We are multi-dimensional beings. I speak of dimensions comprising our physical and psychological attributes, hobbies, interests, habits, humor, taste for 20th-century classicism, etc. The individual dimensions number too many to list.

Now imagine yourself as a point on this highly-dimensional plane. The points closest to you are probably your friends. I say that backwards. Rather, your friends - real friends, that is, are probably among the points closest to you. However, the higher the number of dimensions you project on the plane, the less neighbors you will find around you. It can get lonely on that plane.

Okay, let me back up. For simplicity sake, suppose we are nothing but primitive creatures of two dimensions. You can now visualize this plane and even sketch it on paper. You can scatter a bunch of points on the plane to represent various people you know or don’t know. This is entirely hypothetical.

Let’s think of the *unit density* as the average number of points per unit hyperplane. In 2-dimensions, this unit hyperplane is a simple square of arbitrary unit area. In 3-dimensions this becomes a cube. And so on. The greater the density, the more neighbors you will find, on average, and the more trusted friends you probably have.

Suppose this 2D world now becomes self-aware. The inhabitants realize there’s more to them than representable in two dimensions. Suddenly they conceptualize a third dimension. Bear in mind, the number of inhabitants remains constant, but we now project them onto three dimensions. Guess what? The number of neighbors in your unit hyperplane (a cube) is now notably less. That is, assuming you populated your world not with your clones but with inhabitants of sufficient variety and uniformity. Convince yourself of this fact.

It gets worse. With each increasing dimension, the unit density falls exponentially.

But all mathematical relation aside, the greater the number of dimensions, the less beings in common you will find among your network. You can probably induce this observation to what you know about human beings, compared to say, animals. The loneliness, the solitude, are especially common among those singular beings of particular taste and inclination.

Bear in mind, this dimensional projection of yourself is nothing more than that, a projection. If you have certain friends with whom you share an interest in vinyl records, no multi-dimensional projection will alter that. You will still align among that one dimension. And yet, the higher the dimensionality we imagine ourselves to span, the more complex of an identity we project among ourselves, and the greater difficulty we’ll face in accepting others into our trusted domain. You may align among one dimension, but your singularity suddenly skyrockets in a world that evolves from three to ten or a hundred total dimensions.

If you find yourself victim to this *curse of dimensionality*, find a way to collapse your world to a smaller number of dimensions. It may not alleviate your existentialism struggle, but it will certainly ease the task of reestablishing a trusted circle of contacts.

To further complicate matters, we occupy a world of continuous movement. As points on a plane, we generally don’t remain static. At least in some dimension we find ourselves in gradual movement across time. And this likely is the case across a number of dimensions.

With that noted, our identity is better defined not strictly as a point on a plane, but as a vector; a vector of movement; a vector that illustrates our direction within some discrete time interval. The reliability of our trusted group of friends is now better represented not only by the proximity to each other on the plane, but by the similarity between the vectors.

Let’s take one dimension of commonality, the vinyl records. You may find yourself in relative proximity on that axis with certain friends. But your movement among the axis over time may differ. Their interest may gradually increase, while yours slowly diminishes. With time, you lose commonality along that dimension.

With a higher number of dimensions, the similarity between the movement vectors of the world inhabitants also falls. At one instant, we may coincide across many dimensions even. And yet our vectors may entirely differ. We may be arriving from different points, roughly coincide for a discreet time interval, and in but a brief moment set course for complete divergence.

Be conscious of your movement vector. Communicate about it. It is fundamental to reaching mutual understanding. It is representative of the likelihood that your network and your friends survive the test of time.