The first two sections of Ulysses are by no means easy, but this one steps it up a notch. First of all, Don't Panic! Later parts of the book again become easier, and you can't be expected to get too much out of "Proteus" on a first or even a second read.
First, let's reflect on how far we've come. What makes the first two sections of Ulysses difficult is the sudden un-announced turn, a few pages in, to Stephen's stream-of-consciousness. There isn't any introductory phrase announcing this as interior monologue, e.g. "And then Stephen thought, in a free-wheeling manner based largely upon puns..." As a result, it is hard to distinguish the dialogue and the action of the scene from Stephen's own interior thoughts.
But this isn't just difficulty for the sake of difficulty. Think of it this way. Your girlfriend or boyfriend just broke up with you and you have coffee. Afterward you are trying to determine whether or not they seemed happy. You're trying to be objective about it, but you can't help emphasizing certain things about the scene as a result of your subjective prejudice. Since your ex is supposed to be sorry that they left you and secretly sad, you project your desire to have them seem sad onto the scene and imagine, for instance, a little bit of sadness in their voice that may or may not be there. You have trouble distinguishing the external world – what's actually out there – from the internal world – what's just going on in your head.
This may be a silly example, but knowing how self-absorbed Stephen is we can realize that he's constantly faced with the mad-rush of his own thoughts and external reality going on at the same time. In extreme cases, the two can become indistinguishable.
Now, in "Proteus," the trouble isn't determining the external from the internal or deciding who is talking because it's all Stephen. The difficulty now is just following his train of thought, which can often turn on references that the average reader doesn't know much about. Let's look at just the first paragraph as an example:
The opening: "Ineluctable modality of the visible" alludes to the Aristotelian idea that when we look at something, the thing itself is not part of what we see. We see just a pure form, but the substance – the thing out in the world – is entirely separate. According to Aristotle, this is different than sound, for example, because in sound some of the substance gets mixed up with the pure form in the process of hearing. Vision is unique, then, because what we perceive (the form) and what exists (the substance) are distinct.
When Stephen then thinks of "Signatures of all things" he is thinking of the philosophy of the German mystic Jakob Boehme who maintained that a thing can only be encountered through its opposite. For Stephen, this is tied to the first idea because, in the case of vision, form is opposed to substance. Thus, what Stephen is actually perceiving as he looks around Sandymount Strand is just a signature and not at all the thing itself. Again, the idea is that the world is different, perhaps only distantly related, to how we perceive it.
Stephen then goes on to think about Aristotle's ideas about transparence (the diaphane) and how transparency is something that is common in nature, and is not just a property of specific objects. Transparency is not just limited to things like water and glass; it is everywhere. But, Aristotle being a smart guy and all, he realized that we need a way to keep everything from being see-through. Thus, he suggested that transparency is limited by the color that exists in actual objects.
Stephen then thinks of the philosopher Bishop Berkeley and his theory that there is no such thing as matter, that nothing exists outside of one's own mind (solipsism). Stephen remembers how Aristotle refuted this by just hitting a material object (just like Samuel Johnson did). The basic idea being: "No such thing as matter! Ha! Look, I just kicked a stone and now my toes hurt! I refute you! There is such a thing as matter!"
Stephen then thinks about what is known of Aristotle's biography: that he was a blind millionaire. He goes on to quote a line from Dante in Italian saying that Aristotle was "the master of all those that know," and closes by thinking about the silly distinction that Samuel Johnson made between a gate and a door in his first English Dictionary. This again plays into Stephen's ideas about the distance between what we think of (gates and doors) and what actually exists out in the world (things that we classify neatly as gates and doors, but that may be gates or doors or something else entirely).
Stephen closes his eyes to see if he will still register evidence of the external world.
And that's the first paragraph. We take a deep breath and think of how to sum up the gist of all this in a single sentence. We might say, for example, that Stephen considers ancient ideas about solipsism and the existence of an external world, and wonders how the thoughts in his head relate to the world around him.
Point being: As you read, don't get panicked about all the references or the fact that you sometimes lose track of what's going on (very little happens in this chapter). Recognize that you can delight in the beauty and erudition of Joyce's prose without understanding every last little detail. Think of Stephen as the smartest professor you can imagine whose mind goes faster than the average mind and now he's wandering up and down the beach spitting thoughts in a disordered fashion at 100 miles per hour.
Here are a few of the big ideas you might be on the lookout for as you move through the chapter.
First, what is Proteus? In Greek mythology, Proteus is the shape-shifting son of Poseidon who has the power of prophecy. Menelaus, attempting to return home from the Trojan War, knew that one of the gods had a grudge against him and he wanted to find out which one. To do so, he had to pin down Proteus, who was a shape-shifter and took the form of beasts, water, and fire. But Menelaus held tight and Proteus gave him news of the difficult journey that Odysseus was trying to make home, and of the deaths of Ajax and Agamemnon. Menelaus recounts all of this to Telemachus in Book 4 of the Odyssey.
Here, Stephen's thoughts have a decidedly protean nature, constantly turning from one to the next. He tries to maintain a handle on them just as Menelaus tried to maintain a handle on Proteus, but he can't glance at anything along the beach without thinking of a dozen new references. Stephen's mind is so saturated with knowledge that he sees the whole world as being intertwined with language. Perhaps the key line of the chapter is: "These heavy sands are language tide and wind have silted here" (3.62).
We should note that, though Stephen's thoughts are hyper-abstract in the first part of this chapter, they gradually become more and more focused on the world around him – particularly when he sees the couple with the dog. Though still spinning out beautiful prose, his mind cools down toward the end of the chapter. It is at this point, during the cooling off period, that Stephen gets out of the abstract and becomes focused on the external world, that he actually writes his poem on the rock. After this, Stephen becomes even more a person "in the world" when we find him doing the very ordinary bodily business of going to pee and then picking his nose to make sure no one is watching.
Stephen's thoughts also wander back to his past, and we learn a few more details about his time in Paris with the exiled Irish nationalist Kevin Egan (whom Joyce lists as the Menelaus figure for this episode), and why he was called back to Ireland. This is where we get a real glimpse of Stephen's growing maturity. In Portrait, Stephen takes off for Paris with dreams of the great art that he will produce, and he seems to resent his family and his hometown. Yet, by interacting with Egan, Stephen found that the problems of Ireland followed him straight to Paris. Since Stephen had to return to Ireland as something of a failure, he was greatly humbled. Stephen now manages to joke about his early vanity and ambition. Though this makes him a much more tolerable character, it doesn't hide the fact that his mind is still aflame with something akin to literary genius.
We also get a real sense of how alone Stephen is in this chapter. He opens by thinking about solipsism, and is preoccupied with ideas about decay and images of the man that recently fell off a rock in the bay and was drowned. His thoughts occasionally slip back to his mother and the remorse he feels for not praying over her. Furthermore, when Stephen writes his poem, he realizes that he has no one to give it to and that there is no one to read it. Stephen's artistic ambition and his egotism have cut him off from people, and it does not help that he feels estranged from his father. In Paris, we see that the older Kevin Egan took Stephen under his wing (paralleling the Telemachus-Menelaus relationship in the Odyssey), but Egan was only a temporary surrogate father figure.
The next chapter turns to the actual Ulysses figure of Joyce's novel, Leopold Bloom, who will also become a sort of father figure for Stephen. Perhaps a good last-thought for Proteus is to muse, not only on Stephen's longing for a father, but on the ways that his brilliant intellectualism has not exactly done him a lot of good – it has isolated him from humanity.
What is that word known to all men? Answer: Love.