Our Study
We hopefully captivated you earlier with our question: Why do we notice a large change in light of a room when a second candle is turned on but we don't notice a change at all really if a hundredth candle is turned on?
The simple answer to this question is that, more or less, humans see in a logarithmic manner: The change from log(1) to log(2) is relatively large compared to the change from log(99) to log(100) just like how humans notice a large change in light when a second candle is turned but basically we recognize nothing when a 100th candle is turned on. Even though in both cases, only one candle is being added, the way we perceive this candle changes with more and more candles because we see logarithmically. log(2)-log(1)=.301 but log(100)-log(99)=.00436. And .301/.00436=68.97. So if humans really do see logarithmically, we perceive the change in light when a second candle is turned on 69.97 times more than we perceive the 100th candle turned on...mind-boggling, I know.
So we designed an experiment to see if humans also think logarithmically.
Our experiment was simple really: We took a flashlight and shined it at the test subject for about 1 second; we told the person that this was considered a short burst, but we did not say it was 1 second. We then shined the flashlight at the test subject for about 16 seconds; we told the person that this was considered a long burst, but we did not say it was 16 seconds. We then told the subject that there would now be a series of intermediate bursts, that is bursts in between 1 and 16 seconds. We told the subject to tap the desk when their mind made the decision that the burst was long, that is if it seemed its duration was more than what they considered the middle of the short and long bursts models we showed to them in the beginning. Now, if humans could perceive the time linearly, then every test subject would tap the desk at the midpoint between 1 and 16 seconds, which would be 8.5 seconds. However, 8 of 10 test subjects tapped the desk in between 3-5 seconds, an average of 4 seconds. Hence, most of the test subjects clearly underestimated the midpoint, and this alludes to the fact that, although not totally conclusive, humans think somewhat logarithmically because just like with the candle situation, smaller values seem to be spread out and larger values seem to be compressed. In other words, the test subjects rendered 1-4 seconds like 1-8.5 seconds, so it was more spread out. Yet, the test subject rendered 4-16 seconds like 8.5-16 seconds, so it was more compressed.
The simple answer to this question is that, more or less, humans see in a logarithmic manner: The change from log(1) to log(2) is relatively large compared to the change from log(99) to log(100) just like how humans notice a large change in light when a second candle is turned but basically we recognize nothing when a 100th candle is turned on. Even though in both cases, only one candle is being added, the way we perceive this candle changes with more and more candles because we see logarithmically. log(2)-log(1)=.301 but log(100)-log(99)=.00436. And .301/.00436=68.97. So if humans really do see logarithmically, we perceive the change in light when a second candle is turned on 69.97 times more than we perceive the 100th candle turned on...mind-boggling, I know.
So we designed an experiment to see if humans also think logarithmically.
Our experiment was simple really: We took a flashlight and shined it at the test subject for about 1 second; we told the person that this was considered a short burst, but we did not say it was 1 second. We then shined the flashlight at the test subject for about 16 seconds; we told the person that this was considered a long burst, but we did not say it was 16 seconds. We then told the subject that there would now be a series of intermediate bursts, that is bursts in between 1 and 16 seconds. We told the subject to tap the desk when their mind made the decision that the burst was long, that is if it seemed its duration was more than what they considered the middle of the short and long bursts models we showed to them in the beginning. Now, if humans could perceive the time linearly, then every test subject would tap the desk at the midpoint between 1 and 16 seconds, which would be 8.5 seconds. However, 8 of 10 test subjects tapped the desk in between 3-5 seconds, an average of 4 seconds. Hence, most of the test subjects clearly underestimated the midpoint, and this alludes to the fact that, although not totally conclusive, humans think somewhat logarithmically because just like with the candle situation, smaller values seem to be spread out and larger values seem to be compressed. In other words, the test subjects rendered 1-4 seconds like 1-8.5 seconds, so it was more spread out. Yet, the test subject rendered 4-16 seconds like 8.5-16 seconds, so it was more compressed.
