We decided to investigate in this area. And we found that the Hick's Law is the most suitable to calculate this phenomenon. To prove that we understand this topic on logarithms and to prove that Hick's Law is true, we did an experiment with several friends. (As this is all about human behaviour and human reaction)
We used the formula in Hick's Law, which is T=b x log2 (n+1).
To refresh your memories, T is the time taken to choose from a variety of choices. n is the number of choices given to the person. However, there is one more constant, which is the b. We concluded that b varies from person to person as every human is different. So, how did we execute this 'experiment'?
First we had to find the constant b. We formulated a question for our friend. (Anonymous to protect his identity -- Stated in the report) We gave decided to give him 4 choices of fruits to choose from. (Since we do not know the constant b, we had to work backwards).
Q: Choose with carefully consideration and do not be bias in this test. What would you choose? Orange, Apple, Pineapple or Honeydew?
A: (After 5 seconds) Apple.
And we worked backwards to find out his constant b.
T=b x log2 (4+1) --> 5s=b x log2 (5) --> 5/log2 (5) = b
And b is 2.15338279.
And we can continue with our experiment! Next, we formulated another question. But this time, we gave him 6 choices to choose from. Before we even asked him the question, we calculated and predicted the time he will take to choose from the 6 items.
T=b x log2 (6+1)
T=2.15338279 x log2 (7)
T=6.046559356
Round down to 6s.
Q: Choose among these drinks. Peach Tea, Green Tea, Ice Lemon Tea, H-Two-O, Bubble Tea or Apple Tea?
A: (After 7 seconds) Bubble Tea.
He took 7 seconds to answer this question. Although the answer and the predicted answer was not exactly the same, it was a difference of 1 second. Give and take 1~3 seconds for human reaction, he is in the range of our predicted answer and we have successfully completed our experiment!
However, we were not happy with just 2 questions. We formulated another questions. This time, we gave him 9 choices to choose from.
Again, the formula -->
T=b x log2 (9+1)
T=2.15338279 x log2 (10)
T=7.153382789
Predicted Time taken for him to choose from 9 choices is about 7s.
Q: Choose a brand of a car. Toyota, Honda, Ford, Fiat, Chevrolet, Volkswagon, Mitsubishi, Nissan, Proton.
And indeed, this time, he took 7 seconds to answer!
Isn't it amazing!?
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