### abstract ###
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is
The problem is especially acute when we need to consider artificial systems which are significantly different to humans
In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features
These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines
We believe that this measure formally captures the concept of machine intelligence in the broadest reasonable sense
### introduction ###
Most of us think that we recognise intelligence when we see it, but we are not really sure how to precisely define or measure it
We informally judge the intelligence of others by relying on our past experiences in dealing with people
Naturally, this naive approach is highly subjective and imprecise
A more principled approach would be to use one of the many standard intelligence tests that are available
Contrary to popular wisdom, these tests, when correctly applied by a professional, deliver statistically consistent results and have considerable power to predict the future performance of individuals in many mentally demanding tasks
However, while these tests work well for humans, if we wish to measure the intelligence of other things, perhaps of a monkey or a new machine learning algorithm, they are clearly inappropriate
One response to this problem might be to develop specific kinds of tests for specific kinds of entities; just as intelligence tests for children differ to intelligence tests for adults
While this works well when testing humans of different ages, it comes undone when we need to measure the intelligence of entities which are profoundly different to each other in terms of their cognitive capacities, speed, senses, environments in which they operate, and so on
To measure the intelligence of such diverse systems in a meaningful way we must step back from the specifics of particular systems and establish the underlying fundamentals of what it is that we are really trying to measure
That is, we need to establish a notion of intelligence that goes beyond the specifics of particular kinds of systems
The difficulty of doing this is readily apparent
Consider, for example, the memory and numerical computation tasks that appear in some intelligence tests and which were once regarded as defining hallmarks of human intelligence
We now know that these tasks are absolutely trivial for a machine and thus do not test the machine's intelligence
Indeed even the mentally demanding task of playing chess has been largely reduced to brute force search
As technology advances, our concept of what intelligence is continues to evolve with it
How then are we to develop a concept of intelligence that is applicable to all kinds of systems
Any proposed definition must encompass the essence of human intelligence, as well as other possibilities, in a consistent way
It should not be limited to any particular set of senses, environments or goals, nor should it be limited to any specific kind of hardware, such as silicon or biological neurons
It should be based on principles which are sufficiently fundamental so as to be unlikely to alter over time
Furthermore, the intelligence measure should ideally be formally expressed, objective, and practically realisable
This paper approaches this problem in the following way
In  Section  we consider a range of definitions of human intelligence that have been put forward by well known psychologists
From these we extract the most common and essential features and use them to create an informal definition of intelligence
Section  then introduces the framework which we use to construct our formal measure of intelligence
This framework is formally defined in  Section
In  Section  we use our developed formalism to produce a formal definition of intelligence
Section  closes with a short summary
A preliminary sketch of the ideas in this paper appeared in the poster  CITATION
It can be shown that the intelligence measure presented here is in fact a variant of the Intelligence Order Relation that appears in the theory of AIXI, the provably optimal universal agent  CITATION
A long journal version of this paper is being written in which we give the proposed measure of machine intelligence and its relation to other such tests a much more comprehensive treatment
Naturally, we expect such a bold initiative to be met with resistance
However, we hope that the reader will appreciate the value of our approach: With a formally precise definition put forward we aim to better our understanding of what is a notoriously subjective and slippery concept
