Costly Signals and Sound Money
Connecting Biological Power, the Power Law, and Bitcoin
It's amazing what you can do with your own brain enhanced by AI. I decided to do a deep dive on Jason Lowery's Softwar thesis, the controversial MIT paper arguing that Bitcoin's proof-of-work mechanism is a form of non-lethal power projection, when I noticed a connection I hadn't seen anyone draw. Lowery argues that Bitcoin converts physical energy into digital security, creating the first physical anchor in cyberspace. But before he does that, he reinforces the idea of power at the biological level. Separately, Giovanni Santostasi and Matthew Mezinskis have documented that Bitcoin's price follows a power law or power curve, the same type of scale-invariant pattern found in mammalian metabolic rates, earthquake frequencies, and city growth. Both frameworks describe Bitcoin as a physical system rather than a financial one. I haven't seen anyone connect the idea of power in nature to the scaling power law, and the bridge between them turned out to be signaling theory, a framework from biology and economics that explains why Bitcoin behaves differently from every other form of money in human history.
Power in Nature
Lowery starts in a place most Bitcoin writing never goes: billions of years before the first transaction. Before money, before language, before anything resembling an economy, organisms were already solving the problem of property rights. They solved it with power.
Two bull elk lock antlers in a clearing. The contest is metabolically brutal. Growing those antlers costs the equivalent of regrowing an entire skeleton every year. But the contest itself is not about destruction. It is about information. The weaker animal walks away alive. Resources get allocated. No arbiter, no court, no central authority. The physical cost of the display communicates something that cannot be faked: underlying fitness. An animal that can afford to grow a rack of antlers that weighs forty pounds and still outrun predators, still forage, still survive the winter, is demonstrating capacity that no bluff can replicate.
Lowery traces this pattern from sub-cellular life through complex organisms and up through human civilization. He formalizes it as the Benefit-to-Cost Ratio of Attack: when the cost of attacking exceeds the benefit, property is secure. When it doesn't, property changes hands. This is not metaphor. It is the operating principle behind every territorial boundary in nature, every border between nations, every lock on every door. Security is, and always has been, a function of the physical cost required to violate it.
The Scaling Pattern
Systems governed by physical constraints tend to follow a specific mathematical pattern: the power law. Geoffrey West's work at the Santa Fe Institute documented this across biological systems. A mammal's metabolic rate scales with its body mass raised to the three-quarter power. This relationship holds from shrews to blue whales across eight orders of magnitude.
The pattern extends far beyond biology. City infrastructure scales as a power law. So do river networks, earthquake frequencies, and the branching patterns of trees. Zipf's law shows that word frequency in every natural language follows a power law distribution, constrained by the physics of cognitive processing and communication efficiency. Pareto documented that wealth distribution follows a power law across every society he studied, regardless of political system or historical period. Scientific citation networks follow the same pattern. So does the frequency and severity of wars.
The common thread is not that these are all physical systems in the narrow sense. Cities are socio-technological systems with politics, regulation, human behavior, and sentiment. Language is entirely human-created. Wealth distribution is shaped by tax policy, inheritance law, and revolution. Power laws emerge in all of them because the underlying constraints, whether metabolic, cognitive, infrastructural, or thermodynamic, are physical even when the systems built on top of them are not. Individual-level volatility averages out at scale. The noise is human. The signal is physical.
Giovanni Santostasi, an astrophysicist, observed that Bitcoin's price, hash rate, and user adoption all follow power law distributions. Not just individually, but in relation to each other and to time. Price scales roughly as time to the sixth power. Hash rate scales as time to the twelfth power. Hash rate equals approximately price squared. These are not independent observations. They are a connected feedback loop: adoption drives price via Metcalfe's Law (network value scales with users squared, itself a power law), price attracts mining investment, the difficulty adjustment constrains hash rate growth to a physical parameter, and increased security attracts more adoption. Santostasi's insight is that this feedback loop, governed at every step by physical constraints, is what produces the power law.
