There are three on-off light switches on the wall of the first floor of a building. One of the switches is initially off and controls an incandescent bulb in a lamp on the third floor of the building. The other two switches do not control the bulb or anything else (they are disconnected). How can you find out which one of the three switches turns the light bulb on and off? You can toggle the switches as many times as you want and for as long as you want, but you can walk only once to the third floor to check on the light bulb.
While you're working on that, I'll show you what you look like (no offense!):
(A hint and the solution to the problem are at the bottom of this post.)
It's thrilling when it happens, but what actually causes insight? New research in the Journal of Cognitive Neuroscience takes us one step closer to an answer: up to 8 seconds before people solve problems thought to require insight, a particular set of very fast oscillations are observable above the right frontal lobe.
Sheth, Sandkuehler & Bhattacharya gave 18 subjects a series of "insight problems" like the one at the start of this post, while the electrical activity on subjects' scalp was recorded via a sensor net with 32 electrodes. All the problems shared a number of features:
- no problem required specialized knowledge, nor could any be solved with a predefined procedure
- if the correct solution was described, it would seem obvious (i.e., they were simple puzzles)
- the puzzles weren't well known, and didn't require pen/paper to solve
To get the gist of this, contrast these criteria with algebra problems (which do require specialized knowledge, can be solved with predefined procedures, often with the help of pen and paper, and do not have typically yield answers that are transparently correct). If subjects hadnt' solved a problem within 60-90s, they were given a hint. After an additional 60-90s, or until subjects felt they'd solved the problem, subjects first indicated whether they felt a sensation of insight (on a scale from 0-10), and then verbally described their solution. Data from the sensor net were transformed with Morlet wavelets to quantify the power of oscillations at particular frequencies on the scalp, and then subjected to something like principal components analysis (a technique the authors call "PARAFAC," a form of factor analysis used to identify the "scalp topography, spectral frequency, and temporal dynamics that provide maximum discriminatory power between two compared conditions.")
The results showed two primary effects discriminating correct from incorrect solutions: a decrease in the power of frequencies between 15-25 Hz (the so-called "beta-band", sometimes implicated in active maintenance) over posterior regions, and an increase in the power of frequencies between 30-75 Hz (the so-called "gamma-band", implicated in higher cognitive functioning) over right frontal regions. The beta-band reduction was more prominent in:
1) solved problems relative to unsolved problems;
2) solved problems where no hint had been provided relative to those with hints;
3) solved problems with a hint relative to those remaining unsolved despite the hint,
4) in problems solved with a strong feeling of insight relative to those without this feeling.
Similar results were found for increases in the gamma-band, in every case except for #3, in which gamma band increases were actually more pronounced for problems remaining unsolved despite the hint. The authors suggest this could reflect that the "transformative thought" underlying insight is reduced by hints - particularly when those hints lead to a solution. Perhaps subjects are engaging in a larger number of transformative thought processes (just the wrong ones) following a hint that does not ultimately yield a successful solution.
Many of these oscillatory changes preceded subjects' responses by several seconds (up to 8 seconds, in the case of the gamma-band increases), leading to the suggestion that this reflects unconscious processing (as discussed at the Economist). i think the flaw in this reasoning is made clear with a simple example.
Let's suppose that some subjects were allowed to close their eyes instead of reading the problems. Clearly we would be able to determine which subjects were most likely to solve the problems long before any actually solved them, likely by looking at activity in the visual cortex. However, we would not say that this activity in the visual cortex reflects unconscious processing. The best evidence we have that insight problems reflect "unconscious" processing is that people have difficulty reporting how they solve them - in other words, the brain data add little to this debate.
There are a number of other caveats to the research as well. First, no one really knows what processes any of these oscillations reflect, nor do we know their sources. Second, the changes in oscillatory power are inherently ambiguous, because they can reflect many underlying changes in the brain: an change in neuronal firing rates, a change in the coherence with which neurons are firing (without changes in rate), or a change in the phase coherence across multiple frequencies with which neurons are firing. Third, and most critically, Sheth et al used an unusual baseline condition in calculating the changes in oscillatory power: the time during which subjects were reading the problems.
The problem with this baseline can be easily illustrated. Let's suppose that subjects who ultimately solve the problems undergo more "transformational thought" while they're first reading the problem. This seems like a reasonable assumption, given that one's understanding of the problem is likely to be restructured as you integrate the various constraints, and that to the extent this occurs one is more likely to actually solve the problem. Thus, these "better subjects" will show less beta-band power during their (mostly correct) solutions (relative to baseline) than the "worse subjects" will show during their (mostly incorrect or undiscovered) solutions (relative to baseline). Whether this particular example applies in the case of Sheth et al is hard to say, but it illustrates the general problem of using such a cognitively "high-level" baseline, and highlights the underlying ambiguity with what these oscillations actually mean.
If you still haven't solved the problem, here's your hint: Turn one switch on for an hour and then turn it off. The solution is in the comments.
