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Pound of Feathers, Pound of Gold

2 Post author: Annoyance 23 October 2009 05:48PM

Which weighs more:  a pound of feathers, or a pound of gold?

Close consideration of this riddle - and the conditions under which people tend to get it wrong - is helpful in understanding the limits of human rationality.  It is a specific example which leads us to general principles of rationality failure.

These sorts of riddles and similar interpersonal language tricks (such as "Stupid says what?") are especially popular among children but not among adults.  Why is this the case?  Partly because adults are more likely to have previously encountered and become familiar with their patterns, but there are other factors - including one very relevant one.  Children tend to have less-developed capacities of impulse control.

It takes very little analysis to discover the 'trick' in the question; the concepts involved are relatively simple.  But we're confronted with the fact that people do answer it incorrectly, and that by manipulating aspects of the context in which the question is delivered, we can significantly increase the chance people will fall for it.  What does this imply?  That analysis is not being conducted in the erroneous cases, and that context is a contributing factor to whether people successfully engage in conceptual analysis.  Specifically, that context determines whether people will counter their impulses long enough for analysis to be completed.

The key to these sorts of riddles is time pressure.  If people feel free to take as much time as they like thinking over the question, they rarely fall for the trick.  But if they're trying to answer rapidly, they'll screw up.  Examples of situations that often result in such behavior include:  competing against others to see who can be correct first, trying to demonstrate competence by investing little effort in answering, or encountering the question as part of a limited-duration examination.  If several superficially-similar questions whose answer depends on retrieving facts from memory rather than performing logical analysis of the question are asked before the riddle is presented, that also tends to result in a wrong response.

The error occurs because of our weight-related associations with the concepts of 'feathers' and 'gold', our conditioned assumptions about the sorts of questions people are likely to ask, and a failure to inhibit the first impulses towards response.  Feathers are far less dense than gold; any given volume of feathers will weigh far less than the same volume of the metal.  Questions about a property rarely contain their own answers in a trivial way - we do not expect the defined quantities in the question to be equivalent relative to the property being asked about.  And - this is the most vital aspect - it takes longer for our brains to process the question at a conceptual level than it does to activate our associations.

In the state of nature, organisms are often under intense pressure to produce results quickly.  If they take too long, the resource they're trying to exploit may be taken by a competitor - or worse, they may become exploited resources by a predator.  So stimulus-response methods which produce generally-useful reactions tend to be favored over extremely accurate and precisely analysis that takes longer.  As a consequence, natural modes of though available to humans favor rapid responses more than rigorous correctness - and in much the same way that the limits of our visual processing systems lead to optical illusions, which can be understood and thus constructed, the limits of our conceptual processing lead to inherent tendencies towards fallacies of reason, which can be exploited to produce riddles and language gags.

Just as other aspects of our behavioral response involve the repression of rudimentary reflexes, our thinking involves the inhibition of associational activation and reflexive reactions.  The "more advanced" cognitive functions can take place only because the simpler, less resource-intensive, and faster functions are prevented from initiating responses before them.

In the wrestling match between the modern functions and the ancient ones they try to control, the more subtle and advanced features are at a distinct disadvantage.  Which brings us to the next post.

Comments (15)

Comment author: Aurini 23 October 2009 11:15:57PM 5 points [-]

One of the major purposes of any sort of combat training (martial arts or military) is to instil pre-designed behavioural patterns that will be effective in the majority of probable encounters; the same thing goes for interpersonal relations, and intellectual heuristics. I suspect that we'll never be done with these sorts of tricks in one form or another, since having the assortment of batch-files which leads to these errors will generally be more efficient than trying to run Slackware. That said, it's obvious how our innate set, customized as it is to the ancestral environment, is absolutely awful for scientific thinking. I think they're a large part of the reason why thermodynamics is such a mystical field for most people, when the inherent concepts are so incredibly simple.

Comment author: Psychohistorian 23 October 2009 06:43:14PM 5 points [-]

Questions about a property rarely contain their own answers in a trivial way

I think this fact may explain most of the reaction; the answer is slipped into the question with a couple words that don't interrupt the flow. The questions is pointless, but we don't expect questions to be pointless, so we don't really hear it right or interpret it correctly, and we answer the question that would actually make sense.

Comment author: gwern 23 October 2009 07:51:29PM 0 points [-]

What is the question that makes sense? 'Does a cubic meter of feathers weigh more than a cubic meter of gold'? A cubic foot?