Matthew Mezinskis independently documented the same pattern and has tracked it since 2018, showing that for roughly every 13% increase in days since Bitcoin's genesis block, the power trend price doubles. The fit holds across fifteen-plus years with an R-squared above 95%. Santostasi argued explicitly that Bitcoin should be studied with the tools of physics, not finance, because its feedback loops make it behave like a physical system.
A common objection is that Bitcoin is not a physical system but a socio-technological one, shaped by human behavior, regulation, and sentiment. This objection proves less than it appears to. Cities are also socio-technological systems. They have politics, zoning disputes, corruption, speculative real estate bubbles, and every other form of human noise. They still follow power laws. The reason is that the underlying constraints, infrastructure networks, energy distribution, transportation geometry, are physical. Human behavior sits on top of those constraints and creates volatility around the trend. It does not alter the trend. A Bitcoin node running in someone's house, untouched for months, is validating transactions and enforcing consensus rules right now without human involvement. A home miner is hashing on the network right now without human involvement. The protocol runs whether anyone is watching or not. Sentiment impacts price, which in turn influences hash rate and the difficulty adjustment through miner economics. But the difficulty adjustment is the mechanism that preserves the signal's integrity through those cycles, adapting the energy cost to maintain the system's structural properties. What sentiment cannot alter is the supply schedule, the protocol rules, or the structural relationship between hash rate and network security. The system bends with sentiment. It does not break. The power law describes the physical layer. Price is a noisy derivative of it.
The standard explanation for Bitcoin's power law behavior is straightforward: Bitcoin is physically anchored. Mining requires real energy. The difficulty adjustment enforces thermodynamic cost. Supply is perfectly inelastic. These properties make Bitcoin behave more like a geological or biological process than a financial asset, and physical processes follow power laws. But this explanation is incomplete. Gold also requires real energy to extract. Gold mining is physically constrained, geologically scarce, and thermodynamically costly. Gold does not follow a power law. It has appreciated roughly 8x over fifty years, tracking inflation with modest real gains. If physical constraint alone explained power law behavior, gold should exhibit it too. Something else is going on.
What Makes a Signal Honest
In 1973, Michael Spence published a paper on job market signaling that would eventually earn him a Nobel Prize. His insight was that a college degree functions as a costly signal. Not because education necessarily makes workers more productive, but because the degree is differentially costly to obtain. A rigorous program is harder for low-ability candidates to complete than high-ability ones. Because the cost falls asymmetrically, the signal carries honest information. Employers can use it to sort candidates even if the education itself adds no direct productive value.
Spence identified three properties that make any signal effective. It must be costly to produce. The cost must fall disproportionately on those who would fake it. And it must be observable by the receiver. When all three hold, the signal is honest and the information it carries is reliable. When any of them breaks down, the signal degrades and participants lose the ability to distinguish quality from noise.
In Spence's framework, a signal is any costly, observable action that communicates private information about underlying quality to a counterparty who cannot directly observe it. The cost must correlate with the quality being communicated, or the signal degrades. This is the definition that connects everything in this article. The elk antlers signal fitness to rivals who cannot directly measure it. The college degree signals ability to employers who cannot directly test it. Money, I will argue, signals real economic value to counterparties who cannot directly verify it. For the remainder of this article, I apply Spence's framework specifically to monetary systems: the signal is the information a form of money communicates about the real economic value it represents. A monetary system whose production costs are high, differential, and observable produces an honest monetary signal. One whose production costs are low, symmetric, and opaque produces a degraded one.
The education example is worth sitting with for a moment, because it is in the process of breaking in real time. If AI makes it trivially easy for a low-ability candidate to produce work that previously required years of training, the cost of the signal is no longer differential. The degree stops sorting for the qualities it used to sort for. The implications for credentialing, hiring, and institutional trust are significant and underexplored. For now, the takeaway is that signal quality is fragile. It depends on the cost structure remaining intact.
