@Setanta,
Lighten up, Setanta. There is no need to get personal. I am here because I enjoy this type of speculative discussion. If this isn't fun for both of us, then why play? It isn't like this matters at all (at least not until we find some Aliens to compare with our speculations).
My point was that none of these things
depend on metallurgy. There is no reason that the lack of metallurgy would have prevented us from developing advanced mathematics.
I proposed that a Calcium Carbonate age might happen in place of a Bronze Age. The important part of the Bronze Age was the availability of a useful building material, Calcium Carbonate could fill the same role. This would allow the development of tools and a hard enough building material to create simple machines.
The study of energy doesn't depend on metallurgy or on fire. There are heat sources in the ocean. The physics of mechanical and potential energy don't have anything to do with heat (or metallurgy).
The scientific method has to do with reason, logic and careful experimentation. I fail to see why metal is at all required for this. Same with genetics. Gregor Mendel advanced the study of genetics by doing experiments with generations of pea plants. I fail to see how an alien Mendel would be prevented from doing the underwater equivalent of these experiments by a lack of metallurgy.
The whole point I am making is that the
order of discovery can be different for alien civilizations that it was for humans. Just because we developed metallurgy before we developed genetics doesn't mean that every alien race in the Universe has to do it in this order (since genetics has nothing to do with metallurgy).
Again, if this isn't enjoyable for you, then please stop. I only will continue if there is someone who finds this sort of speculation interesting.