Normal Distribution
Normal Distribution
Virtually everything within our ken is a continuum and phenomena we experience tend to distribute
normally across a spectrum of continuum. Drop a glass and plot the location of the shards. Most fall
within a small circle around the impact point. Some may be discovered at some distance from that
impact point. Plotted, the results form what we have familiarly learned to call the bell curve. This can
be explained by the laws of physics, as can many such familiar phenomena. But many other
observations demonstrate a similar trend. Human intelligence, size, motivation, talent. Surely there
must be laws that explain the elements of social behavior and human nature in much the same
manner as the laws of physics, or so many have thought. If so such laws have eluded us.
Nonetheless, normal distribution continues to be demonstrated in so much of what we observe.
Looks. There are few beautiful people, and few truly ugly people, and many, many in between. There
are few truly good people, and few truly bad people, and many, many in between. But what is
beautiful and what is ugly? What is good and what is bad? Perceptions vary from individual to
individual, so become personal distributions rather than universal distributions. And thus we have
created words to help us communicate so we can discuss such comparisons. But the words
themselves are only approximations, and hardly ever truly precise. What is intelligence? What is
ruthlessness? What is compassion? Yet such words do provide us the means of roughly
communicating concepts, perceptions; and the result so often approximates a normal distribution.
The problem, of course, is that we attempt to isolate a variable and observe it as if it existed in
isolation, which it does not. Traits of individual personality certainly do not; we only attempt to
observe them as such. We are far too complex to yield to such simplicity. But to do otherwise is too
overwhelming to contemplate. So we slice and dice, and attempt to observe and make judgement in
isolated chunks for which we have created indecisive words. But even so, the words are helpful to
understanding, evaluating and analyzing the complex world in which we find ourselves, and must
live. And each result is, at least in individual minds, reduced to a normal distribution.
The elemental traits of “successful” leaders of society – the elite – are illustrative. For discussion
purposes let’s list a limited number upon which we might tentatively agree: intelligence, charisma,
insight, strength of character, persuasiveness, confidence. Just reviewing the words gives indication
of the difficulty in discussing this thing we call success in leadership.
Intelligence is many things: ability to learn, ability to remember, ability to understand. But more:
ability to grasp concepts and extrapolate their effect on the over all, whatever that might be; ability to
see forward to consequences; ability to develop useful perspectives; even ability to reason. And that
doesn’t begin to tell the story. We attempt to measure some of these things, but only ineffectively; but
when we do, the result is normal distribution. Some have virtually photographic memories; some
remember poorly. Most of us fall somewhere in between, at the top of the bell curve. And some, with
almost perfect memories, have poor perception, or limited understanding, or inability to see to
consequences. Intelligence then is a bewildering amalgamation of many perceived traits to which
we have clumsily assigned words.
Charisma is even worse. What is charisma? Oxford says, “the ability to inspire followers with
devotion and enthusiasm; an attractive aura; great charm. More imprecise words, truly an ICIWISI
kind of thing: I’ll know it when I see it. Insight? Oxford: “the capacity of understanding hidden truths,
etc., especially of character or situations.” Hidden truths? Character: “the collective qualities
especially mental and moral, that distinguish a person.” Persuasiveness: ability to persuade or
influence. Confidence: “a feeling of self-reliance or certainty; a sense of self-reliance or boldness.
So many words, so many vague concepts; but for the population in general, spread over a normal
distribution, most of us in the middle, but some with far greater strengths than others; and some with
almost none at all.
One of my favorites is confidence. Associated words – at least for me – are ego and arrogance. The
useful meaning of ego is self esteem. The person with none can not function; but he with towering
self esteem is so insufferable that we cannot stand him. Yet to be successful one must be closer to
the latter than the former. Arrogance is a word that often describes one whose ego is very strong.
