*
In considering the nature of genius, it is not possible to define it in terms of a single variable - but requires several factors: the three Ps - power, preeminence, and associated with a personality.
1. Genius is a form of power
It is indeed a new source of power that adds to human capability.
An analogy would be that genius is like discovering a new supply of fuel - a new forest, coal seam or oil field. This new power can be used constructively, or destructively - for tools or for weapons.
Genius is somewhat like a local reorganization of reality to create new capability or efficiency, the insights and theory necessary for such a reorganization, or a technology or tool that enables such a reorganization.
But if the primary reality of genius is a new source of power, the secondary effect is to redistribute power - specifically to concentrate power around the results of genius (not necessarily around the genius himself, but concentrate power around the product of genius).
But is should be noticed that the tendency is for this power to diffuse and dilute - so that the consequences of genius spread much more widely than the situation or society in which the originating genius dwelt.
*
2. That power is associated with preeminence
A genius must also be preeminent is his field, must be a person of high ability. Thus, it is not genius when a person is of mediocre ability but merely has power conferred upon him or has a large effect but by accident.
*
3. Genius is personal, that is it originates in a specific person
The power and preeminence of a genius must also be derived from within themselves, must originate from the person - and not merely from his position in a system or institution or from headship of a team (or from some other person - as when somebody else's work is appropriated).
I think the only exception to this is that sometimes genius seems to be genuinely dyadic - a product of the close interaction of two persons neither of who is necessarily a genius alone. Gilbert and Sullivan would be one instance, Crick and Watson is perhaps another. But - as far as I know - this does not scale-up to higher numbers: genius may occasionally be a dyad, but never triadic or more.
*
These criteria are similar to those for a Nobel Prize - a prize is awarded (in general) when an influential breakthrough (corresponding to power) is associated with a particular individual and is the achievement of that person; or up to three people when the prize is awarded for either for establishing a new field via more than one discovery, or awarded for the two or three most significant steps towards as discovery.
However, the Nobel does not have direct reference to preeminence, and some prizes have been given to people who were exceptionally hard-working, or in the right place at the right time, or lucky rather than exceptionally able.
*
Wednesday, 9 October 2013
Friday, 4 October 2013
Thursday, 3 October 2013
Comparing mental age ratio with percentile measures of IQ - the intrinsic imprecision of high IQ measures in adults
*
I dislike the current method of expressing IQ rankings with an average of 100 and a standard deviation of 15 (or 16): in fact I think it is crazy and bizarre, and puts IQ research into a weird scientific category all or its own, while making IQ measurements all but incomprehensible to almost everybody.
Underneath these IQ numbers lies the more useful and comprehensible information about percentiles; and this would be a much better method of expressing intelligence - for example instead of saying an IQ of 130, just state that the person is in the top 2 % of the population (approx).
*
What is wrong with that? - and how much clearer it is.
Nonetheless, such percentages are still incomprehensible to many people, and it might be better to express the information as its reciprocal - that only one in fifty people have this intelligence as high as this or higher.
This gives a clearer sense of IQ differences - because when the average is 100, then an IQ of 130 looks as if it is almost identical to IQ 126 about twice as superior as 115.
But it probably makes more sense to say that an IQ of 130 (in the top 2%) is more like twice as superior as an IQ of 126 (in the top 4%) and about eight times superior to an IQ of 115 (top 16%)
*
But percentiles are still pretty abstract and incomprehensible, and not many people can think that way.
So there is much to be said for the original method of calculating IQ by mental age ratios.
In this system, the performance of a specific child in a specific examination is interpolated into a graph of the average performance of children of different age groups in that examination.
Thus, when an 8 year old child performs at the level of an average 10 year old, he is described as having a mental age of ten (or, if you must! - an IQ of 125 - since 10 is 25% more than 8).
*
Why was this simple and elegant method of measuring intelligence dropped?
Well, in the first place it wasn't - and parents are used to being told their child's Reading Age, which is a straightforward mental age measurement.
