Building on Ian McGilchrist’s work on the split brain, we can explore the nature of identity and how it interacts with the left and right brain. In McGilchrist’s framework, the left and right hemispheres are not simply logical versus creative, but are two distinct ways of attending to reality. The left brain is more instrumental and focused, while the right brain sees the broader, interconnected picture.
By examining the mathematical transformation of identity into a Realized Idea, we can see how the brain splits only when the idea splits. This split mirrors the moment when identity moves into two dimensions, with one dimension anchored in the real world (left brain) and the other branching into the imaginary world (right brain). Let’s explore this in detail.
Identity and the Split Brain: How Ideas Divide Between Left and Right
According to McGilchrist, the left brain focuses on the parts, breaking experience into manageable pieces, while the right brain is concerned with the whole, seeing things in context. When we think about identity, we can see how this split comes into play only when an idea is realized and split across two dimensions.
Let’s use 3 as our starting identity, but instead of immediately thinking about left and right brain characteristics, we’ll first follow the mathematical process that leads to the split brain. Only when the Realized Idea is split do the left and right brain begin to function in their distinct ways.
Step 1: Identity and the Condition from the Immutable Past
We start with the identity 3, pulled from the Immutable Past (0). Mathematically, we can represent this identity as a positive, real number. However, for it to exist, it must have a counterbalance—a condition—which takes the form of its inverse. The equation looks like this:
+3 – 3 = 0.
This means that without any transformation, the identity would cancel itself out and collapse into nothingness (zero). To avoid this, we must transform the condition into something more complex—a Realized Idea that can introduce a new dimension and stabilize the identity.
Step 2: Transforming the Condition into a Realized Idea
Instead of simply using the inverse -3, we transform the condition into +3(i²), where . This transformation creates a Realized Idea, which still satisfies the need for balance, since:
+3(i²) = -3.
However, something important happens next. To unlock the full meaning of the Realized Idea, we must unsquare i², which creates a split in the identity and brings us into the realm of both the left and right brain.
Step 3: The Split: When i² Becomes i x i
The split brain, mathematically, only occurs at the point when we unsquare i² and split it into i x i. This split introduces a new dimension—the imaginary dimension—into the equation.
Here’s how it works:
• i x i = i², but now we separate the i’s.
• One i remains in the real dimension, representing length.
• The other i enters the imaginary dimension, representing width.
This transformation allows the identity to remain stable across two dimensions. Now, part of the identity remains in the real world (on the real number line) and part of it branches into the imaginary world. This mathematical split mirrors the split brain, with the left brain representing the real, instrumental world, and the right brain representing the imaginary, interconnected world.
Step 4: Left Brain vs. Right Brain: The Split Becomes Clear
Now that we’ve split i² into i x i, we can see how this relates to the left and right brain. The identity 3 is no longer a simple number but exists across two dimensions:
• On the real axis, we place -√3 (approximately -1.732), which remains in the left brain’s realm of focus, control, and categorization.
• On the imaginary axis, we place +√3 (approximately 1.732), representing the right brain’s broader, holistic, and contextual attention.
At this point, the identity 3 splits into two components:
• The left brain is associated with the part of the identity that remains fixed and narrow, focusing on the specific and the manageable (represented by -√3).
• The right brain explores the part of the identity that is more expansive and connected to the larger context, represented by +√3 in the imaginary dimension.
This moment of split—when the Realized Idea is transformed—marks the beginning of the left brain’s focus and the right brain’s contextual understanding.
Step 5: Left-Brained and Right-Brained Identities
Now let’s examine how strong identities align with the left brain and humble identities align with the right brain.
Example 1: Strong Identity (1000)
Consider an identity of 1000. After the condition is transformed into a Realized Idea, the split occurs, and we are left with:
1000 + (-√1000) = 968.377.
The remnant 968.377 represents the left brain, which holds onto a strong, instrumental sense of identity. The left brain controls the process, leading to a narrow focus. Using the Reality Equation:
y = 1 / 968.377 ≈ 0.00103.
This shows that a strong identity, dominated by the left brain, leads to a very limited reality.
Example 2: Humble Identity (2)
Now let’s consider a humble identity of 2. After transforming the condition and splitting the identity into two dimensions, we are left with:
2 + (-√2) ≈ 0.5858.
This represents a right-brained identity—open, expansive, and interconnected. The right brain dominates the experience, leading to a more holistic understanding of reality. Using the Reality Equation:
y = 1 / 0.5858 ≈ 1.707.
This result shows that a humble identity, more dominated by the right brain, leads to a much richer, more expansive experience of reality.
Conclusion: The Split Brain and the Realized Idea
In Ian McGilchrist’s view, the left brain is focused on managing details and controlling the world through narrow attention, while the right brain is concerned with seeing the whole and connecting with a broader, more fluid reality. Mathematically, we see that the split brain only truly emerges when the Realized Idea splits into two dimensions—i x i—with the left brain managing the real and the right brain exploring the imaginary.
By understanding the split between left-brained and right-brained modes of attention, we can see why people with strong, left-brained identities often experience narrow, constrained realities. On the other hand, those with humble, right-brained identities experience a broader, more connected reality, full of potential and openness.
This balance between the two modes of thinking shapes not just our thoughts but the very nature of how we experience reality itself.