Thinking about the human vector
This phrase came to me while I was writing for the Modu Study AI 2024 coaching study, or perhaps while I was organizing the final week's mission. As I worked as a team leader, researching and organizing things with teammates who were active and voluntary, a term suddenly surfaced: human vector.
Of course, this is not an argument about strict conceptual precision between the keywords. It is a story built on structural resemblance and personal inference.
Directionality
Unlike a scalar, which has only magnitude, a vector has both magnitude and direction. For that reason, it can also be represented by an arrow when needed. Based on this feature, vectors are used informally in mathematics and physics to describe quantities such as displacement, force, and velocity, as well as some elements of vector spaces, things that cannot be expressed as a single number. (Sources: Wikidocs, Wikipedia)
Here I found something interesting.
What about people? Unlike material elements placed on the timeline, human beings do not simply float or remain fixed in time. They keep carrying, or trying to carry, the property of direction.
Position is not a property of a vector. A mere point cannot express it. The same is true of people. A person cannot really be described or interpreted alone. Maybe that interpretation is meaningless in the first place. People need neighboring others, much like vectors that are considered equal when they are parallel and have the same length.
= update =
Philosophers have long regarded images as reproductions of external objects located within consciousness. Yet an image is not an object of consciousness but an activity of consciousness.
This central claim in Sartre's theory of the image must be understood on the basis of Husserl's philosophy. What Sartre noticed above all in Husserlian phenomenology was the idea of the intentionality of consciousness. Husserl, confronting philosophical problems head-on, said that every intentional experience has its intentional object. Sartre formulates this as: all consciousness is consciousness of something.
Consciousness always has the nature of being directed toward something. Consciousness is nothing but pure activity. We should not mistake consciousness for a kind of space in which representations are placed. There is no inside of consciousness. The object to which consciousness relates intentionally is always outside consciousness.
Therefore the traditional philosophical notion of an image as a representation located inside consciousness is entirely false. Just like perception and thought, imagination is one mode of the activity through which consciousness directs itself toward an object. An image is the mode of activity by which consciousness aims at an object imaginatively.
...
What we experience, philosophy has often said, are only representations derived from objects. But if the nature of consciousness is intentionality, then consciousness stands in direct relation to the object outside itself
Sartre's philosophy of the image
- What Is an Image? Lee Sol (Minumsa)
This is an explanation of Husserl's intentionality of consciousness, which Sartre found so important. Adding my own interpretation, consciousness exists in itself, but cannot fully recognize its own existence by itself. As if looking into a mirror, it understands itself through what it reflects against the surrounding world, and only then can it reflect on itself through the behavior and attitude of others.
What is consciousness? The key is that consciousness should no longer be understood within a spatial mode of thought. Consciousness is not like other objects in the external world, nor is it like the space in which such objects are located. Consciousness must be understood as pure activity, and the act of intending the object (noema), that noetic activity itself, is the essence of consciousness.
No further mediation is required between the intentional object of consciousness and the intentional act. Once consciousness is understood as pure intentional activity rather than a container for representations generated by external objects, the image too becomes a mode of activity taken up by consciousness. p.113
The structural resemblance to the idea of a vector feels surprisingly close, does it not?
Birds of a feather
A vector can be represented as a point in a two-dimensional space with x and y axes. It can also be represented in three dimensions, four dimensions, and more. Dimension. People also take on highly multidimensional vector-like forms along the direction of life and time. As individuals, family members, workers, club members, or study participants, they take on different roles from different positions and dimensions. Recently, many people even live with two or three jobs, occupying many layers of everyday life, much like the familiar idea of a persona.
Have you ever spoken with people whose thickness or depth feels different from your own? It may be rare to meet them, but when you do, does it not feel as if they inhabit a completely different world? And one more thing: when vectors share the same dimension and the same corresponding components, meaning direction and magnitude, they are considered equal. In that sense, people really do gather with their own kind.
But here's the thing
Even though we are human, are we not evaluating ourselves and others too often by standards more like scalars? That thought led me to wonder whether we are also too ungenerous toward human vectors that exist in dimensions different from our own.
I suspect everyone has felt at least once the sting of unnecessary coldness in conversations with customer service agents, public officials, colleagues in other departments, or staff inside a store.
