Science = "What" & "How", Spiritualism = "Why"
Science hasn't yet to quantify and rationalize things like the human spirit, consciousness, evolution, and quantum particle characteristics. The deeper down the rabbit hole they seem to go, the more perplexed they become. Spiritualism usually implies the existing or the 'calling up' of the paranormal, mediums, communication with the idea and so on.
Science and spiritualism are complimentary. Depends on how you look at spiritualism. If we think that spiritualism answers the "why" of things, science answers the “what” and "how" of things, the two can compliment one another. There is no question of relating one to the other. We have a need to now transcend the paradigm of modern scientific inquiry which necessarily includes the metaphysical questions regarding being and existence. By doing so, we can push towards the next stage of evolution, specifically the evolution of consciousness which seeks to re-integrate epistemological patterns of discipline-based inquiry for a collective ontological understanding of life.
Both science and spiritualism stem from one's curiosity. The science is inquisitiveness to know about our being, and spiritualism is to know the purpose of our being; both originate from our desire to know. But they are compartmentalized in a sense that science just knows everything which is matter and spiritualism aims beyond matter. Science just tells us about the practical utility and scope of material things whereas spiritualism tells us about ethics of its use. Both must be grounded in each other.
Both your 'science' and 'spiritualism' are systems of belief and practice with different purposes. Their apparent split seems almost archetypal."Science =What" from wiki: Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. "spirituality = WHY”, it is essentially the unknown, mystical, so far un-understood part of ourselves (our own mind), and we should persistently make efforts (for example, through meditation) to bring as much as possible of that mystical into the realms of knowledge and science (human psychology, human emotions, how our mind works, etc.) and philosophy, in order to harness that "spirituality" towards transforming ourselves, our organizations, and our world.
No knowledge is truly 'known', no learning is truly 'finished'. The 'hard' sciences claim objectivity by way of structured methods and empirical data sets. The spirituality (not based on doctrines but true introspection) does have a practical role in that it could help inform the scientist to 'see the bigger picture', the complexity of all things while simultaneously reflecting on how his/her worldview influences their understanding of what it is they are inquiring about. Perhaps no single individual is capable of truly understanding the bigger picture and thus scientific inquiry NECESSITATES an approach which is transdisciplinary, theoretical and practical, hard and soft, based on concrete evidence and reflective on the process itself. After all, knowledge and learning are the results of a recursive cycle of action/reflection and as such no knowledge is truly 'known', no learning is truly 'finished'
A simple systems way to relate spirituality with science is through philosophy; the three disciplines (science, spiritualism, and philosophy) makes a triad of the highest levels of human knowledge. Science is what we know for sure, it can prove through existing laws of nature world, spirituality is what we know through our connections to the universe, carried largely through unconscious instincts, motives, and intuition. Philosophy is a reasoning discourse that draws from both to give us broad principles of guiding or lives. Science provides the control part of the knowledge system, philosophy as the influence part and spirituality as the appreciative part.
Transdisciplinarity connects science and spirituality as different levels of reality. Through "analogical thinking" indeed related to system sciences (complexity), bridges can be made between all levels of reality. Meaningfully relating the core distinction between 'physical' and 'meta-physical' depends on context. It is based on the nature of the inquiry within the structure of our language and the organization of our thoughts. The right tools can serve us: the wrong ones hinder. There’s also philosophical connection between wholeness and "partners", 'wholeness' means the scientific belief in an object being 'whole' and existing within the physical boundaries observed; 'partness' means all things being linked together in the cosmos through their interdependent relationships.
There’s known known, known unknown, and unknown unknown. The things we know compared to the things we don’t know is just a tip of the iceberg. Humanity as a whole there is enough transcendental wisdom to form the level of spirituality you are seeking. Science and spiritualism provide a different angle to continuous discovery.