The singularity is a speculative notion referring to the point at which exponential innovation generates a fundamental transformation of human civilisation. As Murray Shanahan puts it in on loc 78 of his book The Technological Singularity:

In physics, a singularity is a point in space or time, such as the center of a black hole or the instant of the Big Bang, where mathematics breaks down and our capacity for comprehension along with it. By analogy, a singularity in human history would occur if exponential technological progress brought about such dramatic change that human affairs as we understand them today came to an end. 1 The institutions we take for granted—the economy, the government, the law, the state—these would not survive in their present form. The most basic human values—the sanctity of life, the pursuit of happiness, the freedom to choose—these would be superseded. Our very understanding of what it means to be human—to be an individual, to be alive, to be conscious, to be part of the social order—all this would be thrown into question, not by detached philosophical reflection, but through force of circumstances, real and present.

How we should interpret this notion remains controversial. My own instinct is to see this as a form of techno-religion, delineating the point at which we transcend through our technological creations. But it is also something I feel we need to take seriously in order to understand, particularly how it is a framework for the future shaped by the conditions of late capitalism. It is in this sense that I was intrigued to see acceleration so explicitly invoked as a force which could be harnessed in order to drive this innovation. From pg 44 of the same book:

The last of these options raises the possibility of a whole virtual society of artificial intelligences living in a simulated environment. Liberated from the constraints of real biology and relieved of the need to compete for resources such as food and water, certain things become feasible for a virtual society that are not feasible for a society of agents who are confined to wetware. For example, given sufficient computing resources, a virtual society could operate at hyper-real speeds. Every millisecond that passed in the virtual world could be simulated in, say, one-tenth of a millisecond in the real world. 

If a society of AIs inhabiting such a virtual world were to work on improving themselves or on creating even more intelligent successors, then from the standpoint of the real world their progress would be duly accelerated. And if they were able to direct their technological expertise back out to the real world and help improve the computational substrate on which they depended, then the rate of this acceleration would in turn be accelerated. This is one route to a singularity-like scenario. The result would be explosive technological change, and the consequences would be unpredictable.

My point is not to dispute the scientific plausibility of this but rather to ask how the notions in play come to acquire the resonance they do for those advocating and exploring the prospect of the singularity. 

A bit later in Battle of the Titans, Fred Vogelstein transcribes a talk he saw Eric Schmidt give at a technology conference. From loc 1904-1918:

We have a product that allows 82 you to speak to your phone in English and have it come out in the native language of the person you are talking to. To me this is the stuff of science fiction. Imagine a near future where you never forget anything. [Pocket] computers, with your permission, remember everything—where you’ve been, what you did, who you took pictures of. I used to love getting lost, wandering about without knowing where I was. You can’t get lost anymore. You know your position to the foot, and by the way, so do your friends, with your permission. When you travel, you’re never lonely. Your friends travel with you now. There is always someone to speak to or send a picture to. You’re never bored. You’re never out of ideas because all the world’s information is at your fingertips. And this is not just for the elite. Historically, these kinds of technologies have been available only to the elites and not to the common man. If there was a trickle down, it would happen over a generation. This is a vision accessible to every person on the planet. We’re going to be amazed at how smart and capable all those people are who did not have access to our standard of living, our universities, and our culture. When they come, they are going to teach us things. And they are coming. There are about a billion smartphones in the world, and in emerging markets the growth rate is much faster than it is anywhere else. I am very excited about this.

I don’t think it’s hyperbolic to suggest this vision can and should be analysed using the conceptual resources provided by the Sociology of Religion. In fact Schmidt has apparently used that term himself:

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But what would such a study look like in practice? I don’t think I’m qualified to do it but I’d love to help someone with a background in this area who is interested in this topic. Given the power wielded by devotees of this nascent religion, with only 5 tech companies sitting on $430 billion in cash between them, it seems urgent to better understand how these new elites interpret their own place within the world and orientate themselves to it.

From The Boy Kings, by Katherine Losse, pg 166:

Later on, when I was working directly for Mark and charged with the task of interpreting his thoughts for the world, Mark told me that his dream for Facebook was something like this, to make us all cells in a single organism, communicating automatically in spite of ourselves, perhaps without the need for intention or speech.