Abstract Solutions

Australia v/s Bangladesh
Case1: Australia won the match

Case2: Bangladesh won the match

There is more information in the message-Case2 as compared to that of Case1. But, how can we come up with a precise notion for this intuitive argument?

Consider this problem.How can you compare biodiversity at two different parks?
Say park1 has 10deer, 1 lion and 10 monkeys while park2 has 2lion, 4 deer and 6 monkeys.

This question was answered by setting up a game. Suppose Alice and Bob are the players. Alice is at the national park and Bob is at home. Alice and Bob know the frequencies of all the animals. Bob needs to ask a question to which Alice can only reply Yes/No. Now consider the average number of questions to be asked, to find the answer. If the park has 99.9% deer, Bob would ask "is it a deer" and guess it with a probability of 0.999. The average number of questions to be asked is close 1.However, if all the animals have similar frequencies, it takes more questions.

Consider a simpler example. Suppose Sheldon, a sumo and Mr Bean are wrestling. To find the winner's name I would ask "Is it Mr Sumo?" and the next question would be "Is it Sheldon". I would get my answer, within two questions. However, there is a good chance that  we would obtain the answer in just one step. Thus, the average number of questions will close to 1. If all the players are well matches, with one-third chance, a question will suffice and with two-third of a chance two questions will be needed and the average number of questions would be equal to 1.66

Leaving the math and the abstractions aside. The central argument is- Can we define the problems properly and seek sophisticated and robust solutions using the power of abstraction, like how we did, in this example?

Business Research

How can Alice tell a secret to Bob, such that Charlie can't listen?

What if all that Alice knows about Bob is his signature?

This problem, of cryptography, is translated into a riddle. Alice has a Kohinoor Diamond. She needs to send it to Bob, using a courier Charlie. There is no other medium of communication. Alice has a lock, box, diamond and a key. She can use the courier any number of times. How does she send the diamond, without sending the diamond.

We can solve it backwards.Bob had the box and he took the diamond safely. It must have been locked and the key wasn't sent, so the lock must have been put by Bob. So, in the previous step, Bob put a second lock.

The protocol is simple. Alice sends a locked box which is locked by Bob, with his own lock. Bob sends the box back to Alice, who unlocks her own lock and then sends it back to him. Bob opens his lock and takes his diamond.

Note: It took a significant amount of time to arrive at this solution.The one who solved it, got the idea during a voyage. This method is a mere interpretation/reconstruction of the solution.

Business Research- Can we ask for questions in business management and seek scientific solutions for problems like this?

In the next post, we shall discuss an elegant solution to the problem of developing a rigorous notion of information(Entropy).