I suspect the human brain is capable of combining data in a way that allows it to arrive at correct conclusions at a higher degree of accuracy than what at first seems to be possible given the limitations of the data it used to come to that conclusion. By writing an app I can precisely control the data given to the user to measure these effects.
In the app there will be 3 types of tests each of which will be repeated many times. The first test presents the user with a circle then a different circle appears of different size and the user is asked which was larger. The second test is the same except it is a sound and the user is asked which was lower pitched. The third test combines these two tests into one: a circle appears with a beep then disappears then another circle with a beep appears. The user is then asked which one was lower pitched and larger (the lower pitch will always be paired with the larger circle).
From this data graphs can be plotted that have % difference in size vs probability it is correctly selected and so on. But what’s most interesting is trying to predict the results of the third test using only the data from the first two tests. Suppose a user has a 66% accuracy in the first two tests when the stimuli differs in intensity by 10%. What is the best accuracy he could be expected to reach in the third test when both stimuli differ by 10%? Keep in mind users can guess.
It’s tempting to say 66%, but this is not true. If in the first two tests the user is 66% confident his answer is correct 100% of the time then this would be true. But what’s interesting is that it could be the case that 33% of the time the user is 100% confident in his guess and 66% of the time he makes a blind guess. To calculate his expected accuracy we first work out the probability that he does encounter a stimuli he is certain about, which is 1 – (2/3) * (2/3) = 55.5%, then we calcualte the probability he doesn’t encounter a stimuli he is certain about then half it (as in this case he is guessing so has a 50/50 shot) which is (2/3) * (2/3) * 0.5 = 22.2%. Now add these together to get 77.7% accuracy.
If the human mind is independently analysing the sound and size stimuli, it is impossible to achieve an accuracy above 77.7%. But if there is some process in the human brain combines stimuli it becomes possible to achieve a higher degree of accuracy. My suspicion is that it’s possible the human brain does do this, and it may be possible to surpass the 77.7% limit for such a user.
An example of how this could be possible is to think of neurons as a bucket that fires when the water overflows the top. If you give it a test of size or pitch alone the neuron may be filled to 80% capacity, but if you do both at the same time it may overflow to 160% and fire away, leading the person to reach a conclusion. This isn’t meant to be an explanation of how I think the mind works, it is merely meant to be an example showing how there could exist mechanisms that mean it is not totally impossible to achieve above 77.7% accuracy.
In summary, I set out to investigate whether the human brain is capable of using data in a way that makes the utility of the data greater than the sum of its parts.