You’ve heard it said that there is no such thing as normal.  But you’ve also heard the word normal used regularly in conversation, and you’ve used it yourself, which means it has some kind of useful definition—useful even to you.  If normal doesn’t exist, then what do you mean when you use the word?

If you’re not sure, then you’re probably using the word wrongly.  Most people use most words incorrectly.  But just because you define the word incorrectly or vaguely and use it incorrectly or vaguely doesn’t mean that the word does not have a correct and valid definition out there somewhere.  If a word is useful despite your misuse of it, this is an indication that it has a good definition; you just don’t know what that definition is.

The word “normal” as two definitions, one you instinctively but imperfectly recognize, and one which you probably don’t know and which would be of little use to you.

The latter is the geometric definition.  A ray is normal to a plane if it sticks out of that plane at all right angles.  The Washington Monument is normal to the National Mall (for now).  The leaning tower of Piza is no longer normal to the ground on which it stands.  You try to hammer a nail into the wall on a vector normal to the wall, but you fail and it goes in crooked.  This definition is not generally what you mean when you use “normal” in conversation, and you probably had no idea that the word “normal” could mean “existing at right angles to a given reference.”

What you mean when you use the word normal is that a given attribute has a value equal to or nearly equal to the peak value of that attribute’s normal distribution.  Each man in a given group has a height, and their heights will fall along a normal distribution curve (also known as a bell curve), with a few outliers being short, a few being tall, but most being about average.  For a group of American men, let us say that’s about 5’ 9”.  It may be that no one in your group is exactly 5’ 9”, but most will cluster around that height, and the farther you go from that height in either direction, the fewer exemplars you will find.  The peak of the bell curve occurs at 5’ 9” in our example, and you, as a casual conversationalist, rightly refer to that as the normal height for a person in that group.

So normal (as you want to use the word and as you casually do use the word) does exist, and it has a perfectly functional and useful definition.  So why is it popular to say that normal does not exist, or that there is no such thing as a normal person?

A story is told to Student Naval Aviators the U. S. Military was first trying to develop flight equipment (flight suits, vests, helmets, etc. as well as cockpit designs with seat heights, pedal distances, instrument panel heights, etc.), military engineers conducted a statistical analysis of that segment of the American populace which was suitable for military aviation and determined the average value for those men in every relevant anthrometric parameter.  For all men suitable to military aviation, the military determined the average height, the average leg length from floor to hip, the average length of the lower leg, the average length of the upper length, the average length of the spine, the average length of the arm, the upper arm, the lower arms, the average width, breadth, and depth of the head, the average interpupillary distance—you name it.  For every important measurement, the engineers determined the average (the “normal” value) amongst their potential recruits.  They then built equipment to fit the average (“normal”) person in each of these dimensions.  Of course, they were surprised in the end to discover that the equipment they had built fit exactly no one.  Not a single recruit could wear their gear or sit in their carefully engineered cockpits.  Why?  Can we say then that not a single normal person existed?  Can we say there is no such thing as normal?

Of course normal existed.  In each of these dimensions, these attributes, the candidate pool displayed a normal distribution.  Among these candidates, there was an average (“normal”) head width, and the candidates demonstrated a normal distribution about that average, such that a helmet designed to fit that normal head with acceptable tolerances did indeed fit most of their candidates.

What they failed to anticipate, which seems obvious in retrospect, is that there was no guarantee that the people who were within one or two standard deviations of normal head width would be the same people who were within one or two standard deviations of normal lower arm length.  As people are randomly distributed along a normal distribution curve with respect to each of their attributes, there will inevitably be some who are “normal” in one attribute (fall close to the average) but “abnormal” (statistical outliers, far from the average) in another attribute.

In fact, that is the other definition of a distribution curve.  I say it illustrates the distribution of the population, or I can say it illustrates the odds of any one individual having a given value in that attribute.  If 95% of the population is within two standard deviations of normal and 5% lies farther than two standard deviations from normal, then I can just as well say that any given individual (in the absence of additional predictive information) has a 95% chance of falling within two standard deviations of normal and a 5% chance to being an outlier, greater than two standard deviations from normal.  If all attributes are randomly distributed each according to its own normal curve, then a person who might have a perfectly normal head width has a 5% chance of being more than two standard deviations from the normal arm length, with arms either “abnormally” short or “abnormally” long.

The more parameters I add for consideration, the more likely it is that a given individual, though normal in most respects, will be abnormal in at least one.

So, the military discovered, there is a perfectly meaningful, useful, and true sense of what is “normal,” but only for each individual attribute, and if you measure for enough attributes, every individual will eventually be found to be abnormal in at least one of those attributes.  In other words, you can say meaningfully and truthfully that a person is normal or abnormal, but only with respect to one particular attribute at a time, and those people who are normal with respect to one attribute are not guaranteed to be normal with respect to another attribute.

That is why people struggle to understand the concept of normal.  They fail to realize that it only has meaning with respect to a defined attribute, and—perhaps more importantly for the use of the word in conversation—they fail to realize that each time they use the word “normal,” they are implicitly defining an attribute, even if they don’t realize they are doing so.  When you say, “She is so weird!” what you’re actually saying is that she is a statistical outlier with respect to some specific attribute which is relevant to you and your friends at that moment, but you haven’t specified that attribute explicitly.  You’re assuming a common frame of reference within your tribe, or creating one, and disregarding the fact that with respect to some other attribute, you’d be the weird one.  This is a natural behavior for tribal animals which are always, instinctively, looking to isolate and destroy their weakest members.

Meanwhile, when you say, “There’s no such thing as a normal person,” you are leaving off a critical half of the statement:  “—with respect to all possible attributes.”  With respect to any one attribute, there are normal people and abnormal people, and that is quite useful information.