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that light bulb thing got me thinking. However, you've got a huge assumption in there, in thinking that you can "feel the temperature" of the light bulb to see what switch it is. some light bulbs give off no heat whatsover, so the experiment is flawed as it has a cultural bias in thinking heat is given off in the bulb. also, what if the conditions in the room allowed the light bulb to be cooled, as you got to the third floor? just something to think about!
Solution:
You turn the first switch on and leave it on for an hour. Then you turn it off and turn the second switch on, leave the third switch in the off position, and you go upstairs. If the bulb is on, then itâs switch number two, which is the one thatâs on. If the bulb is off and itâs cold, then it is switch number three (the switch you never touched) that controls that light. If the bulb is off but itâs hot, then it is switch number one.
The solution is correct for my first impression of the problem statement, but a second close reading provides a simpler solution to the actual problem statement: The ONE switch intially in the off position controls the light.
So, why not walk outside and look up at the 3rd floor window to see if the light is on???!!! I know, I know, there may not be a window and the light may be interior,but my feeble brain could only come up with that one !
How about this?
Turn switch #1 on, leaving 2 and 3 off.
Climb up to the third floor and look at the lamp.
If the bulb is on, switch #1 is the winner.
If the bulb is off, move the lamp to a window that faces the street.
Go back down to the first floor.
Turn switch #1 off, switch #2 on.
Go outside, look up to the third-floor window to see if the bulb is on. If it is, switch #2 is the winner, if not, #3 is.
How about just getting a voltmeter, unscrewing the switch cover and check to see which switch has voltage. The two that are disconnected have no potential across the leads.
i think you guys are missing the point! :) nice solutions though.
They aren't missing the point; they're drawing our attention to the fact that the terms of the problem are not well-defined in the question itself. The question never disallows voltmeters or moving the bulb; similarly, a critic of the proposed solution could say that a typical bulb may cool off enough by the time one climbs two flights of stairs that someone might not be able to feel whether the bulb had recently been on.
To say that they are "missing the point" is to deny the fact that they've seen perfectly valid alternative explanations.
If someone solves the problem differently than the way the author intended, does that make their answers incorrect? It's always easier to dismiss answers that are different than the one you wanted than to acknowledge that you didn't foresee ambiguity in your question. A well-designed and well-worded problem would be unambiguous.
Though I scrapped it when I thought of the standard solution, the first idea to come to mind involved tying knots in a piece of heavy twine, tied around a light switch in the "up" position. When its weight is nearly sufficient to pull the switch, allow the bottom of the twine to dangle into a bottle of water, so that the water gradually soaks the twine. Flip one of the other two switches. Now go upstairs, and if the light is on, it is the switch you flipped - otherwise wait a while, and if the light turns on by itself... it is the twined switch. (If all three switches begin in the down position the procedure is similar but we wait for the light to turn off).
Of course, this solution is unappealing due to unreliability and the need for twine, water, and careful calibration.
But to respect the topic of the blog entry, I should add that at the moment I scrapped the idea, all that I was consciously aware of was the image of the twine tied around the light switch, which I pictured myself somehow pulling from the third floor. Yet after I hit upon the other solution and skimmed the article and comments... the plan above was fully developed. This is matched by the subjective perception that ideas are turned loose to develop on their own in some remote corner of the mind, then return to consciousness once they have ripened.
I get the point. The conclusions were not supported by the data. Someone is awfully presumptuous, but much of neuroscience is change something, observe, change something else, observe, interpret. You put a challenge question on the internet, so you get to put up with the solutions.
Step 1. Go to the power meter (that is assumed to be accessible and exist), count the amount of power used in 120 seconds.
Step 2. Flip switch 1, repeat step 1. If the amount of power consumed has changed, switch 1 controls the light.
Step 3. If step two didn't solve it, flip switch 2, repeat step 1. If the amount of power consumed has changed, switch 2 controls the light, if not switch 3 controls the light.
It's much faster than the given solution and does not assume that the building has windows on the third floor or require a tiresome trip all the way up to the third floor. It only assumes that the building has an electric meter (what with light switches, light sockets and all). Another solution would be to turn off all switches, go upstairs and short circuit the light socket flip a switch then check the fuse box before flipping the next one. Whichever switch causes the fuse to blow controls the light.
I get the point. The conclusions were not supported by the data. Someone is awfully presumptuous, but much of neuroscience is change something, observe, change something else, observe, interpret. You put a challenge question on the internet, so you get to put up with the solutions.
Step 1. Go to the power meter (that is assumed to be accessible and exist), count the amount of power used in 120 seconds.
Step 2. Flip switch 1, repeat step 1. If the amount of power consumed has changed, switch 1 controls the light.
Step 3. If step two didn't solve it, flip switch 2, repeat step 1. If the amount of power consumed has changed, switch 2 controls the light, if not switch 3 controls the light.
It's much faster than the given solution and does not assume that the building has windows on the third floor or require a tiresome trip all the way up to the third floor. It only assumes that the building has an electric meter (what with light switches, light sockets and all). Another solution would be to turn off all switches, go upstairs and short circuit the light socket flip a switch then check the fuse box before flipping the next one. Whichever switch causes the fuse to blow controls the light.
