Solve et Coagula
Since the earliest times, philosophers have been searching for the underlying patterns of order. Having no ambition to explain everything, I want to point out one omnipresent mechanism. We find it in Spiritual development, we find it in psychotherapy and we find it- yes, even in quantum physics. In the latter understanding, there is a well known duality of wave and particle (light exists as a wave and a particle at the same time, modern physics tells us). A wave has no limits, it spreads everywhere and we can't measure it. In the moment we try to measure it, or to interact with it consciously, it disappears everywhere except at the point of observation i.e measurement. On that point it changes into a particle which has particular characteristics.
But long before quantum physics, alchemy pointed to its most important operation:
Solve et Coagula. "Solve" or "solutio" refers to the breaking down of elements and "Coagula" refers to their coming together. In the process of transmuting base metal into gold or arriving at the Philosopher's stone, this contained both literal and hidden meaning. Esoterically, "solve" referred to the dissolving of hardened positions, negative states of body and mind , thereby dissolving and vanishing negative energetic charge. "Coagula" referred to the coagulation of dispersed elements into an integrated whole, representing the new synthesis. Solve et Coagula expresses transmutation from base to a finer state, the perpetual goal of spiritual growth and human evolution.
Thus in the widest meaning of the term, Solve means dissolve, disperse, dilute. Coagulate, by definition, is "to gather or form into a mass or group".
So, the real meaning of these three words ("Solve et Coagula") is the formula that the alchemists used to effect this transformation. It could be described as a process where something is broken down to its elements, a process which produces energy that compels reconstitution in a purer form.
The same meaning we find in the well known scientific terms: Analysis and synthesis. We first break something down into its parts and then make a new, better or more acceptable whole. A result of this process is the release of energy.
Even in some particular occult systems we find this realization. For example in thelema, A. Crowley speaks of the duality of Nuit and Hadit. Nuit is the "goddess of the infinite space" (meaning the wave) and Hadit is the point (which means the particle).
What all this has to do with our job, i.e. human evolution, Spiritual technology, therapy etc.? Well, we apply what we know. We know we are not able to work with a wave, we must transform it into a particle. We can't work with some indefinite problem, for example a fear. First we must quantify it through observing it and "measuring it". We ask our client what is the location of his fear? Shape? Dimensions? Age? Colour ? Level of consciousness etc. Doing it, for example with some fear, we can see that endless and formless wave changes into a quite concrete "particle". A particle is something we are able to assist in the transforming of.
Asking for the particulars of our client's problem is the coagula phase. Afterward we apply the adequate method, we disperse it, freeing it's energetic charge (solve) , the client regroups and again we come out of the process with the new "particle" - a measurable, transformed purer state which is positive and desirable.