Uniqueness is a measure of rareness and not arbitrariness.

What, then, makes an artifact unique? Uniqueness, like most words we could choose, comes with some everyday bias that needs to first be dispelled, for it is often used to describe arbitrary distinctions. Colloquially, we call a teen with wild rebellious clothes and a face full of ornaments unique. We call off-the-wall ideas unique. And we call an artistic creation unique, even when we think that it is nothing at all special. We sometimes go so far as to suggest that anything which slightly distinguishes one work from another makes it unique. But these arbitrary distinctions have nothing to do with real uniqueness. There are thousands, perhaps millions of slight variations among teenage styles, weird ideas, or even art works sold at on a highway's shoulder. If everything that is arbitrarily distinguished is unique, then everything would be unique, and we would have lost a wonderful word and a wonderful idea.  

No! Uniqueness is what distinguishes special works of artisans and craftspeople, of artists and scientists, of scholars and inventors. Unique is the opposite of arbitrary. It applies to what is rare. It is a measure of special ness. It is not arbitrariness because, to an extraordinary degree, people agree on which artifacts are unique. I would also argue that uniqueness is not in the mind of the beholder; it is not a perception; it is not different for each person or each group. Uniqueness is fundamental, recognizable by most people within a short time, and broadly agreed upon within and between cultures. Unique, as its linguistic root implies, is one - singularity.

We all have the same fundamental sense of what is unique.

I am not, certainly not, suggesting that we don't have to learn to appreciate uniqueness. But once people are familiar with a collection of artifacts, either physical or conceptual, they have a very high degree of agreement on which are unique and which are not. We create museums to house those things that are unique, whether they be great works of art, beautiful gems, or well-formed ‘primitive’ artifacts. People from the world over come to see and admire them, consider them special, and regard them as the foremost reflection of our humanity. Worldwide, we believe in the same theories and patterns of nature. We visit the same tourist attractions no matter what country we come from. And while styles differ among cultures, and we may not all agree on which styles we like or prize; a wonderful work, a beautiful creation, a striking artifact is unique whatever its style, whatever its pedigree, wherever it may be found. No matter what our tastes, if we ask people to list the greatest human works, we would find broad consensus. An artifact is valuable because it is unique, and because we agree on what is unique.

Uniqueness is external and not internal.

It has been common for us to believe in relativism as we have since the beginning of the 20th century, a natural consequence of a plural entities period. Cultural relativism remains to many a standard for judging new works - that each of us individually and culturally perceives the world through our own eyes and that each of these perceptions must be respected. We easily say that each of us perceives our environment differently. I would not argue that this view is wrong- it is the perception of the plural environments knowledge builders. Rather, I would argue that we will focus now on a fundamentally different vision; that there are artifacts which we all agree are unique and that these will become the significant building blocks of knowledge. Once we begin to construct the world of unique artifacts, the common singularity fundamental to uniqueness will overwhelm the minor differences and relativism of individual perceptions.

In which we get to the heart of the theory  

Forms of Uniqueness 

Difference

Sameness

Matching

If humans see uniqueness in the same ways, and I would argue that we do, then we would logically expect to be able to enumerate and define the forms of uniqueness. If uniqueness is well-defined, then we should be able to find some simple standards by which we judge whether an artifact we make or see is unique. Then, what makes an artifact unique? The most obvious answer is that it is different. If an artifact is different, fundamentally different, from other artifacts then it is unique. For if an artifact is significantly different from all other artifacts, then it must be rare and if it is rare then it is unique.  

Uniqueness as difference is one absolute, one form in which an artifact can be distinctive. At the other end of the spectrum are artifacts that are absolutely the same. Like identical twins, these too are equally rare and distinctive. Sameness, like difference, is unique.

And if both difference and sameness are unique, then their combination, matching will also be unique. When artifacts match perfectly they are certainly unique and certainly as rare and distinctive as difference and sameness.

These are the three, and only three, forms of uniqueness: difference, sameness, matching. An artifact is unique because it is different in a significant respect from other artifacts. An artifact is unique because it is the same in some significant way among other artifacts. An artifact is unique because it matches, or produces a match, between other artifacts. Of all the artifacts that exist or that we can create, only those that are fundamentally different, that are inherently the same, or that match can be called unique. These are the only ways we compare artifacts, by how different, how similar, how close a match there are. These are the ways we determine uniqueness.

Difference 

It is amazing how good we are at picking out the most valuable diamond in a group of cut stones, or a masterpiece in a collection of artworks, or a good idea from all the ones we throwaway. From the time we are toddlers we are given difference problems to solve. In "Sesame Street," "Which of these things is not like the others. Which of these things doesn't belong?" is repeated daily. And obviously, uniqueness is just that, which one of these is not like the others. We are naturally capable and constantly taught to recognize differences. Difference means that the artifact stands out in our minds; that it is separate from all other artifacts; that it is distinct. We certainly judge an artifact to be unique on the basis of difference.

Sameness

We crave continuity; a car without dents, a newly painted room, a lawn looking like golf course greens. It is amazing how much time and effort human beings spend on producing continuity, smoothness, evenness, sameness. We are lovers of patterns, creating them for all kinds of decoration. We tile, tessellate, search for and create symmetry, weave, and in general make patterns of all kinds. We like our artifacts to share, to have something in common, to replicate elements: silverware to have the same design, shapes to be repeated in an oriental rug, themes to be replayed in our music. And just as we teach our children what things are not like the others, we also expend serious energy teaching them when things are the same: these things are all round, they are all blue, those are all baby animals. Indeed, the Sesame Street "difference game" is often turned into a "sameness game." Artifacts are unique when they have or produce continuity, consistency, and design; they are unique when they have sameness. When we search for uniqueness we find it in commonality as well as individuality. Our jewelry can highlight a single, unique stone, or a common collection, a large diamond or a string of pearls. We can judge the uniqueness of artifacts on the basis of sameness and search for common properties or qualities.

Matching

We also love artifacts that are a perfect fit and consider them to be of great worth and unique. We mate, we join, we create symmetries, we explore yin and yang, and we make intricate designs based on matching of colors, shapes, sizes. Whether we clothe ourselves, decorate our dwellings, or produce beautiful things, we are concerned with making artifacts fit together. We also teach our young to make matches, giving them puzzles to put together from a very early age. When we decorate we start out by selecting shapes or artifacts that are distinct, that are different. We group them together into commonalties looking for sameness and continuity. And then we try to get these common groups to fit together, to match. Matching creates the union between artifacts that are both different and the same. A unique match takes two artifacts that are fundamentally different - often opposites - and joins them by finding something that creates sameness between them. That is in large measure what we do when we fall in love.

These are the only forms of uniqueness. They are the basis for the construction of all knowledge.

Thus these are the three forms of uniqueness; difference, sameness, matching. Artifacts - both physical and conceptual - are unique when they are different, when they are the same, or when they match others. We find these three forms of uniqueness in many different areas. As we have already seen they make up the games we teach our babies. They are the heart of most tests of IQ as well as the cornerstones of puzzles that test our mental muscle. It does not matter whether we are constructing physical or conceptual artifacts; we make them unique when we make them different, the same, or matching. We make artifacts in the same way whether we use our hands or our minds, because, we are always using our minds. Nor does it matter whether the artifacts we are constructing are our everyday dishes or our fine china, little explanations, or our great theories; they all take the same forms of uniqueness. Whether we build or we judge artifacts, we search for uniqueness, and that uniqueness can only take the form of difference, sameness, or matching.