The Dance Between “What Is” and “What Can Be Made”: A Practical Guide to Modern Thought Through Euclid

Introduction: Are You the Puppet or the Puppeteer?

The ultimate goal of modern philosophy, as well as Mahayana Buddhism, can be summarized in a single phrase: to become the puppeteer, not the puppet.

Without realizing it, we often live our lives manipulated by the strings of a particular way of thinking. For instance, the commonsense belief that the world “is” made of objective realities is one powerful puppet—this is Realism. The sophisticated idea that the world “can be made” or constructed through language and social rules is another—this is Structuralism.

A “puppeteer” is a proactive practitioner who understands that neither viewpoint is an absolute truth and learns to use them freely according to the situation. In modern thought, this intellectual freedom is called Post-structuralism; in Buddhism, it is known as Madhyamaka (“The Middle Way”). This is not an esoteric theory but a practical skill for achieving intellectual liberty.

So, how does one become a puppeteer? The greatest textbook for this training is none other than Euclid’s Elements, a work that has been the foundation of Western intellectual tradition for over two millennia.

**Why Euclid’s Elements is the Perfect Textbook**

Inscribed at the gate of Plato’s Academy were the words, “Let no one ignorant of geometry enter here.” For centuries, geometry was considered the bedrock of logical thought. The fact that Euclid’s Elements is the second best-selling book in history, surpassed only by the Bible, speaks to its profound influence.

The reason for this is that the Elements is more than a book about shapes; it presents an entire operating system for thought—a system for how to perceive the world and construct logical arguments. And astonishingly, this OS is a masterful hybrid, skillfully combining two distinct modes of thinking: Realism, which believes in “what is,” and Structuralism, which defines “what can be made.”

Deconstructing Euclid’s Hybrid Genius

Euclidean geometry is built upon three sets of rules: Definitions, Axioms (or Common Notions), and Postulates. By analyzing these, we can clearly see the two faces of his hybrid thought.

1. Believing in “What Is”: The Realist Foundation 🏛️

First, Euclid establishes an unshakable starting point by presenting certain concepts as truths that are “already there.”

The Foundational Definitions:
- “A point is that which has no part.”
- “A line is breadthless length.” These definitions are profoundly Realist (or Platonic). They attempt to describe the essence of perfect “points” and “lines” as if they exist in some ideal realm, independent of us.
The Axioms (Common Notions):
- “Things which are equal to the same thing are also equal to one another.”
- “The whole is greater than the part.” These are presented as self-evident truths, applicable to all sciences. They are the undeniable “rules of being.”

2. Defining “What Can Be Made”: The Structuralist Blueprint 🏗️

Next, using these “given” elements, Euclid establishes the rules of operation and construction—defining “what is permissible to do.”

The Relational Definitions:
- “The ends of a line are points.”
- “An angle is the inclination of two lines to one another.”
- “Parallel lines are straight lines which… never meet.” These definitions are Structuralist. They do not define an object’s essence but its relationship to other elements. An angle is not a thing, but a relationship; parallelism is not a property of one line, but a relationship between two.
The Postulates (Permission to Construct):
- “To draw a straight line from any point to any point.”
- “To describe a circle with any center and radius.” These are not statements about what exists, but rules about what we are allowed to create with our tools (a straightedge and a compass). This anticipates the philosophy of Constructivism in mathematics, where an object’s existence is guaranteed only by one’s ability to construct it.

Euclid, therefore, first lays down the truths of “what is” and then provides the rules for “what can be made,” building his entire logical system on this brilliant combination.

The Great Unbundling: From Hybrid to Specialist in Modern Math

Modern mathematics evolved by taking the two sides of Euclid’s hybrid model and pursuing each to its logical extreme.

Formalism (led by Hilbert): Sought to eliminate the ambiguity of Euclid’s definitions. It treated mathematics as a formal game of manipulating symbols according to axioms, without asking what those symbols “truly are.” It was a more conscious and rigorous way of handling “what is” by treating it as a set of formal givens.
Intuitionism (led by Brouwer): Elevated Euclid’s “what can be made” side into a core principle. It asserts that a mathematical object exists only if one can provide a concrete procedure for constructing it.

These schools of thought can be seen as specialists, each deeply exploring one side of the original Euclidean hybrid.

From Puppet to Puppeteer: The Practical Art of “Skillful Means”

Let us return to our initial question: How do we become the puppeteer? The answer lies in training ourselves to consciously switch between the Realist perspective (“what is”) and the Structuralist perspective (“what can be made”).

The State of the Puppet:
- To think, “This is just how reality is, so nothing can be done,” is to be a puppet of Realism.
- To think, “The rules and the system determine everything, so the individual is powerless,” is to be a puppet of Structuralism.
The Practice of the Puppeteer: The puppeteer skillfully switches between two questions depending on the situation:
1. The Courage to Assume “What Is”: In a complex situation, one must have the courage to form a hypothesis—to say, “Let’s assume this is the case for now” (Realism) in order to get a quick overview. This is the act of forming a hypothesis in research or a provisional diagnosis in a clinic.
2. The Prudence to Verify “What Can Be Made”: One must then have the prudence to test that hypothesis by breaking it down into concrete, verifiable steps and procedures (Structuralism). This is the act of designing an experiment or a treatment protocol.

This round-trip journey—from a leap of faith to rigorous verification—is the practical application of the freedom from fixed viewpoints taught by Post-structuralism and Buddhist Madhyamaka. It is a technique for an intellectually agile and resilient way of life, where both Western and Eastern philosophies converge.

Conclusion

Euclid’s Elements is not just an ancient math textbook. It is a foundational guide that demonstrates how to combine two fundamental modes of thought: the acceptance of “what is” and the construction of “what can be made.”

Consciously practicing this round-trip motion is the surest path to freeing ourselves from the ideological “puppets” that seek to control us. It is the path to becoming the “puppeteer” of our own thoughts, capable of navigating the world with clarity, creativity, and freedom.

The Dance Between “What Is” and “What Can Be Made”: A Practical Guide to Modern Thought Through Euclid