If you are super-confused about what all the coin-tossing and yarrow stalks in this book is about, you've come to the right place. Because, before we can talk about the I Ching as a symbol, we've got to talk about what it is. Man in the High Castle does a pretty good job of telling us what the I Ching is, but in case you got distracted by the whole "Nazis winning World War II" thing, here's a short reminder.
What It Is
It's an old Chinese book that is used for fortunetelling. That's the basics and that's all we feel comfortable talking about; like, we're not going to get into the question of how old it is, since some stories say it's from 3000 BC and some evidence shows the oldest manuscript is from 475 BC. So, there's just a little disagreement there.
But here's what people agree on about what it is and how to use it: the I Ching contains 64 symbols (called hexagrams); each hexagram is made up of six lines—or, depending on your point of view, made up of two trigrams (which are themselves made up of three lines). A line is either unbroken (a Yang line) or broken (a Yin line). And, on top of that, a line is either fixed-static or moving. A moving line switches between Yang and Yin and carries a special message. To get each line, you do something to get a random answer, like tossing coins, with each coin toss telling you if you've got an unbroken or broken line, and whether that line is fixed or moving. Once you figure out which hexagram you have, you can turn to the I Ching itself to read what the hexagram means, as well as any commentary that might come with that hexagram. (For a video example, check out this.)
Ready for an example from the book? In Chapter Four, Frank asks the I Ching if he should go into business with Ed and he gets these lines
The bottom line was a Seven, and so was the second and then the third. […] Then line Four, an eight. Yin. And line Five, also eight, a yin line. […] He threw the three coins.
Yin. A six. It was Peace. (4.47-8)
If we were going to draw that hexagram, it would look like this. But if you were ever confused why both 6 and 8 were yin lines, that's because 6 is one of those darn moving lines. Which is why Frank first reads the judgment of this hexagram, and then reads the extra message of that moving line.
So What's the Symbolism?
The I Ching is a Chinese book brought by Japanese immigrants and adopted by a Jew and some Americans. Childan makes this point when he's at his most racist. The Japanese may have brought the I Ching to America after the war, but it was originally a Chinese book (7.87). For Childan, this is just proof that (ugh) "Only the white races endowed with creativity" (7.88). (Childan makes that statement even after just noting that the I Ching was Chinese—he's not going to let a little self-contradiction get in the way of his racism.)
But for us, we can see that the I Ching isn't being "forced down our throats," as Childan claims. Rather, a bunch of people use the I Ching of their own free will: Hawthorne Abendsen, Frank and Juliana Frink, Tagomi. So the I Ching doesn't seem like a symbol of imperialism, as Childan thinks of it. It's more like a symbol of cultural borrowing and exchange. Leave it to Childan to be upset over sharing.
The Interconnectedness of All Things
The I Ching is one element that keeps reappearing in every story line. Frank uses it in the art plot, Tagomi uses it in the spy plot, and Juliana uses it in the art-spy plot. There are even times when different people get almost the same fortune from the I Ching. For instance, Tagomi gets hexagram 47 with no moving lines, and only a few paragraphs later, Frank Frink gets the same hexagram, only with one moving line (6.244-248). Dick puts those two hexagrams really close together, so it's easy to see how the I Ching pops up all over the book.
But the people who use the Oracle also talk about it explicitly as tying all these things together. Almost the first time we see the I Ching, Frank tells us that the hexagram he get is:
Random, and yet rooted in the moment in which he lived, in which his life was bound up with all other lives and particles in the universe […]
He, Juliana, the factory on Gough Street, the Trade Missions that ruled, the exploration of the planets, the billion chemical heaps in Africa that were now not even corpses, the aspirations of the thousands around him in the shanty warrens of San Francisco, the mad creatures in Berlin with their calm faces and manic plans—all connected in this moment of casting the yarrow stalks to select the exact wisdom appropriate in a book begun in the thirtieth century B.C. (1.72)
This might seem like a real cosmic vision, dude. Correction: this is a real cosmic vision, seeing all of life's separate particulars as part of one big situation. As Tedeki explains to Baynes, this sort of vision can give one "an external frame of reference" (12.222) on one's own life because it gives one a historical view.
History and Fate—Both Cosmic and Personal
So, lastly, the I Ching is a symbol seriously tied to the themes of fate and history. In The Man in the High Castle, the I Ching may tell one's future or one's role in the universe. And it can tell one if one should go into business or other less cosmic questions like that. (We've never used it to help us write a paper, but it might be helpful there.) For more on this, check the "Fate" and "History" themes.