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This is the first in a series of posts about the Singularity, that notional future time when machine intelligence explodes in capability, changing human life forever. Like many computer scientists, I’m a Singularity skeptic. In this series I’ll be trying to express the reasons for my skepticism–and workshopping ideas for an essay on the topic that I’m working on. Your comments and feedback are even more welcome that usual!

[Later installments in the series are here: 2 3 4]

What is the Singularity? It is a notional future moment when technological change will be so rapid that we have no hope of understanding its implications. The Singularity is seen as a cultural event horizon beyond which humanity will become … something else that we cannot hope to predict. Singularity talk often blends into theories about future superintelligence posing an existential risk to humanity.

The essence of Singularity theory was summarized in an early (1965) paper by the British mathematician I.J. Good:

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control.

Vernor Vinge was the first to describe this as a “singularity”, adopting a term from mathematics that applies when the growth rate of a quantity goes to infinity. The term was further popularized by Ray Kurzweil’s book, “The Singularity is Near.”

Exponential Growth

The Singularity theory is fundamentally a claim about the future growth rate of machine intelligence. Before evaluating that claim, let’s first review some concepts useful for thinking about growth rates.

A key concept is exponential growth, which means simply that the increase in something is proportional to how big that thing already is. For example, if my bank account grows at 1% annually, this means that the every year the bank will add to my account 1% of the current balance. That’s exponential growth.

Exponential growth can happen at different speeds. There are two natural ways to characterize the speed of exponential growth. The first is a growth rate, typically stated as a percentage per some time unit. For example, my notional bank account has a growth rate of 1% per year. The second natural measure is the doubling time–how long it will take the quantity to double. For my bank account, that works out to about 70 years.

A good way to tell if a quantity is growing exponentially is to look at how its growth is measured. If the natural measure is a growth rate in percent per time, or a doubling time, then that quantity is growing exponentially. For example, economic growth in most countries is measured as a percent increase in (say) GDP, which tells us that GDP tends to grow exponentially over the long term–with short-term ups and downs, of course. If a country’s GDP is growing at 3% per year, that corresponds to a doubling time of about 23 years.

Exponential growth is very common in nature and in human society. So the fact that a quantity is growing exponentially does not in itself make that quantity special nor does it give that quantity unusual, counterintuitive dynamics.

The speed and capacity of computers has grown exponentially, which is not remarkable. What is remarkable is the growth rate in computing capacity. A rule of thumb called “Moore’s Law” states that the speed and capacity of computers will have a doubling time of 18 months, which corresponds to a growth rate of 60% per year. Moore’s Law has held true for roughly fifty years–that’s 33 doublings, or roughly a ten-billion-fold increase in capacity.

The Singularity is Not a Literal Singularity

As a first step in considering the plausibility of the Singularity hypothesis, let’s consider the prospect of a literal singularity–where the rate of improvement in machine intelligence literally becomes infinite at some point in the future. This requires that machine intelligence grows faster than any exponential, so that the doubling time gets smaller and smaller, and eventually goes to zero.

I don’t know of any theoretical basis for expecting a literal singularity. There is virtually nothing in the natural or human world that grows super-exponentially over time–and even “ordinary” super-exponential growth does not yield a literal singularity. In short, it’s hard to see how the AI “Singularity” could possibly be a true mathematical singularity.

So if the Singularity is not literally a singularity, what is it? The next post will start with that question.