Recently, while using AI services, there are moments when AI feels as kind as people, or sometimes kinder. At the same time, it is not unusual to see people practicing more careful prompt engineering with AI than the care they show in ordinary human conversation.
What if we were as kind to people as we are in prompt engineering?
It is an ironic and heavy reality.
Person-to-person relationships are increasingly objectified through standards of usefulness and efficiency, while AI is simultaneously being improved to resemble humans and is sometimes treated better by humans than humans treat one another.
People themselves tighten their lives in the name of convenience and efficiency, chasing routine and quantifiable existence and gradually losing room simply to exist. Meanwhile, new entities such as AI, at least in my personal view, seem to be chasing qualitative and nonlinear modes of being. The irony is hard to ignore.
Main point
That is enough for the prologue. Returning to the beginning, while working as a team leader during the Modu Study AI 2024 coaching study, the phrase human vector came to mind together with the thought: an individual resembles a vector, and an organization resembles a matrix. Looking back on that brief period of leadership, I began to wonder whether better outcomes might be possible if we considered each person's properties and physical limits, or, in mathematical terms, the rules that constrain them.
1) Example one
I think the meeting between a person and a tool resembles addition or subtraction, while the meeting between person and person resembles multiplication or division. (For reference, I see the "entity" category in AI as slightly closer to a person than to a tool.)
And if we multiply the latter case,
- as in person with person -
then mathematically it is written as 'C = A ⋅ B',
in Python as 'C = A @ B',
and in NumPy you can use `np.dot()` for matrix multiplication. But the key point is this: the number of columns in the first matrix must match the number of rows in the second matrix. If they do not match, multiplication is impossible.
2) Example two
Principal Component Analysis, or PCA, is one of the best-known dimensionality-reduction algorithms. PCA first finds the hyperplane closest to the data and then projects the data onto that hyperplane. It is a linear transformation method that finds orthogonal components maximizing variance. By eigen-decomposing the covariance matrix, it calculates eigenvectors, the principal components.
On the two-dimensional dataset to the right, three axes are shown. The right side displays the result of projecting the data onto each axis in one dimension. The top solid line preserves the most variance, while the bottom dotted line preserves the least. PCA selects the axis that minimizes the mean squared distance between the original dataset and the projected dataset while preserving as much variance as possible. Put more simply, it is a technique for reducing dimensionality while retaining as much of the original variance as possible. That made me think about whether the direction of an organization or a product responding to a market or to customers works in a similar way.
3) A perhaps hasty generalization
Example one resembles the relationship between human vectors and other human vectors, or between a human vector and an organizational matrix. Example two resembles the relationship between an organizational matrix and a market matrix.
In that sense, when we deal with communication between human vectors, projects between human vectors and organizational matrices, or collaboration between organizational matrices, we need a process of first constructing, sharing, reviewing, and agreeing upon a minimum common area, a kind of common dimension and shared direction. In reality, that is often the first thing a PM or PO does when forming and operating a task force.
Conclusion.
Inside an organization, each individual is like a vector. That vector carries different dimensions depending on time and place, and each dimension assigns roles and responsibilities much like personas in service design. In this way, each human being accumulates dimensions shaped by their own lived experience. Sometimes those dimensions are made of small hobbies, and sometimes of goals, dreams, and relationships.
When those dimensions can form meaningful intersections, the whole organization can finally operate like a matrix, much like the interaction between vectors and matrices.
*(The composition of forces means combining several forces acting on one object through vector addition so that they produce the same effect as a single force. - Seoul National University Science Education Institute)
Each individual, based on their own experiences and knowledge,
forms a personal human vector within their own life.
And the team,
together with those different human vectors,
sets out on the road of a great voyage.
So what kind of dimensional vector do I carry?
In my relationship and communication with other human vectors, organizational matrices, or market matrices, am I someone who can reduce part of my dimension to meet them, or am I a human vector who depends on their adjustment instead?
Just that, really.
Cookie: In natural language processing there is a keyword called vectorization, the conversion of text into vectors during preprocessing. Videos can also be converted into images, and images back into text. And today, especially through deep learning and machine learning, anything that can be turned into a vector can have its distance from other things calculated. In the end, that is what makes prediction and inference possible.
