Did you know that if you're a completely average person, in personality traits, memory, and intellegence, there are about 145,000 people just like you on planet earth, or about 13,000 here in the USA . Identical!! Like a twin, and even more. This sounds like a lot, but it is really quite a small proportion, about 36 in one million. Here we look at the numbers - some very tiny and some astronomically big.
Preamble – Do you want to live forever? You will, but perhaps not in the way you think – or want. In a previous report, The Immortality Paradox, (http://used-ideas.blogspot.com/2012/06/immortality-paradox.html) it was demonstrated from a human viewpoint, that immortality is rather problematic simply from mental capacities consideration. But there is another way. (Note, we leave of religious, deist, theist, considerations that identify an immortal soul, as they take us far afield of our point here.) Have you ever said something like this. “You know that Karen is just like Susie. If they looked alike they could be identical twins. Probably you have. We all know folks that are really, really similar to others. Sometimes, we remark on this as unique, and perhaps it is in small populations, but when we consider large populations, there are many, many people almost identical.
Who are you, anyway? Background factors such as education, sense of determination, life shaping events notwithstanding, you are a personality of many traits, a brain, a memory, bound and shaped by experiences and abilities – all wrapped up in a physical container.
What are really your personality and our mental abilities? According to some accounts, you have seventy distinct personality characteristics. Roy Posner, (http://www.gurusoftware.com/gurunet/personal/factors.htm), splits them into categories or subscales of (a) attitudes (73), (b) miscellaneous attributes (95), (c) social endowments (11), and (d) skills (23), where the numbers in parentheses indicate the individual traits in the respective category. Just a few of the attitudes and their negatives are
If one were classified with each of these (though the overlap is considerable) as “on” or “off,” that is you have it or you don’t, with no gradations in between there would be 2(73+95+11+23) = 2202 completely different personalities. This is a big number, about a six followed by sixty zeros, or to three places (6.43)x1060. How big is that? Well, as of 2009, the entire World Wide Web was estimated to contain close to 500 exabytes of data. This is a half zettabyte. Let’s say it is now, in 2012, a full zetabyte, which is 1021 bytes. Cubing that gives 1063 just over the number of complete personalities – actually about 100 times it. By comparison, the population of the world is about 4x109 (about four billion, 4,000,000,000). It should be clear from these numbers, the chances of there being an identical-in-all-ways-twin for you is infinitesimally remote – unless that person is just that, biologically. But, looking at all these traits reveals many come in bunches. There simply cannot be a person with arbitrary trait values. Let's look a little deeper
The Big Five. The Big Five are five distinct personality traits that most psychologists believe classify your personality with high probability. The goal of personality traits thoeries has been to predict behavior. This has been extraordinarily difficult, until the tests of the theories ceased trying to predict individual actions but aggregates of them. Then prediction became more reliable. These five are the so-called The Big Five framework of personality traits from Costa & McCrae, 1992 has emerged as a robust model for understanding the relationship between personality and various academic behaviors.[1] The Big Five personality traits from Costa & McCrae, 1992, have been rediscovered more than one time – always the same - are:
Assumption #1. Each of these traits is divided into a scale of eleven degrees ranging over the extremes. So, there are eleven degrees each of openness, conscientiousness, etc.
Thus, we now have five traits each with eleven degrees. So, from the Big Five and Assumption #1 there are so far only 115 (= 11 x 11 x 11 x 11 x 11) or 161051 different personality types to consider. Next, we introduce two more personality types, or physical attributes that profoundly influence how the personality types are manifest. The first is your intelligence and the second is your memory. For memory, we use a similar scale graded from 0 to 10, just as for the personality traits.
For intelligence, we use the controversial measure, the Intelligence Quotient, IQ. There is so much literature on the IQ test, we consider only a gross summary as provided in the Wikipedia. See, http://wilderdom.com/intelligence/IQWhatScoresMean.html. Basically, the consensus is that 99.5% of all people have an IQ in the range between 60 and 140. We restrict the IQ range from 0 to 200, and this includes just about everyone.
Assumption #2. Intelligence is measured by the IQ score divided into 13 levels. As with personality traits, any value at the extremes indicates a very, very rare individual - from idiot to genius. Your memory is divided into 11 categories, with a five indicating a strictly average memory. Extremes, 0-3 and 7-10 again are very rare.
What are the results? We assign probabilities to each level. The probability tables are below.
