Pop-up ads and mechanised call centres may be annoying and faintly sinister, but they are whimsical delights compared with the technological cataclysm that some scientists believe could happen "around 2045". Known as the Singularity, it represents the moment when computers become so advanced that they "escape the limitations of the human brain", booting themselves into ever-higher levels of intelligence and rendering our current idea of humanity redundant. Taking his title from Emily Dickinson  a figure any computer might struggle to replicate  Appleyard argues that the human mind can't be quite so easily captured as the techno-moguls like to think. The range and pace of his book are at times dizzying, drawing Cheryl Cole, Bill Gates and CS Lewis, among others, into an alarming survey of the computer age's immersive power. Appleyard enjoys playing Morpheus in The Matrix, plying the reader with red pills and leading them to see beyond the joys of "unboxing" their latest gadget. It's fitting, however, that a book that dissects the modern obsession with connectivity and information leaves your circuits a bit overloaded.

"A carrot is a carrot, and nothing more is known." These words, from a dying Chekhov, are quoted by Bryan Appleyard in this pop-science book which aims to uncover the hidden link between robots, the 2008 financial crash, Cheryl Cole and almost everything else. The Russian writer was talking about the futility of pondering the meaning of life, and Appleyard uses the quote to say that breaking something down doesn't always help define it. Consciousness can't be reduced entirely to brain goo, however closely we study MRI scans; and computer-modelling the atoms of a carrot won't help when it comes to gardening.

This, roughly speaking, is complexity. Chaos theory means it's hard to forecast the weather because of butterflies in Tokyo, but complexity theory says that even if we had all the information about everything in the world, it would still be impossible because emergent properties  such as the consciousness that emerges from the brain  can't always be deduced from the underlying data. And complexity isn't the same as complication: our planet is complex, with systems and cycles that interlock; a bad film is complicated because its parts don't cohere.

The author goes on to say that a complex world demands complex thinking, and that we are simplifying things with moronic celeb culture, tweets, texts, online profiles, automatic telephone prompts and the kind of financial thinking that resulted in the 2008 crash. He repeatedly says we are becoming more like machines  but that's when he strays away from science and into hyperbole, describing MRI scans as an "assault on the self", pacemakers as "a form of cyborgism", and Tiger Woods's "robotic" TV apology two years ago as his "software for the day".

Appleyard, a feature writer for the Sunday Times, backs up his frightening vision with research from recent books about technology, and includes interviews with artsy types such as Aaron Sorkin and Marilynne Robinson as well as scientists and programmers. The picture is persuasive in its broad sweeps but confusing in its details: it's never properly explained, for example, why David Hockney's iPad art is complex, and therefore good, when computer games are labelled as simple and therefore bad. What we're left with is a guiding principle that's basic enough to trip up on its own logic: simple isn't always best.