For one who is confident is usually (but not always) so for some valid reason. Specifically, he finds
himself on the high end of the bell curve in a number of these characteristics, realizes it and is quite
impressed by the fact, another attribute of human nature, or as they say colloquially, if you’ve got it,
flaunt it. They do, because they can. The arrogant flaunt it, and thus are “aggressively assertive,
presumptive or overbearing.” Another related word is ruthlessness. Synonyms include tough,
severe, and relentless; but also pitiless, brutal, vicious and inhuman. A leader must possess
sufficient ruthlessness to be able to accomplish things that need to be accomplished, firing an
incompetent but likeable subordinate, for example. But to be inhuman, savage or brutal would be
considered to be unacceptable in these times, even though probably necessary in times past. Again
we see the continuum of meaning about which a normal distribution, or distributions, can be
constructed.
Why is this a useful concept to understand? Because it deflects us from a black-white view of the
world and of our fellow man. Or as some are prone to say, there are good and bad in all of us. But
even more important, there is often likely to be blurry right or wrong when it comes to many concepts
related to people and their society. Myriad opinions will necessarily abound, and for us to survive
they must be blended into a fabric that embraces all.
An understanding of the normal distribution of life’s forces predisposes us to expect diversity of
opinion, perspective, ability and capability of comprehending and understanding. It doesn’t tell us
what to do with it; that is a far more complex challenge. But it does prepare us for the fact that it will
always be there, and must be dealt with in every facet of our social existence.
Let us move to an even more critical aspect of the normal distribution of life’s forces: freedom versus
discipline (education), freedom versus order (government), rights versus responsibility. Deriving
from the lack of equality of man, it has been alleged that if we divided everything in the world among
all its people, within some short period of time a small number would control it all again –
apocryphal, but thought provoking . Progressive governance, then, (supposedly) strives to balance
the extremes, compromise among the competing needs, and find what is best for the most: to find
the center (median) of the normal distribution of any opposed concepts. Of course, we are again
reminded of the difficulty in isolating, and that’s what makes the process so complex and
challenging to achieve.
What’s best for the most? And who decides? And on what basis? Normal distribution. Of course
people are different from shards of broken glass. The shards are governed by the laws of physics;
the people’s needs and wants are governed by what they believe to be their own free will and
interests. Ignorance and gullibility will result in that more likely being what someone has told them, i.
e. some form of propaganda, but the result is the same, and will take the form of a normal
distribution. However, the normal distribution will be valid only for the elements under consideration
at a moment in time.
And people want what they think is in their best interests. In education they want freedom, until there
is no discipline, and then they decry the lack of discipline – or the poor results that come from not
having it. So do people want their rights and their freedom, until discipline and order is lacking, and
then they decry the lack of security that it generates. Thus compromise defines the balance point; the
median of a normal distribution and the line drawn in the sand to delineate where the extremes
blend into the middle ground.
The problem, I believe, is that power brokers feel they need to take a stand to differentiate
themselves from all the others. No one likes compromise and few respect those that seek to find
the point of balance; all prefer their own extremism, no matter how moderate they pretend it to be. As
a result they choose their point to the right or left of balance and attempt to move the balance in their
direction. Who would support the expert who agrees that both sides have a valid point? The normal
distribution of life is not necessarily something we strive for, but something that results despite our
individual efforts to force a solution favorable to us. The shards do not seek their resting place, but
find it nonetheless. Human nature does not seek to find the balance point, but reluctantly finds it
forced upon them, as, through a continuing process, they attempt to force the balance point in the
direction of their interests. The normal distribution of ideas and opinions is not fixed, but continually
readjusts itself in response to the forces under which it is formed.
To understand the complexity of man, consider a thousand positions, each with its own normal
distribution that changes continually and instantaneously. Nor are any of these normal distributions
even necessarily consistent on an individual basis. What a seething, churning mass is the world of
human ideas and desires. Each of us wants what we think is best, for us, though we seldom really
know what that is, since our knowledge is limited to perceptions, and we likely do not – can not –
consider all the ramifications of our position over time. Is it any wonder that the compromise
depicted by a normal distribution is not a popular result?
Traits, ideas, positions; all normally distributed, with everyone trying to influence or change them to
achieve best personal advantage. None static; many poorly understood, or easily influenced by
others. Good looks, good music, fashion, politics, ideas, motives; formulated under pressure and
influence into some form of normal distribution. We are equal in no way; we see the world through
different eyes; our wants, needs, desires forming the basis of the influence pressures. And still
coming out normally distributed. What a marvel.