To clarify this table, let us suppose you believe your self to be very, very inventive, say about an 8 on the scale. The probability of this occuring in the general population is 0.049, or at the rate of 49 of every 1000 people. If you believe your self to be average on memory, say about a 5 on the scale, the probability of this occuring in the general population is 0.236, or about one in four.
It would be difficult to divide the scale between each of these attributes into 11 parts. Here is how it might look. Keep in mind the extreme values are just that; you probably don't know anyone in the top three and/or bottom three subscales.
The IQ's are standard. The probabilities used are cited in the literature. In this case, we use 13 subscales. The extremes, -1 and 11, are in the ranges, including the idiot and super genius, respectively. Personally, I know only about one person that fits the genius scale. Not me. :)
The Probabilities. The probabilities in both tables are computed using what statistically is called the normal distribution. Another way would be to use the uniform distribution, that would make all possibilities the same. The number of geniuses is the same as the number of average people, and so on. This would be the same as in flipping a coin ten times, the chance of getting all ten heads is the same as any mixture of heads and tails. This is not intuitive. And similarly, this is not the way traits generally behave. There is a concentration about the middle; the extremes are more rare. The probabilities in the table express this. The normal curve has a distribution just like in the graphic below, as a probability density function. In fact, this is exactly the curve used to compute the probabilities in the personality trait table.
Computing the numbers. We assume all seven traits are independent. This means the probabilities multiply. So, we might select a person with traits 5,6,5,6,6,4,8. Select the probabilities and multiply them together. Then multiply by the population. It is easier to see this in the following example. Suppose we have two coins of different values, e.g. a nickel and a dime, or 1 € and 2 € coins. When flipping both together the probability of getting two heads is 1/2 * 1/2 = 1/4. This is because the outcomes are independent, i.e. the outcome for one of the coins is independent of the other.
As an aside... An alternative to the normal distribution is the uniform distribution. This means we assign equal probabilities to each case. In the case of the IQ, this means we would assume there are an equal number of geniuses as average types, something none of us would agree about. The normal distribution is, curiously, the way nature operates when confronted with multiples of independent trials measuring the same thing. This is a mathematical conclusion, the proof of which would take us far beyond the simple application we are pursuing.
Special cases: It is always interesting (and fun) to look at and conjecture at special cases of folks. Bear in mind that individuals in this profession or set of attributes may have slightly different profiles. These do add up to get the full populations.
0. Averages: The average, above average and below average categories contribute to about 146,726,000 of the total four billion of the world population. If we include the full normal range, those way above to way below categories, this model accounts for 1,383,108,000 of the world population. This does at the same time contribute a considerable population but leaves out very, very many. We conclude that more than half the world population has at least one personality trait or IQ well beyond the normal ranges. To compute these values, we sum the probabilities over the respective ranges and then take to the sixth power, multiply by the IQ probability sum, and then multiply by 4,000,000,000,000.
1. Sociopaths: Note by selection values as small as 3 and as large as 8 takes us to the extreme edges of the particular personality trait. Naturally, we could do ranges, as above, on the scores/values, increasing by a lot the world population.
Conclusions.
Preamble – Do you want to live forever? You will, but perhaps not in the way you think – or want. In a previous report, The Immortality Paradox, (http://used-ideas.blogspot.com/2012/06/immortality-paradox.html) it was demonstrated from a human viewpoint, that immortality is rather problematic simply from mental capacities consideration. But there is another way. (Note, we leave of religious, deist, theist, considerations that identify an immortal soul, as they take us far afield of our point here.) Have you ever said something like this. “You know that Karen is just like Susie. If they looked alike they could be identical twins. Probably you have. We all know folks that are really, really similar to others. Sometimes, we remark on this as unique, and perhaps it is in small populations, but when we consider large populations, there are many, many people almost identical.
Who are you, anyway? Background factors such as education, sense of determination, life shaping events notwithstanding, you are a personality of many traits, a brain, a memory, bound and shaped by experiences and abilities – all wrapped up in a physical container.
