Our Relationship with Ideas: The Geometry of Bias
Our relationship with ideas is already shaping reality by the time we become conscious of what we are experiencing.
That is the central point. We encounter the world from within a relationship that is already active. Its direction and intensity are part of the experience itself.
The Reality Equation is the framework I use to explore this:
Reality equals Actual divided by Expectation.
The equation describes the reality of an entity. An entity can be a person, a bird, a nation, or a solar system. For this discussion, we will stay with the human being. Your own experience gives you somewhere to begin.
The relationship with ideas lives in the denominator.
Expectation Has Two Components
We usually hear “expectation” and think about prediction. We expect someone to arrive at a particular time. We expect a conversation to go a certain way. We expect an event to unfold according to a familiar pattern.
In the Reality Equation, prediction is one component of expectation.
Expectation is represented as a complex number, with a real component and an imaginary component. The real component represents prediction. The imaginary component represents our relationship with ideas.
“Imaginary” is a mathematical term here. It names a component of the model. That component participates in determining the reality we experience.
This gives us a distinction worth holding onto. Two people can predict the same thing and still experience it differently. Agreement about what will happen leaves open the question of their relationship with the ideas involved.
To see that relationship more clearly, let’s put a circle on the chalkboard.
A Circle of Ideas
Imagine a unit circle, a circle with a radius of one. Its circumference contains infinitely many points. In this picture, each point represents an idea.
Draw an arrow from the center to a point on the circumference. The arrow has a length and a direction. Every arrow reaching the circumference has the same length, but each points somewhere different.
Now we have a way to picture a domain of ideas and the relationships within it.
The geometric illustration asks us to look at the combined effect of those relationships. We add contributions tip to tail and examine the resulting vector.
Its direction tells us where the relationship is oriented. Its magnitude tells us how strong the net effect is.
Consider an arrow of length four pointing at sixty degrees. You can see two things immediately: where it points and how far it reaches. Direction and intensity are different properties. We need both.
The unit circle remains a unit circle. The combined vector can extend beyond it because several contributions can reinforce one another.
Balance Can Produce Zero
Start with two arrows of equal length. One points straight up at ninety degrees. The other points straight down at 270 degrees.
Add them together. Their sum is zero.
Both contributions are present. Both participate in producing that result. Zero describes their balance.
That distinction becomes important when we apply the picture to ideas. Imagine an ideal relationship in which every directional contribution is balanced by an equal contribution in the opposite direction. The net effect has no preferred direction.
Within this model, that is the image of an unbiased relationship.
We should be careful about what we infer from the result. A zero by itself does not reveal every relationship that produced it. But the balanced example shows why zero can coexist with extensive participation. We can be looking at an abundance of relationships held in balance.
Now return to our two arrows and remove the downward-pointing contribution.
The upward-pointing arrow remains. The net result has a direction.
This is a useful way to understand bias: an imbalance in the relationship.
The remaining contribution did not become longer. Its counterbalancing contribution was removed. What is absent can matter as much as what is present.
How Bias Becomes Intense
A strong directional effect can also arise through reinforcement.
Imagine several arrows pointing in nearly the same direction. Add them tip to tail. Their contributions accumulate, producing a longer resultant vector.
In the geometric picture, we can now distinguish the direction of a bias from its intensity.
Two people can be oriented toward similar ideas with very different intensity. Two others can have equally intense relationships that point in different directions.
Saying that someone “has a bias” leaves much of the relationship unexplained. Toward what? With what intensity? What is reinforcing that direction? What is missing from the balance?
These questions give us something more precise to examine.
The geometry makes the distinction visible. The equation places its consequence inside expectation. In complex arithmetic, the denominator affects both the magnitude and the direction of the quotient. Its contribution remains part of the result.
In the Reality Equation, the result is what the entity experiences as reality.
The Same Wedding
Consider two people attending the same wedding.
For this example, hold Actual constant. They are at the same ceremony, hearing the same words and witnessing the same event.
Now hold the predictive component of expectation constant as well. Both know what is going to happen. Both expect the vows, the exchange of rings, and the celebration.
Their relationship with ideas can still differ.
The ideas engaged by the ceremony meet a different orientation and a different intensity in each person. The imaginary component of expectation therefore differs, even though the event and their predictions have been held constant.
Within the equation, their realities differ.
This is why a disagreement about an experience can run deeper than a disagreement about the sequence of events. Two people can agree about what happened and still be describing genuinely different experiences of it.
The difference is already present while the wedding is happening.
Ideas Have People
“Ideas have people. People don’t have ideas.”
I use this formulation to interrupt a deeply familiar habit: treating the mind as a factory that manufactures ideas.
The premise of this framework is that the domain of ideas precedes the particular human being who encounters it. We enter into relationships with ideas. Those relationships have direction, intensity, and consequences.
The geometric picture helps us approach that premise. At a particular moment, the combined relationship has a particular orientation. That orientation participates in expectation, and expectation participates in reality.
Our conscious experience is on the left-hand side of the equation. The relationship producing it is largely outside our awareness.
We do not first stand outside reality, inspect every contribution, select an angle, and then begin to experience. By the time we ask what is happening, we are already experiencing it.
The relationship with ideas is already at work.
A Moment in a Continuing Relationship
A diagram gives us a snapshot.
We draw a vector, assign it a magnitude, and identify its angle. We have frozen a moment so that we can examine a relationship.
The living relationship continues.
This matters because a description of someone’s orientation at one moment should not become a permanent definition of that person. The snapshot tells us about the relationship being examined. It does not contain the whole life of the entity.
The practical consequence is a different way of approaching disagreement.
When another person describes the same event differently, the event is only part of what we need to understand. Their relationship with ideas is participating in the experience, just as ours is participating in our own.
And our certainty does not place us outside that relationship.
The ideas shaping our reality can be hardest to recognize when the reality they produce feels most obvious.
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