When people talk about Byatt, they tend to dwell on her academicism, on her allusions and quotes, on her historicism. But if this were all there were to Byatt, no one would read her. What makes Byatt a wonderful writer is that she has a tremendous sense of how the world works, how situations and relationships that seemed promising slowly unravel, how smart people can do stupid things, and how things and people who at first seem hopeless can wind up being wonderful. She understands process, and she understands complexity.
Babel Tower is about how people devoted to the life of the mind can survive in a society which is hostile to that life. Much of the book is taken up with trials, because a major character in this book is "society", which may be personified by juries, by expert witnesses, by journalists. Her character, Frederica, escapes from a marriage which first stultifies her mind, and then threatens to kill her. On a meagre living, she constructs a life and a support system that will give her young son what he needs, mentally and physically. But her husband is wealthy, and what he offers the boy seems superficially more wholesome, so in the trials for divorce and custody, Frederica is judged essentially for her surface, for what her life looks like from the outside.
In a parallel subplot, the writer Jude Mason has written a book that is judged for obscenity. But Mason wrote it as a moral book which tells the lessons he has learned in life. He is a vagrant. He was sexually abused in childhood. He understands how people torture those they love. In the book's obscenity trial, Mason, his neuroses, his appearance, and his intentions are judged and condemned; when his book is banned, he himself is banned.
And in the early part of the book, we have a debate about how children should be educated, and what they should learn. The proponents of throwing out classical and grammatical training win, and it is a blow for the life of the mind. In the end of the book we see the results.
Babel Tower has several interesting themes: 1) the way society reduces and [clouds] a person's identity, and the effect it has on them; 2) depravity and sadism as an integral part of human nature, where cruelty is the backside to love; 3) gender and class double-standards; 4) the debate of what constitutes a good education; 5) the impossibility of creating coherency between the disparate elements of your life, and what this does to you.
Byatt is a wise, courageous thinker who can turn a battle of ideas into an enthralling page-turner. But her understanding of life is what makes her work great.
Babel Tower was a great book. But you should read its prequel first, Still Life.