In nature, humans seldom grow tails, and yet, for some, the proof is in the seeing. There are persons with small tails, with the striated muscle and nervous wiring that they can move said tail.
Perhaps most of us here have seen the video clip of it in action.
Human Tail Video
The greater odds of having such stem from the fact, that even those without a visible tail may in fact have the neural wiring to operate one if it was there. The most likely source of actual biological tails is probably going to be something grown from stem cells. Now that the places in which they can be found are beginning to proliferate, it is only experimentation with them that will show what is possible.
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I am unsure how many humans can move their ears. I used to believe that everyone could. Well, I can. And if someone can move a human ear, then probably with the right kind of bioengineering, an ear can be created to suit someone who already has the wiring to make use of such an ear and the associated muscle tissue were it provided.
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Regarding Stalking Cat aka Dennis Avner. He seems to be perfectly comfortable and at home with his body mods. He is a nice fellow too. I would not be surprised if such visible ones impact the ability to find work with some employers, though I would point out that Dennis does have work.
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Body mods such as tattoos, piercings and others that emulate tribal and social relationships are pretty ancient in human culture. The degree, nature and amount of such that a given person has can affect how they are perceived in the human world. The very same mods that elicit aspersion in one social circle, may for the very same person, have exactly the opposite affect in other social circles.
Having said that, such body mods are socially a far cry from full scale bioengineering. While I cannot really anticipate what will or will not ultimately be doable in actuallity, I can speculate upon its social aspects. Now some folks may find cosmetic changes in the area of tattoos, inserts and implants to be offputting, they do not really make humans look alien, just different.
However
Creating new, functional organs and totally rebuilding people might create a subclass of persons who really do seem alien. Now whether this perception will be deep or even permanent, is hard to nail down precisely, but we can look at history and human nature and extrapolate.
Many of us live in societies that are more or less open and flexible. Even so we encounter from time to time persons and groups of persons whose paradigms are closed, inflexible and sometimes inimicable to other portions of our own societies. Sometimes these people are quiet and do not display their feelings, other times these people are strident and in our faces about them. Also, in groups, sometimes even the quiet ones will fall into step with the group attitudes and become quite aggressive.
A significant portion of humanity lives in societies which are very closed and traditional. This is not to knock tradition in general terms, but to remind us that traditions are habits. They can be neutral, good, bad or a blend of these. They can range from tolerant to wildly intolerant. Flexible to stonily inflexible. Traditional solutions for non-conforming individuals can range from the benign to the deadly. And in some cases, even mild non-conformity can trigger deadly reactions.
Persons bearing customization that genuinely makes them look 'other'. Other than human, can place them in classes where they become vulnerable to other factors of human perception. Humans can be pretty accurately described as pack animals. Dividing into groups easily identified as 'us' and 'them'. Vilification and separation into such groups is a fine and refined art. The world around us is doing it constantly.
One of the more common paths of such dividing into such groupings and is to identify non-members of one's group as 'animals'. Notwithstanding that humans are animals too, this is easily overlooked, for the basic underlying premise is that 'we are us' and that 'they are them'. Worthiness of kindness and consideration is thereafter amplified along the lines of 'how much USness they have' or 'how much THEMness they have'. Typically the less human and less of 'us' that they are, the more disposable and dispensable they are.
Consider, that at least in the Western cultures, the history is full of images, icons and acts basically boiling down to mankind being at War With Nature. Total war in many respects. Even today, with nations and peoples being presumably more educated than ever before, we remain about as ethnocentric as we have ever been. So, if being of the wrong ethnicity or belief system is entirely sufficient to justify mass murder, how much easier is it to dehumanize someone who has to the eye and perception surrendered in all or part, their own humanity ?
"They are animals !" Is not so far fetched a cry of hatred to visualize and hear in the mind, is it ? Even permissive societies go through periodic social and cultural convulsions. In the last century alone, one could go on a world tour of current and past convulsions based on delirious hatred and murder for the most questionable of causes and rationalizations. This is a genetically hardwired in part of human nature. It is horrifically ugly and not likely to go away anytime soon.
So consider nations, peoples, governments. If we take a close and honest look at pretty much ALL of them, we can see certain things practiced pretty routinely. Laws on the books both new and old whose express or oblique purpose is to coerce normative behaviour. Normative behaviour ? Yeah. Conformity to what whomever in the position of power is able to determine is appropriate way for individuals and groups to live.
The world is rife with laws whose only real purpose is the coercion under penalty of whatever, to force persons to conform. Vast numbers of these laws regulate and prohibit activities which by any measure of human social interaction are harmless. In other words, alleged crimes which have no victims. Actually such laws do create victms, for nonconformists are punished and sometimes very severely.
Personally I think a world in which people would have the most imaginative and creative body customizations would be rather fascinating. But for those who have them, and cannot avoid taking their body mods wherever they go, and thus cannot have a day off from being 'different', I should think the world will be a most interesting place.