Comment author: Psychohistorian 24 October 2009 12:12:38AM 2 points [-]

It doesn't make sense because the answer is so obvious, no one is likely to genuinely ask for a comparison between the weight of the two objects. There's a definite "Duh" answer. By contrast, "Which is heavier, lead or mercury?" or "feathers or dry leaves?" would not (in most cases) prime a "duh" answer, so people listen the question more carefully.

I'll admit there's a lot more to it, but I think that our understanding of the question is influenced by how its meaning is processed. If we hear "heavier... gold... feathers" we give an automatic response; if we hear "heavier... lead... mercury" we don't give the same automatic response, since the answer is not automatic - I'm pretty sure it's lead, but I wouldn't wager a large sum of money on it at very low odds, which I would do with gold being heavier (by volume) than feathers.

Comment author: Annoyance 23 October 2009 07:51:04PM 0 points [-]

There's more to it, of course. Ask the question with substances that don't produce strong associations regarding "weight" (really, density), and people tend not to get it wrong no matter how much time pressure is involved.

Comment author: komponisto 23 October 2009 08:51:41PM *  5 points [-]

Which weighs more: a pound of feathers, or a pound of gold?

[...rationality discussion...]

I must be missing something. I thought the point of this riddle was the difference between avoirdupois and Troy weight -- a simple matter of (rather esoteric) factual knowledge not contained in the structure of the question.

Comment author: knb 23 October 2009 11:34:33PM *  3 points [-]

The point of the riddle, as I've always heard it, is to take advantage of the fact that we're primed to think of an even amount of lead and feathers (by volume, presumably) as having different weights due to density, we forget that the weight is the given variable.

I believe this is the incarnation of the riddle that Annoyance is referencing. I always heard the materials in this riddle as feathers and lead, probably because lead has strong associations with heaviness and density. Maybe there are two different riddles using the same materials.

EDIT: After looking it up, I can see that there are two different but similar riddles with feathers/metal. One has to do with troy weight/avoirdupois weight, the other with density.

http://answers.yahoo.com/question/index?qid=20070925160232AAR2Arr

Note that someone suggested the same riddle as you, and others answered the question as posed.

Comment author: CronoDAS 26 October 2009 02:48:50AM 2 points [-]

The "duh" version is usually stated as "Which weighs more: a ton of bricks, or a ton of feathers?" Or, at least, that's the way I usually heard it.

Comment author: billswift 23 October 2009 10:30:42PM *  0 points [-]

Another way of looking at it is an ambiguity between two close but not identical meanings of "pound". Which is why it is tricky, not really because it's esoteric. Also, it's not really all that esoteric, most people learn about the difference as kids, mostly through this riddle.

Comment author: Annoyance 24 October 2009 04:19:28PM 0 points [-]

That is an absolutely charming interpretation, and one that makes a lot of sense. However, in my experience, it's not how the riddle is commonly used.

That would be a great way to show off your knowledge of jeweler's weights, though.

Comment author: gwern 23 October 2009 07:52:47PM 1 point [-]

It's worth noting that philosophers perform much better on these kinds of tests than equivalently educated or intelligent persons: http://experimentalphilosophy.typepad.com/experimental_philosophy/2009/09/philosophers-just-aint-twitterers.html

Comment author: DanArmak 24 October 2009 12:19:48AM 3 points [-]

Perhaps this is because philosophers do expect to be asked pointless questions, or ones where the answer is held to be self evident? :-)

Comment author: gwern 24 October 2009 12:23:25AM 2 points [-]

Well, it shouldn't have to do with expectations. Suppose you're a normal person taking those sample questions - shouldn't you expect 'trick questions' of some sort? (If I were taking a math test and was asked what is 50+50, I'd double-check several times...)

So they should have no disadvantage compared to the philosophers; I think this really is just a case of philosophers being more used to carefully checking through the language of the question, its presuppositions etc. and their own solution, and being better at it. Which should come as no surprise, since this is basically most of philosophy (as an activity)!

Comment author: Alicorn 23 October 2009 06:59:18PM 1 point [-]

It's just begging for a link: Retarded Tests

Comment author: ellenjanuary 24 October 2009 05:55:16PM 0 points [-]

I love this place. At first I said to myself, "Duh!" Then I was like, there's a trick involved... :) Perhaps I can reward a thought with a thought... isn't it also true that a pound of feathers will weigh more? ;)