Polanyi's idea of Personal Knowledge is closely related to Tacit Knowledge, which is knowledge that we possess but cannot express in words. Polanyi famously stated, "We know more than we can tell."
No wonder he was in disagreement with Wittgenstein who said:
"What can be said at all can be said clearly, and what we cannot talk about we must pass over in silence"
Ludwig Wittgenstein - Tractatus Logico-philosophicus
According to Polanyi, Personal Knowledge always includes Tacit Knowledge, which cannot be fully explained verbally. He would probably be more sympathetic to Taoism,
"The Tao that can be told is not the eternal Tao;
The name that can be named is not the eternal name"Tao Te Ching
By the way, Tacit Knowledge is distinct from the "Unknown Known" because, although we are aware of Tacit Knowledge, we cannot express it verbally.
Examples of Tacit Knowledge include: Face recognition, bicycle riding, and playing piano.
In these examples, the individual has repeated experience and has internalized the knowledge to the point where it becomes automatic.
Adriaan D. de Groot, the Dutch psychologist who studied the thinking of chess players, discovered that especially grandmasters employ a lot of Tacit Knowledge.
The structure of Tacit Knowledge always has two parts, the proximal and the distal elements.
The proximal element is the closer, and the distal the farther away. The association is like a directed arrow from the proximal to the distal. And while we are fully aware of the distal element, we are not aware of the proximal element.
This structure is the defining characteristic of Tacit Knowledge.
In the case of recognizing a familiar face in the crowd, the proximal is the facial features of the person, and the distal is the person that we know.
For the piano maestro, the proximal is the fingers playing the keyboard, and the distal is the music produced. To play well, attention must not be on the fingers (fingers have a memory of their own from practice) but on the music and the emotional content.
In Personal Knowledge, people say "Writing forces us to think clearly". We believe this, and incorporate this into our personal Knowledge Base, because we have experienced it many times ourselves.
The knowledge "Writing forces us to think clearly" has its roots in Tacit Knowledge, which is incorporated into our Personal Knowledge, and expressed and shared widely, so that it becomes objective knowledge.
In general, the Act of Knowing is always Tacit Knowledge.
Creativity is also related to Tacit Knowledge. For example, an artist with a deep understanding of color theory and painting techniques, combined with their own personal experiences and observations, can use their tacit knowledge to produce a truly unique and creative work of art.
Michael Polanyi derived his whole philosophy from the ideas of Personal and Tacit Knowledge. It is a very wide subject, we have barely touched the subject here.