Prelude: Two Voices
On January 3, 2009, someone whose identity no one knows wrote a rule into a piece of code:
For every 210,000 blocks produced, the issuance of new coins is halved.
The rule gives no reason. It doesn’t explain why 210,000, doesn’t explain why halving rather than some other decay. It simply exists, like an axiom.
Seventeen years later, on some night in 2026, I sat in front of my screen and wrote down a rule of my own:
Monthly contribution = base amount × (reference price / current price)^k
My rule has no reason either — I mean, of course it has reasons; I could talk about them for three hours. But the moment I wrote it down and decided to obey it, it became an axiom. It began to constrain me, the way that rule of 210,000 constrains the entire network.
Two rules, seventeen years apart, one inside a machine, one inside my head.
What this essay wants to say is: they are the same thing.
And more than that — what happens between them is, precisely, a fugue.
Part One: Bach’s Problem
What Is a Fugue
A fugue begins with a subject. A short melody, a few notes, unremarkable on its own.
Then a second voice enters. It sings the same subject, but transposed up a fifth. This is called the answer.
A third voice enters. A fourth. Each entry is the same subject, but at a different pitch, at a different moment.
What you hear now is no longer a single melody. What you hear is multiple copies of the same melody chasing one another.
And the miraculous part is: they must all be harmonious at the same time.
Once the subject is transposed and laid over the original, they cannot clash. They must hold simultaneously both vertically (harmony) and horizontally (melody).
This is an extraordinarily severe constraint. Bach spent a lifetime dancing inside it.
Retrograde, Inversion, Augmentation
But Bach was not satisfied with this.
In The Musical Offering, he wrote a Crab Canon. The second voice of this piece is the first voice played backwards, from end to beginning.
Turn the score around, and it is still itself.
In The Art of Fugue, he used inversion: every ascending interval of the subject becomes descending, every descending one becomes ascending. The melody is mirrored — yet it can still coexist harmoniously with the original.
And there is augmentation: the same subject, played at twice the note values. It slows down, but the skeleton stays the same.
A subject can be transposed, inverted, reversed, stretched — and it remains itself.
Here a philosophical question appears, and a large one at that:
What is “itself”?
If a melody played backwards is still it, mirrored is still it, slowed by half is still it — then what, exactly, is “it”?
“It” is not that string of notes. “It” is the structure of relationships among those notes.
The notes change. The relationships do not.
This is the first thing we need to grasp: what remains invariant under transformation is what is essential.
Physicists call this symmetry. Noether’s theorem tells us: every symmetry corresponds to a conserved quantity.
And in music, it is called a fugue.
Part Two: Gödel’s Crack
Can a System Speak About Itself
In 1931, Kurt Gödel did something that, at the time, looked exceedingly strange.
He assigned a number to every symbol, every formula, every proof in a mathematical system. The plus sign is some number, the equals sign is some number, and the statement “1+1=2” as a whole is also an (enormous) number.
And so, statements about mathematics became statements about numbers.
And a mathematical system studies numbers in the first place.
So now, the mathematical system can speak about itself.
With this key, Gödel constructed a sentence. Once encoded, the sentence says:
“This sentence is not provable within this system.”
Stop and think about that sentence.
If it can be proved — then what it says is false (because it says it is not provable). A system that can prove a false proposition is inconsistent.
If it cannot be proved — then what it says is true. And so there exists, within this system, a proposition that is true but cannot be proved.
Two roads: either contradiction, or incompleteness.
Any sufficiently powerful formal system cannot be both complete and consistent.
The Point Is Not the Conclusion, but the Method
Most people remember the conclusion. But the real shock lies in how Gödel did it.
What he did was: make the system point at itself.
As long as a system is powerful enough to describe its own structure, it can always construct a self-referential sentence — and that sentence will tear it open.
Complex enough to speak about itself, and it is doomed to be wounded by itself.
This is not a bug you can avoid by “designing the system better.” This is the fate of any sufficiently complex system.
Part Three: Escher’s Hands
Escher drew a pair of hands.
The left hand holds a pen, drawing the cuff of the right hand. The right hand holds a pen, drawing the cuff of the left hand.
They draw each other into existence.
And when you look at the drawing, you can’t help asking: then who drew these two hands?
The answer is outside the picture. Escher drew them.
