There's an extraordinary chapter in The Education of Henry Adams in which the author recounts his first encounter with the dynamo, the central piece of high technology displayed at the Paris Exposition of 1900. The chapter's title - "The Virgin and the Dynamo" - is an attempt to convey Adams's feeling that the 20th century would be as obsessed by electrical machines as the Middle Ages were by the Virgin Mary.

It was a fanciful notion, but not entirely wide of the mark, for the dynamo was what made our modern, electricity-based civilisation possible. The internet is its contemporary equivalent: it is the invention that threatens and promises to transform our future, and is just as awe-inspiring in its power and scope and potential.

But how can one convey this? A standard ploy is to quote the astonishing statistics of the thing. Nobody really knows how many people use the net, but the best estimates suggest a user population of about 300 million - equivalent to the combined populations of several major industrial nations. And while nobody knows how many web pages there are, last week one of the major search engines (Google) claimed to have indexed a billion.

The trouble with these stupefying statistics is that they do not adequately convey the scale of the phenomenon. What does it actually mean to have 300 million people online? Who can imagine such a thing? Immanuel Kant once observed that the capacity to "take in" great magnitudes is ultimately aesthetic, rather than purely logical. He illustrated this with a French general's account of how, on a visit to the great Pyramids, he was unsure about how truly to feel the emotional impact of their sheer enormity. Approach too close and you see only stone upon stone and miss the full sweep from base to apex; move too far away, on the other hand, and you lose the sense of awe that something so vast was constructed block by back-breaking block.

However, internet demographic data are discounted and adjusted, although we have long passed the point where it was sensible to conjecture that the thing might turn out to be the CB radio de nos jours. This is no passing fad, but a fundamental transformation of our communications environment. This is for real. We have hitched a ride on a rocket, and none of us has a clue where it's heading.

As such, asking whether the net is a good or a bad thing is a waste of time. People once asked similar rhetorical questions about electricity and the telephone. A much more interesting question is: what is the net? The conventional answer is that it's a "global network of computer networks", but there are several things wrong with this.

The first is the implication that the internet is some kind of global machine. Now, a machine is something that can be switched off. Could you switch off the net? Answer: only in principle. It would involve shutting down a large proportion of the most powerful computers on the planet.

The net is an obvious application of Metcalfe's Law (named after the inventor of the Ethernet networking system), which says that the power of a network increases as the square of the number of computers connected to it. In fact, the internet's burgeoning population of densely interconnected computers leads some people to ask whether this is something that is quali-tatively different from anything that has gone before. For example, in a provocative book, Darwin Among the Machines, George Dyson argues that, collectively, the networked computers that now surround us in their millions constitute a form of intelligent life - one that is evolving in ways we may never understand.

Dyson portrays the net as a globally networked, electronic, sentient being. The central thrust of his book is that the net is qualitatively different from other technological systems such as the electricity grid. He thinks it might have "emergent" behaviours that we do not (cannot?) anticipate - that is to say, behaviours that cannot be predicted through analysis at any level simpler than that of the system as a whole. In a way, this is just an extension of the view that what we call "intelligence" is really an emergent property of another densely interconnected entity - the human brain. Although simple in comparison with the brain, it is possible that, one day, the internet's intricately interrelated systems will produce new forms of artificial intelligence.

But you don't need to resort to speculation of this sort to explain why the net is different from anything we've seen before. Because the conventional definition of it as a global network of computer networks contains an elementary schoolboy mistake: it makes no mention of people.

The net is really a system that links a vast number of computers and people, and it is the people who make it really interesting. They use it for many things that human beings like to do, but mostly they use the net to communicate. And it is the phenomenon of hundreds of millions of people communicating via such an efficient and uncensored medium that gives the net its special character - and its extraordinary power.

Howard Rheingold, who is the nearest thing cyberspace has to an elder statesman, maintains that, essentially, people use the network in two ways: for entertainment and information; and to form what he calls "virtual communities". Anybody who has spent time on the net knows of the extraordinary opportunities it provides for reaching out and helping others. "Here are a few people to talk to about the menace of cyberspace," fumes Rheingold, with heavy irony: "the Alzheimer's caregiver afraid to leave the house who dials in nightly to a support group; the bright student in a one-room Saskatchewan school house researching a paper four hours from the nearest library; the suicidally depressed gay teenager; Aids patients sharing the latest treatment information; political activists using the net to report, persuade, inform; and the disabled, ill and elderly, whose minds are alive but who can't leave their beds. For them and for potentially millions of others like them, cyberspace is not just a lifeline, it can be better than the offline world."

The coherence of the net is sometimes its most surprising quality. After all, it has no central authority; no body determines who can join it and under what conditions. Anyone can hook up a computer to the net. The thing is unimaginably complex - and yet it works astonishingly well, passing enormous volumes of data every day with remarkable reliability. It is an example of a self-organising system, of something where there is order without control.

Whenever I think about the net, what comes to mind is a line from W B Yeats's poem "Easter 1916" - "A terrible beauty is born". It was his metaphor for the resurgence of Irish nationalism, which followed the armed uprising against British rule at Easter of that year. In military and ideological terms, the insurrection was a fiasco, but the clumsy execution of the rebel leaders stirred some deep instinct in the Irish people that finally led them to throw off the colonial yoke. It was this awakening that Yeats sought to capture in his famous phrase - it expressed the perception that a genie had been released from a bottle.

Similarly with the net. A force of unimaginable power is loose in our world, and we are as yet barely aware of it. It is already changing the way we communicate, work, trade, entertain and learn; soon it will transform the way we live and earn. Perhaps it will even change the way we think. It will undermine established industries and create new ones. It challenges traditional notions of sovereignty and makes a mockery of national frontiers. It accelerates the rate of technological change to the point where even those who ride the crest of the wave complain of "change fatigue".

In its conjunction of the words "terrible" and "beauty", Yeats's phrase has a strange ambiguity. His critics focus on the noun and read into it the glorification of blood-soaked Irish nationalism, the ideology that found its modern expression in the terrorism of the IRA. But the adjective is equally plangent. It implies that there was something awe-inspiring, as well as terrifying, in the sleeping giant awoken by the British.

Much the same might be said about the net. Like all powerful technologies, it has an immense capacity for good and evil. It gives freedom of speech its biggest boost since the US Constitution got its First Amendment; but, by the same token, it gives racists, paedophiles and pornographers a distribution system beyond their wildest dreams. The liberty it allows me to live and work almost anywhere is the upside of the freedom it gives employers to lay off office staff and contract out their duties to teleworkers on the other side of the world. The net enables us to create virtual communities of geographically dispersed people with common interests; but the industries it supplants once supported real communities of people living in close proximity to one another.

The truth is that the net is wonderful in what it can do for us, and terrifying in what it might do to us. Yeats got it just about right: a terrible beauty has been born.

John Naughton leads the Open University's "Going Digital" project and is a Fellow of Wolfson College, Cambridge. A Brief History of the Future: the origins of the internet, his book on the significance of the internet, is published by Weidenfeld & Nicolson