs for the claims, the implication could only be true in the model (they are not necessarily entailments).
The waters are muddied further still when the hypothesis itself is phrased as an implication.
EDIT
It also strikes me that for your line of reasoning to hold, it is not sufficient that Pd1 = Pd2 are small, but instead `Pd1 = 0 = Pd2`, in order to justify this line:
Which is tantamount to saying Is it not?EDIT (2)
Ignore that, it is not tantamount, it is a weaker condition.
First of all, if you know that
then the following two terms are logically equivalent: Also, for the proof which I gave it is sufficient that Pd1 = Pd2. It does not need them to be zero.This is backwards. It should be
It's not "if these assumptions hold, the hypothesis is true". It's "for this hypothesis to be true, these assumptions must hold".Suppose you have the hypothesis that Bruce Wayne is Superman. Then you see the two of them in the same room together. It's still possible that Bruce Wayne is Superman, but only if he has an identical twin. Your credence that Bruce Wayne is Superman should decrease accordingly.
Assumptions are the left-hand side of an implication, by definition. (And the right-hand side is called "conclusion".)
The relevant statement here is not "for this hypothesis to be true, these assumptions must hold".
It is: "for this hypothesis to be derived this way, these assumptions must hold".
There is always the possibility that a hypothesis can be proved in a different way from different assumptions.
Unless, of course, your theory not only proves "(A1 & A2 & ... & Ak) -> H" but "(A1 & A2 & ... & Ak) <-> H". That is, if your theory shows that your hypothesis does not only follow from the assumptions, but is equivalent to its assumptions. That's quite a rare case, though.
I'm using the word "assumption" in a natural way. (Also in the way that it's used in Occam's razor.) If you have a definition that says I'm using it wrong, then your definition is silly.
* I have heard this defined as hypothetical baggage or implicit baggage. ie. if CO2 is not increasing temperature then why not?
If I think Bruce Wayne is Superman, I might base that on the fact that they're both physically very fit; that one would need to be very rich in order to have the kind of technology that is indistinguishable from alien powers; that Bruce Wayne's parents were murdered, and this could conceivably draw him to a life of fighting crime, which is a thing Superman does.
That sort of thing leads me to form the hypothesis: "Bruce Wayne is Superman".
But that sort of thing isn't what Occam's razor is about. It's about things that we haven't observed to be true, but which would need to be true for the hypothesis to hold. You should prefer a hypothesis that requires fewer such things.
If I see Bruce Wayne and Superman in the same room, then in order for Bruce Wayne to be Superman, he must have an identical twin. I haven't observed him to have one, but that's what the hypothesis requires. Accordingly, my confidence in the hypothesis decreases.
In other words, the claim "Assuming Q, I prove P" does not mean (to me) that Q must hold in order for P to hold, but rather that one way to show that P is true is to show that Q is true.
[1]: https://en.wikipedia.org/wiki/Structural_rule
In the search for a cure for head ache, some guy took aspirin and did a magic rite, and he was cured; another guy just took aspirin and he was cured. Both account can be reproduced, and so far have worked. Therefore when doing analysis you can ignore the bit about magic, while it may be relevant in some mystical sense (the spirits are more happy if you do it, whatever), it is unnecessary to explain the cure from head ache.
Also, i like Hanlon’s Razor. "Never attribute to malice that which is adequately explained by stupidity." Generalizing here, but people _are_ stupid.
See also BIC (Bayesian Information Criterium) for selecting models.
> 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.
Rocks falls downwards since masses attracts each other.
Rocks falls downwards due to invisible ghosts making masses attract each other.
Both of these theories have the same amount of evidence supporting them, but one is strictly simpler than the other. If one theory isn't a simple reduction of the other then Occam's razor doesn't apply, but in those cases it is usually possible to make experiments which disproves one of them.
Occams razor does not ask that you accept the simplest explanation. It asks that one take into account as many, and only as many factors as necessary to explain a phenom. It does not promote fallacy or lessen rigour. It is a "loose leash but a tight chain"
As originally defined, it stated: Entities should not be multiplied without necessity(Entia non sunt multiplicanda praeter necessitatem).
Bertrand Russel held the principle in high regard. This quote from Newton encapsulates its application: "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." and simplified for scientists in this form: ""when you have two competing theories that make exactly the same predictions, the simpler one is the better" http://math.ucr.edu/home/baez/physics/General/occam.html
There is a line of scholarship that believes William of Occam (c1287-1347) never made the quote attributed to him. http://www.logicmuseum.com/authors/other/mythofockham.htm
What is termed Occams razor by vog asQuirrel asmad and others is a statistical/logicians derivative not really of concern to most people.
this is an extraneous assumption in your theory. and thus, in humorously recursive fashion, i have used occam's razor to disprove your conclusion about occam's razor not being useful. needless to say , a theory with fewer assumptions about this discussion doesn't assume that the people having it are smart. (i'm not saying they are stupid!!! ...how about the default non assumption that they are merely average )
DISPROVE THAT! :)
Which they don't, therefore you can't say Occam's razor isn't useful. :) funny
You cant do a 'premature' optimization and not even attempt to piece together a theory that sounds complex, when maybe that is currently the only theory that explains the phenomenon.
The collection of data can have assumptions built in that you are unaware of. If you aren't thinking about the earth moving when measuring the orbits of the other planets the data shows that the orbits are pretty crazy.
Likewise when we measure at the quantum level things seem pretty crazy, things in two places at once, etc. Saying "Once something is small enough it can behave completely differently from what we observe at larger scales" is a pretty big assumption.
String theory trades some assumptions for others to rationalize some of the 'crazy behaviour' at small scales.
https://www.google.com/search?q=occam%27s%20razor%20string%2...
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.
Never a bad idea
Because the idea is that the theory will be tweaked anyway. Nothing's gonna be perfect on the first try.
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.
1. Process-knowledge. Arts and practical stuff, say, agriculture, construction, boatbuilding, sailing, etc.
2. Fuels & combustion, generally. Wood, plant and animal oils, charcoal, coal, petroleum, steam, otto, deisel, turbine engines.
3. Materials. Functions dependent on specific properties, and abundance of materials they're based on.
4. Power and transmission.
5. Sensing, perception, symbolic representation & manipulation.
6. Systematic knowledge. Science, geography, history.
7. Governance, management, business, & institutions.
8. Scaling and network technologies. Cities, transport, communications, computers.
9. Sinks & unintended consequences. Pollution, effluvia, systems disruption, and their management.
"Thought technology" probably falls into scientific knowledge (models) or symbolic processing.
Thoughts?
More: https://ello.co/dredmorbius/post/klsjjjzzl9plqxz-ms8nww
For example, rocket / grenade / arrow spam in TF2, or Lucio / Hanzo / Symmetra projectile spam in Overwatch. In this context, spamming is just firing in the general direction of the enemy, hoping that some of the rounds will hit.
Maybe this generalizes to repeated application of some cheap technique that has a low probability of success, where the low chances of success are compensated by the low amount of effort per 'shot' required -- but I can't think of any more examples.
Though I think I'd agree that it's technically a different model, but related.
I personally use cost-benefit analyses for every non-trivial decision in my life.
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
Overall, a superb list.