But the world inside the picture has no concept of an “outside.” Within the drawing, this is a closed, self-sufficient, inescapable loop.
Hofstadter calls this a strange loop:
You move up (or down) a hierarchy, and as you go, you find yourself back where you started.
Print Gallery is fiercer still: a man stands in a gallery looking at a painting; the painting shows a city; in the city there’s a building; in the building there’s a gallery; in the gallery stands a man — himself.
At the very center of the picture, Escher left a white void, and signed his name.
Because there, the drawing could go no further.
That void is Gödel’s crack.
Part Four: First Modulation — The Metronome in the Code
Now set these three things down and return to the rule.
Every 210,000 blocks, one halving.
What this rule does is manufacture time inside a system that has no time.
The blockchain itself has no concept of a “year.” It doesn’t know how many times the Earth has circled the Sun. It only knows blocks.
But the difficulty-adjustment mechanism anchors block time at roughly ten minutes. And so 210,000 blocks ≈ four years.
A purely mathematical rule seeped into physical time.
And this seepage produced a consequence that I consider the most profound part of the whole affair:
It created a beat.
Not a beat in the metaphorical sense. A real, predictable, periodic pulse. Once every four years, the flow of new coins is halved, like a giant heart contracting.
And price — that thing determined by the greed, fear, leverage, and liquidations of millions of people, that thing which looks utterly chaotic —
it follows this beat.
Imperfectly. With lag. Sometimes early, sometimes late. But it follows.
Three halvings, three bull-bear cycles. The sample is small, small enough to make any serious statistician frown. But that shape is there.
Why This Keeps Me Awake
Because it means: a rule that was written down by a human, arbitrary, without reason, has nonetheless resonated a cycle out of the collective behavior of millions.
The number 210,000 has no natural meaning whatsoever. It corresponds to no physical constant. Satoshi could have written 200,000, could have written 250,000.
But he wrote 210,000, and so the world breathes on a four-year cycle.
A rule is not a description of the world. A rule creates a part of the world.
This is Bach’s subject. An arbitrary, brief melodic fragment — the instant it is written down, it begins to demand that the entire piece organize itself around it.
The halving is the subject. The market cycle is the answer.
Part Five: Second Modulation — My Rule, and a Loop I Didn’t See Coming
Now it’s my turn.
I saw that beat. I believe (with appropriate skepticism) that it is real. And so I wrote down my rule:
Contribution = base × (reference price / current price)^k
What kind of rule is this?
It is an answer to the beat.
The lower the price, the more I buy. The shape of this function is an encoding of my belief that “the cycle will press the price down to some low point.”
I turned my belief into a mathematical function.
And once it was written, something strange happened:
This function no longer needs me to believe in it.
It runs on its own. When the price falls to 44,000, it puts in more money. It doesn’t ask whether I still believe in the four-year cycle today. It doesn’t care how panicked I am at 3 a.m. after seeing one big red candle.
I externalized my judgment into a machine that doesn’t need me.
But Here Is a Strange Loop
The purpose of designing this set of rules was to spare me from making judgments in moments of panic.
Because I don’t trust the me that panics.
But — who wrote the rules?
I did.
Using the same brain. The brain I don’t trust.
I merely used it in a relatively calm moment, then froze the result, so that it could constrain the future me who is not calm.
This is a self-referential structure.
An element inside the system (me) generated a rule that constrains that system (including me).
And here the Gödelian crack appears:
“I should not make judgments in panic” — this is itself a judgment.
“My rule doesn’t require me to predict the bottom” — but “the bottom is worth predicting” and “the bottom lies between 35k and 50k” are beliefs already encoded into the reference price P_ref and the aggressiveness k.
I thought I had escaped prediction. I had only hidden the prediction inside the parameters.
A parameter is a frozen prediction.
This hole I cannot patch. There is no way to design a rule that “contains no judgment at all,” because the design is itself a judgment.
I did not escape the loop. I only drew the loop a little larger.
Part Six: The Confluence of Three Voices
Now place the three things side by side.
Bach: an arbitrary subject, once written, generates the entire structure of the piece through transposition, inversion, augmentation. The subject does not describe the piece; the subject generates the piece.
Satoshi: an arbitrary number (210,000), once written, generates a four-year cycle through difficulty adjustment, block rhythm, supply shock. The rule does not describe the market; the rule generates the market’s beat.