What are really your personality and our mental abilities? According to some accounts, you have seventy distinct personality characteristics. Roy Posner, (http://www.gurusoftware.com/gurunet/personal/factors.htm), splits them into categories or subscales of (a) attitudes (73), (b) miscellaneous attributes (95), (c) social endowments (11), and (d) skills (23), where the numbers in parentheses indicate the individual traits in the respective category. Just a few of the attitudes and their negatives are
| honest | dishonest, deceiving, lying |
| humble | arrogant, conceited, ego-centric |
| interested | indifferent, uncaring |
| involved | complacent, indifferent |
| jealous, not | jealous, envious, covetous |
| kind | unkind, uncaring, cruel, mean |
If one were classified with each of these (though the overlap is considerable) as “on” or “off,” that is you have it or you don’t, with no gradations in between there would be 2(73+95+11+23) = 2202 completely different personalities. This is a big number, about a six followed by sixty zeros, or to three places (6.43)x1060. How big is that? Well, as of 2009, the entire World Wide Web was estimated to contain close to 500 exabytes of data. This is a half zettabyte. Let’s say it is now, in 2012, a full zetabyte, which is 1021 bytes. Cubing that gives 1063 just over the number of complete personalities – actually about 100 times it. By comparison, the population of the world is about 4x109 (about four billion, 4,000,000,000). It should be clear from these numbers, the chances of there being an identical-in-all-ways-twin for you is infinitesimally remote – unless that person is just that, biologically. But, looking at all these traits reveals many come in bunches. There simply cannot be a person with arbitrary trait values. Let's look a little deeper
The Big Five. The Big Five are five distinct personality traits that most psychologists believe classify your personality with high probability. The goal of personality traits thoeries has been to predict behavior. This has been extraordinarily difficult, until the tests of the theories ceased trying to predict individual actions but aggregates of them. Then prediction became more reliable. These five are the so-called The Big Five framework of personality traits from Costa & McCrae, 1992 has emerged as a robust model for understanding the relationship between personality and various academic behaviors.[1] The Big Five personality traits from Costa & McCrae, 1992, have been rediscovered more than one time – always the same - are:
- Openness (inventive/curious vs. consistent/cautious)
- Conscientiousness (efficient/organized vs. easy-going/careless)
- Extraversion (outgoing/energetic vs. solitary/reserved)
- Agreeableness (friendly/compassionate vs. cold/unkind)
- Neuroticism (secure/confident vs. sensitive/nervous)
Assumption #1. Each of these traits is divided into a scale of eleven degrees ranging over the extremes. So, there are eleven degrees each of openness, conscientiousness, etc.
Thus, we now have five traits each with eleven degrees. So, from the Big Five and Assumption #1 there are so far only 115 (= 11 x 11 x 11 x 11 x 11) or 161051 different personality types to consider. Next, we introduce two more personality types, or physical attributes that profoundly influence how the personality types are manifest. The first is your intelligence and the second is your memory. For memory, we use a similar scale graded from 0 to 10, just as for the personality traits.
For intelligence, we use the controversial measure, the Intelligence Quotient, IQ. There is so much literature on the IQ test, we consider only a gross summary as provided in the Wikipedia. See, http://wilderdom.com/intelligence/IQWhatScoresMean.html. Basically, the consensus is that 99.5% of all people have an IQ in the range between 60 and 140. We restrict the IQ range from 0 to 200, and this includes just about everyone.
Assumption #2. Intelligence is measured by the IQ score divided into 13 levels. As with personality traits, any value at the extremes indicates a very, very rare individual - from idiot to genius. Your memory is divided into 11 categories, with a five indicating a strictly average memory. Extremes, 0-3 and 7-10 again are very rare.
What are the results? We assign probabilities to each level. The probability tables are below.
Personality Trait Table
| |||||||||||||
| Attribute | Low range |
Scale
| High range | ||||||||||
| Openess | Cautious |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Inventive |
| Conscientiousness | Careless |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Efficient |
| Extraversion | Solitary |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Outgoing |
| Agreeableness | Cold |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Friendly |
| Neuroticism | Sensitive |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Secure |
| Memory | Very poor |
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
| Near photographic |
| Probabilities | 0.003 | 0.014 | 0.049 | 0.117 | 0.198 | 0.236 | 0.198 | 0.117 | 0.049 | 0.014 | 0.003 | ||
To clarify this table, let us suppose you believe your self to be very, very inventive, say about an 8 on the scale. The probability of this occuring in the general population is 0.049, or at the rate of 49 of every 1000 people. If you believe your self to be average on memory, say about a 5 on the scale, the probability of this occuring in the general population is 0.236, or about one in four.
It would be difficult to divide the scale between each of these attributes into 11 parts. Here is how it might look. Keep in mind the extreme values are just that; you probably don't know anyone in the top three and/or bottom three subscales.
