Thursday, November 05, 2009

Books, Hooke and economics

In an otherwise very entertaining article on historic books Miranda Devine makes the following statement;

Hooke accused Newton of commandeering his work, and as a result Newton wrote him out of Principia. Their rivalry probably drove both men to greater things but history only remembers one. Hooke was brilliant. He was also reportedly very short, covered in smallpox scars and crippled with scoliosis. No picture of him exists, and it is said the only portrait, housed at the Royal Society, disappeared when Newton became president.

It was in his last barbed letter to Hooke that Newton's most famous quote appears: "If I have seen further it is by standing on the shoulders of Giants." Newton's malicious point, biographers say, is that Hooke, being short, is not one of the giants to which Newton refers.

This is a witty portrayal of the relationship between Hooke and Newton, but errs in claiming that "history only remembers one". In fact, history remembers Hooke well, especially through Hooke's Law. This law is best known as stating that the force on a spring is proportional to the extent it is stretched. This has its most common application in a simple spring scales wherein a spring is stretched by a weight placed upon it and thus the force exerted can be assesed by how much the spring stretches (and relying on gravitational force being the same across the planet the mass can be derived).

The point at which the spring sits is an equilibrium of the force of gravity and the force of the spring. The law can then be used to calculate the oscillations that will be followed by a spring that is temporarily stretched beyond its equilibrium then released - it will oscillate around its equilibrium point though losses from various factors (heat loss in the spring, atmospheric resistance) will eventually bring the spring to rest at its equlibrium.

In fact Hooke's Law is probably one of the best examples for showing how the attempts by economists to create a science by mimicking physics has thus far failed. Economics abounds with analyses that will demonstrate the direction of a force. An economy or market subject to a "shock" can be shown to head in a cetain direction (price movements, quantity traded etc) to return to equilibrium. But nowhere does it explain in theory the magnitude of these forces.

To the extent that the economic forecasting "biz" does so, it does it on the basis of complex models that have been calibrated by understanding the path of correction in the past.

There are some further interesting consequences. For example, if you create a system of thre or more springs attached to one object on a plane surface so that no two springs are directly opposed, and displace the object so that it is no longer in equilibrium, the behaviour of the object can (I think) become chaotic within the mathematical meaning of the term.

Robert Hooke has only been forgotten by those who don't really want to understand science.


Vic N said...

The magnificent "In Our Time" did a great podcast on this recently.....

Vic N said...

and having just started economics in my MBA course...and loving it!!.....the Hookey comparison to price elasticity and equilibrium was interesting.....the forces only computed historically...