But the main problem is in relation to adult IQs.
It is easy to calculate mental ages for most young children - but the performance in tests reaches a maximum plateau sometime in the teens (and later for men than women) - which means that mental age calculations can only be used to calculate average or below-average performance in adults.
*
However, although the use of percentile measurements among high ability adults would appear to be a good solution; the method is something of a fraud, because the calculated values of intelligence are almost always extrapolated rather than interpolated.
What I mean is that, in most IQ tests, the percentage prevalence of performance at high levels is not known from direct measurement, but is extrapolated on the assumption that performance has a normal distribution.
Just imagine what it means to say that a person has an IQ of 145 - approximately the 0.1 percentile, or one in a thousand of the randomly sampled total population?
To know the actual performance of the top 0.1 percent, it would be necessary to measure several people at this level - maybe twelve? To get twelve people who are in the top 0.1 percent it would be necessary to test 12,000 randomly selected people - except that to be reasonably sure of getting 12 in a random sample you would need to have a larger sample than that... maybe 48,000 people or more?
Whatever the decision, at any rate this is a huge IQ test study, and a study of this size cannot possibly (in practice) be random, or anything like it. And if a total enumeration of the population (i.e. a census) was attempted, then there could not be a precise measure of IQ since the test would need to be short and simple.
Indeed, the situation is even worse! - because any test simple and short enough to be do-able by those of low intelligence would be unable to discriminate precisely among those of high intelligence.
Yet, any test which was difficult enough to be able to discriminate among adults of high IQ, would not be able to be normed accurately against tests suitable for lower IQ.
*
My point is that the allocation of numerical values to high levels of adult intelligence, which is made rational by the percentile method of calculation, must be taken with some bucketloads of salt.
The only high IQ measures that are both clearly understandable and relatively assumption-free are mental age calculations done on young children.
Differences in high levels of adult IQ are indeed measurable; but these differences cannot precisely be allocated percentiles with respect to the whole population, nor can they be understood in terms of mental age.
When it comes to high adult intelligence we can only say that it is high (e.g. within the top one or two percent), and that the IQ of Dr X is higher or lower than Professor Y - but we cannot say much more than than.
*
I dislike the current method of expressing IQ rankings with an average of 100 and a standard deviation of 15 (or 16): in fact I think it is crazy and bizarre, and puts IQ research into a weird scientific category all or its own, while making IQ measurements all but incomprehensible to almost everybody.
Underneath these IQ numbers lies the more useful and comprehensible information about percentiles; and this would be a much better method of expressing intelligence - for example instead of saying an IQ of 130, just state that the person is in the top 2 % of the population (approx).
*
What is wrong with that? - and how much clearer it is.
Nonetheless, such percentages are still incomprehensible to many people, and it might be better to express the information as its reciprocal - that only one in fifty people have this intelligence as high as this or higher.
This gives a clearer sense of IQ differences - because when the average is 100, then an IQ of 130 looks as if it is almost identical to IQ 126 about twice as superior as 115.
But it probably makes more sense to say that an IQ of 130 (in the top 2%) is more like twice as superior as an IQ of 126 (in the top 4%) and about eight times superior to an IQ of 115 (top 16%)
*
But percentiles are still pretty abstract and incomprehensible, and not many people can think that way.
So there is much to be said for the original method of calculating IQ by mental age ratios.
In this system, the performance of a specific child in a specific examination is interpolated into a graph of the average performance of children of different age groups in that examination.
Thus, when an 8 year old child performs at the level of an average 10 year old, he is described as having a mental age of ten (or, if you must! - an IQ of 125 - since 10 is 25% more than 8).
*
Why was this simple and elegant method of measuring intelligence dropped?
Well, in the first place it wasn't - and parents are used to being told their child's Reading Age, which is a straightforward mental age measurement.
But the main problem is in relation to adult IQs.
