Euler’s equation is scary.

There are numerous resources explaining it from an intuitive mathematical perspective, my favorite being 3Blue1Brown’s dynamic approach. In this blog, I intend to explore this equation from a purely philosophical angle, because it might be the key to proving the existence of a higher being who purposefully designed our perception of the universe in a specific way.

Let’s define continuity as the opposite of discreteness (or, alternatively, infinite discreteness).

e – Dynamic Continuity

dictates the concept of dynamic continuity in nature in 2 ways:

• Bounded Monotonic Dynamics: Consider a monotonic process (i.e., growth/decay) that transitions from an initial state to an end state. If we partition this process into discrete states, the transition rate between states becomes inversely proportional to the number of partitions. As the number of states approaches infinity, the transition rate approaches the constant . This is proven by .
• Unbounded Monotonic Dynamics: Consider an initial state with position . If at each moment, the state transitions at a velocity identical to the position , the continuous dynamics of this process are governed by the number . This is proven by .

π – Static Continuity

dictates the concept of static continuity in nature. A circle, unique among geometric shapes, has no vertices. Alternatively, it can be seen as having infinite vertices and edges when divided into infinitely small partitions. is the ratio of a circle’s circumference to its diameter. Any geometric analysis involving continuous shapes fundamentally relies on , while shapes defined by discrete vertices do not.

i – Alternative Reality

is the most controversial element of Euler’s equation. Unlike and which have intrinsic nature, is a human-defined construct hypothesizing the existence of . It is independent of the current reality, and it opens the gate to an alternative reality. Despite its abstract nature, is indispensable in various physical fields, including electrical engineering, quantum mechanics, and fluid dynamics. While consistency does not prove existence in nature, it suggests that even if is a mathematical artifact, its conceptual significance and practical indispensability lend it a form of existence within our logical framework. The indispensability argument states that entities that are indispensable to our best scientific theories should be considered real.

0&1 – Physical Reality

0 and 1 are typically overlooked in this equation because they are just two constants, which may seem nothing special compared to the other 3 numbers. However, 0 and 1 are literally the fabric of the mathematical and existential reality in our conceptual framework. From an existence’s perspective, 0 represents non-existence, and 1 represents existence. The superposition of 1s creates new existences. Conceptually, -1 denotes anti-existence, implying the negation or loss of a certain existence.

Is there a God?

In a very abstract sense, Euler’s equation states that the combination of dynamic continuity , static continuity (or geometric infinity) , and alternative reality results in the concept of anti-existence. And if this weird combination superposes with an existence in the physical reality, it all becomes nothing.

Wait… What?

From a Platonic perspective, this equation can be interpreted as the evidence of an underlying, timeless reality that our physical world merely approximates. And this reality is a purposeful design by a higher being. Meanwhile, from a nihilistic perspective, this equation can be interpreted as a joke lol. The convergence of these fundamental constants, which are “discovered” by humans using human-invented tools in a human-invented conceptual framework, into an expression of nothingness literally symbolizes the inherent meaninglessness of existence.

Is Euler’s equation a key evidence to support the claim that there is a higher being above us and that we are just slaves with no free will living in a fixated world defined by the rules they created? As a Zen Buddhist who is slightly tilted toward optimistic nihilism, I stand firmly on the side of the agnostic neutral ground. It’s a 50-50. We need more evidence.

But hol’ up. Let’s just assume the 50% is true. There is a higher being. Then does that mean we can create Artificial Consciousness (AC) who formulate their own conceptual framework from their perceptions of a reality designed by us?

Can we create Artificial Consciousness?

If we are to create AC, Euler’s equation may serve as a metaphorical blueprint. Just some very basic examples that come to my mind right now:

• e – Dynamic Adaptation: Just as represents dynamic continuity in natural processes such as growth/decay of neural signals, an AC must learn, adapt, and evolve. In fact, the existing ML algorithms exploit the nature of for learning and adaptation to the given task bounded by their training data.
• π – Cyclical Processes: is closely related to the cyclical nature of neural oscillations, which are crucial for synchronizing different brain regions. We might be able to implement cyclic processes and feedback loops to help create a more integrated and coherent form of intelligence so that it may develop into consciousness.
• i – Abstraction: introduces a complex dimension akin to the brain’s ability to process and integrate abstract information for thinking and imagination. Yes we are able to get a bunch of embeddings from those gigantic neural networks with numerical values no one understands. Yes they somehow function well for some reason no one knows. But they don’t have consciousness. They don’t even have superintelligence. They are fundamentally function approximation via probabilistic estimation. Why can humans reach far better concept abstraction with a much larger memory storage capacity using a significantly smaller number of neurons? What if these artificial embeddings are constrained in a fixed structure and value range? What if the latent space for abstract concepts is not accessible with matrices but some topological structure that we haven’t invented yet? What if the value range itself should be expanded to one or more imaginary spaces? If we want to build AC, incorporating mechanisms to handle abstract concepts and perform complex reasoning is critical.
• 0/1 – The Fabric: One thing I know for sure is that, no matter how it goes in the future, 0/1 will be the fundamental building block of AC. 0/1 already represent the spike patterns in neurodynamics. Although quantum mechanics suggest a non-binary reality that we live in, a binary abstraction helped us survive and invent phenomenal technologies throughout human history.

If Euler’s equation hints at a higher order or purpose in our universe, can we imitate what the higher being did to us?