First, esoteric knowledge is explored using the full capacities of the human brain, both conscious and unconscious, analytical and intuitive. Rather than directing our attention and awareness to sensory information arising from our physical surroundings, we direct our attention inwardly so to explore and discover answers to questions such as these:
(1) What is the nature of the connection between my body-brain and my inner mind?
(2) What are the capabilities of the unconscious mind and how does it function?
(3) What are the capabilities of the conscious mind and how does it function?
(4) What is the proper method for utilizing these two minds in the esoteric exploration of our inner worlds?
(5) What are effective methods for teaching people how to communicate meaningfully with each other about these inner experiences?
(6) What does it mean when we experience interactions with personalized deities or powers?
(7) Are inner, esoteric experiences totally unique to each and every person (secondary to cultural biases and personal life-experiences) making comparisons impossible or are such experiences essentially universal phenomena (similar brain function) arising from observing and experiencing the actuality of a common nonphysical and spiritual universe?
Second, even though the areas of explorations differ between students of a mystery school and students of mundane science (one being introspective and subjective, the other extrospective and objective), the techniques applied for gathering, organizing and analyzing data, using this data for constructing models and hypotheses are quite similar. This concurrence should not come as a surprise, since the scientific method of asking and answering questions actually arose (and was taught and guarded) within the early Egyptian mystery schools, later being introduced into the mundane world during the birth of modern science in the Renaissance.
Another major difference between mundane scientific and esoteric studies concerns how each area deals with the subject of infinities, limitless quantities. As we saw before, modern science deals solely with components and component-interactions limited to existence within the boundaries of physical matter and energy. By physical matter and energy, I am referring only to those quantities which can be measured and quantified using instruments constructed out of the same physical components. Energies which are beyond the capabilities of measurement by any physical instrument, such as the energies of spirituality, are excluded by default.
Therefore, science operates within the world of finite objects, as is the case with most branches of mathematics, making its advances in technology and understanding by adding sequential rungs to a ladder leading high into the heavens. Each advance is simply another rung upon the ladder–a ladder not leading anywhere in particular.
Esotericism operates within the inner world of multilayered sets of infinite objects and concepts. For example, in kabbalah creation can be described by a tree composed of ten distinct levels or worlds interconnected in a specific manner. Each of these levels represent unique, spiritual forces or powers established by the Creator so to help the souls of mankind return from materiality to the Creator. Since each of these levels arise from and reflect a portion of the absolute infinity of the Creator, by necessity, each is infinite. Moreover, it is a property that movement between a lower infinity to a higher infinity is impossible using only the elements comprising the lower infinity. We saw this before when we discussed the fact that it is impossible for us to reach an infinity using discrete number theory. For example, we can never count to the end of all the integers existing on the number line since no matter how long we count, we can also count one more. Consequently, though our number continues to enlarge with each additional integer, we will never reach the end state, for the end state is not a number but a collection or set containing all integers. This infinity or infinite set was called aleph zero by the father of modern set theory, George Cantor. The numbers contained within this set are its elements, but no one element is equivalent to the set itself. Therefore, it is not quite correct to say that infinity is a real number which is so large that to matter what we do to it, its size does not change. Aleph zero is a whole onto itself which only appears limited on viewing it from our material perspective.