Synchronicity
Synchronicity is the word that has been used to describe fateful alignments of random chance and personal expectation. Sometimes synchronicity is misunderstood directly as irony because it is so unexpected that what was seemingly chance has occurred. This happened to Taleb when she published a book online with no expectation of getting famous, but then she did get famous. Of course secretly, she did desire that or perhaps even believe it could happen, but the chances of it actually happening are synchronous to her destiny of being a writer, she feels. Therefore, the irony of synchronicity is that life has a feeling of being destined.
Unlikely facts are normal
If our sense of destiny brings us into contrary expectations, Taleb invites us to believe in the impossible because actually, unlikely facts are the norm. That is ironic by definition, because the norm should be what is normally expected, but in a universe with a planet like ours orbiting a sun for no explicit reason, the truth is that life itself is statistically improbable. Remembering that reality does not honor our personal opinion of "likelihood" is an important aspect of what this book offers.
The book publication
The ironic facts of Taleb's life are that she wanted to be a writer but did not believe she could. Then, by a random process, she was elevated to a position of fame by a publishing company who randomly discovered her. The unlikeliness of her publication is reason to publish one's own work, because it could happen for any one of us. The reality is that statistically, it doesn't—most books go right into oblivion and no one reads them. However, reality has a way of reward those who take risks; that is what the reader gleans by moralizing this irony.
The false division of fact or fiction
The author takes a stand with all those literary minds before her who address the issue of truth as fact and fiction. Fiction is not a "lie," but rather, fiction allows a mode of interpretation called narrative: concepts and ideas can be treated through a dynamic artistic process for a better analysis of the elements of truth. That means that facts must be somewhat consistent with the narrative process of understanding reality. As a neuroscientist, Taleb knows intimately how strikingly impossible reality is: she studies the most impossible object of all nature: the human brain.
Reality as narrative experience
As a brain-scientist, Taleb offers some facts about reality and perception. Rather than viewing the brain as a tabula rasa engine, the brain is better viewed as a machine through which the body reconciles external circumstances to an internal desire for survival and success. That process of natural survival and success defines the reality around us because our perception of reality is governed by that narrative process of responding to new threats or strategizing, etc. The point is that Taleb treats the reality that can be known as a narrative process, so that it becomes worth taking risks. This raises an excellent question: What is the difference between the reality we observe and the objective reality? The difference is undeterminable and so the book ends on an unlikely note: Reality does not actually have to exist in order for our experiences of reality to exist.