The Correct Use of Analogy

by SilentCal1 min read16th Jul 201415 comments


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In response to: Failure by AnalogySurface Analogies and Deep Causes

Analogy gets a bad rap around here, and not without reason. The kinds of argument from analogy condemned in the above links fully deserve the condemnation they get. Still, I think it's too easy to read them and walk away thinking "Boo analogy!" when not all uses of analogy are bad. The human brain seems to have hardware support for thinking in analogies, and I don't think this capability is a waste of resources, even in our highly non-ancestral environment. So, assuming that the linked posts do a sufficient job detailing the abuse and misuse of analogy, I'm going to go over some legitimate uses.


The first thing analogy is really good for is description. Take the plum pudding atomic model. I still remember this falsified proposal of negative 'raisins' in positive 'dough' largely because of the analogy, and I don't think anyone ever attempted to use it to argue for the existence of tiny subnuclear particles corresponding to cinnamon. 

But this is only a modest example of what analogy can do. The following is an example that I think starts to show the true power: my comment on Robin Hanson's 'Don't Be "Rationalist"'. To summarize, Robin argued that since you can't be rationalist about everything you should budget your rationality and only be rational about the most important things; I replied that maybe rationality is like weightlifting, where your strength is finite yet it increases with use. That comment is probably the most successful thing I've ever written on the rationalist internet in terms of the attention it received, including direct praise from Eliezer and a shoutout in a Scott Alexander (yvain) post, and it's pretty much just an analogy.

Here's another example, this time from Eliezer. As part of the AI-Foom debate, he tells the story of Fermi's nuclear experiments, and in particular his precise knowledge of when a pile would go supercritical.

What do the above analogies accomplish? They provide counterexamples to universal claims. In my case, Robin's inference that rationality should be spent sparingly proceeded from the stated premise that no one is perfectly rational about anything, and weightlifting was a counterexample to the implicit claim 'a finite capacity should always be directed solely towards important goals'. If you look above my comment, anon had already said that the conclusion hadn't been proven, but without the counterexample this claim had much less impact.

In Eliezer's case, "you can never predict an unprecedented unbounded growth" is the kind of claim that sounds really convincing. "You haven't actually proved that" is a weak-sounding retort; "Fermi did it" immediately wins the point. 

The final thing analogies do really well is crystallize patterns. For an example of this, let's turn to... Failure by Analogy. Yep, the anti-analogy posts are themselves written almost entirely via analogy! Alchemists who glaze lead with lemons and would-be aviators who put beaks on their machines are invoked to crystallize the pattern of 'reasoning by similarity'. The post then makes the case that neural-net worshippers are reasoning by similarity in just the same way, making the same fundamental error.

It's this capacity that makes analogies so dangerous. Crystallizing a pattern can be so mentally satisfying that you don't stop to question whether the pattern applies. The antidote to this is the question, "Why do you believe X is like Y?" Assessing the answer and judging deep similarities from superficial ones may not always be easy, but just by asking you'll catch the cases where there is no justification at all.


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For those interested, Douglas Hofstadter (of the famous Gödel, Escher, Bach) wrote recently a book called Surfaces and Essences: Analogy as the Fuel and Fire of Thinking which develops the thesis that analogy is the core and fuel of thinking, and does it quite brilliantly.

I'm only half-way through the book yet, but so far I liked it very much, the first part on language for example develops somewhat similar ideas, but with a quite different viewpoint, than the "Humans Guide to Words" Sequence on Less Wrong, and both complement each other well.

I'm also reading this book, and I'm actually finding it profoundly unimpressive. Basically it's a 500-page collection of examples, with very little theoretical content. The worst thing, though, is that its hypothesis seems to fundamentally undermine itself. Hofstadter and Sander claim that concepts and analogy are the same phenomenon. But they also say that concepts are very flexible, non-rigid things, and that we expand and contract their boundaries whenever it's convenient for reasoning, and that we do this by making analogies between the original concept (or its instances) and some new concept (or its instances). And I agree with that. But that means that it's essentially meaningless to claim that "concepts and analogy are the same thing". We can draw an analogy between the phenomenon we typically call "categorization" and the phenomenon we typically call "analogy", and I think it's very useful to do so. But deciding whether they're the same phenomenon is just a question of how fine-grained you want your categories to be, and that will depend on the specific reasoning task you're engaged in. So I'm just massively frustrated with the authors for not acknowledging the meaninglessness of their thesis. If they just said "it's useful to think of analogy and categorization as instances of a single phenomenon" then I'd totally agree. But they don't. They say that analogy and categorization are literally the same thing. Arggggghhhh.

(Metaphors We Live By, on the other hand, is one of my favorite books in the universe. It changed my life and I highly recommend it. (Edit: ok that sounds kind of exaggeraty. It changed my life because I study language and it gave me a totally different way of thinking about language.))

If you're interested in the actual software implementations of his ideas, I'd also highly recommend Fluid Concepts and Creative Analogies, as a review of some very interesting technical projects. The program 'Copycat' (and iterations such as Metacat ) is particularly noteworthy.

Similar: Metaphors We Live By by George Lakoff and Mark Johnson. A good antidote to much analytical philosophy, even while oversimplifying many of their targets.

Also by Lakoff, Where Mathematics Comes From as a case study of the way we use analogies (metaphors, rather) in a complex domain. The underlying power of analogical reasoning seems to lie in its ability to map from "far" to "near" domains and thinking styles. Since "near"-style thinking has distinctive properties, this ends up being quite useful.

