How can a small group of people have a big impact on the world? Develop a machine or service that is self-replicating or self-amplifying.
In a mundane way, artifacts such as iPhones and even shovels engage in human-catalyzed self-replication. People see them, then want them, then offer their money for them (or build them themselves, in a few cases), which provides the economic juice necessary to increase production and maintain the infrastructure necessary for that self-replication, like the Apple Store.
Self-replication can be relatively easy as long as the substrate is designed to contain components not much less complex than the finished product. For instance, the self-replicating robot built at Cornell self-replicates not from scratch, but rather from a set of pre-engineered blocks not much simpler than the robot itself. Using a hierarchy of such self-replicators, where each step is relatively simple but results in the creation of more complex components used in the next stage of self-replication, could provide a bootstrappable pathway to self-replicating infrastructures. Such a scheme also makes recycling easier -- if a large machine falls apart, perhaps only some of its components need by discarded, and the rest can be reused.
At the root of a substantial number of transhumanists' wild visions appears to be confidence that self-replicating factories will ultimately be produced. Otherwise, it is hard to imagine how society would acquire the necessary wealth to implement changes of the type that transhumanists discuss. In fact, it appears to me that modern transhumanism evolved in large part out of enthusiasm for the idea of molecular nanotechnology in the mid-1990s. The ongoing philosophical connection of transhumanism to other Enlightenment movements is more of a post hoc project designed to make transhumanism palatable and comprehensible to larger groups.
At its core, I believe that transhumanism's greatest accomplishment is identifying self-replicating and self-amplifying processes as humanity's greatest opportunity and hazard of the 21st century -- technology with the potential to allow us to transcend our material, physiological, and psychological limitations or, if handled poorly, cause a reprise of the Permian-Triassic extinction. You don't have to be a transhumanist to appreciate this insight; you only need to be convinced that self-replicating machines are technically plausible at some point in the near or mid-term future. Indeed, a substantial minority of tech-oriented people seem open to the possibility. Here is a poll from a 2005 CNN article on RepRap:
Even more exciting to me than self-replication is the power of self-amplification. I define self-amplification as a growing optimization process that extends its own infrastructure in a diverse way rather than simple self-replication, where "infrastructure" is defined as both core structures and the peripheral structures that support them. Humanity is an interesting edge case here, at the boundary of what I would consider the transition from self-replication to self-amplification. We are able to create diverse artifacts, but our ability to inject diversity into our own bodies and minds through self-transformation or directed evolution is extremely limited.
There is an opportunity here for the development of a mathematical model that quantifies the information and structural content produced by a given self-replicating or self-amplifying entity. Humans like to think that we exhibit nearly infinite variety in the creation of artifacts, but this is untrue. We mostly create artifacts that we have cultural and evolutionary predispositions to create. If we realized how constrained our information-producing tendencies are, it would help us become a more mature species through better self-reflection.