It is easy to calculate mental ages for most young children - but the performance in tests reaches a maximum plateau sometime in the teens (and later for men than women) - which means that mental age calculations can only be used to calculate average or below-average performance in adults.
*
However, although the use of percentile measurements among high ability adults would appear to be a good solution; the method is something of a fraud, because the calculated values of intelligence are almost always extrapolated rather than interpolated.
What I mean is that, in most IQ tests, the percentage prevalence of performance at high levels is not known from direct measurement, but is extrapolated on the assumption that performance has a normal distribution.
Just imagine what it means to say that a person has an IQ of 145 - approximately the 0.1 percentile, or one in a thousand of the randomly sampled total population?
To know the actual performance of the top 0.1 percent, it would be necessary to measure several people at this level - maybe twelve? To get twelve people who are in the top 0.1 percent it would be necessary to test 12,000 randomly selected people - except that to be reasonably sure of getting 12 in a random sample you would need to have a larger sample than that... maybe 48,000 people or more?
Whatever the decision, at any rate this is a huge IQ test study, and a study of this size cannot possibly (in practice) be random, or anything like it. And if a total enumeration of the population (i.e. a census) was attempted, then there could not be a precise measure of IQ since the test would need to be short and simple.
Indeed, the situation is even worse! - because any test simple and short enough to be do-able by those of low intelligence would be unable to discriminate precisely among those of high intelligence.
Yet, any test which was difficult enough to be able to discriminate among adults of high IQ, would not be able to be normed accurately against tests suitable for lower IQ.
*
My point is that the allocation of numerical values to high levels of adult intelligence, which is made rational by the percentile method of calculation, must be taken with some bucketloads of salt.
The only high IQ measures that are both clearly understandable and relatively assumption-free are mental age calculations done on young children.
Differences in high levels of adult IQ are indeed measurable; but these differences cannot precisely be allocated percentiles with respect to the whole population, nor can they be understood in terms of mental age.
When it comes to high adult intelligence we can only say that it is high (e.g. within the top one or two percent), and that the IQ of Dr X is higher or lower than Professor Y - but we cannot say much more than than.
*
Wednesday, 2 October 2013
How big is the IQ cognitive elite?
*
For Herrnstein and Murray publishing The Bell Curve in 1996, the cognitive elite comprised those of:
IQ 125 and above, or 5% of the population - that is one person in twenty.
But for Cyril Burt writing in 1924^, the cognitive comprised those of:
IQ 150 or above, or 0.1% of the population - that is one person in a thousand.
So Burt's elite was fifty times more elite than Herrnstein and Murray's!
*
A small part of this difference is due to Burt using the 'mental ratio' method of calculating IQ - which is that an IQ of 150 is attributed when a child's performance in intelligence testing is the same as the average child fifty percent older (up to a plateau of about 14-16 years old) - for example when an 8 year old performs at level of an average 12 year old.
By contrast, H&M use the 'percentile' method of calculating IQ - which tests a (supposedly population-representative) sample of subjects and puts their results into rank order and then fits onto this a normal distribution curve with 100 IQ points as the mean average and a standard deviation of 15 - such that the IQ of an individual is a statement of their percentile position if the normal distribution assumptions are assumed to be true and if extrapolation beyond the available data is regarded as valid.
(I will soon post a comparison and critique of ratio versus percentile methods of measuring IQ, especially higher than average IQ, separately.)
*
But this accounts for only about 5 IQ points difference in Burt's standard (i.e. Burt's IQ of 150 would be approx. equal to H&M's IQ of 146).
There just is a very big difference in the size of the cognitive elite; and an equally profound difference in the kind of jobs that people of different intelligences ought to be doing.
('Ought' - that is - from Burt's late 19th-early 20th century Left-wing Fabian eugenic meritocratic perspective of optimal rational efficiency.)
*
Burt has eight grades of intelligence, which I will here express in terms of rounded percentiles.
1. Top 0.1 % - Higher Professional: appropriate for university scholarships and honours degrees - occupations include university academics, doctors, lawyers, higher administrators in business and civil service.
