One of the strands of this debate is overt. It concerns the sorts of measures Gordon Brown announced in the Budget last week - tax incentives for small firms to carry out more R&D, extending first year capital allowances, offering relief on employer loans of computers, and so on. The principle underlying such measures is that growth requires investment. Investment builds the necessary capacity, and also embodies new technological developments.
These were just the latest measures by a government which clearly recognises the importance of science and technology. It is careful to avoid opening itself to the charge that it is picking winners - the ghost of the doomed Ministry of Technology, created in 1964 and fanning the "white heat of technology" for six years looms large. However, it has significantly increased its science budget, set about creating an environment that will encourage the commercial development of new ideas, and appointed in Lord Sainsbury a Minister for Science who is passionately interested in science.
The theory of economic growth has always recognised the importance of the amount of investment - both the "neoclassical" theory and the more recent "endogenous" growth theory. And there is a strong empirical correlation between the share of investment in GDP and the growth of GDP over the long term, although certainly not over the business cycle. The recent experience of South East Asian countries suggests over-investment is possible, but no country that has achieved big leaps forward in incomes per head, and basic measures of development such as mortality rates and literacy rates has done so without high levels of investment.
However, attempts to measure how much growth can be attributed to investment and how much to other causes has always found that by far the biggest chunk is the result of technological change - in reality, the bit left over after all the growth that can be assigned to higher levels of capital and more labour input has been accounted for. This motivated the modern growth theory, which tries to explain how technology moves forward as an economy grows, contributing to more growth.
A classic statement of this "endogenous" growth theory, set out in 1990 by Paul Romer, a US academic, incorporates a group of skilled workers who generate ideas. They - or their employers - need to earn a return on their ideas, requiring the protection of patent and copyright law.
For, once an idea exists, it is out there, free to copy without some legal protection. As Professor Danny Quah of the London School of Economics points out (in the latest journal of the Society of Business Economists), in our increasingly weightless economies, such protections are even more important, for more and more goods do not even get used up physically. Once a new medicine is injected it is used, so charging at the point of use is practicable. But software code or music is cheap and easy to copy; getting people to pay for it, and safeguarding the financial reward that keeps innovators producing new software or music, is tricky.
Sustaining the pace of technological innovation in the advanced economies is therefore something of a challenge. There are new difficulties on top of the age-old problem of encouraging innovation, using every means from improving the education system to creating incentives for enterprise; for it is becoming increasingly difficult to guarantee high enough rewards to sustain the pace of invention.
This takes us neatly back to the second, crucial strand of the current policy debate. And that is about the place of science in society. There is clearly a small-c conservative and romantic backlash against some of the scientific developments that will prove crucial in determining whether living standards in both advanced and developing countries can rise in the 21st century as they have in the 20th, and whether they can do it in a cleaner and less resource-intensive way. It is the first time in a generation that attitudes to scientific and technological innovation have been so polarised.
Rather than pretend to a magisterial objectivity on this debate, I should state that I am on the side of science and technology. Without advances in scientific knowledge and their embodiment in our everyday lives, we would all be poorer, unhealthier, would lose more of our children to illness, die younger - and, moreover, be more ground down and bored. Economic progress is about making human lives better in the most fundamental ways, and that does not happen without scientific progress.
However, there is clearly a big question about the role of the profit motive in the kinds of scientific advance we are seeing now. The returns to, say, genetic modification of food need to be high enough to encourage genuinely helpful technological advances. But they must not be so high that they either drive companies to cut corners on safety or even give the appearance of doing so.
There is a further issue, and that is the property rights inherent in weightless resources such as genetic code. Who owns the DNA of an Amazonian plant? The native people who live in the area? The Brazilian Government on behalf of all the Brazilian people? The rancher who owns the land? The multinational that decodes the plant material? Or is it part of the common human heritage?
We do not begin to have right answers to these questions from any standpoint, least of all that of maximising economic growth. But economics does indicate that some degree of private appropriation of profit will be necessary in order to trigger the scientific and technical development.
As the ferocity of the rows over our own development of GM foods and the rights of US multinationals to export such products to Europe indicates, the need for a debate has become urgent.