Having finally read this book, I must say that I am at a loss to explain why so many people hate it. It's pretty much what it says on the box: Russell considers the impact of science on society, and, unsurprisingly, argues that that impact has had both positive and negative aspects. Perhaps critics are reacting to the tone, which, as usual with Russell, is disengaged and ironic; this despite the fact that he believes that what he is saying is desperately important to our continued survival, as a civilization and possibly as a species.
On the positive side of the balance sheet, Russell has two main items. First, and I think most importantly to him, he argues that a scientific world-view, based on observation and logic, is better than one based on revelation and authority. Russell is a philosopher who passionately loves Truth as an abstract virtue. He prefers a system in which people strive to discover Truth ahead of one in which they believe what authority figures (kings, priests, politicians) tell them to believe. Second, he makes the obvious point that technology developed through science, in particular modern medicine, has vastly decreased human suffering over the last few hundred years.
On the negative side, Russell pulls no punches when he describes how science can, and very often is, used as a tool of oppression. The more advanced technology becomes, the more it tends to concentrate power in the hands of a small elite. He makes reasonable projections about where this trend is likely to lead, and comes up with dismaying conclusions. Unless we can become less selfish, and develop a way to formulate and actually implement responsible global goals, we may not survive very much longer. Some people interpret this as arguing for the installation of a scientific world dictatorship, but I do not think the text supports that reading. Russell is simply saying that, if we don't get our act together and stop putting narrow partisan interests first, we are likely to destroy the planet. He explicitly says that he thinks the most likely outcome is that we will be unable to deviate from our current course, and that we will consequently choose death. Developments since the time of writing do not obviously invalidate his line of reasoning.
As already noted, Russell likes to be ironic, and it seems to me that some people are not properly appreciating this. Please read the following key passage and decide for yourself what you think Russell's opinions are concerning the indoctrination of citizens by their governments:
I think the subject which will be of most important politically is mass psychology. Mass psychology is, scientifically speaking, not a very advanced study, and so far its professors have not been in universities: they have been advertisers, politicians, and, above all, dictators. This study is immensely useful to practical men, whether they wish to become rich or to acquire the government. It is, of course, as a science, founded upon individual psychology, but hitherto it has employed rule-of-thumb methods which were based on a kind of intuitive common sense. Its importance has been enormously increased by the growth of modern methods of propaganda. Of these the most influential is what is called "education". Religion plays a part, though a diminishing one; the press, the cinema and the radio play an increasing part.
What is essential in mass psychology is the art of persuasion. If you compare a speech of Hitler's with a speech of (say) Edmund Burke, you will see what strides have been made in the art since the eighteenth century. What went wrong formerly was that people had read in books that man is a rational animal, and framed their arguments on this hypothesis. We now know that limelight and a brass band do more to persuade than can be done by the most elegant train of syllogisms. It may be hoped that in time anybody will be able to persuade anybody of anything if he can catch the patient young and is provided by the State with money and equipment.
This subject will make great strides when it is taken up by scientists under a scientific dictatorship. Anaxagoras maintained that snow is black, but no one believed him. The social psychologists of the future will have a number of classes of school children on whom they will try different methods of producing an unshakable conviction that snow is black. Various results will soon be arrived at. First, that the influence of home is obstructive. Second, that not much can be done unless indoctrination begins before the age of ten. Third, that verses set to music and repeatedly intoned are very effective. Fourth, that the opinion that snow is white must be held to display a morbid taste for eccentricity. But I anticipate. It is for future scientists to make these maxims precise and discover exactly how much it costs per head to make children believe that snow is black, and how much less it would cost to make them believe it is dark grey.
Although this science will be diligently studied, it will be rigidly confined to the governing class. The populance will not be allowed to know how its convictions were generated. When the technique has been perfected, every government that has been in charge of education for a generation will be able to control its subjects securely without the need of armies or policemen. As yet there is only one country which has succeeded in creating this politician's paradise.
Russell's book is short and still very topical. If you want to read it, there is an online version here