QUOTE
A singularity on the far side of it (eg. us to the steam engine) never appears as a singularity, we can see the cause-effect relationship involved, but from the other side, it's very difficult to conceive of those technologies and their impact on society.
I think your definition of singularity is extremely narrow for this discussion. I think an appropriate definition for a singularity is a period of inflection where the dominant structure of human civilization changes in such a way that a person on one side event is unable to succeed in the civilization on the other side without difficult and extensive retraining.
The steam engine didn't revolutionize human civilization by itself, nor did the silicon chip. Any one technology can't bring about a fundamental shift in the structure of human societies. There are four main revolutions in human history, as I see it. Everything else represents side effects or emergent properties of those revolutions. You can think of them as the "four singularities", if that makes any sense at all:
Technology: Technology isn't just the computer you're looking, it's any tool, system, or method that makes your life easier. It's also the
study of those things to attempt to make them better. It's the practice of taking a stone hand axe and attaching a handle to it for more leverage. Iterative, constant improvement in tools, systems, and methods is the biggest difference between pre-Stone Age humans and us.
Agriculture: Agricultural civilizations allow for specialization, increased population, selective breeding of helpful organisms. It roots people to a geographic area and swells the number of things the collective can own because they don't need to carry it all. Territory and war become more important. Craft and manufacturing emerge. Philosophy and science become possible.
Writing: Skillwires in the pre-matrix days. Writing evolved in parallel to many other human innovations, and so perhaps doesn't represent a single period or short event, but is transformative enough that it bears mentioning. It represents a way to statically capture complex ideas for posterity. As the ancient axiom goes, we stand "on the shoulders of giants, so that we can see more than they, and things at a greater distance." It is because of writing that civilization doesn't slide backwards too far before catching itself.
Capitalism: Prior to the informal rise of capitalism (it didn't have a name until Marx and his contemporaries coined the term in the late 19th century), much of commerce was dictated by protectionist guilds and corporations. Guilds would maintain strict limits on production, discouraged innovation, and pushed out anyone who wasn't a member. Corporations were state-sanctioned monopolies that operated in a competition-free environment. Capitalism is mitigated competition and acts as a multiplier for technology, agriculture, and writing -- popular and useful ideas, products, and services float to the top. Capitalism is the mother of the industrial revolution and is strongly correlated with populism. Because of capitalism, the poorest 1% on earth lives a longer, freer, wealthier life than the richest 1% 250 years ago.
I think if I were to offer up a fifth, it would be germ theory--understanding that illness is caused by tiny organisms is extremely powerful and informative. It makes antibiotics, surgery, antiseptics, vaccines, and basic medicine possible. A post-germ theory world is fundamentally different than a pre-germ theory world.