Richard Melson

July 2006

Entropy: Islamic Finance

http://www.islamic-finance.com/item3_f.htm

'Entropy' is a term that is used to represent the amount of disorder in a physical system. When physicists say that 'entropy is increasing' they are describing the tendency of all physical systems towards greater disorder, a tendency that is encapsulated in the first two laws of thermodynamics. Together these laws indicate that, as time passes, a closed system incurs a constant total of energy, but that the distribution of such energy becomes more even. Though entropy is always increasing, its rate of increase varies from one system to the next. Fruit rots within a matter of days once picked, buildings become dilapidated within a matter of years if unattended and minerals in the earth's crust remain for millennia with little sign of deterioration.

Whilst the entropic process distinguishes itself as an irrevocable and qualitative process that represents decay, to say that entropy increases irrevocably is not the same as saying that the effects of the entropy process cannot be reversed. By consuming energy from the external environment, a physical system may halt or reverse its tendency towards greater disorder. The plant consumes energy and nutrients from the external physical system that is the environment. In this manner the plant creates a highly ordered structure - fruit. Similarly, the repair men consume energy and materials in maintaining the building. However, precisely because of the consumption of external matter and energy in these processes, entropy in the external physical system will increase. In evidence of this fact, land becomes less fertile as crops grow and workmen's tools wear out in the process of construction. As a result of such processes, the net amount of entropy must increase and thereby the entropy law remains valid.

It was Schrodinger who first proposed that any life bearing structure maintains itself by consuming low entropy from the environment and transforming it into higher entropy. Given that average entropy in a physical system is always increasing at a natural rate, it must be true that man's activity, in establishing lower degrees of entropy in some components of his physical environment, inevitably accelerates the increase of entropy in other components.

Georgescu-Roegen in the Entropy Law and the Economic System (1971) develops this idea and informs us that, on the physical level, the observable purpose of man's activity in increasing entropy is to enhance the quality of his existence.

To put it bluntly, low entropy resources are transformed into high entropy waste plus the enjoyment of life.

The entropy process dominates almost every facet of the economic process. If we are then to ignore it in our economic analysis, we are doomed to failure before we begin.

Early classical models of physics, developed by Newton and applied so successfully to the world of machines and mechanical processes, inspired economists to seek similar mechanical descriptions within their own field of endeavour. However, mechanical processes are by nature revocable. A ball can be picked up if dropped. Today, such mechanical ideas are dominant in economic analysis. Meanwhile, the entropy law, when applied to the economic process, involves an irrevocable uni-directional flow from low entropy resource to high entropy waste. Such a concept opposes the classical mechanical view of revocability in economic processes, and the circular flow arguments used by modern economists to describe economic activity.

Much modern analysis treats the economic system in a mechanical way that assumes change to be revocable, or in some formula bound way that assumes a determinate process.

In criticism of this approach, Marshall comments in Principles of Economics :
'...biology, not mechanics, is the true Mecca of the economist'

We must accept that our economic activity does not take place in a closed physical system. Even on a global scale we receive low entropy energy from the Sun daily, and free of charge. This very fact makes our land valuable and productive and allows humans to live, but rarely does it appear in econometric models.

The impact of sunlight upon the earth is that of the external input of energy into a physical system that we reviewed earlier. With this idea in mind, it becomes increasingly obvious that it is the free energy of the sun that must in some form or other be consumed in order to combat the increase of entropy in earth bound structures and allow the enjoyment of life to proceed. For example, it is the sunlight of past millennia that allows man to increase his enjoyment of life through the burning of coal. It is the sunlight of the present that allows him to grow crops and experience the seasons.

If society aims for higher levels of enjoyment, it may do so by consuming greater amounts of past sunlight, or catching present sunlight in a more efficient way. Each approach will inevitably result in an increase of entropy in the system that is comprised of Sun and earth, but the effects of that increased entropy are to be seen in different places. Few on earth care for the higher entropy that results in the Sun as it converts hydrogen into helium. Far more of us care for global warming as coal is burnt to fire our power stations. Here in a nutshell is the environmental choice that faces our modern world. It is a choice that pits sustainable development against un-sustainable development, renewable resource against non-renewable resource.

The Guardian leader page from March 25th. 1995 comments :

Global warming is, above all, an index of the rate at which the world squanders its resources and of the resulting disturbance to natural ecological balances maintained for millions of years. No one can seriously deny that energy is now being consumed on a scale never achieved by humanity before. The only question - and it is the critical one - is whether it can be stopped and how.

I contend that fresh air, clean rivers and a stable climate have a high priority in society's hierarchy of wants, but that society may not fully realise their value until they have been lost for ever. If such a gloomy outcome does materialise it will be in part due to the striving of mankind to supplement a flow of sunlight energy that is now deemed insufficient to meet his requirements for the enjoyment of life. As decades pass, the entropic consequences of this new avarice grow ever clearer.

My proposition is that the conventions of the modern interest based financial system ignore the fact of entropy in the physical system. In so doing, such conventions may actually encourage entropy to increase faster in our environment. Elsewhere on this web site, I have illustrated this phenomenon with a simple example from the world of discounted cash-flow analysis. One of the pertinent issues that arises from that illustration relates to the real interest rate, as follows.

In a simple barter economy, an individual would hold surplus wealth in the form of physical assets. Depending upon the nature of the asset, there is no way for such an individual to avoid certain costs related to the storage of that wealth. A further cost may arise over time since the quality of the stored assets will be subject to the fact that entropy is increasing. Of course the owner of such wealth may decide instead to lend it to an individual who wishes to engage in a productive process of some kind. The costs associated with holding those assets may not seem to be a disadvantage from a borrower's point of view if a profit can be made when, say, a borrowed ox ploughs a field. It is however important to consider exactly what kind of ox such a borrower must repay. Should it be the same ox that was borrowed, or should it be an ox equal in age and health to the one that first left the lender's farm?

In a modern interest based economy, 100 borrowed must be repaid to the sum of 100 plus interest. In so structuring our financial conventions we are effectively saying that an ox equal in age and health to the original must be repaid, plus interest. One flaw in such a convention is that the lender of the ox passes on, to the borrower, costs which he himself would otherwise have had to bear. 100 of money lent at interest does not obey the same law as the 100 of physical assets that such money must buy in order to fund the interest charge. As Frederick Soddy would put it, in the application of compound interest, a given monetary value can merrily march the path of geometric increment towards infinity. Due to increasing entropy, physical wealth follows the path of compound decrement toward, but never quite reaching, zero. The parallel within our barter economy is that whilst our financier may store his assets and find upon later inspection that they have deteriorated, in a loan transaction those very assets may exist for him merely as a non-depreciating entry on a loan document.

In Money versus Man (1933), Soddy comments:

'... the ruling passion of the age is to convert wealth into debt in order to derive a permanent future income from it - to convert wealth that perishes into debt that endures, debt that does not rot, costs nothing to maintain, and brings in perennial interest'.

If the stipulations of a compound interest money loan were applied to a loan of physical capital, then such would remain un-degraded throughout the life of a loan whilst at the same time generating new wealth. This new wealth in turn would not depreciate and would itself be expected to yield further wealth in sympathy with the compound process. Such a state of affairs would be wonderful were it attainable but, due to the entropy principle, it isn't. Perpetual wealth creation from a single stock of non-depreciating capital will remain impossible so long as the laws of thermodynamics hold true.

Abridged from The Problem With Interest

(Ta-Ha Publishers, London, 1997)

Islamic Finance: Interest & Entropy

July 14, 2006