The irony of forgotten memory
Jack starts this novel as a symbol for dramatic irony itself, because his experience of reality is warped by syphilis; he is extremely plagued by amnesia but is chronically remembering important information as time goes on. This is dramatic irony, because the reader also does not know what Jack is capable of. In moments of clarity, he takes extreme and precise action because of his experiences, and even when his point of view is subjective or wrong, the action tends to improve his station in life.
The golden treasure lost
When the pirates obtain a ship smuggling what they thought was silver, it turns out to be gold. This is the archetypal discovery that every pirate longs for, but in this case, it turns into a liability and they are easily exploited. The irony is that they finally get what they always want without the means to exploit the treasure to their profit. Jack solves this irony for himself personally by improving his station until the same queen pirate who stole his treasure gives it back. He is ready for it then.
The rise to power
Jack's rise to power is ironic through and through. By the time he is a king in India, the reader has to do a double take. How did this person go from absolute chaos and slavery to being a king in India? The rise to power is a commentary on the capacity of a human being. He rises to power in a way that shows that fate has good fortune to bestow as well as bad fortune. The rise to power is balanced by Eliza's own unique rise to power.
Eliza's secret
Eliza has a secret that is essentially ironic. She knows that Jack was willing to kill out of his loyalty and love for her, but secretly she is like Helen of Troy. When life changes around Eliza, she is perfectly flexible and adaptive. Her secret is that she is emotionally ingratiating without loyalty; she exploits the sexual chemistry she has with other people, without feeling attachment toward them. By the end of this, she has also risen to power using this ethically dubious strategy. She is like a female Ulysses in terms of her wile.
Newton's dramatic irony
The ending of this book is a poignant irony for students of history. Isaac Newton is an alchemist and prophetic person in general who was already incredibly accomplished by the time Eliza makes his acquaintance. Newton elevates the drama of the book by suggesting an ultimate irony; he believes that secretly, a universal theory of reality could be derived. He is a religious mystic and a student of Hebrew, Greek, the theories of mysticism, and gnosticism, and he is a skillful alchemist and mathematician. The drama arises from the group around him who believes he is simply going insane. The irony is solved by the reader if they know the history of math; Newton goes on to discover the theory: it is what we now call Calculus. Leibniz also receives his due shout-out, because he also discovered the same theory on the same day.