What is power, and do academics have any? asks Susan Greenfield.

When I and seven other people drawn from business, public service, politics and the media started to compile a list of the 300 most powerful people in Britain for a recent Channel Four/Observer venture, academics were not in the front of anyone's mind. Broad categories in the initial papers directed our thinking towards the obvious monoliths of government, media and commerce. Science lurked as a sub-section of "culture".

But no one could really blame the production team. The critical issue is how you define power. Surely it does not automatically need an object but can be intransitive too - an intrinsic quality, like a well-developed muscle, or a six-litre engine, or indeed an agile and well-exercised brain wrestling unclaimed in a dark library corner with the nuances of a speech, a long-gone event or a persistent literary metaphor. Implicit in such power may well be a potential to influence someone or something, but whether or not this potential is realised does not detract from the power itself, unless the thought is lost. Yet because of the knee-jerk definition of power less as an intrinsic quality than as the overt ability to influence others, academics as a general class were non-starters.

The average academic's power extends to revising a core curriculum, thrashing out a new course or setting priorities for internal funding allocations. But these achievements are small beer compared with the sweep of influence on those directing the opinions, beliefs, spending and even the lives or deaths of millions. Given that professors of humanities, as well as vice-chancellors, made such a feeble mark, there must be some additional reason why scientists and economists, at any rate, should have made any kind of impression at all on the list.

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Economists have power of a sort in influencing world money markets. And we all know about scientists' power, or perceived abuse of it, as regards BSE, global warming and genetically engineered food. But in neither case is the power very serious. No scientist dictates government policy. No university economist issues daily instructions to a biddable Gordon Brown. We academic scientists and economists are supposed to have all the answers, and are therefore the ones to blame when things go wrong. But whereas the power of our politicians is normally balanced by law, we academic authorities have the worst of all worlds - all the responsibility without any power at all.

Even if power is defined merely in terms of fame, academics still would not feature. The lifestyle is hardly the stuff of dreams for those readily impressed by style pointers ranging from the Spice Girls to Alan Shearer. But if the ability to influence others is what counts, then academics may have much more power than the list suggested.

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At the initial discussion weekend, we panellists were each asked to present a film about an individual we personally perceived as powerful. I chose the mathematician Sir Roger Penrose specifically because his work was the most theoretical, the least directly related to obvious spheres of power.

The subjects of other films were either well known or marshalled millions of pounds. By contrast, my softly spoken and modest hero might have seemed an anticlimax. But as the ideas on space and time unfolded and were linked to the basics of brain function and human consciousness and as Stephen Hawking pressed home the message in his stark electronic voice that paradigm shifts in science were, though abstract, of untold future potential, a silence fell around our table. I was thrilled that the excitement and far-reaching implications of ideas were at least nudging at the accepted, here-today-gone-tomorrow, tinselly power of the political heavyweights.

My point is, and was, that the most powerful power is subterranean. "No one tells me how to make up my mind," protested one commissioner colleague. But surely the brain-washing techniques and education systems of the totalitarian regimes of this century testify to the most powerful vehicle for power - the human brain. Academics are far from being consciously in the business of indoctrination. But traditionally we do traffic in ideas, and ideas, once seeded, can influence action without anyone forcing the issue.

Perhaps our powerful power is slipping as the trend in the self-conscious, audit climate tips arguably more towards the swallowing of rote facts. Nonetheless, the advertisement in which celebrities name early mentors showing that "everyone remembers a good teacher" may make us pause in considering how and to whom to ascribe true power.

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So why does everyone, including academics, refuse to regard academics as powerful? First, the power is not directly and readily attributable. How much did Eric Anderson, for example, directly influence Tony Blair? And, before the advertisement, who would have known anyway? Second, there is a tendency nowadays for the national curriculum and hard-pressed, and increasingly vocationally oriented, university courses to emphasise mere facts at the expense of truly powerful, mind-stretching concepts. Third, academia is still perceived in terms of its clerical roots to admonish the materialistic real world, with its business card efficiency, and business-class travel, in favour of that scruffy, secular monk, the absent-minded professor, the very embodiment of abrogation of power.

The Power List was popular because it appealed to all ages and sectors of society from playground to factory floor to board room. For a while, when the programme was being advertised and aired, I was suddenly a lot more in demand at parties, with the Power List as the inevitable opening conversational gambit. And if that's not power - then at least it's show-biz.

Susan Greenfield is director of the Royal Institution.

ACADEMICS WHO APPEARED IN THE POWER LIST

(ranking in brackets)

Stephen Hawking, author of A Brief History of Time (68)

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Roger Penrose, quantum theorist (83)

Alec Jeffreys, geneticist (118)

Robert Winston, fertility expert (121)

Richard Doll, epidemiologist (122)

Steve Jones, geneticist (137)

Richard Peto, epidemiologist (140)

Richard Dawkins, author of The Selfish Gene (141)

Anthony Giddens, director of the LSE (156)

Colin Blakemore, professor of physiology (178)

* Academics who should have appeared: Keith Thomas former president of the British Academy

Owen Chadwick ecclesiastical historian

Max Beloff, historian and constitutional expert

Martha Nussbaum, philosopher

Amartya Sen, Nobel prize-winning economist

Derek Parfit, philosopher

John Bailey, literary critic

Simon Schama, historian and writer

Charles Handy, former professor, London Business School

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Brian Morris, former professor of English

(Suggestions by David Cannadine, director of the Institute of Historical Research; Marina Warner, cultural historian; Jonathan Glover, philosopher and director of King's College, London Centre of Medical Law and Ethics; Terence Hawkes, professor of English, University of Wales, Cardiff; and Cary Cooper, professor of clinical psychology at UMIST School of Management).