Virtually everything within our ken is a continuum and phenomena we experience tend to distribute
normally across a spectrum of continuum. Drop a glass and plot the location of the shards. Most fall
within a small circle around the impact point. Some may be discovered at some distance from that
impact point. Plotted, the results form what we have familiarly learned to call the bell curve. This can
be explained by the laws of physics, as can many such familiar phenomena. But many other
observations demonstrate a similar trend. Human intelligence, size, motivation, talent. Surely there
must be laws that explain the elements of social behavior and human nature in much the same
manner as the laws of physics, or so many have thought. If so such laws have eluded us.
Nonetheless, normal distribution continues to be demonstrated in so much of what we observe.
Looks. There are few beautiful people, and few truly ugly people, and many, many in between. There
are few truly good people, and few truly bad people, and many, many in between. But what is
beautiful and what is ugly? What is good and what is bad? Perceptions vary from individual to
individual, so become personal distributions rather than universal distributions. And thus we have
created words to help us communicate so we can discuss such comparisons. But the words
themselves are only approximations, and hardly ever truly precise. What is intelligence? What is
ruthlessness? What is compassion? Yet such words do provide us the means of roughly
communicating concepts, perceptions; and the result so often approximates a normal distribution.
The problem, of course, is that we attempt to isolate a variable and observe it as if it existed in
isolation, which it does not. Traits of individual personality certainly do not; we only attempt to
observe them as such. We are far too complex to yield to such simplicity. But to do otherwise is too
overwhelming to contemplate. So we slice and dice, and attempt to observe and make judgement in
isolated chunks for which we have created indecisive words. But even so, the words are helpful to
understanding, evaluating and analyzing the complex world in which we find ourselves, and must
live. And each result is, at least in individual minds, reduced to a normal distribution.
The elemental traits of “successful” leaders of society – the elite – are illustrative. For discussion
purposes let’s list a limited number upon which we might tentatively agree: intelligence, charisma,
insight, strength of character, persuasiveness, confidence. Just reviewing the words gives indication
of the difficulty in discussing this thing we call success in leadership.
Intelligence is many things: ability to learn, ability to remember, ability to understand. But more:
ability to grasp concepts and extrapolate their effect on the over all, whatever that might be; ability to
see forward to consequences; ability to develop useful perspectives; even ability to reason. And that
doesn’t begin to tell the story. We attempt to measure some of these things, but only ineffectively; but
when we do, the result is normal distribution. Some have virtually photographic memories; some
remember poorly. Most of us fall somewhere in between, at the top of the bell curve. And some, with
almost perfect memories, have poor perception, or limited understanding, or inability to see to
consequences. Intelligence then is a bewildering amalgamation of many perceived traits to which
we have clumsily assigned words.
Charisma is even worse. What is charisma? Oxford says, “the ability to inspire followers with
devotion and enthusiasm; an attractive aura; great charm. More imprecise words, truly an ICIWISI
kind of thing: I’ll know it when I see it. Insight? Oxford: “the capacity of understanding hidden truths,
etc., especially of character or situations.” Hidden truths? Character: “the collective qualities
especially mental and moral, that distinguish a person.” Persuasiveness: ability to persuade or
influence. Confidence: “a feeling of self-reliance or certainty; a sense of self-reliance or boldness.
So many words, so many vague concepts; but for the population in general, spread over a normal
distribution, most of us in the middle, but some with far greater strengths than others; and some with
almost none at all.
One of my favorites is confidence. Associated words – at least for me – are ego and arrogance. The
useful meaning of ego is self esteem. The person with none can not function; but he with towering
self esteem is so insufferable that we cannot stand him. Yet to be successful one must be closer to
the latter than the former. Arrogance is a word that often describes one whose ego is very strong.
