Refined from http://tuscanycircle.net/post/iq ...

• -6σ
  Functioning is absolutely minimal.
  Incapable of self-maintenance in any way.
  Can't even be toilet-trained.

 

• -5σ: Profound retardation.
  Once known as "idiots", this group are without understanding or ordinary mental capacity.
  Need constant care and supervision.
  An IQ of -5σ is the beginning of a semblance of humanity (consciousness).
  Cats are at this level.

 

• -4σ: Severely retarded.
  Once called "imbeciles".
  Congenitally weak-minded, they cannot profit from academic training at all.
  Cannot be employed in sheltered workshops.
  Must be supervised domestically.
  Demonstrate little or no social and communication skills but they can be trained in basic health habits.
  Smart dogs are estimated to have IQs at this level.

 

• -3σ: Moderately retarded.
  Limited support is essential and with extended special education a maximum of fourth grade could be attained by age 18.
  Their thinking does not involve much in the way of logic.
  Their ethical thinking has to involve conditioning.
  There is the beginning of a quid pro quo sort of morality.
  Their social and communication skills are fair but there is little self-awareness.
  They can function vocationally in a sheltered workshop (and perhaps lawn-mowing, if you don't mind them losing fingers).
  Cannot live independently.
  Average adult chimpanzee has a general intelligence level corresponding to this category.

 

• -2σ: Mildly retarded.
  Mental age 12 for normal adults.
  Once called "morons" or "feeble-minded".
  With special education, a maximum of sixth grade is possible by age 18.
  Are inevitably functionally illiterate even if they have been taught to read for at least four years.
  Real (if superficial and concrete) logic appears in this category.
  Conventional morality also begins to appear - this group perceive as good whatever pleases significant others and the bad as anything that displeases them.
  At least some intermittent outside assistance is necessary.
  Their communication and social skills are reasonable. (By social/communication this does not refer to negotiation skills or wit, but basics such as washing hands, dressing, brushing teeth, using toilet paper, looking at the person addressing them and finding the local doctor.)
  They are socially and vocationally adequate (at menial labor) given special training and supervision.
  Many are able to lead a relatively independent life.
  At an IQ of -2σ or below, the law regards them as being too stupid to know the difference between right and wrong.

 

• -1σ: Dull.
  Life is tough at this level.
  Learning is slow, simple and needs to be supervised closely to be effective.
  Those with IQs below -1.3σ will probably never be functionally literate and the rest will not understand anything more complex than a popular magazine.
  Their reasoning is very superficial.
  Morality is of a primitive conventional sort - good and bad depends on how significant others view good and bad.
  The vast majority of serious social problems are associated with people in this category because there are so many of them and they are just smart enough to be let loose.
  People in this category commit about 75 percent of all petty and violent crimes.
  Anything other than unskilled labor is a trial, though simple semi-skilled work is possible.
  These tend to overestimate themselves by at least an additional standard deviation, believing they're at least average.

 

• Mean (0σ): Mediocre
  The average person.
  Learning varies from explicit coaching with hands-on experience to study guides and textbook work with some practical experience.
  Their reading level is, at best, news stories (not editorials), popular magazines and novels.
  Morality is conventional - a matter of serving the social order and tradition or doing your duty as defined by some authority - church, teacher, parent, or state.
  Able to function at the level of skilled blue-collar, clerical, sales, police work, and teaching.
  This large group are the glue of society, but, given the wrong authority, they will do horrible things in the name of morality.
  These tend to overestimate themselves by at least an additional standard deviation.

 

• +1σ: Bright.
  They can learn via the typical university format of lectures and textbooks.
  Their typical reading level is editorials, magazines such as Time and The Economist, and classical novels.
  Abstract, "what-if" hypothetical thinking begins in this group but is still superficial.
  Principled morality also begins in this group, that is, they can see there are non-arbitrary principles or laws that should govern ethical behavior and thought.
  Their best work level is that of most professors, low- to middle-level management and military officers, sub-standard to fair professionals and some elected politicians.
  This group makes up the moral, intellectual, and practical leadership assistants of society.
  These tend to overestimate themselves by at least an additional standard deviation.

 

• +2σ: Superior.
  This category and all those above them don't require assistance to learn.
  They can find the information and master the methods themselves.
  Reading philosophy and legal tracts with comprehension is possible.
  Morality is decidedly a matter of principles for this group but nevertheless they tend to accept established systems.
  This group forms the bulk of the better doctors, lawyers, engineers, accountants and other professionals, United States presidents, CEOs of large companies, and some of the better professors.
  Tend to be the keepers, and transmitters of knowledge and the higher points of any culture, but can't create it themselves.
  These tend to overestimate themselves by at least an additional standard deviation.

