There Will Be No Technological Singularity

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On Monday, I looked at the possibility of artificial intelligence through the perspective of history: the history of the field and of expert conjecture. That analysis revealed that, up until now, predictions of AI emergence have had little correlation with progress in the field. The predicted arrival of machine intelligence by many experts has generally always been "roughly 20 years from the present."

Today, I want to look at current predictions, specifically, at the details of today's most popular prognostication for the future of AI, an idea called the technological singularity. This concept posits that AI is inevitable in the near future, due to the sheer rate at which computers improve in speed and cost.

Over the past several years, many futurists, notably Ray Kurzweil, have advanced this theory. In 2000, he surmised that many humans will start to believe that computers are as smart as them by roughly 2019. In 2005, he clarified his forecast, saying that by 2029 a machine would pass the Turing test. What chances do these modern "about 20 years away" predictions have? The answer lies in the nature of singularities in mathematics and science.

"Singularity" is a technical math term. A singularity is a feature of a mathematical function where the function increases sharply, and its value becomes infinitely high. ("Nears" or "goes to" infinity is a term used by physicists, referencing the study of these situations by the methods of calculus.)

A singularity.png
A function with a singularity, becoming infinitely large at the number one.

This is like what happens when you divide one number by a smaller and smaller second number; as your divisor nears zero, the answer becomes larger and larger. One divided by .1 is 10, 1/0.01 is 100, 1/0.001 is 1000,  and so on. If you get close enough to dividing by zero, the answer would be nearly infinity. A bit abstract right?

There is a reason that we don't intuitively grasp phenomena described by infinite singularities very easily: they don't occur in real life! (Well, one possible exception is the black hole; but even the Big Bang did not involve a singularity.)

The point is: Whenever the mathematics of physics tell us to expect something nearly infinitely large, infinitely small, infinitely fast, or infinitely easy, it means that our laws have broken down. Our mathematical models no longer reflect reality correctly. This is precisely the case for the technological singularity and its prediction of effectively infinite computer power.

A few examples illustrate this point. 

The physics of vibrations has mathematical solutions which describe resonance. Humming a certain note in a bare-walled room or parking garage will cause the surroundings to vibrate; that particular hummed pitch is the resonant frequency. A simple application of physics to this situation would say that the resonance will grow and grow, until it is infinitely strong. In this model, if you hum long enough, the strength (amplitude) of the resonance will tend towards infinitely large, tearing apart the walls, your body, and eventually the air itself. But obviously, this doesn't happen.

Newton's universal law of gravitation says that as objects move closer together, their gravitational pull on each other increases, eventually becoming infinite. However, in reality, objects are only able to come so close together before their atoms repel each other and stop the pull. There is no infinite gravity. (Except, again, possibly black holes; no one knows what is at the heart of a black hole.)

An example from applying mathematics to biology is less abstract. When a population of an animal species that procreates quickly finds itself in a situation with abundant food and few predators, an exponential growth in population occurs. If each animal has, say, five offspring, and those offspring have five offspring, and those offspring have five offspring, then after a few generations, there are 625, 3125, 15625... animals. The population approaches a "singularity" as the number of animals starts to become infinitely large. Are an infinite number of rabbits actually born? No. Food or territory runs out, and the mathematical model of exponential reproduction fails to describe reality anymore. Instead, growth follows a "logistic curve":

exponential vs logistic growth.png
Logistic growth is the black curve. At first, exponential growth (red) looks almost identical, but logistic growth levels off while exponential growth continues forever.

Initially, things look like an exponential curve, but they level off when realistic constraints on growth begin to take effect.

All systems that we look at have this property: reality sets in and stops a singularity from occurring. A stone dropped towards the earth does not hit the surface infinitely hard, the room you hum in does not tear itself apart, there are not an infinite number of rabbits in the world, etc.

Our technological progress has been incredible. In fact, it will probably continue to grow at an exponential pace for some time. However, eventually some worldly factor will step in and slow the exponential growth. (Critics will rightly point out that previous estimates of when this might happen have failed.) However, the answer of "infinity" from a mathematical model is never correct, as there is always a limiting factor. Whether we reach it soon, or in many many years, we will eventually reach it.

Given how far we are from understanding even a simple worm's brain, much less the human brain, this leveling off will almost certainly occur before our computing power swells to the necessary point to create an artificial human mind. Maybe some day we will succeed in creating AI, but don't hold your breath or freeze your brain. Technological singularity will not bring it any time soon.

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