The Handicap Principle
Two years after Spence, biologist Amotz Zahavi extended the same logic into the natural world with the handicap principle. Peacock tails, elk antlers, elaborate birdsong: these are all costly signals that function precisely because they appear wasteful. Only genuinely fit organisms can afford the metabolic expense of growing a three-foot tail and still surviving. The wastefulness is the point. It is what makes the signal unfakeable.
This closes the loop back to Lowery. The elk antlers are not just a power projection mechanism. They are a signaling mechanism. The physical cost of the display is what makes the information it carries reliable. Power and signal are not separate phenomena. The signal is the power, expressed in a form that communicates without requiring lethal combat every time two organisms encounter each other.
Zahavi's framework applies to any system where participants need to communicate quality, capability, or commitment under conditions where lying would be advantageous. Job markets. Mating displays. And, it turns out, money.
Fitness Signals and Resource Signals
The distinction between two types of costly signals sharpens the analysis considerably.
Zahavi's handicap principle describes fitness signals. The peacock tail, the elk antler, the metabolically expensive display: these communicate something about the organism's underlying quality. The signal says, "I am so fit that I can afford this handicap and still thrive." The signal must be continuously renewed. An elk grows new antlers every year. The cost is ongoing. The information is current.
Thorstein Veblen described a different kind of display in 1899: conspicuous consumption. The elaborate court, the gold-plated palace, the feast that could feed a village. These are resource signals, not fitness signals. They communicate stockpile size, not ongoing quality. The signal says, "I have accumulated so much that I can afford to waste some." A resource signal can persist long after the capacity that generated it has disappeared. A dynasty can display inherited wealth for centuries without any member demonstrating the fitness that originally produced it.
The distinction matters because the two types degrade differently. A Zahavi signal is anchored to ongoing biological fitness. You cannot fake metabolic capacity. Each renewal of the signal carries fresh information. A Veblen signal is anchored to accumulated stock, and it is culturally contingent. Its information content decays over time because it tells you about the past, not the present.
The Signal in Money
Apply both frameworks, Spence's three criteria and the Zahavi-Veblen distinction, across monetary systems and the differences are stark.
Bitcoin. Costly to produce? Yes. Mining requires real energy expenditure, currently tens of thousands of dollars per coin in electricity and hardware. Differentially costly to fake? Yes. An attacker attempting to forge the signal through a 51% attack must outspend the entire network. The cost falls overwhelmingly on the dishonest actor. Observable? Completely. Hash rate, difficulty, block times, and total supply are publicly verifiable by anyone running a node, in real time, anywhere on Earth. Bitcoin satisfies all three of Spence's criteria. Under the Zahavi-Veblen spectrum, Bitcoin operates at the protocol level as a fitness signal. Every block requires fresh energy expenditure that demonstrates ongoing network fitness. The signal is continuous, not point-in-time. It does not decouple from its physical anchor.
Gold. Costly to produce? Yes. Real energy and labor are required for extraction. Differentially costly to fake? Partially. Counterfeiting is possible, tungsten-core bars have been documented, and verification requires specialized equipment. More importantly, gold supply responds to price. When gold doubles, marginal deposits become economic, exploration spending increases, and production rises over a multi-year lag. The energy anchor stretches. Observable? Poorly. Production costs vary by mine and are reported by companies with financial incentives to manage those numbers. Total above-ground stock is estimated, not verified. Estimates range by tens of thousands of tonnes depending on the source. Gold satisfies the first criterion, partially satisfies the second, and largely fails the third. Under the Zahavi-Veblen spectrum, gold began its monetary life as a fitness signal. Extracting it required real productive capacity. Possessing gold signaled that you or your ancestors had the fitness to acquire it. Over centuries, gold has migrated toward a resource signal. Central banks sitting on gold reserves are demonstrating stockpile size, not productive fitness. The signal has moved from "we can produce" to "we have accumulated." The information content has degraded accordingly.
