On the definition of intelligence


There are many people that claim that we still do not agree on a definition of intelligence (and thus what constitutes an artificial intelligence), with the usual argument that intelligence means something different for different people or that we still do not understand everything about (human or animal) intelligence. In fact, in the article What is artificial intelligence? (2007), John McCarthy, one of the official founders of the AI field, states

The problem is that we cannot yet characterize in general what kinds of computational procedures we want to call intelligent. We understand some of the mechanisms of intelligence and not others.

To understand all mechanisms of intelligence, some people, such as Jeff Hawkins, have been studying the human brain (which is the main example of a system that is associated with intelligence).

We might not know how we are intelligent (i.e. how the human brain makes us intelligent), but this does not mean that we can’t come up with a general definition of intelligence that comprises all forms of intelligence (that people could possibly refer to). In other words, you do not need to fully understand all mechanisms of intelligence in order to attempt to provide a general definition of intelligence. For example, theoretical physicists (such as Albert Einstein) do not need to understand all the details of physics in order to come up with general laws of physics that are applicable in most cases and that explain many phenomena.

Universal Intelligence

There has been at least one quite serious attempt to formally define intelligence (and machine intelligence), so that it comprises all forms of intelligence that people could refer to.

In the paper Universal Intelligence: A Definition of Machine Intelligence (2007), Legg and Hutter, after having researched many previously given definitions of intelligence, informally define intelligence as follows

Intelligence measures an agent’s ability to achieve goals in a wide range of environments

This definition favors systems that are able to solve many tasks, which are often known as artificial general intelligences (AGIs), than systems that are only able to solve a specific task, sometimes known as narrow AIs.

Mathematical Formalization

To understand why this is the case, let’s look at their simple mathematical formalization of this definition (section 3.3 of the paper)

\[\Gamma(\pi) := \sum_{\mu \in E} \frac{1}{2^{K(\mu)}} V_{\mu}^{\pi}\]


  • \(\Gamma(\pi)\) is the universal intelligence of agent \(\pi\)
  • \(E\) is the space of all computable reward summable environmental measures with respect to the reference machine \(U\) (roughly speaking, the space of all environments)
  • \(\mu\) is the environment (or task/problem)
  • \(V_{\mu}^{\pi}\) is the ability of the agent \(\pi\) to achieve goals in the environment \(\mu\)
  • \(K(\mu)\) is the Kolmogorov complexity of the environment \(\mu\)


We can immediately notice that the intelligence of an agent is a weighted combination of the ability to achieve goals in the environments (which represent the tasks/problems to be solved), where each weight is inversely proportional to the complexity of the environment (i.e. the difficulty of describing/solving the corresponding task). In other words, \(\Gamma(\pi)\) is defined as an expectation of \(V_{\mu}^{\pi}\) with respect to the probability distribution \(\frac{1}{2^{K(\mu)}}\), which Legg and Hutter call the universal distribution.

So, the higher the complexity of an environment, the less the ability of the agent to achieve goals in this environment contributes to the intelligence of the agent. In other words, the ability to solve a very difficult task successfully might not be enough to have high intelligence. You can have higher intelligence by solving many but simpler problems. Of course, an intelligent agent that solves all tasks optimally would be the optimal or perfect agent. AIXI, developed and formalized by Hutter, is actually an optimal agent (in some sense), but, unfortunately, it is incomputable (because it uses the Kolmogorov complexity)1.

Consequently, according to this definition, we could say that all animals (and maybe even other biological organisms) are more intelligent than, for example, AlphaGo or DeepBlue, because all animals solve many problems, although they might not be as difficult as Go, while AlphaGo only solves Go 2.

Open Questions

I like this definition of universal intelligence because it implies that humans (and other animals) are more (generally) intelligent than AlphaGo or any other computer program, but it raises at least 1-2 questions:

  1. How would we measure the difficulty of a real-world environment?

  2. So, in practice, can we really compare an animal with AlphaGo? Yes, we can with intelligent tests like the Turing test, but can we do it with \(\Gamma(\pi)\)? The answer to this question clearly depends on the answer to the question above.

Intelligence Tests

In the paper, they also discuss issues like intelligence tests and their relation to the definition of intelligence: that is, is an intelligence test sufficient to define intelligence, or is an intelligence test and a definition of intelligence distinct concepts?


In my view, it is unproductive to come up with new definitions of intelligence (unless it’s more generally applicable than the universal intelligence) or to avoid choosing one definition with the excuse that we don’t know what intelligence is. I know what intelligence is. It’s measured by \(\Gamma(\pi)\). So, I don’t need to know how we can create an agent that is (highly) intelligent before I know what intelligence is. It’s not matter of liking or not a definition, it’s a matter of defining a set of axioms or hypotheses and deriving other properties from them or test those hypotheses, respectively.

  1. \(\Gamma(\pi)\) is also a function of the Kolmogorov complexity, but this is just a definition, i.e. it does not directly give you the instructions to develop intelligent agents. 

  2. Note that, according to this definition, AlphaGo is still intelligent, but just not as intelligent as animals.