Value
|
Subscales
| |
0
| Absolutely to the extreme | Below Average |
1
| Extreme | |
2
| Exceptionally below average | |
3
| Way below average | |
4
| Below average | |
5
| Average | |
6
| Above average | Above Average |
7
| Way above average | |
8
| Exceptionally above average | |
9
| Extreme | |
10
| Absolutely to the extreme |
The IQ's are standard. The probabilities used are cited in the literature. In this case, we use 13 subscales. The extremes, -1 and 11, are in the ranges, including the idiot and super genius, respectively. Personally, I know only about one person that fits the genius scale. Not me. :)
Intelligent Quotient (IQ) Table
| |||||||
| Value |
5
|
4 or 6
|
3 or 7
|
2 or 8
|
1 or 9
|
0 or 10
|
-1 or 11
|
| Top Range |
96-103
|
104-111
|
112-119
|
120-127
|
128-135
|
136-143
|
144-200
|
| Bottom Range |
88-95
|
80-87
|
72-79
|
64-71
|
56-63
|
0-55
| |
| Probabilities |
0.210
|
0.183
|
0.121
|
0.060
|
0.023
|
0.007
|
0.0017
|
The Probabilities. The probabilities in both tables are computed using what statistically is called the normal distribution. Another way would be to use the uniform distribution, that would make all possibilities the same. The number of geniuses is the same as the number of average people, and so on. This would be the same as in flipping a coin ten times, the chance of getting all ten heads is the same as any mixture of heads and tails. This is not intuitive. And similarly, this is not the way traits generally behave. There is a concentration about the middle; the extremes are more rare. The probabilities in the table express this. The normal curve has a distribution just like in the graphic below, as a probability density function. In fact, this is exactly the curve used to compute the probabilities in the personality trait table.
Computing the numbers. We assume all seven traits are independent. This means the probabilities multiply. So, we might select a person with traits 5,6,5,6,6,4,8. Select the probabilities and multiply them together. Then multiply by the population. It is easier to see this in the following example. Suppose we have two coins of different values, e.g. a nickel and a dime, or 1 € and 2 € coins. When flipping both together the probability of getting two heads is 1/2 * 1/2 = 1/4. This is because the outcomes are independent, i.e. the outcome for one of the coins is independent of the other.
As an aside... An alternative to the normal distribution is the uniform distribution. This means we assign equal probabilities to each case. In the case of the IQ, this means we would assume there are an equal number of geniuses as average types, something none of us would agree about. The normal distribution is, curiously, the way nature operates when confronted with multiples of independent trials measuring the same thing. This is a mathematical conclusion, the proof of which would take us far beyond the simple application we are pursuing.
0. Averages: The average, above average and below average categories contribute to about 146,726,000 of the total four billion of the world population. If we include the full normal range, those way above to way below categories, this model accounts for 1,383,108,000 of the world population. This does at the same time contribute a considerable population but leaves out very, very many. We conclude that more than half the world population has at least one personality trait or IQ well beyond the normal ranges. To compute these values, we sum the probabilities over the respective ranges and then take to the sixth power, multiply by the IQ probability sum, and then multiply by 4,000,000,000,000.
1. Sociopaths: Note by selection values as small as 3 and as large as 8 takes us to the extreme edges of the particular personality trait. Naturally, we could do ranges, as above, on the scores/values, increasing by a lot the world population.
Attribute
|
Score
|
| Openess |
7
|
| Conscientiousness |
3
|
| Extraversion |
8
|
| Agreeableness |
5
|
| Neuroticism |
7
|
| Memory |
8
|
| IQ |
120-127
|
Attribute
|
Score
|
| Openess |
6
|
| Conscientiousness |
6
|
| Extraversion |
5
|
| Agreeableness |
7
|
| Neuroticism |
6
|
| Memory |
6
|
| IQ |
112-119
|
Attribute
|
Score
|
| Openess |
6
|
| Conscientiousness |
6
|
| Extraversion |
4
|
| Agreeableness |
7
|
| Neuroticism |
6
|
| Memory |
8
|
| IQ |
136-143
|
- Naturally, you may disagree with the numbers. But... What is your personality profile? How many "twins" do you have? Simply assign a value for each personality traits, multiply together the associated probabilities, and then multiply by the population at hand. I have been using 4,000,000,000 for the world population.
Conclusions.
- Everyone should have their personality profile made - just like we all have an IQ. It clearly will help you know better who you are. You will be able to track your personality profile throughout your life.
- With it, teachers can know better how to teach individuals and classes.
- Employers will better be able to identify the applicant they will hire.
- Police will better develop suspect lists for specific types of crimes.
- It is always fun playing with numbers, especially big ones.
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