Fiat currency. Costly to produce? At the margin, no. Created by keystroke. A bank creates new money by making a loan entry. A central bank creates reserves by changing a number in a database. An important objection here: the fiat system's maintenance cost is enormous. The US military, the global banking compliance apparatus, the legal system, these require real resources and real energy. The dollar is not backed by nothing. It is backed by geopolitical power. But under Spence's framework, what matters for signal quality is the marginal cost of production, not the fixed cost of system maintenance. The Fed can create $4 trillion in new monetary units without proportionally increasing military spending or compliance overhead. The marginal cost of signal production is near zero even when the fixed cost of the system is high. Differentially costly to fake? No. The issuer and the counterfeiter use functionally identical mechanisms: entering numbers into a ledger. Under the eurodollar system, any bank anywhere in the world with a dollar-denominated balance sheet can create new dollar-denominated claims through lending. Observable? Marginally. M2 is published in the United States, but shadow banking, eurodollar creation, offshore credit expansion, and off-balance-sheet structures make the true supply of dollar-denominated money unknowable. Fiat fails all three of Spence's criteria at the margin of production. Under the Zahavi-Veblen spectrum, fiat currency is overwhelmingly a resource signal. The dollar's reserve currency status does not signal productive fitness. It signals military hegemony and institutional inertia. The signal is accepted not because it is honest, but because the power behind it is sufficient to enforce acceptance.
This produces a four-tier monetary signal hierarchy, understood as a spectrum rather than a set of absolute categories. At the top: protocol-level Zahavi, continuous, unfakeable, fully observable. Bitcoin. Below that: degraded Zahavi migrating toward Veblen. Gold. Below that: Veblen with minimal fitness component at the margin. Fiat. And at the bottom: Veblen signals backed by nothing but narrative and enforcement. Specific fiat currencies in terminal decline.
Why Bitcoin Follows the Power Law and Gold Doesn't
Now we can answer the question from earlier.
The standard explanation for Bitcoin's power law behavior is physical constraint: energy, difficulty adjustment, inelastic supply. That explanation is correct but incomplete. Gold is also physically constrained. Gold mining also requires energy. Gold supply is also relatively inelastic. Yet gold does not follow a power law.
The missing variable is signal quality. Power law dynamics emerge in systems where the signal is continuously renewed, physically anchored, and never decoupled from the underlying fitness it represents. Bitcoin's proof-of-work satisfies all of these conditions. Every block is a fresh demonstration of energy expenditure. The difficulty adjustment ensures that the cost of producing the signal scales with the network's growth. The signal does not degrade because the protocol does not allow it to coast on past performance.
The Metcalfe's Law connection reinforces this. Network value scaling with users squared is itself a power law. If adoption follows a power law in time, and value scales as a power law of adoption, the composition produces the price power law. But Metcalfe's Law alone doesn't explain why some networks sustain the pattern and others don't. The internet does: node growth, bandwidth consumption, and traffic distribution all follow power law distributions decades after the network matured, because the infrastructure layer is physical. Fiber optic cables, router capacity, spectrum allocation, data center energy consumption. The content layer is human. The infrastructure layer is not. Facebook's user growth followed a Metcalfe pattern during its growth phase but the valuation decoupled, because Facebook has no physical anchor. The cost of adding a user is near zero. There is no difficulty adjustment. Value depends on attention and advertising revenue, which are narrative-driven and manipulable by policy. The Metcalfe pattern held during growth and then broke because nothing physical kept it coupled. Bitcoin's network value stays coupled to the Metcalfe trajectory because proof of work anchors it to a physical cost function at every step. Metcalfe provides the network effect. The difficulty adjustment provides the physical anchor. Signal quality is why the two stay coupled.
