Will more money mean better care?

As such, he says, it is highly "resistant to change" - meaning that even big changes in investment may have little discernable effect.

While doctors and politicians have for decades likened the NHS to a "black hole", swallowing extra investment without trace, this represents the first attempt to explain why this might be so.

Mr Papadopoulos uses "complexity theory", a mathematical method used to try to predict the behaviour of highly complex systems.

In order to overcome the resistance, the government would have to spend much more - perhaps even double or treble the 50-odd billion a year they spend at the moment

Marios Papadopoulos, report author

The atmosphere is a good example of such a system - the laws of physics may help scientists reliably predict what will happen when one gas particle interacts with another - but these laws cannot be used to predict the weather.

The weather system is too complex simply because there are too many particles interacting with each other.

The NHS, says Mr Papadopoulos, is currently in a state called "edge of chaos" - neither ordered, nor completely chaotic.

In this state, even relatively large outside changes may produce only tiny changes to the system itself.

The surgeon's analysis looked at the Department of Health's own quarterly waiting list figures over a period of a few years, examining lists for general surgery, orthopaedics, and neurosurgery.

He says that despite extra investment pumped in following the NHS Plan, any changes in waiting lists were "fluctuations" rather than a discernable trend.

Hard to change

He told BBC News Online that this suggested that the NHS was in the "edge of chaos" bracket.

"This means that, in common with other complex systems in this state, it is highly resistant to change."

There are many reasons why the NHS may resist any attempts to make it run more efficiently or handle more patients.

If an extra consultant is added to a unit, for example, instead of treating more patients, GPs may simply start referring more frequently, or the consultants decide to spend more time with each individual patient.

Banning some consultants from private practice so they are tied to the NHS, he said, was also unlikely to have much effect, as waiting lists would "reorganise themselves" to remain at the same length.

"Chaos and complexity theory suggest that no matter how many managers are appointed they will be unable to enhance efficiency, and that increasing control and uniformity may shift the NHS from an efficient, self-organised critical system to a mediocre, highly-ordered one."

Underfunding

He said that decades of underspending by successive governments had pushed the NHS to "the edge of chaos", and that even a substantial injection of money would be unlikely to have much effect.

He said: "It won't be enough. In order to overcome the resistance, the government would have to spend much more - perhaps even double or treble the 50-odd billion a year they spend at the moment."

Waiting list falls

Other European health systems, he said, had been able to avoid moving towards this "edge of chaos" state by receiving reasonable levels of funding year on year.

The government is unlikely to agree with Mr Papdopoulos' assessment of their impact on waiting times since coming into office.

Health Secretary Alan Milburn is still confident that a three month maximum for heart bypass surgery is possible over the next few years.

However, long waits remain in some other specialties.