2. Top 2 percent - Lower Professional: appropriate for secondary (high) school education, but not for college or university. Occupations include elementary school teachers and higher level clerks.
3. Top 15 percent - Clerks and Highly Skilled Workers: higher elementary education, leaving school about 14 years old; the occupations are of 'intelligent, but moderately routine character' - such as highly skilled manual workers and most clerks.
4. Top 50 percent (above average, but below the above groups - comprising about 35% of total population) - Skilled workers and most Commercial Positions: occupations in skilled labour such as shopkeepers, small scale tradesman, shop assistants for large firms.
5. The approx 35-40% who fall just below the average (that is, IQ roughly between 85 and 100) - Semi-skilled Labour: such as (I guess) underground coal miners, shipyard workers, steel workers, farm foremen.
6. Those above the bottom 4% but below the group of semi-skilled (that is, IQ roughly between 70 and 85) - Unskilled Labour - (I guess) farm workers, navvies, most labourers.
7. & 8 The bottom 4% described as "Casual Labour, Imbeciles and Idiots": are those who are more or less mentally handicapped - some can be basic domestic servants and rural labourers, most are incapable of work and presumably live under family care or in institutions.
*
What is striking about Burt's classification is how minute are the elite; and what a high intellectual standard, compared with nowadays, he expects would be required for each level of occupation.
This fits with my idea that nowadays we are living in an over-promoted society
http://iqpersonalitygenius.blogspot.co.uk/search?q=over-promoted
Compared with about a century ago, the average cognitive competence of occupational strata has decline by at least one of Burt's categories, sometimes more like two categories.
Part of this is due to the inflationary expansion of the upper categories - which means that people have higher level occupations in name, but not in terms of what they actually do; and part of it is due to the decline in general intelligence over these period, such that the proportion of the population in each high level category has declined.
For example, intelligence at Burt's highest level was attained by one in a thousand as measured in 1924; but this level would now probably now be attained by only one in five or ten thousand (or less).
*
Burt envisaged a society with a small and very able cognitive elite, selected and allocated afresh each generation; and the mass of people doing manual labour and routine clerical jobs.
Yet we apparently see in the modern West is a society in which only a small proportion do manual labour (due to increased use of machines and computerization) and a third or more of people do what appear to be higher level jobs in Burt's categories 1 and 2.
I think the meritocrats of Burt's era would interpret this in terms of a massive expansion of make-work - instead of making unemployed the mass of the manual and routine clerical workers displaced by mechanization and computers, they have been allocated pretend work at a higher level than they are competent to accomplish.
*
What the early meritocrats would not have envisaged, since they lived in a much more honest society than ours, was that we could have this current situation of massive over-promotion, gross inflation of occupational status, and incomprehensibly vast erosion of the value of educational qualifications - and yet to deny outright that this is the case: indeed to pretend that the average person in a given category is smarter, better educated and more competent!
**
^Burt C. The principles of vocational guidance. British Journal of Psychology. 1924; 14: 336-352.
For Herrnstein and Murray publishing The Bell Curve in 1996, the cognitive elite comprised those of:
IQ 125 and above, or 5% of the population - that is one person in twenty.
But for Cyril Burt writing in 1924^, the cognitive comprised those of:
IQ 150 or above, or 0.1% of the population - that is one person in a thousand.
So Burt's elite was fifty times more elite than Herrnstein and Murray's!
*
A small part of this difference is due to Burt using the 'mental ratio' method of calculating IQ - which is that an IQ of 150 is attributed when a child's performance in intelligence testing is the same as the average child fifty percent older (up to a plateau of about 14-16 years old) - for example when an 8 year old performs at level of an average 12 year old.
By contrast, H&M use the 'percentile' method of calculating IQ - which tests a (supposedly population-representative) sample of subjects and puts their results into rank order and then fits onto this a normal distribution curve with 100 IQ points as the mean average and a standard deviation of 15 - such that the IQ of an individual is a statement of their percentile position if the normal distribution assumptions are assumed to be true and if extrapolation beyond the available data is regarded as valid.