For one who is confident is usually (but not always) so for some valid reason. Specifically, he finds
himself on the high end of the bell curve in a number of these characteristics, realizes it and is quite
impressed by the fact, another attribute of human nature, or as they say colloquially, if you’ve got it,
flaunt it. They do, because they can. The arrogant flaunt it, and thus are “aggressively assertive,
presumptive or overbearing.” Another related word is ruthlessness. Synonyms include tough,
severe, and relentless; but also pitiless, brutal, vicious and inhuman. A leader must possess
sufficient ruthlessness to be able to accomplish things that need to be accomplished, firing an
incompetent but likeable subordinate, for example. But to be inhuman, savage or brutal would be
considered to be unacceptable in these times, even though probably necessary in times past. Again
we see the continuum of meaning about which a normal distribution, or distributions, can be
constructed.
Why is this a useful concept to understand? Because it deflects us from a black-white view of the
world and of our fellow man. Or as some are prone to say, there are good and bad in all of us. But
even more important, there is often likely to be blurry right or wrong when it comes to many concepts
related to people and their society. Myriad opinions will necessarily abound, and for us to survive
they must be blended into a fabric that embraces all.
An understanding of the normal distribution of life’s forces predisposes us to expect diversity of
opinion, perspective, ability and capability of comprehending and understanding. It doesn’t tell us
what to do with it; that is a far more complex challenge. But it does prepare us for the fact that it will
always be there, and must be dealt with in every facet of our social existence.
Let us move to an even more critical aspect of the normal distribution of life’s forces: freedom versus
discipline (education), freedom versus order (government), rights versus responsibility. Deriving
from the lack of equality of man, it has been alleged that if we divided everything in the world among
all its people, within some short period of time a small number would control it all again –
apocryphal, but thought provoking . Progressive governance, then, (supposedly) strives to balance
the extremes, compromise among the competing needs, and find what is best for the most: to find
the center (median) of the normal distribution of any opposed concepts. Of course, we are again
reminded of the difficulty in isolating, and that’s what makes the process so complex and
challenging to achieve.
What’s best for the most? And who decides? And on what basis? Normal distribution. Of course
people are different from shards of broken glass. The shards are governed by the laws of physics;
the people’s needs and wants are governed by what they believe to be their own free will and
interests. Ignorance and gullibility will result in that more likely being what someone has told them, i.
e. some form of propaganda, but the result is the same, and will take the form of a normal
distribution. However, the normal distribution will be valid only for the elements under consideration
at a moment in time.
And people want what they think is in their best interests. In education they want freedom, until there
is no discipline, and then they decry the lack of discipline – or the poor results that come from not
having it. So do people want their rights and their freedom, until discipline and order is lacking, and
then they decry the lack of security that it generates. Thus compromise defines the balance point; the
median of a normal distribution and the line drawn in the sand to delineate where the extremes
blend into the middle ground.
The problem, I believe, is that power brokers feel they need to take a stand to differentiate
themselves from all the others. No one likes compromise and few respect those that seek to find
the point of balance; all prefer their own extremism, no matter how moderate they pretend it to be. As
a result they choose their point to the right or left of balance and attempt to move the balance in their
direction. Who would support the expert who agrees that both sides have a valid point? The normal
distribution of life is not necessarily something we strive for, but something that results despite our
individual efforts to force a solution favorable to us. The shards do not seek their resting place, but
find it nonetheless. Human nature does not seek to find the balance point, but reluctantly finds it
forced upon them, as, through a continuing process, they attempt to force the balance point in the
direction of their interests. The normal distribution of ideas and opinions is not fixed, but continually
readjusts itself in response to the forces under which it is formed.
To understand the complexity of man, consider a thousand positions, each with its own normal
distribution that changes continually and instantaneously. Nor are any of these normal distributions
even necessarily consistent on an individual basis. What a seething, churning mass is the world of
human ideas and desires. Each of us wants what we think is best, for us, though we seldom really
know what that is, since our knowledge is limited to perceptions, and we likely do not – can not –
consider all the ramifications of our position over time. Is it any wonder that the compromise
depicted by a normal distribution is not a popular result?
Traits, ideas, positions; all normally distributed, with everyone trying to influence or change them to
achieve best personal advantage. None static; many poorly understood, or easily influenced by
others. Good looks, good music, fashion, politics, ideas, motives; formulated under pressure and
influence into some form of normal distribution. We are equal in no way; we see the world through
different eyes; our wants, needs, desires forming the basis of the influence pressures. And still
coming out normally distributed. What a marvel.