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Narratives don't come much grander than the current scientific view of the history of the Universe - a 14 billion-year saga so far, with many billions more to come. Against that backdrop, the totality of human history is a brief span indeed. But for us, that infinitesimal interval is the really interesting part.

Any sketch that relates cosmic history to human affairs has to be organised around some concept that justifies devoting as much space to the last 4 million years, as this book does, as to the previous thousands of millions. The unifying concept here is complexity, a quality - it is hard to define it as a quantity - that has emerged in stages over cosmic history, and whose development is most marked under special, marginal conditions.

It seems, perhaps, a suspiciously convenient way of putting human beings at the centre of the story, as the human brain is the most complex object in the known Universe. But this is inescapable. More complex weavings of matter and energy may exist somewhere, but we have yet to encounter them. We are limited by our own vantage point, and by the great size and age of the Universe. Looking out is always looking back: the further we look, the older the information - limited by lightspeed - that we can receive. As Fred Spier puts it, "the closer we come to the present, the less we know about the universe at large".

University of Amsterdam lecturer Spier is one of a small band of exponents of big history, or maybe Big History, the effort to put the whole story together in an academically rigorous way. As he outlines here, it is an enterprise in the spirit of Alexander von Humboldt and Robert Chambers, 19th-century pioneers in trying to relate a natural history of the Universe. It is also familiar to contemporary readers of popular science, but has as yet only a few footholds in universities, and none as far as I know in Britain.

As outlined here, big history is a story stripped back to essentials. Complexity is sustained by flows of matter and energy. New forms of complexity are created in special conditions - Spier calls them "Goldilocks circumstances" - and sustained if the right conditions endure. Around these ideas, he organises a clear, broad-brush (very broad!) account taking in some familiar items. The Big Bang and the origins of matter, the formation of stars, galaxies and planets, the emergence of life, multicellular organisms, consciousness, language, society, culture and civilisation are all described in these terms.

The narrative is progressive, in its way, as complexity increases through a series of levels of organisation. But it does not depict progress as inevitable. The continual repetition that this or that development depended on Goldilocks circumstances begins to produce a feeling that this is a catch-all description, not an explanatory principle. But it does emphasise how complexity often demands unusual conditions whose continuation is highly contingent.

That in turn leads to a final chapter on the future, which is marked by contemporary concerns about whether the level of complexity our current society has attained is sustainable.

All in all, big history may be the academy's best hope for those who dream of consilience. As Spier says, "Big history integrates all the studies of the past into a novel and coherent perspective." A cosmic backdrop to Earthly affairs may induce a sense of humility. It also makes one appreciate how remarkable it is that the fragile parcel of evolved complexity between our ears, enduring for perhaps a hundred years, can contemplate the entire sweep of the Universe from which it arose. Either way, it would be good to see a place for big history in UK higher education.

Personally, I think everyone should have access to this story, and I would put it at the heart of the national curriculum as well. Perhaps UK education secretary Michael Gove, who one gathers has plans to reform history teaching in schools to convey more of a story, could put it on the agenda. But I fear that from this point of view, Mr Gove's notion of history is rather small.