Why worry about which one works? Just turn all three on.
Dane, the problem doesn't seem to say whether it's obvious from looking at the switches what the state of each on is... eg switch one might be in the up position and be on, while switch two might be in the up position and be off... so you assume too much.
I think everyone's missed the point. The answer is in the question:
"One of the switches is initially off and controls an incandescent bulb in a lamp on the third floor of the building."
It's the one that's in the off position :)
The connected switch starts in the off position.
The other two switches do nothing.
So, flip all switches and go home.
The trip upstairs is unnecessary.
How about this one: for many standard light switches you can slowly ease the position of the switch to a point where it is so close to making physical contact, that you reach the dielectric breakdown of air and you can hear sparks arc across the gap between the metal contacts. If they are the right type of switch, it should be rather easy to find the live one in a few seconds of gentle switch flipping and listening.
This worked for all the switches in my apartment that can be switched between on and off in a smooth arc rather than snapping quickly into place.
I think the fact that an incandescent light was specified directs the reader to use the solution of feeling the bulb for residual warmth
Great puzzle. I'm waiting for another!
I second that, a good mental challenge.
The statement "one of the switches was initially off and controls an incandescent bulb in a lamp on the third floor of the building" does not necessarily lead one to conclude that the other switches that did not do anything were in the "on" position, rather it could simply be looked upon as the author clarifying to the person trying to solve the test the the lamp starts in the off position. Furthermore anyone who possesses knowledge about house wiring knows that there are things such as 3-way switches, absent clarification, would not assume that just because a switch is up or down that it's on or off.
I therefore think that testing the heat of the bulb is the more likely correct answer. If the switchers were dimmers, one might also be able to feel the heat from the dimmer.
How about you don't go upstairs at all. You just call a co-worker on his/her cell phone from yours, have them go to the 3rd floor lamp while you flip the switches one by one and ask them to tell you when the light goes on. Mission accomplished in 1 minute!
Being someone who tends to intellectually "rush in" before really internalizing the constraints, I focused on the harder problem, where you don't know the initial state of the lamp, and you don't know whether the up/down state of the wired switch corresponds to lamp on/off.
I came up with 4 solutions, some of which were similar to those already described:
1) remove/destroy coverplate, flip a switch wildly and look for sparks, etc. (we neglect the too easy solution of checking which one switch has wires connected!)
2) remove coverplate, lick thumb and forefinger and rapidly probe the pair of terminals on one switch, etc. The unpleasant buzz won't kill ya, and you have a 2/3 chance of no buzz at all.
3) make use of the building power meter as described above. relies on knowing some circuit theory, and that all other circuits on the meter stay idle.
4) (my fave) binary search of temperature change: for an hour, flip one switch at a 50% duty cycle, flip a second with a 75% (which may actually be 25%) duty cycle, and leave 3rd alone, then:
cold or max temp ==> the switch left alone
intermediate temp ==> will map to one of 3 distinct temperatures, 1 for 50%, and two for the 25% and 75% cases.
yes, a thermometer and some calibration is required...
2 ways came to my mind:
1. to go outside and check the bulb from a window [hopefully there, since there isn't any comment about a windowless house, and we know usually houses have windows!], and if the light of bulb is weak, we can wait until night and check it better. even since there is no forbidding rules about enhancements, we can borrow a handy cam with NightVision [infrared sensor] option, to check the very weak light from a far window, easily.
2. we can go upstairs once and locate a dropping water can over the bulb, in a position that water doesn't go to wires, and dropps only on the bulb.... then from downstairs we can turn on switches and wait for a good while until bulb gets hot to burn and explode by cold water... then by hearing the sound we can conclude that it was ON. if the bulb is little, we can use hearing enhancements, since there are no restrictions: we can locate a connected and turned on mobile phone beside the lamp to hear the weak sound of breaking. we can position a microphone etc.
I am not a grad student, or anything like that. I do find the human brain fascinating however having experienced a craniotonomy on my right temporal lobe for an AVM and just recently a removal of a Meningioma Tumor on my right Frontal Lobe. I have to say, that what we truly know about the human brain is actually very little, and the answers posted here prove as much! Everyone has different ideas, answers and takes on the original question, which in fact did not give direct pirameters for finding out which bulb was the correct one. It did start out good however, but did not finish well. If we were not to move the lamp, or use a voltometer, it should have been stated. I must say bravo to all those who used their imaginations and the FOUR LOBES of their wonderful MINDS to give insightful answers. Touche'....
I am not a grad student, or anything like that. I do find the human brain fascinating however having experienced a craniotonomy on my right temporal lobe for an AVM and just recently a removal of a Meningioma Tumor on my right Frontal Lobe. I have to say, that what we truly know about the human brain is actually very little, and the answers posted here prove as much! Everyone has different ideas, answers and takes on the original question, which in fact did not give direct pirameters for finding out which bulb was the correct one. It did start out good however, but did not finish well. If we were not to move the lamp, or use a voltometer, it should have been stated. I must say bravo to all those who used their imaginations and the FOUR LOBES of their wonderful MINDS to give insightful answers. Touche'....