First, a fable.
A long time ago, pleased with one of his courtiers, a king offered him any present he would ask for. The courtier said, quite modestly, that he was not a material man. But if the king was to insist, then he should order his servants to get a chess board.
‘A chess board?’ asked the king. ‘Whatever for?’
‘My lord,’ said the courtier, ‘please arrange for your servants to place one grain of rice on the first square of the chess board, two on the next, four on the one next to it, and so on, each time doubling the number of grains placed on the previous square. At the end of the exercise, if you could arrange for the total rice on the chess board to be transported to my house, I would be most grateful.’
The king looked doubtful. ‘Is that all you want? Are you certain I could not give you a better present?’
The courtier smiled and shook his head.
Only after the king began the process that the courtier had laid out did he realize his folly. The numbers started innocuously enough: 2, 4, 6, 8, 16, 32, 64… but soon they began to swell. By the time they reached the twentieth square, they had to place 1048576 grains on it. At the twenty-fourth square, the royal granary had to be emptied. For a sense of perspective, the total number of grains that the king would have had to give the courtier if he had followed through the task to completion would exceed the number of electrons in the known universe.
Human beings are linear thinkers. When we look into the future or at the past, we tend to project from our present situations backwards, in a linear fashion.
Is this always a problem? No. Many of life’s situations are linear, so it works well. If you need two handfuls of grain to feed one adult, you will most likely need four handfuls to feed two, and six to feed three. If one acre of land yields two tonnes of rice, two acres of the same land will probably yield four. If one cow gave one litre of milk per day, two cows will probably give two.
Unfortunately, the real world doesn’t work on a linear path. There are many social constructs that we’ve set up that refuse to be restricted by a straight line. The most common of these is money.
Here are two quotes by Albert Bartlett, an American Professor of Physics:
The greatest shortcoming of the human race is its inability to understand the exponential function.
And on growth:
We must realize that growth is but an adolescent phase of life which stops when physical maturity is reached. If growth continues in the period of maturity it is called obesity or cancer.
Some examples from the world of money
- It’s common to hear economists and politicians say that a country has been ‘steadily’ growing at a rate of x%. That gives us, the listeners, the impression that the growth rate is constant. In our minds, we picture a straight line. But in reality, a ‘steady’ growth of x% is not linear. It’s an exponential function. Like the grains on the chess board in our story, it requires exponentially more resources to maintain the same percentage level of growth.
- Our lives run n the principle that more is good. If one car makes us twice as happy, we reason that buying a second car will make us four times as happy, and so on. If one house gives us a certain amount of pleasure, our second house should bring us twice that amount, and our third three times that amount and so on. But human happiness is not a linear function. As Maslow said, more is good only until the point at which our basic needs are met. From then on, more brings less and less happiness.
- We underestimate the power of compound interest. We think small savings will not add up to much in the long run, and we think that small loans don’t matter. We think that 100 rupees saved over 12 months equals 1200 rupees, whereas in reality it equals 1257 rupees (at 8.75%). Even our debts blindside us for this very reason, because our mental calculations are all linear.
A few things we could do to conquer this bias
1. Understand that there is no such thing as continuous growth. The Earth’s natural resources are finite. Infinite growth – which our modern economics demand – cannot come from finite resources.
2. Consciously remind ourselves that more is not always better. After we’ve reached a certain stage in our economic lives, more is very often worse.
3. Take note of what Albert Einstein said: Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.
Over to you, now. How else do you think the exponential function trips us up? Do you have any more examples to add to the ones I posit above? What steps do you take to cover for this bias?
Image Courtesy: Independent