Oh my answer to "why they can't fit together like a puzzle" - -
I missed that comment before.
They can't because they're each following different rules with
different assumptions. Will there be a Unity of Science? Perhaps
someday, perhaps there will never be. It's equally likely that,
should religion-as-we-know-it be abolished, should the courts
systems of truth-verification be abolished and replaced by the
sciences... should countries adopt Science as their Only Way...
that there will be Science Wars between disciplines and
competing hypothesis, countries going to war over yet more
ideologies.
I see no reason why, if the Sciences were the top dog, which
they likely will be one day, that they won't also fight, as all
powerful ideologies seem to eventually fight, usually over
minutae of differences.