The Principle of Constraint
Revealing the Rungs on Reality’s Ladder
June 2025
Part 0 in the Recursive Observation Series
I. Preface: When the Arrowhead Drops
There are discoveries that reward diligence, and there are those that fall into your hand, sharp and improbable, like an arrowhead revealed by chance after striking a block of flint. Sometimes what you find is not what you set out to make; it is better.
This is the spirit of what follows.
The essays in this series began as an attempt to clarify the paradoxes of quantum mechanics. What emerged, unexpectedly, was a principle with the power to dissolve not just quantum puzzles, but mysteries throughout science and beyond. The principle you’ll meet here doesn’t just dissolve the mysteries of quantum theory; it offers a lens through which to see all structure, physical, informational, and even biological, as the recursive solution to layered constraints.
It is a principle as plain as geometry, as indifferent as an inert gas, and as reliable as a stone tool:
Reality is defined by constraint.
What exists, exists only by fitting all the rules at once. There is no process, no “collapse,” no contest, only the set of solutions, under the current system of constraints. Each rung on reality’s ladder reveals new structure, not by adding more substance, but by tightening the web of constraints.
II. What We Mean by “System” and “Structure”
In this series, we use these terms in a precise and sometimes stricter sense than usual:
- A system is the set of all constraints, as rules, relationships, or principles, that define what is possible in a given context.
Here, “system” always means the set of all constraints, present, remembered, or anticipated, that are active from a given perspective. - A structure is whatever satisfies all of those constraints at once.
“Structure” is whatever satisfies those constraints at once. This applies whether the constraints are immediate (as in geometric examples), inherited (as in memory), or even projective (as in anticipation or law).
This may be stricter than ordinary usage, where “system” can just mean “a collection of things” and “structure” might mean “any arrangement.” Here, we care only about the solution set:
What exists, exists because it fits every rule of the system, with nothing left over.
III. Three Opening Thought Experiments
1. Geometry and Constraint:
Think of all possible shapes. Add the constraint “polygonal,” and you immediately pare away everything else. Add the constraint “vertices on a circle,” and the solution set narrows further. There is no process, no pruning, no “transition states”, just a change in what is, now that the rules have changed.
2. Orion’s Rectangle:
Consider the four stars that form the corners of Orion. If Betelgeuse were to collapse into a black hole, the rectangle ceases to exist, not through any process, nor by a signal passing between the stars, but simply by redefinition of what “visible” means for the observer.
Time and distance are irrelevant: the rectangle’s existence depends only on the perspective (the system of constraints) in play. The set of viable structures has changed, instantly and everywhere, because the system’s constraints have changed. What was a rectangle is now nothing more than three isolated points, no transition nor any information transfer required.
3. Information and Constraint:
Imagine a sequence of bits. Each “1” or “0” is a constraint on the possible messages that could be sent. As more bits are specified, the space of possible messages shrinks, not by a process, but by the logic of constraint. When all bits are fixed, the solution set is a single message: structure as total constraint satisfaction.
Structural Notes:
In all these cases, the analogy is not just illustrative; it is structurally exact. Only those members that satisfy all current constraints are real within the system. Where the analogy would break down, so would the logic of our approach.
Not all features of a system depend on physical process or signaling. Some exist only as consequences of constraints, instantly and everywhere those constraints are defined. In this series, “system” always means: a perspective defined by constraints; “structure” always means: what is possible from that perspective.
IV. Why This Matters for More Than Quantum Mechanics
The essays that follow will revisit the deepest puzzles of quantum theory, wavefunction collapse, measurement, observation, and more. These words, inherited from a century of physics, have accumulated metaphysical baggage and confusion. They often suggest process, agency, or the intervention of a conscious observer.
But through the lens of constraint and solution, we will see these mysteries with new clarity. “Collapse” will become a statement about which structures are possible under the current constraints. “Observation” will mean nothing more than the addition of new constraints, and the solution set changing accordingly.
As we’ll see, it is through interaction that systems gain new constraints and that the universe narrows the set of what is possible. But this logic will also guide us in tackling puzzles of memory (why the past is remembered), irreversibility (why time has an arrow), adaptation (how structures learn and persist), and even the emergence of space, time, and law.
What seems mysterious in quantum mechanics is often just a confusion about what system is being described, and what structure is being selected. The same clarity applies, sometimes in surprising ways, to thermodynamics, computation, biology, and beyond.
V. A Caution and an Invitation
These essays will use language familiar from quantum physics, but each term (“collapse,” “observer,” “possibility”) will be rigorously redefined by constraint. We aim to transcend the pitfalls of metaphor: our analogies are only as valid as the structural identity they preserve. Where the analogy runs out, so does the explanation.
As the essays climb, we’ll use the same rigor to interpret not just collapse or observation, but memory, learning, anticipation, and even the emergence of space and time themselves.
If, as you read, you find paradoxes dissolving, not through cleverness, but through clarity, then perhaps you will have picked up something sharp and simple, too.
VI. A Note on “Structure” and Abstract Spaces
In these essays, we use the word “structure” in a very specific sense: not just to mean an arrangement of things in physical space, but to describe whatever satisfies all the constraints of the system in play. Sometimes, structure does correspond to a physical shape or layout. More often, it refers to a kind of geometry in an abstract space, a landscape defined by rules, relationships, and possible connections.
As you read further, watch for the term “structure” applied to phenomena that may have no spatial geometry at all, an organism’s DNA, a computer’s program state, or the possible histories of a physical system. In every case, what persists is what fits the active constraints, whether they are spatial, informational, historical, or otherwise.
When we speak of “structure,” then, we mean the pattern, visible or hidden, that emerges when every rule is satisfied at once. It may help to imagine this as a “shape” not just in three dimensions, but in a space where every constraint is an axis, and what is real is what occupies the intersection of them all.