Tuesday, March 18, 2014

L.A.M. on a Number Sequence

Let’s play a game. I will reveal to you a sequence of 3 numbers and your task is to determine the rule of this sequence. To help you come up with your conclusion, you can list your own set of 3 numbers and I will answer with either a yes or a no. Based on my answer, you should be able to gain information to determine the pattern of the sequence.

Got it?

Here goes.

My sequence is………………………………………..
2, 4, 8

Ok, I’ll give you a bit of time to come up with your own sequence. On second thought, as this is a blog and not an interactive medium, let me try to second guess the sequences you have come up with.
I believe most of you would have come up with

3, 6, 12
4, 8, 16
16, 32, 64
5, 10, 20

If you came up with any of the above sets of numbers, you are correct! Your sets of numbers do follow my pattern. So what is the rule?

If you said that the rule is to multiply each preceding number by 2 to get the subsequent number in the sequence, your answer is wrong.

Ok this is rather puzzling. In your mind, you are pretty sure that the pattern follows a X2 rule, where each preceding number is multiplied by 2. You run through the calculations again:

2 X 2 = 4
4 X 2 = 8

There is no mistake. Whatever sequences you have thrown up follow a X2 rule and they have been proven to be correct. You throw up more numbers that follows this X2 rule

20, 40, 80
64, 128, 256
7, 14, 28

All of the above are correct. But if you are going to say that the rule is a X2 rule. You are still wrong.

You think for a long time and are on the verge of giving up. Finally, you throw up some random numbers in frustration.

1, 2, 3
5, 6, 7
2, 4, 6

Your pattern is…………………………………………………. correct. 

Now this is even more confusing. These numbers don’t follow a X2 rule but yet they are correct. Could it be that your original hypothesis that the numbers follow a X2 rule is wrong? You list another set of random numbers, throwing in some other unlikely combinations such as negatives and descending orders

2, 4, -8
5, 4, 3
6, 2,7

It took you a moment to register, but almost instinctively, you have figured out the answer. The rule is a sequence of ascending numbers.

Now on closer reflection, you realize one thing. This game is all about obtaining information and when it comes to information, a positive confirmation that your hypothesis is correct is less valuable than information showing that your hypothesis is wrong. If you had thought of sequences to confirm whether your hypothesis is wrong earlier such as throwing up numbers that do not follow a X2 rule or numbers in descending order, you would have reached the correct conclusion earlier. 

Similarly when faced with questions, we are constantly on the lookout for information that confirms existing beliefs. In a debate, we also find ourselves leaning towards arguments or people who agree with our preconceived opinions. 

However, depending on positive confirmation or surrounding ourselves with yes-men, only serves to give us a confirmation bias. A confirmation bias is a tendency for people to favor information that confirms their beliefs or hypothesis. People display this bias when they gather or remember information selectively or when they interpret it in a biased way. You displayed confirmation bias when you started out the exercise by listing sequences that affirms your existing belief that the numbers follow a X2 rule.

Confirmation biases contribute to overconfidence in personal beliefs and can maintain or strengthen beliefs in the face of contrary evidence. This can lead to poor decisions in an organizational context. It leads to continuing with client or personal relationship that are no longer profitable or healthy or continuing to invest in a stock whose share price is falling.

The most valuable information is information that disproves you. Similarly, the most valuable opinions are the opinions that challenge your beliefs. In order to dispel confirmation bias, we need to be open to contrary evidence and to seek data or evidence that contradicts our existing hypothesis. 

So, the next time you find yourself leaning towards an opinion or information that affirms your existing beliefs; take some time to consider the negative or controversial information. You never know if it could lead to a paradigm shift.


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