I came across this term while I was writing my post about Socrates’s ‘An Unexamined Life is Not Worth Living’ quotation.
I identified with the term radical self-understanding since it seems that it is an activity in which I am engaged. My activity could also be described with other terms: radical narcissism, obsessive self-reflection, pissing up a rope, etc… I decided to see if this term, as described by Abraham Heschel  is related to what I do.
Heschel’s definition of radical self-understanding
Heschel characterizes radical self-understanding as one of two types of philosophy. Different than the philosophy that analyzes the content of thinking – e.g. what one is thinking about – he describes radical self-understanding as thinking about thinking. “[R]adical self-understanding [is] a process of analyzing the act of thinking, as a process of introspection, of watching the intellectual self in action.” [emphasis in original] 
What is the purpose of ‘watching the intellectual self in action’? According to Heschel, the purpose is two-fold: 1) to recognize one’s ideas and concepts; 2) to recognize through depth of thinking, the relationship between one’s self and reality
If my summary does not express Heschel’s point adequately, here are his words: “Radical self-understanding must embrace not only the fruits of thinking, namely the concepts and symbols, but also the root of thinking, the depth of insight, the moments of immediacy in the communion of the self with reality.” 
Fruits and roots: a nice encapsulation of Heschel’s concept of radical self-understanding.
Am I a radical self-understander?
If I have been engaged in radically self-understanding, I would have fruits of my thinking, concepts and symbols as well as a feeling of connection of my self with reality.
My thinking, as a youth, centered on trying to mold myself to a template of what I thought life should be. There was no “communion of the self with reality” on this front. Instead of communion with reality, I had feelings of alienation.
Adult self- understanding
On the other hand, during my youth I had also given the situation of my brother a great deal of thought. My brother Mike is autistic, low functioning and has never spoken. On the surface, my thoughts – questions, really – are dispassionate, e.g. “I wonder what could have caused Mike to not pay attention to anyone else; what part of the brain could make him slap his head and bite his hand; how is it that he has vocal cords, yet does not have language; am I like him?”
What are the concepts and symbols associated with this thinking?
- My brother is different;
- My brother is not understandable;
- My brother is a human being,
- My brother and I are from the same parents.
What is the root, the depth of insight I can gather from my thinking? Here is where I hit a brick wall. When I try “communing with reality” on this front, it doesn’t work. There is no communion; there is a discontinuity. My brother’s mind is so different I have no inkling of his reality. I know that his reality and mine do not overlap to any degree other than, we both get hungry and we both feel pain if we touch a hot stove.
God in Search of Man
This is the title of Heschel’s book, wherein he discusses radical self-understanding. The rest of his book discusses the philosophy of religion, self-understanding of religion, and other concepts that interest me only peripherally.
Although I haven’t read the entire book, I doubt if Heschel’s text would give me any acceptable answer to the one major thought about my brother: Why is Michael the way he is?
God in search of man? Phooey. One would think s/he’d be able to find my brother.
 Heschel, A. God in Search of Man New York. Octagon Books 1976 print
 Ibid pg 6
 Ibid pg 6