‍Symmetry, Asymmetry, and the Birth of Computational Time

Introduction | Before Discussing Bitcoin, Ask a More Fundamental Question

Before discussing Bitcoin, we need to ask a more fundamental question: “Where does the fundamental driving force of the world come from?” It comes neither from absolute symmetry, nor from pure chaos, but from— within the constraints of global symmetry, the spontaneously generated, continuously dissipated, and measurable asymmetry inside a system.

Water to fish, wind to birds, information to Bitcoin. They all follow the same structure.

I. Starting from Noether’s Theorem: Symmetry Determines Invariants

Noether’s theorem reveals one of the most profound facts in modern physics:

Time translation symmetry ⟹ conservation of energy

Space translation symmetry ⟹ conservation of momentum

The meta-structure behind it is:

As long as a system remains invariant under a certain transformation, there must exist a global conserved quantity.

This idea is not limited to physical systems.

It applies equally to—game systems and computational systems.

II. Information Symmetry: The Only Prerequisite for Unique Convergence of Nash Equilibrium

In game theory, Nash gave a conclusion that appears strict, yet is extremely important:

Only under conditions of information symmetry and strictly competitive payoffs can non-cooperative games converge to a unique equilibrium.

Once information becomes asymmetric:

Private information emerges

Identity or permissions arise

Coalition games form

The system will inevitably move toward multiple equilibria and path dependence,

and can ultimately rely only on external arbitration to maintain order.

III. An Extended Noether Theorem: Information Symmetry ⟹ Unique Convergence

This implies a profound correspondence:

The status of information symmetry in game systems is equivalent to the status of time symmetry in physical systems.

We can regard this as an extended Noether theorem:

Information symmetry ⟹ unique convergence of Nash equilibrium

This is not rhetoric, but structural isomorphism.

IV. Satoshi Nakamoto’s Key Choice: Preserving Information Symmetry Instead of Introducing Privilege

The first fundamental principle of the Nakamoto consensus mechanism is not hash power, nor the blockchain itself, but:

Maintaining global information symmetry at the consensus layer.

In Bitcoin:

Rules are symmetric to all nodes

Verification is symmetric to all nodes

Identity, status, and permissions do not participate in consensus

Therefore, the entire network participates in a truly non-cooperative game,

thus possessing the possibility of unique convergence to a Nash equilibrium.

This step directly excluded all consensus mechanisms that rely on identity sets, voting power, or committee structures.

V. The Double-Spending Paradox: How to Avoid Arbitration Under Information Symmetry?

The question then arises:

Under complete information symmetry, with no third-party arbitration, how can double-spending attacks be prevented?

Satoshi’s answer was not to break information symmetry,

but to introduce another dimension of asymmetry—

computational asymmetry.

VI. The Benchmark Function: Measurable Computational Asymmetry

By encapsulating a one-way hash function, Satoshi constructed a Benchmark function whose core characteristics are:

Hard to generate: requires exponential nonce searching

Easy to verify: verification completed with a single hash

Unforgeable cost: hash power and energy cannot be rolled back

This is: a continuously occurring, measurable local computational asymmetry under the constraint of global information symmetry.

It is neither privilege nor knowledge advantage,

but a purely physical cost differential that can be quantified.

VII. The Birth of Time: 10 Minutes as the Scale Constant of the Computational World (the Benchmark function is used to maintain a constant 10 minutes)

The difficulty adjustment mechanism keeps block production at approximately one block every 10 minutes:

Hash power increases ⟹ difficulty increases

Hash power decreases ⟹ difficulty decreases

The key is not the value “10 minutes” itself, but that:

this time scale remains invariant under environmental changes.

Thus, 10 minutes becomes—

the computational time ruler shared by all nodes.

VIII. Isomorphism with Relativity: Scale Invariance

Structurally, this is completely isomorphic to the invariance of the speed of light in relativity:

The speed of light is not invariant because the world is static,

but because it serves as a scale constant shared by all inertial frames.

Likewise:

Bitcoin’s 10 minutes is not because hash power is constant,

but because the time scale is dynamically maintained.

Only when the scale is invariant can time be established.

IX. A Unified Perspective: Life, Flight, and Computational Time

Returning to the original unified structure:

Fish: the continuity of water provides global symmetry; asymmetric head–tail movement generates free motion

Birds: the continuity of air provides global symmetry; phase asymmetry of wings generates flight

Bitcoin: information symmetry stabilizes unique convergence of Nash equilibrium; computational asymmetry generates the direction of time

They follow the same principle:

Global symmetry provides coordinate stability; spontaneous symmetry breaking provides directional动力.

Conclusion | Bitcoin Is the First Verifiable “Computational Time System”

Bitcoin is not a “more efficient payment tool.”

It is a system that— under conditions of information symmetry, generates time and history through measurable computational asymmetry.

If the speed of light defines the time structure of the physical world,

then the 10-minute block defines the time structure of Bitcoin’s computational world.

This is the true philosophical principle of the Nakamoto consensus mechanism.