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Normalcy is very subjective. In many cultures and in different countries there are different ideas about what is normal and what is unusual. In many respects, social pressure decides what is normal and what is not. There are a few things that are generally considered unnatural, but most of cuture is arbitrary.
Embracing change seduces acceptance. Just look at the changes during the past fifty years. I sense a different form of humanity from that of my youth. Not all bad. One thing for certain, we will always have control mechanisms (governments) in place to calibrate on overt savagery. We will be more unhappy because of an aspiring sophistication that will mechanically arbitrate (covert savagery) within our species from which governments will not be immune.
Children raised with animals mimic that ethos, are all animals unhappy?
Define normal. For me, normal is majority. If the majority of us suddenly sprouted wings or tails or horns, it would be normal, because it is the same for majority, for most other people. We compare ourselves to other people every day - what is the benchmark from just 'normal looking' to 'drop-dead gorgeous'? There is no criteria, no little box that says 'flawless skin' and 'beautiful curly red hair' or 'dark, mysterious grey eyes' that you can tick and then announce yourself to fulfill the requirements for being a stunning beauty. The benchmark is the comparison between yourself and your peers. If you are better looking then your peers, you will automatically equate that to being better looking that the norm, and thus will term this as 'pretty'.
A search on Google defines the definition of normal as conforming to a standard; usual, typical, or expected. So with that being the definition the question then is who and/or what sets the standard for conformation? The bottom line, the very definition of normal illustrates its relevancy. The customs created are relevant to those who create them.
Within a society, people are compared to other human beings in that society, whose behaviors will all fall into a certain range that is considered "normal." Each culture is compared to each other, and one that has a particular quirk or behavior that differs is not "normal" as compared to the rest of Earth's cultures, but its citizens are "normal" in relation to one another. But we can't only compare to ourselves- what is normal for humans may not be normal for animals, and vice versa. The female praying mantis, for example, kills the male after mating. This is normal for these insects, but would not be normal for us! When we can call something "normal" in one situation and not in another, then we are looking at something that is relative. Almost any behavior can be looked at in this way.
So no it's not relative. But it's incredibly naive and promotes blind conformity when people try to use "that's not normal" as an argument like Mayor Bloomberg recently did with cigarettes. Why should I care if something is or is not normal? Shouldn't we all just do what's right and not care about normality? What if racism, bigotry, homophobia, antisemitism, rape, what if those were all normal should we then support them? What if love and kindness were abnormal should we oppose them? So while normality may not be relative appealing to it is a logical fallacy that people should stop using.
Although normalcy can be defined as what is normal behavior for each individual person, the concept of normalcy is not completely relative because there is a range of activities and behaviors that is considered to be "normal" for all human beings who reside within a specific community, city, or country, etc.
The idea of something being normal comes about because so many people adhere to it. Therefore, it cannot be completely relative. While it is difficult in some cases to determine what is normal, in most cases there is an understood value or behavior that is equated with normal which is what people react to.