Goldilocks and the elephant
R. Shankar, The Institute of Mathematical Sciences, Chennai
Goldilocks was a little girl with golden hair. She got lost in a forest one day. Tired and hungry she came to a house that belonged to a family of bears. When she went in, see saw three bowls of porridge on the table. A large one (for Karadiappa), a medium sized one (for Karadiamma) and a small one (for Karadipapa). She tasted the large one and found it was too hot, the medium one was too cold but the small one was just the right temperature. The story goes on but I am not going to tell it to you. It is a well-known story and I am sure you can find some-one who knows it.
What I am going to tell you is the lesser known story of what happened a few years later. Goldilocks came to India for a holiday and went to visit the wildlife sanctury in Mudumalai near Ooty. There she was taken for an elephant ride into the forest to spot animals. The young elephant on which she rode was called Vikram. Goldilocks and Vikram became friends. She told him about her experience with the bears and he told her about his life in the elephant camp of the Mudumalai wildlife sanctury.
After Goldilocks left, Vikram was thinking about what she said and became very puzzled. The large bowl of porridge was the hottest, the medium bowl was the coldest and the smallest one was of medium temperature ! How can that be ? Was it not more natural for the medium sized bowl to be of medium temperature ?
He thought a little more. Firstly, why was the temperature of the porridge in the three bowls different ? "When the porridge was made and poured out into the three bowls", he reasoned, "all of it would have been of the same temperature. Then they will start to cool. Now I know that if I take out one teaspoonful of the porridge and hold it in the air, it will cool much faster than the the porridge in the bowls. So small amounts should cool faster than larger amounts. So the medium sized bowl should have been of medium temperature. Was Goldilocks actually mistaken ?" 
Vikram was an elephant with scientific temper. He felt that he had to try it out practically before coming to any conclusions. So he went discuss the problem with his good friend Lakshmi, who was the daughter of one of the mahouts in the elephant camp. Lakshmi was also puzzled. But she pointed out that, "Actually, it is not only the amount of porridge that matters. When we drink tea or coffee, we pour it out from the tumbler to the dabara (a sort of bowl) and the same amount of coffee cools faster. So the shape of the container also matters". Being of a scientific bent herself, she also felt that they had to try it out practically.
So they went to Lakshmi's house and asked her mother if they could use the kitchen for some time. After finding out what they wanted to do, her mother said "OK! But you must leave the kitchen as neat and tidy as you found it". Lakshmi and Vikram promised to clean up everything after they finished their experiments and started their work. They decided to heat water, pour different amounts into two containers, one big, one small, and check which cooled faster. Vikram was of course outside the house. He stood near the kitchen window and with his trunk he could reach inside to help Lakshmi. The tip of his trunk was much more sensitive than Lakshmi's fingers so he could easily make out which container was cooling faster.
They did many such experiments and kept discussing the results. In a couple of hours the whole thing was clear to them. They understood what were the features that controlled the rate of cooling of a hot liquid and that Goldilocks could indeed have been right. Then they cleaned up the kitchen and left, a young elephant and a young girl with the feeling of deep satisfaction that comes from having solved a difficult problem.
You too can get that feeling of satisfaction. Do the experiments and write to us (at the JM address given) describing what you did in order to answer the question: Under what circumstances could the porridge in the medium sized bowl have been cooler than the porridge in the small bowl ? We will publish the best answer that we get.