h a l f b a k e r yKeep out of reach of children.
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Background
A transform is a mathematical tool for mapping a problem from one domain into another. The problem can be solved easily in the other domain, and the solution can then be mapped back to the original domain (for example Laplace transforms).
A mnemonic is a learning and memory technique
that maps information into a form that is easier to remember.
The idea
My (admittedly vague) idea is that some problems could be mapped (in a similar way to a transform or mnemonic) into different domains which may make solving the problem easier.
Chess example
A game of chess is won by anticipating the other player's moves. It is relatively easy to see one move ahead, but (exponentially?) more difficult to see two or more moves ahead.
What if the branching possibilities of chess moves were mapped onto something that the human mind understands instinctively? For example a ski slope where the possible chess moves are mapped onto the possible routes to travel.
Other possible uses would be: diplomacy, sport, logistics.
Even if this has no practical application, it might make a good plot device (in a similar style to the recent Sherlock Holmes movies).
Wason Selection Task
http://www.philosop.../wason/Default.aspx
Take the test, online. [Loris, Jun 15 2012]
The Murders in the Rue Morgue
http://poestories.com/read/murders
"Dupin," said I, gravely, "this is beyond my comprehension. I do not hesitate to say that I am amazed, and can scarcely credit my senses. How was it possible you should know I was thinking of ___ ?" Here I paused, to ascertain beyond a doubt whether he really knew of whom I thought." [rcarty, Jun 15 2012]
[link]
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Analogies and hypotheticals serve a similar purpose.
Not clear what the invention is here, though. |
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Analogical reasoning and problem solving transform (I'll call it PST) share the characteristic that they both use mapping from one situation to another. They differ in that the mapping in PST is algorithmic (one-to-one mapping), whereas analogical reasoning is not. Analogical reasoning works well in some situations (e.g. law and social science) but not in others (e.g. chess). |
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//recruiting online gamers to solve the game and therefore the original problem.// |
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Sounds very "Ender's Game" |
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There's a fairly well-known example of this in the following form: |
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Suppose you're shown four cards, with "A","B","1" and "2" on the visible faces. You are told that cards have a number on one side and a letter on the other. You need to determine whether cards with a vowel on one side have an even number on the other side. Which cards do you need to turn over to test this? |
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People generally struggle with this problem. |
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Now suppose that you're a shop inspector, and you must make sure that a shop is not selling alcohol to people under a legally defined age. There are four transactions which you can review:
a person of indeterminate age, buying vodka;
a person indeterminate age, buying vegetable oil;
a child, whose purchase you can't see;
an adult, whose purchase you can't see.
Which transactions do you need to check? |
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People generally find this very easy to solve.
The interesting thing is that this is logically equivalent to the first problem. |
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So it turns out that human brains are tuned to parse agent behaviour. This is why it's helpful to consider e.g. genes as sentient entities. |
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[Loris] That's an interesting pair of problems. I agree that the card problem takes a little more thought, but it seems to me that it is more difficult simply because it is worded in a way that it requires more logic parsing. |
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If the card problem was changed to be, "Which cards need to be checked to see if there are any cards that have a vowel on one side and an odd number on the other," the answer is obvious and no more difficult than the other problem: "Which transactions need to be checked to find out if a child purchased alcohol." |
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The first problem is difficult because the logic needs to be parsed into a simpler form. The efficient solution is to look for violations of the stated requirement, not attempt to verify directly that the requirement is met. The context of the second problem implies that we are looking for violations, so the solution is intuitive to most people. |
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I think the most interesting thing about this set of problems is that it makes people think that they are not as good at solving conceptualized/mathematical problems as they are at solving real-world problems, when in reality, the only difficulty with the more abstract version is that the problem statement is obfuscated with logic. |
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//I agree that the card problem takes a little more thought, but it seems to me that it is more difficult simply because it is worded in a way that it requires more logic parsing.// |
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If that is the case, it is entirely down to my rendition - I assume that the original researchers would have taken more care over their phrasing. I took some care, but it was late at night and I was more concerned to get the logic and equivalence of the two problems correct. |
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I'm not really clear on the distinction you're trying to make in your third paragraph. It seems to end with the conclusion I stated - human brains are tuned to deal with interpreting actions and behaviour. |
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I see this as being partially baked as flowcharts. These are essentially maps that can be found in virtually every domain and lay-out courses of action based on almost every conceivable eventuality. As per the plot device idea at the end, Edgar Alan Poe's Sherlock Holmes predecessor used a similar method to read the mind of... bah I'll just find a link. |
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Link is up. If you have an hour or so to spare, I'd suggest reading the entire story. It's a pretty awesome work. If you really couldn't be damned about the story then maybe just the first 1500 words. |
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I've now found a link to what I was on about before. It's called the Wason Selection Task. I think it's worth playing. |
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Current results are that around 22% of players got the abstractly phrased problem correct, but 57% got it right when it was described in terms of detecting cheats. |
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Wasn't there a Phillip K Dick story where the protagonist thought he was just living out his life and playing some kind of game (was it a crossword every day) and it transpired that he was actually solving math problems for directing some kind of high tech war, but he didn't know it? |
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[Loris], thanks for the link to the Wason Selection Task. I stand by my original analysis. I'd say that your rendition was good enough. Your wording of the first question was logically equivalent to theirs: "If a card has a circle on one side, then it has the colour yellow on the other side". Your wording of the second question was different, but the wording was irrelevant because the majority of people already know the rules for serving alcoholic beverages. Many people are not that great at logic, but the condition, "If a person drinks an alcoholic drink, then they must be over the age of 21 years old," sounds like it matches existing law with which they are familiar. The implications of the law have already been worked out in most people's mind through experience, stories, etc. I would point out, that the law is written more like: people under 21 are not allowed to drink. The way it is stated it sounds like somehow a person will hit a time warp and suddenly age if they drink some alcohol, but since we know that can't happen, it doesn't confuse us. However with the other selection tasks the wording is the same yet the impossibility of the misinterpretation is not as obvious. |
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To put this another way, someone should try the test with cards showing a girl, a boy, a skirt and some pants with the requirement: "If a student is a girl, they must wear a skirt." This is the exact same logic, and on first glance it appear to match traditional school dress code requirements, but from a logic point of view it allows boys to wear skirts or pants. I suspect that this would score lower than any of the others (unless you limited your samples to cultures where boys often wear skirts). |
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You could easily say that my new question is a trick question. I agree. It uses social norms to guide you to the incorrect answer, but the beverage question uses social norms to guide you to the correct answer, so it is equally invalid. |
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The Wason Selection Task is actually a good example for this idea. If it is possible to find an analogous problem that has already been solved, that makes it easy to solve. I would say that verifying that the problem is truly analogous is just as difficult (or more difficult) than solving the original problem. |
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But I think it is incorrect to saying that the Wason Selection Task shows that people are better at solving problems involving agents and action like you said, or as the link says: "they argue that the human mind has evolved to detect violations of conditional rules, when these violations involve cheating on a social exchange." The Wason Selection Task does show that if people correctly guess that a problem is the same as a problem they have already solved, the answer is easy, but I say any confidence in such an answer is misplaced if it is based on a guess. In the case of my trick dress code question, I predict that many people would incorrectly guess that the problem matches one that has already been solved and end up with the wrong answer. Maybe I’ll see if the owner of that site can add my question to his quiz. |
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I was intrigued to read that people actually get the Watson task wrong! |
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[squeakth], if there was such a story (and it does sound
vaguely familiar), then either Dick or Orson Scott Card was
ripping the other off. |
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Which is actually a commonly accepted practice in science
fiction, of course. |
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