Soul-to-soul connection is the most mysterious. There are people in my spiritual life that I have never met but I love them. I have never seen or met Baba (Shrii Shrii Anandamurti) physically but I loved him. Baba was and still is my guru. You can love someone without ever seeing that person.
Soul-to-soul connection is clearly evident when you are in love. You see the beloved in your dreams. You see the beloved whenever you close your eyes. You know that there is a soul-to-soul connection when you feel the intense pain of separation and the intense longing to unite with the beloved.
Mind-to-mind connection is more obvious and is becoming more obvious on the web. I would describe mind-to-mind connections as asynchronous interactions. Mind-to-mind interactions do not take place in real-time. The time dimension is relaxed. I can read your blog post many days after you finished writing it and click on the “like” button. Similarly, a scientist can read another scientist’s paper months or perhaps years later and respond in kind.
There are other types of mysterious connections. We are connected to the Cosmic Soul and we are connected to the the Cosmic Mind as well. The causal layer of the human mind (Atimanas Kosha, Vigyanamaya Kosha and Hiranmaya Kosha) which is the innermost layer is the same as the causal layer of the Cosmic Mind. Human beings are connected through the Cosmic Mind.
Another mysterious connection is due to strongly emotional interactions in the past lives. Some people we meet in this life are people we interacted with in the past lives. We feel the connection but we cannot find rational explanations for it.
In the physical world there are many different types of connectivity:
connectivity as in DNA similarity: connectivity due to common origins. Human beings are connected because they share common DNA.
connectivity as in structural similarity: connectivity due to common environment.
connectivity as in behavioral similarity: common conditioning (common training or education) creates a different kind of connectivity.
connectivity as in historical similarity: common histories, being connected in the past may have lingering effects in the present.
connectivity as in correlation: some medium facilitates the connection. The connection is not strong enough to be causal.
connectivity as in coupling: more direct connection by causal interaction
connectivity as in co-movement: staying connected in time, evolving together
connectivity as in synaptic coupling: one-to-many connections leading to amazing information processing capabilities
connectivity as in being in a bound state: electrons and protons in an atom are connected because they are bound by the electromagnetic force. Quarks inside a proton are connected because they are bound by the strong nuclear force. Every physical entity including human beings of this galaxy are connected because of gravity. Gravity binds and connects.