(I will soon post a comparison and critique of ratio versus percentile methods of measuring IQ, especially higher than average IQ, separately.)
*
But this accounts for only about 5 IQ points difference in Burt's standard (i.e. Burt's IQ of 150 would be approx. equal to H&M's IQ of 146).
There just is a very big difference in the size of the cognitive elite; and an equally profound difference in the kind of jobs that people of different intelligences ought to be doing.
('Ought' - that is - from Burt's late 19th-early 20th century Left-wing Fabian eugenic meritocratic perspective of optimal rational efficiency.)
*
Burt has eight grades of intelligence, which I will here express in terms of rounded percentiles.
1. Top 0.1 % - Higher Professional: appropriate for university scholarships and honours degrees - occupations include university academics, doctors, lawyers, higher administrators in business and civil service.
2. Top 2 percent - Lower Professional: appropriate for secondary (high) school education, but not for college or university. Occupations include elementary school teachers and higher level clerks.
3. Top 15 percent - Clerks and Highly Skilled Workers: higher elementary education, leaving school about 14 years old; the occupations are of 'intelligent, but moderately routine character' - such as highly skilled manual workers and most clerks.
4. Top 50 percent (above average, but below the above groups - comprising about 35% of total population) - Skilled workers and most Commercial Positions: occupations in skilled labour such as shopkeepers, small scale tradesman, shop assistants for large firms.
5. The approx 35-40% who fall just below the average (that is, IQ roughly between 85 and 100) - Semi-skilled Labour: such as (I guess) underground coal miners, shipyard workers, steel workers, farm foremen.
6. Those above the bottom 4% but below the group of semi-skilled (that is, IQ roughly between 70 and 85) - Unskilled Labour - (I guess) farm workers, navvies, most labourers.
7. & 8 The bottom 4% described as "Casual Labour, Imbeciles and Idiots": are those who are more or less mentally handicapped - some can be basic domestic servants and rural labourers, most are incapable of work and presumably live under family care or in institutions.
*
What is striking about Burt's classification is how minute are the elite; and what a high intellectual standard, compared with nowadays, he expects would be required for each level of occupation.
This fits with my idea that nowadays we are living in an over-promoted society
http://iqpersonalitygenius.blogspot.co.uk/search?q=over-promoted
Compared with about a century ago, the average cognitive competence of occupational strata has decline by at least one of Burt's categories, sometimes more like two categories.
Part of this is due to the inflationary expansion of the upper categories - which means that people have higher level occupations in name, but not in terms of what they actually do; and part of it is due to the decline in general intelligence over these period, such that the proportion of the population in each high level category has declined.
For example, intelligence at Burt's highest level was attained by one in a thousand as measured in 1924; but this level would now probably now be attained by only one in five or ten thousand (or less).
*
Burt envisaged a society with a small and very able cognitive elite, selected and allocated afresh each generation; and the mass of people doing manual labour and routine clerical jobs.
Yet we apparently see in the modern West is a society in which only a small proportion do manual labour (due to increased use of machines and computerization) and a third or more of people do what appear to be higher level jobs in Burt's categories 1 and 2.
I think the meritocrats of Burt's era would interpret this in terms of a massive expansion of make-work - instead of making unemployed the mass of the manual and routine clerical workers displaced by mechanization and computers, they have been allocated pretend work at a higher level than they are competent to accomplish.
*
What the early meritocrats would not have envisaged, since they lived in a much more honest society than ours, was that we could have this current situation of massive over-promotion, gross inflation of occupational status, and incomprehensibly vast erosion of the value of educational qualifications - and yet to deny outright that this is the case: indeed to pretend that the average person in a given category is smarter, better educated and more competent!
**
^Burt C. The principles of vocational guidance. British Journal of Psychology. 1924; 14: 336-352.
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