In an interview on September 2021 Daniel Kahneman, the Nobel Prize laureate said that he was working to understand the reason why intelligent people mistake simple riddles.
He used the following example: if a bat and ball cost 1.10$, and we know that the bat cost 1$ more than the ball, how much does the ball cost? 50% of Harvard students say the same as most people and answer: 10c. This is the wrong answer since the math would be that the total cost of the baseball bat and the ball will be 1.20$. The right answer is 0.05c as the next equation shows: X+(X+1)=1.10 or 1.10-X=X+1; eliminating 1 leaves X=0.10-X, thus, we are left with X=0.10/2=0.05c. So, how come some of the brightest minds in a top university answer wrongfully to a question that if they will think it through, they will undoubtfully answer correctly? The reason for that question relates to so many different decision-making problems everyone encounters in our quotidian life. As so many of us, we tend to deduct the 1$ difference between the bat and the ball from the total amount of 1.10$, which indeed leaves 0.10$. However, the decisive data in the equation is that the 1.10$ is the total price of both items and not a simple comparison between them.
Thinking in duality is the cause of that simple and honest mistake. From the one hand we tend to see the total cost (1.10$) and from the other hand we compare two items with a difference of 1.00$ between them, that will lead to the immediate erroneous conclusion of a ball price of 10c. Applying the trispective method we take under consideration a third detail, which in this case will be the transaction. If I pay X money for a ball and then I pay the same price of the ball plus 1.00$, I will receive a ball and bat for 1.10$. That transaction will have to be divided to the price of 0.05$, adding to it 1.00$, meaning 1.05$ that will in fact sum up to a total of 1.10$ for the ball and the bat. Hence, the difficulty occurs when we resolve to a simple and immediate basic calculation satisfying ourselves with a deduction of the 1.00$ from the totality.
So far is the obvious reflection that can be made, but the surprise is why even when the person knows that it is a riddle and thus the answer will most probably not be the obvious one, it is still strenuous to reach the correct one? Most people, including very intelligent ones, will simply tire in the thought process and murmur the faulty reply of 10c. Thus comes the methodology of the applying trispectivism forcing upon the process the third element in two ways:
1. There most be another number other than 1 and 0.1.
2. There most be another element other than the individual prices and the total price of the two elements.
Combining those two factors will increase the odd to find the correct answer in the fastest time without overthinking it and satisfy with the chance of an obvious one. The other number is a missing one and the added element is the transaction. Let´s break it down: if I pay the missing number and add to that the number 1, I get the two items for 1.10, thus the missing number must be 0.05. A quick check resolve in 0.05+1+1.05=1.10.
Think about it for a minute longer and then try the next two riddles:
If five machines made five gadgets in five minutes, how much time would it take for 100 machines to make 100 gadgets?
A beautiful lake is covered with lily pads. We know that each day the lily pads doubled in size, and it took 48 days for the lily pads to cover all of the lake. How long took for the lily pads to cover half of the lake?
Did you reach the correct answer?
(5 minutes / 47 days)
Let´s check the thought process and the application of trispectivism.
In the first riddle we know that 1. The number should not be 100 minutes; and 2. To get to the right answer we must separate the elements that constitute the riddle and check their interconnectivity. Which is why we avoid the immediate thought of one machine produces one gadget in a minute but the total time for the same number of machines to produce the same number of gadgets is 5 minutes. Thus, the correct answer will be that no matter how many machines there are, as long as they produce the same number of gadgets, it will always be 5 minutes. The number 5 is different from the number 100 that our immediate brain insisted on as the correct answer.
In the second riddle we know that 1. The number will not be the division in half of the number of days (24); and 2. We must separate the elements. Here´s what we do while applying the trispectivist mindset: we look at each lily pads as an interconnect individual unit and we ask ourselves if each one of them across half of the lake doubles in size in a day, how long it will take them to cover the lake? The answer is 1 day. That day we deduct from the 48 days given to us as data (48-1=47). The answer is 47 days, and it is indeed different than the number 24 our binary mind insisted on. And what about if it took them 60 days, or 100 days? In any case it will be the total number of days minus that day.
NB. If from the first second you thought about the correct answer, it is anormal though it doesn´t mean that you will do as good with other riddles that involve logic more than numbers. Either way, trispectivism is something we can all work at and improve our immediate brain functioning.