I think the immortal spirit means what you call the spark of life. Most religions will tell you that all spirits are connected with the root source as god.
It's a metaphysical way of talking about existence, or the fact of being. Interesting fact, the hebrew word YWHW or whatever means 'he who is'...
There's just one problem with the word science today. It's changed from being pure facts such as math or physical laws, basically the STEM field, to studies that are voted democratically such as economy, psychology etc. I use the word studies on purpose. Yes those are 'sciences' in common language, but those are theories that are even less likely to accurate. The STEM field is complex enough, now add the human factor and the philosophy behind why we do things and you find answers that can be 'proven' in both ways, it depends just on how you present (and collect) the stats and facts