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posted 18 Apr 2012, 22:00 by John Brown   [ updated 3 Feb 2015, 14:35 ]
"... the goal is that the formal notion match the intuitive one in all the easy cases; 
resolve the hard ones in ways which don't make us boggle; 
and let us frame simple and fruitful generalizations."
Shalizi (2001) paraphrasing Quine (1961) 

Intelligence is an evolved characteristic which has arisen as a result of natural selection. A formalization of intelligence should be cast in these terms, to capture the essence of why brains came about. 

I consider that ...

intelligence is observed as the rate at which a device increases its efficiency in an environment.

i e = δη / δt

Thinking about intelligence in terms of efficiency, stems from the perspective that evolution through natural selection is something of an "arms race" to obtain scarce resources, and to avoid hazards. Those organisms which are more efficient in their reproductive endeavours hold a competitive edge. If an organism can alter it's response to it's environment in such a way that increases the resource obtained, then it has become more effective. If the gain outweighs the cost, then the organism has become more efficient, and requires less resources overall.

"... every evolutionary advantage in nervous systems has come at a cost", and "the development and operation of a brain is tremendously expensive in terms of the energy required(Allman 2000). However, the fact that brains have evolved, demonstrates that they deliver a reproductive advantage"Brains exist because the distribution of resources necessary for survival and the hazards that threaten survival vary in space and time. There would be little need for a nervous system in an immobile organism or an organism that lived in regular and predictable surroundings.(Allman 2000). For example, fruit has higher energy and is easier to digest than the more readily available leaves. However, fruit is more widely dispersed in space and time, and subject to greater competition.

One organism can be more efficient than another, without being more intelligent. A dessert plant may survive and proliferate over many years on a meagre ration of water, while a pair of horses are unlikely to survive a single gestation period at the same location. The dessert plant boasts exceptional water efficiency. The horses, with their capacity for movement, may range broadly in search of water, and water may indeed be located at great cost. However, on a subsequent occasion the horses, with their capacity for memory, vision and smell, will likely travel by a much more efficient route to the water source. The plant remains more efficient, but the horses have increased their efficiency.

Intelligence is something more than the capacity for movement. A female wasp Sphex seals her eggs in a prepared burrow alongside a paralized cricket which serves as food for the wasp grubs. The Sphex follows a routine which involves dragging the cricket to the threshold of the burrow, entering the burrow and then re-emerging to drag the cricket inside. If a researcher moves the cricket a little distance away while the wasp is in the burrow, then the Sphex will repeat the whole routine of dragging, entering, emerging. On one occasion a researcher and wasp repeated the routine forty times (Hofstadter 1996). The Sphex is capable of elaborate movement, but has a limited capacity to improve the efficiency of that routine movement. 

Brains enable gains in efficiency, but are not limited to that, any more than a tongue is limited to agitating food.

Efficiency is a general concept relating to the expenditure required to achieve some outcome - in terms applicable to the task at hand. This general notion is given varying degrees of formalism in physics, economics and rather loosely in the examples in this article. While evolution by natural selection has been referred to as a "blind" process without purpose (Dawkins 1987 1999), this same process can also be viewed as a fierce competition. Efficiency in these competitive terms might be defined broadly in terms of the resources required to make replicas of a strand of DNA. The flexibility (and value) in the notion of efficiency flows through into that of intelligence - in terms of the objective, and the resources under consideration.

This notion of intelligence is tied to a particular environment, such that one may compare the intelligence of two devices within a single environment. Unfortunately, it does nothing to assist us to compare the intelligence of devices in different environments. The traditional game of chess can be viewed as a simple environment within which two potentially intelligent players may compete. There are also variants of this game environment which limit the amount of time available for making each move. It seems readily apparent that intelligence (increased efficiency over time) in the traditional game will largely translate to the fast chess environment. However, fast chess will clearly favour a slightly different intelligence. Consider further altering the chess environment such that players need not wait for their turn, but may make up to one move per second. The manner in which a player might increase their efficiency over time alters significantly. Consider the intelligence of a dedicated chess player in a poker environment, in judo ......... or in Africa. The nature of intelligence is closely related to the nature of the environment.

This notion of Intelligence offers a good match to our intuition:
  • Rocks interact with the environment in a consistent unchanging manner, and hence there is no intelligence.
  • Plants typically interact with the environment only very slowly, or in a repetitive manner. Each individual plant in a species exhibits very similar efficiency, and without significant improvements during the plant's lifespan. Intelligence of plants is vanishingly small.
  • Dogs are able to "learn new tricks" as it were; changing the way that they behave to obtain a reward. Dogs are intelligent.
  • Crows of New Caledonia are able to fashion a tool from a novel material (wire) and use it to extract a grub from an inconveniently shaped hole (Bluff et al 2007). Crows are intelligent.
  • People are intelligent when they "design a better [more efficient] mousetrap", and not so intelligent when they repeatedly pull the handle of a poker machine against the odds.
  • Turing machines operate in complete isolation of the environment for the duration of a deterministic undertaking. There is no capacity to improve efficiency, and hence no intelligence. 
  • Searle's Chinese room operates on a fixed set of instructions with no facility for improving efficiency, and hence there is no intelligence.
  • Chess playing computers which become stronger over time in response to their gaming environment are intelligent.
Recognising intelligence as increasing efficiency over time accords well with our intuition. Inspecting intelligence through this lens provides clarity in some instances where the lack of an accepted formalization has fuelled debate. Efficiency is a suitably flexible notion which bundles an objective with the necessary resources. Intelligence is explicitly tied to an efficiency in a particular environment.

Allman,J. (2000), Evolving Brains. W. H. Freeman. 
Bluff,L. Weir,A. Rutz,C. Wimpenny,J. Kacelnik,A. (2007), Tool-related Cognition in New Caledonian Crows. University of Oxford.
Dawkins,R. (1999), The Extended Phenotype. Oxford University Press.
Dawkins,R. (1987), The Selfish Gene. Oxford University Press.
Hofstadter,D. (1996), Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books.
Quine, W (1961), From a Logical Point of View: Logico-Philosophical Essays. Cambridge, Mass.: Harvard University Press, 2nd edn. First edition, 1953.
Shalizi,C. (2001), Causal Architecture, Complexity and Self-Organization in Time Series and Cellular Automata.