 

• +3σ: Brilliant.
  Highly regarded original academic work rarely occurs with lower IQs.
  Some in this group exceed the average university student in academic competence while still in primary school.
  They garner most academic honors such as Rhodes scholarships and maths Olympiads.
  They can read anything and probably read philosophy for pleasure.
  Most professional mathematicians, physicists, philosophers and some judges or very senior counsel can be found in this group.
  Many Nobel laureates and some historical geniuses are also to be found here.
  People in this category make up society's intellectual leaders.
  Most original ideas start with these people.
  However their contribution tends to be in bits and pieces rather than a whole new system or new way of seeing things.
  Particularly true of those choosing not to reside within academia, they tend to marvel at how poorly most people (with lower IQ) cope with life's common trials, properly recognizing such challenges as par for the course.
  One in 1,000 people.
  Beginning to be truly rare, these can underestimate themselves by almost a standard deviation in an unbelieving attempt to reduce disparity.

 

• +4σ: Genius.
  Most exceed the average postgraduate in academic competence - even professors - while still in primary school and probably knew more than their teachers from about fourth grade.
  They can and do read philosophy for pleasure well before puberty and can read at the university level before the average person can comprehend a primary reader (that is, "I see a cat").
  The smarter Nobel Prize winners and most historical geniuses (people such as Einstein, Hawkins, Byron, Milton, Kant, Newton, Bertrand Russell, Ayn Rand) are to be found in this category.
  They are the source of virtually all of humanity's advances.
  A common experience with people in this category or higher is that they are not wanted - the masses (including the professional classes) find them an affront of some sort.
  Fewer than 1 in ten thousand.
  Fortunately, they are plentiful in absolute numbers, so many of them do rise above the envy and hostility.
  Pride in their accomplishments notwithstanding, these can underestimate themselves by a standard deviation as well as overestimate others by as much.

 

• +5σ: Freakish.
  While still of primary school age, only around one in 1,000 professors can look them in the eye intellectually, social pigeonholing notwithstanding.
  Fewer than one in a million people are this intelligent.
  They are seldom understood or appreciated.
  Often perceived as arrogant (may be intentional or unintentional); besides being broadly adept, they may never encounter anyone with a higher IQ.
  Most feel profoundly isolated from society - even when they are appreciated.
  A large proportion of this group opt out of society and never make revolutionary contributions in the standard academic fields or professions.
  It seems to be very difficult to motivate them to play the academic/scholarly/professional game because they regard even the most venerable of traditions and institutions as absurd or silly.
  Consider that even the mind of the average professor appears to them like the mind of the average bricklayer would appear to the professor.
  Even complex human behavior, individually and en masse, may be depressingly predictable to these.
  Being significantly rare, these tend to underestimate themselves by up to two standard deviations and often overestimate others, in an unbelieving attempt to reduce marked disparity (Copernican principle of intelligence).

 

• +6σ
  In all of history only about a dozen people have been this smart.

 

Think of intelligence as a balloon. Its volume can be thought of as the totality of intellectual capability. Another way of looking at the balloon is by measuring its skin's distance from center. However, not all intellect balloons are spherical. Some have protrusions in one or two areas, suggesting greater than average ability in those areas. Such protrusions, though, do not necessarily imply greater volume overall.

So what does IQ measure? That depends upon the test, the application, the anecdote, etc. People like Sidis may be extremely bright in a key areas (e.g., math, language), indicating protrusions that do indeed extend very far from center in those ares. This does not necessarily suggest, though, that the overall volume of his intellectual balloon is as great. In other words, in those limited areas, Sidis may have had a 6σ IQ, but his overall IQ (not limited to math and language, for example) may have been only 4σ. This is just an example. (I never knew Sidis or the specific tests of his IQ.) My experience with autistic savants (e.g., "Rain Man") is lacking, but I imagine these to be like balloons with giant protrusions in one area, perhaps two, but an overall volume that may even be less than average. Their measured IQs then, may be near the top of the scale or mediocre, depending upon what's tested or how.

Perhaps IQ should be expanded to be more than a mere scalar. Perhaps there should be an array of quantifiers, one for each area of excellence corresponding to balloon protrusions, plus an additional quantifier for overall intelligence corresponding to balloon volume. I believe most IQ tests are quite poor, though, at best testing merely some common areas of protrusions and merely hinting at overall volume, but with little to no distinctive qualification. I imagine improving such exams would be a daunting task, given the complexity that is intellect.