Perhaps you could see trying to think of analogies as sampling randomly in conceptspace from a reference class that the concept you are interested in belongs to.

Imagine a big book of short computer programs that simulate real-life phenomena. I'm working on a new program for a particular phenomenon I'm trying to model. I don't have much data about my phenomenon, and I'm trying to figure out if a recursive function (say) would accurately model the phenomenon. By looking through my book of programs, I can look at the frequency with which recursive functions seem to pop up when modeling reality and adjust my credence that the phenomenon can be modeled with a recursive function accordingly.

Choosing only to look at pages for phenomena that have some kind of isomorphism with the one I'm trying to model amounts to sampling from a smaller set of data points from a tighter reference class.

This suggests an obvious way to improve on reasoning by analogy: try to come up with a bunch of analogies, in a way that involves minimal motivated cognition (to ensure a representative sample), and then look at the fraction of the analogies for which a particular proposition holds (perhaps weighting more isomorphic analogies more heavily).

I wouldn't trust myself to sample randomly, so I prefer an adversarial approach: try to generate analogies that support each conclusion, then use them to figure out what evidence to look for.

+1 for adversarial approaches in general. I find that I'm more creative thinking of arguments if I'm trying to think of arguments to support a particular conclusion. So in order to gain maximum insight, I should try to think of all possible conclusions and then brainstorm arguments in favor of each.

I like the idea of coming up with lots of analogies and averaging them or seeing if they predict things in common.

Analogies are pervasive in thought. I was under the impression that cognitive scientists basically agree that a large portion of our thought is analogical, and that we would be completely lost without our capacity for analogy? But perhaps I've only been exposed to a narrow subsection of cognitive science, and there are many other cognitive scientists who disagree? Dunno.

But anyway I find it useful to think of analogy in terms of hierarchical modeling. Suppose you have a bunch of categories, but you don't see any relation between them. So maybe you know the categories "dog" and "sheep" and so on, and you understand both what typical dogs and sheep look like, and how a random dog or sheep is likely to vary from its category's prototype. But then suppose you learn a new category, such as "goat". If you keep categories totally separate in your mind, then when you first see a goat, you won't relate it to anything you already know. And so you'll have to see a whole bunch of goats before you get the idea of what goats are like in general. But if you have some notion of categories being similar to one another, then when you see your first goat, you can think to yourself "oh, this looks kind of like a sheep, so I expect the category of goats to look kind of like the category of sheep". That is, after seeing one goat and observing that it has four legs, you can predict that pretty much all goats also have four legs. That's because you know that number-of-legs is a property that doesn't vary much in the category "sheep", and you expect the category "goat" to be similar to the category "sheep". (Source: go read this paper, it is glorious.)

Anyway I basically think of analogy as a way of doing hierarchical modeling. You're trying to understand some situation X, and you identify some other situation Y, and then you can draw conclusions about X based on your knowledge of Y and on the similarities between the two situations. So yes, analogy is an imprecise reasoning mechanism that occasionally makes errors. But that's because analogy is part of the general class of inductive reasoning techniques.

Perhaps a better title would have been "The Correct System-II Use of Analogy", or "The Correct Use of Analogy in Intellectual Debate." What you're saying is true about day-to-day/on-the-fly thinking, but written argument requires a higher standard.

It seems like there's a paradox about attacking analogies: if you say "Here are examples of Argument by Analogy not being valid, so your Argument by Analogy is not valid", you're engaging in Argument by Analogy yourself. It's also not clear what the point of mentioning the airplanes with beaks is. If people were saying "Birds have beaks, therefore planes must need beaks", that would be poor logic, but if people were saying "Birds have beaks, so we should try beaks", that's quite reasonable. It's all well and good to look with hindsight at people trying something that turned out to not be right and laugh at how silly they are, but being willing to try out different hypotheses even if people are going to think you look silly if the hypotheses are wrong is an important skill.

EY keeps adding the qualifier "surface" to the term "similarities", but that's largely begging the question. "Analogies based on invalid bases are invalid" is a bit of a tautology.

It's also frustrating how people insist on pretending that analogies are comparing the elements of the analogy, rather the relationship between the elements. For instance, SSM advocates argued that the Full Faith and Credit clause compelled states to recognize SSMs from other states. Obama pointed out that there was case law saying that states don't have to recognize marriages that violate their age of consent or consanguinity laws. Dan Savage then proceeded to accuse Obama of comparing homosexuality to pedophilia and incest. Make comparisons between robbery and rape, and feminists will accuse you of comparing women's bodies to personal property.

The human brain seems to have hardware support for thinking in analogies, and I don't think this capability is a waste of resources, even in our highly non-ancestral environment [...] Take the plum pudding atomic model. I still remember this falsified proposal of negative 'raisins' in positive 'dough' largely because of the analogy...

I think this part is really important. It seems like humans really do have hardware for analogies and that leads to better retention of information that you analogize. Of course using analogies to try do derive new information about the original subject is a fallacy (and I think that's where most of the animosity toward analogies on LW stems from), but drawing an analogy is an invaluable tool for understanding and remembering things. It forces you to think things through on a mechanistic level and gives an easy path to retrieval.

What do the above analogies accomplish? They provide counterexamples to universal claims.

Excellent point.

Related -- here are some attempts to formalize and understand analogy from a category theoretic perspective: