According to Greek legend, Zeus sent two eagles flying off in different directions to meet at the center or the navel – the omphalos – of the world. The idea of the world having a navel, and more specifically, of there being an umbilical cord that runs back through time to connect to that navel, is one that recurs throughout Ulysses. The omphalos idea is part of a bigger network of thoughts in the novel – all having to do with pregnancy, motherhood, and reproduction.
In "Proteus," Stephen thinks, "The cords of all link back, strandentwining cable of all flesh. That is why mystic monks. Will you be as gods? Gaze in your omphalos. Hello. Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one" (3.6).
Though brief, the thought is quite dense and complicated. First, Stephen thinks of mystic monks trying to have an experience of the world itself. The whole mystical idea (in a nutshell) is that there is a certain experience that cannot be put into words, and after you have that experience you realize that up until then your existence had been quite superficial. It is as if there is an ideal metaphysical (fancy philosophical word meaning having to do with the nature of existence) world that most of us do not have access to.
Sometimes, the mystical idea gets conflated with the notion of a simpler way of life, as if there was a time when man's existence was much more pure and in tune with the world. In Christianity, this is Eden before the fall of Adam. Now, Stephen thinks of himself as an over-educated guy staring into his navel (as the saying goes), but then imagines the umbilical cord as a telephone cord that will allow him to call back to Eden – this simpler way of life – using the Greek letters "Aleph, alpha: nought, nought, one."
Stephen's omphalos thought is only one of many images having to do with pregnancy, motherhood, and the female form. Think of the Dead Sea being compared to a vagina in "Lotus Eaters," or Mulligan joking about being pregnant in "Oxen of the Sun," or "Circe" where Bloom actually gives birth to eight children.
But to get to the crux of the matter: The book seems to suggest that there is a disconnect between the male and female experience of life. The disconnect mainly has to do with birth and the process of procreation. Whereas men simply have to donate their sperm and then are removed from the birthing process, women have to let the child grow inside their womb for nine months and then go through very painful labor before the child is born. The result is that women feel in touch with the reproduction process while men feel left out. In terms of bodily experience, the father is so removed from reproduction that it takes a great act of imagination for him to conceive of what it must be like to have a child.
So the idea is that men have to find some way to compensate for being left out of the creative process. Whereas Freud says that women are envious of men's penises, Joyce flips that around and says, "No, actually men are jealous of women's ability to give birth." This is all quite simplified, but let's simplify it further: women give birth; men write books.
In terms of symbolism and imagery, the result is that the creative process is compared to the gestation period a woman goes through as she prepares to give birth. This is nowhere as apparent as in "Oxen of the Sun," when all of the men are gathered at the maternity hospital waiting to hear news of Mina Purefoy giving birth. In the episode, Joyce stylistically re-enacts the development of the English language from direct translations of early Latinate prose up to modern Dublin slang. In the words of a drunken Stephen Dedalus, "In a woman's womb word is made flesh but in the spirit of the maker all flesh that passes becomes the word that shall not pass away" (14.21). Let's dub it fetus-envy.