Edition: New English Library, 1981
Review number: 576
As Heinlein got older, his books became more self-indulgent; Number of the Beast is interesting when tracing his development as a writer because it marks out the particular ways in which that would become manifest, though there are traces of it in some of his earlier writing. It is easy to criticise this book, which only hangs together very loosely, but it is still in the main an enjoyable read and has some interesting features.
Jacob Burroughs is an engineer and physicist who has created a time machine, which also allows access to a multitude of alternate universes as called for by his theory of time and space (in which there are three time co-ordinates to match the three spatial ones). Enemies - aliens already familiar with this mechanism - discredit his work and then try to kill him, and he only escapes with his family by the skin of his teeth.
Making Jacob the centre of the story is convenient for summarising how it begins, but he is not the dominant character of the novel. The four members of his family are all more or less equally important for most of it, though his wife Hilda gradually occupies the spotlight more and more of the time.
Though the arch style in which the first part is told is frequently annoying - occasionally it is as amusing as it is intended to be - the real self indulgence only become apparent when Heinlein begins to chronicle the other universes to where his central characters travel. Without justification (and that is important in science fiction), he makes these universes worlds which are described in the fiction of the Burroughs' home universe, and so they include Oz, Lilliput, Camelot and various pieces of science fiction. Then, in the third part, the universe is that of much of Heinlein's own writing: they meet characters from others of his novels, most importantly Lazarus Long, a long term favourite of the author.
It is from this point that the novel really begins to fall apart, until it ends on an incoherent note at a vast conference attended by delegates from an incredible number of fictional universes. Having many characters from other Heinlein novels does not really help matters, as it merely emphasises how few different ones he was capable of creating.
It is possible to criticise the physics behind the novel, even from a pre-string theory point of view. Burroughs' model of the universe has six co-ordinates, of which four are experienced at a time (three spatial, one temporal). He is able to rotate relative to these, and so for example experience duration on what is normally a spatial co-ordinate. The time axis is different from the others. It has a direction associated with it and, assuming some variant of big bang theory to hold, a minimal value. Neither of these properties holds for the spatial co-ordinates, and this makes a transformation which turns one into the other rather suspect. The original motivation for the idea of six co-ordinates is that there shouldn't be an asymmetry between the number of spatial and the number of temporal co-ordinates. However, this asymmetry is no sooner removed than it is re-introduced, as it is pointed out that we only experience one temporal dimension at a time, even though we see three spatial ones.
Another problem may only lie in the way that things are explained. Heinlein uses the system as though the co-ordinates for the universes need to be what is called orthogonal - at right angles to one another. This is not the case; they only need to be linearly independent - none of them able to be made up as combinations of the others - to ensure that six co-ordinates can pick out any point. There is also no particular direction which is more important than any of the others; we only tend to think automatically in the (approximately) orthogonal set up, left and forwards because we live oriented by a gravitiational field (so up and down make sense).
There are other, less critical errors: Heinlein seems to have misunderstood Cantor's set theory so much that he really should not have used it, for example.
I suspect that for many the annoyances in The Number of the Beast will outweigh its merits, but I still find it enjoyable, one of those books to which I return when I am ill or tired.