Debt & the magical mathematics of Brahmagupta

7th March 2015

Author: George Cooper

At Equitile we believe it is impossible to understand either macroeconomics or financial markets without first understanding the role of money and debt in the economic system. It would not be an overstatement to say we are obsessed with debt. For those with the time to spare Andrew’s recent book Debtonator and my own Origin of Financial Crises discuss our thoughts on the role of debt in society and the financial markets. For those wanting a quicker, slightly light hearted, explanation of the linkages between money, debt, financial instability and economic growth the following may be of interest:

(A light hearted look at the darker side of money)

Today few people in the West know of the 7th century Indian mathematician and astronomer Brahmagupta. This is a pity because he has a fair claim to have made the most important discovery in the history of mathematics.

Brahmagupta discovered nothing. More specifically he was the first mathematician to recognize the significance of zero – that it was a distinct number in its own right. Brahmagupta did not stop at nothing, he also saw that zero could be split into two equal but opposite components.

Zero, according to Brahmagupta, was the number which resulted from adding any number to its negative partner.

Zero is the sum of five and minus five, fifty and minus fifty, or of any arbitrarily large number and its negative partner.

Zero = X – X

This insight allowed Brahmagupta to become the first person to understand how to calculate with negative numbers. Today most of the rules laid out by Brahmagupta for calculating with zero and negatives still form the bedrock of modern mathematics. (He struggled a bit with infinities and with dividing by zero – an area which still causes problems for some today).

Brahmagupta’s conceptual trick, splitting nothing into two equal but opposite components, continues helping us make sense of the world in surprising ways. On the biggest of all scales cosmologists use it as a way to conceptualize how the universe was created from nothing, in the big bang, and may one day return to nothing, in a big crunch. On the smallest scale particle physicists use Brahmagupta’s idea to explain how matter is created from nothing. Particles, we now know, can be created from nothing provided they are created together with their equal and opposite anti-particles.

Scientists at the CERN particle collider now routinely create particles and their anti-particles – electrons and positrons for example – which they then collide together at speeds approaching that of light in order to create even more exotic particles.

The very high speeds of these collisions are necessary in order to provide the huge amounts of energy required to generate the mass of the newly formed particles and their anti-particles. Much of the energy of these collisions is, converted into the mass of the resulting particle-pairs according to Einstein’s famous E=MC2 formula. Energy is consumed when particles are created and then released again when the particles and anti-particles eventually recombine to annihilate one another.

Surprising as it may sound Brahmagupta’s mathematics and the process of creating matter and anti-matter can help us think more clearly about the workings of our modern monetary system. It may even help us understand where macroeconomic policy is going wrong.

The connection between the mathematics of zero and that of finance becomes apparent when one looks at the language originally used by Brahmagupta to describe his mathematical laws. The following are three examples of his laws:

A debt minus zero is a debt.

A fortune minus zero is a fortune.

A fortune subtracted from zero is a debt

Note that Brahmagupta choses to call his positive numbers fortunes and his negative numbers debts. He recognized, as do modern day accountants, that the combination of a fortune with an equally sized debt was exactly zero.

Recognizing that equally sized fortunes and debts sum to zero and therefore can be created from zero is the key to demystifying our banking and monetary system.

It is often said that banks have the power to create money from thin air and that this is the source of their fantastic profits. Although this is true it is, quite literally, only half of the story.

The scientists at CERN can create matter from nothing only if they also create its offsetting opposite anti-matter. Similarly banks are only able to create money from thin air provided they create, at the same time, the offsetting opposite amount of anti-money, otherwise known as debt.

In short our modern banks are the particle accelerators of the financial system. They conjure money and anti-money, fortunes and debts, from nothing.

It is informative to extend this analogy a little further. When particles and anti-particles are created from nothing energy is ‘consumed’ and when they later recombine to annihilate one another this energy is then re-released. There is an analogous, though opposite, process of energy capture and release associated with the creation and destruction of money and debt.

When a bank makes a loan it splits zero into a fortune (money) and its equivalent debt. This process releases new spending power into the economy producing a burst of economic energy. Conversely when, at a later date, the money is recombined to annihilate the debt, both money and debt vanish and an equivalent amount of spending power, economic energy, is withdrawn from the economy.

At any given time, if the amount of credit being created roughly balances with the amount being destroyed the spending power within the economy will remain roughly constant and the economy will be stable. On the other hand, if there is an imbalance between credit creation and credit destruction the economy will be unstable. An excess of credit creation – new money and new debt – will amplify economic activity. Conversely an excess of credit destruction – repaying old debts – will attenuate economic activity.

From the remorseless logic of Brahmagupta’s mathematics it follows, any economic boom generated by high levels of debt creation will have the seeds of its own destruction within it. These credit-creation fuelled booms will inevitably lead to their partner, a credit-destruction driven bust – otherwise known as a debt deflation cycle.

This simple way of thinking about how our monetary and banking system works helps explain what has gone wrong with monetary policy over recent years.

People are generally more confident when the economy is stable and growing. And as a rule people are more willing to borrow when they are confident. Therefore when times are good both borrowing and spending rises creating a self-reinforcing boost to economic activity. The process of borrowing and spending becomes a self-fulfilling, positive feedback loop. The more we spend the more we borrow, the more we spend. Put differently there is a paradox of gluttony whereby the more we consume the more we can consume.

Unfortunately this process also works in the opposite direction. If confidence falls we begin to reduce our borrowing levels by paying down previously accumulated debts. This removes spending power from the economy thereby reducing economic activity, providing a self-ratifying justification for the original fall in confidence. This is Keynes’s famous self-reinforcing paradox of thrift – the less we spend the less we have to spend.

These self-reinforcing credit expansions and contractions are what the American Economist Hyman Minsky described in his financial instability hypothesis. The moment at which we flip from a credit expansion phase to a credit contraction phase is the now famous Minsky-Moment. Alternatively these are the same credit cycles described by the Austrian school of economics. Unfortunately these cycles are not part of mainstream economic thinking which continues, erroneously, to believe the economy is a naturally self-stabilizing system.

Unfortunately there is a troublesome interaction between these credit cycles and the political cycle.

We tend to be more content during periods of robust economic growth and more discontent during periods of weaker growth. Naturally we are also inclined to re-elect the incumbent government when we are content and disinclined to do so when discontent. This voting pattern produces a powerful incentive for governments to adopt policies designed encourage credit expansion, especially ahead of an election.

Our own voting patterns have trained our political leaders, like Pavlov’s dog, to seek a relentless but ultimately unsustainable credit expansion. However, when policy makers seek to engineer an economic boost through credit expansion they are also, due to the mathematics of Brahmagupta, engineering a future economic slump. This helps us understand where the deflationary forces currently taking hold in the Eurozone have come from. These are, in large part, the inevitable consequence of previous monetary policy designed to engineer credit expansion.

The next time you see the term ‘Money Supply Growth’ it may be worth pausing for a moment to reflect on the ideas of an obscure 7th century Indian mathematician and think instead of the term ‘Debt Supply Growth’.


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