Me: a belief about the cycle, once encoded into a function, generates the whole of my behavior for the next two years through k, P_ref, the cap, the threshold. The function does not describe my judgment; the function replaces my judgment.
Three levels, one structure:
A rule, once written down and once obeyed, begins to generate a world.
And at every level, the same crack exists:
- In Bach’s piece, where does the subject come from? Bach wrote it. And Bach is not inside the piece.
- In Bitcoin’s cycle, where does 210,000 come from? Satoshi wrote it. And Satoshi is not on the chain.
- In my rule, where do k and P_ref come from? I wrote them. And the “me who writes the rule” is not inside the rule.
Every self-sufficient system requires an author it cannot contain.
Escher left a void at the center of the picture and signed his name.
That void is where the author stands.
Part Seven: Rhythm, and Why It Might Not Be Coincidence
I want to say a riskier thought. It may be wrong, but I want to say it.
Why can a rule mesh with the world?
The standard answer is: because the world already has structure, and the rule merely discovered it.
But the Bitcoin example tells us this is not so. 210,000 was not discovered; it was stipulated. This cycle did not exist before Satoshi wrote it.
The rule created that structure.
So the question becomes: why can an arbitrarily stipulated rule stably generate a cycle out of the chaos of millions of free wills?
My guess is:
Because periodicity is not a property of the world, but a property of a “constrained process.”
Any system, as long as it has:
- a feedback mechanism (price influences behavior, behavior influences price),
- a delay (information propagation, decision, execution all take time),
- a periodic external pulse (the halving),
will oscillate.
This is not finance; this is cybernetics. A negative-feedback system with delay necessarily oscillates — this is mathematics, not market psychology.
The halving provides the pulse. Human nature provides the delay.
The cycle is the product of the two.
And this also explains why the four-year cycle may be failing: ETFs and institutional capital have changed the delay structure. Their reactions are faster, their leverage more regulated, their forced-liquidation thresholds clearer.
If the delay has changed, the frequency and amplitude of the oscillation will change.
It is not that “the cycle is broken.” It is that “the transfer function of this control system has been rewritten.”
Part Eight: And So, Music
Return to Bach.
Why does a fugue sound “right”?
Not because it conforms to some rule of harmony — rules are man-made, and they have changed many times.
It is because the fugue gives you a subject, and then lets your brain predict how it will return.
And it always returns — but never in the way you expect.
Expectation, and the tiny frustration of expectation.
This is the essence of rhythm.
A perfectly regular beat (tick-tock, tick-tock) is boring, because it is fully predictable. A purely random sound is noise, because it is fully unpredictable.
Music lives in between.
And the market, too, lives in between.
If Bitcoin’s cycle were perfectly predictable, it would cease to exist — everyone would buy at the same instant, and arbitrage would erase everything in a flash.
It is precisely because the cycle “roughly exists but is not precise” that it is both worth betting on and impossible to fully squeeze dry.
In that “roughly” lives all my opportunity, and all my risk.
It is the subject’s answer — the same melody, but transposed; you recognize it, yet you don’t know on which beat it will land.
Coda: A Problem I Cannot Solve
That night, after I had placed the limit orders, I switched off the screen and sat in the dark.
One sentence kept circling in my head. It is the beginning of this essay, and its end:
I designed a system that doesn’t need me — and that design was made by me.
I cannot escape.
Bach cannot escape — he must write the subject from outside the piece. Satoshi cannot escape — he must fix 210,000 from outside the chain. Gödel tells us that any sufficiently complex system cannot escape — it must contain truths it cannot prove.
And I, sitting here, write down k = 2.0.
Where does that 2.0 come from?
From me.
Then on what grounds do I trust me?
On no grounds.
I merely, in a sufficiently calm moment, wrote it down as best I could — and then decided to obey.
This is not a triumph of reason. It is a strange, almost religious act — I handed myself over to a rule I wrote myself.
Like a musician handing himself over to a metronome.
The metronome does not know what music is. It only ticks.
But it is precisely because of that tick that music becomes possible.
Ricercar.
In Italian, the word means “to search.” Bach used it to name the most complex fugue in The Musical Offering.
We have been searching all along. Searching for the subject that ties everything together.
And each time we think we’ve found it, we discover — that subject is one we sang ourselves.