Creating an app to investigate a theory about how humans process data

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.


Solution to pascal’s wager

For those who don’t know, Pascal’s wager is an attempt to make a logical argument for believing in god. The idea is that if you agree that heaven has infinite value, it follows that if your belief is that the probability god exists is greater than 0 (and even Richard Dawkins would only rate himself at 6 out of 7 in the strength of his belief that god does not exist) then the value of believing in god is infinite, because any non zero number multiplied by infinity is infinity – if you assign a probability of 0.01 of god existing then the value of believing in him to reach heaven is 0.01 * infinity = infinity. For more information, check out the wikipedia article.

Allowing the possibilities of states that have infinite value (such as heaven) implies that any decisions that can both potentially lead to reaching these infinitely valuable states necessarily have equal value. For example, exercising for 50 minutes and punching one’s self in the face are both of equal value to someone who believes that the probability of reaching heaven after doing either of these things is not exactly 0.

Assigning a future state the value of infinity in decision systems has a very powerful destructive effect. Because a future state of infinite value has a non-zero probability of being reached, all the parent nodes have infinite value too and that will ultimately lead to theĀ current node also having infinite value, meaning that there will be indifference to all current decisions. Thereby making it not much of a decision system anymore because itĀ has no way to discern between any choices.

Those who do believe in states of infinite value but don’t believe that all decisions that don’t rule out the possibility of reaching all values of infinite states have equal value are forced into resolving the contradiction. Either they must accept that essentially all decisions have equal value to them, or they must deny the existence of the possibility of states that have infinite value – it’s not consistent to hold both beliefs. And it’s my belief that denying the existence of states of infinite value is the most intuitive decision that most people already agree with. I don’t have any proof that this is the correct assumption, but I think most people would agree with me that anything that results in almost all decisions having exactly the same value is not valid.

While adding in a new rule for decisions systems is a heavy handed approach to solving what seems to be a small problem in Pascal’s Wager, it actually solves the problems of the destructive forces infinities have on decision systems.

At this point you may be thinking “but wait, if heaven does last infinity long and each year has a value greater than 0, it’s value must be infinite”. In that case I would like to outline how it is possible that even though heaven can last infinitely long, it does not necessarily have infinite value even though each year has a positive value. Consider the series 1/2 + 1/4 + 1/8 + … Does it add up to infinity? It doesn’t, here’s a visual proof

Things that have an infinitely long existence in the temporal realm do not necessarily have infinite value even though each instance of that point of time has a value greater than 0.

Similarly, you can assign a probability distribution of the value of an unknown entity such that it never adds up to infinity. E.g. the probability it is worth 1 is 1/2, the probability it’s worth 2 is 1/4 and so on. This is another way to assign a positive probability to all possible values of an unknown entity without requiring you to be absolutely certain that it is not worth more than a given amount (i.e. not needing to assign a probability that it has a value above x to be exactly 0).

In summary, this post is meant to outline the fact that you must either accept that almost all decisions have the same value or that states that have infinite value do not exist.