The implication is that price may not be the primary power law at all. Hash rate is. Santostasi's data shows hash rate scaling as time to the twelfth power with hash rate approximately equal to price squared. Cost to produce a bitcoin is a direct function of hash rate, difficulty, and energy cost. Price oscillates around cost to produce because miners are the marginal sellers, which is empirically observable in the miner capitulation floors that define every bear market bottom. The causal chain runs from the physical layer upward: hash rate (power law) produces cost to produce (derivative of hash rate) produces price (noisy derivative of cost to produce). Nobody has yet isolated cost-to-produce as an independent power law fit, but the causal chain suggests it should be one, and that price oscillates around it in exactly the way the power law's corridor predicts. If this is correct, then the power law's predictive power lives not in the price chart but in the physical layer underneath it. Price is the signal plus noise. Hash rate is the signal.
Gold broke off the power law trajectory when its signal migrated from Zahavi to Veblen. When gold was primarily acquired through active extraction, requiring the demonstrable fitness of the society doing the extracting, it may have exhibited tighter scaling dynamics. As gold shifted to a store-of-value role, where the signal communicates accumulated stock rather than ongoing productive capacity, the connection between physical cost and signal quality loosened. Central bank gold reserves are the purest expression of this: the gold sits in a vault demonstrating nothing about the current fitness of the entity holding it. The signal has decoupled from its anchor.
An objection arises here: Bitcoin sitting in cold storage looks the same. A stockpile demonstrating nothing about the holder's current fitness. But the monetary signal quality is not a property of individual holding behavior. It is a property of the system. Every ten minutes, the Bitcoin network produces a fresh block requiring real energy expenditure. No holder, no miner, no government can alter the supply schedule or forge transaction validity without bearing a cost that exceeds the benefit. Gold has no equivalent mechanism. Gold's monetary integrity depends on the institutions that custody, assay, and account for it, and those institutions can and do manipulate the signal: paper gold, fractional reserve lending of allocated bars, central bank revaluation, confiscation. The gold itself is inert. It proves nothing about the monetary system built on top of it. Bitcoin's protocol proves itself every ten minutes whether anyone is watching or not. That continuous, institution-independent renewal of the signal is what produces scale-invariant growth. Without it, there is no mechanism for a power law to emerge.
Fiat-denominated asset prices do not follow power laws because they are not physically constrained at the margin. They are narrative-driven, policy-driven, and manipulable by the entities that control the signal. A Federal Reserve meeting can reprice every dollar-denominated asset on Earth overnight. No amount of institutional action can reprice Bitcoin's difficulty adjustment or supply schedule. The power law is the empirical signature of an honest signal operating in a system where the cost structure cannot be manipulated at the protocol level. It is what scaling looks like when the signal is anchored to physics.
Returns Denominated in a Degraded Signal
If fiat money is a degraded signal, then any return denominated in fiat carries limited information about whether real wealth was created or destroyed. A portfolio that returns 10% nominally in dollars could represent 10% real wealth creation, or 0% creation plus 10% debasement, or negative 5% real destruction plus 15% debasement. The degraded signal cannot distinguish between these scenarios. Hayek's insight that prices aggregate dispersed information across millions of actors depends on an honest unit of measurement. Denominate everything in a degraded signal and the price discovery mechanism weakens. You get malinvestment, asset bubbles, zombie companies surviving on cheap credit, and capital misallocation at scale.
Jeff Snider's work on the eurodollar system documents this phenomenon in practice. The Federal Reserve does not control the dollar supply. Offshore dollar-denominated credit creation operates outside the Fed's jurisdiction, visibility, and control. When a bank in London creates a dollar-denominated loan to a company in Singapore, that is new dollar supply that appears in no Federal Reserve database. The signal is not just degraded at the margin. It is unattributable and unmeasurable.
If you want to know whether economic activity is creating real wealth, denominate it in the most honest available signal. Denominate the S&P 500 in Bitcoin and you see that equity investors have been losing purchasing power for most of Bitcoin's existence. The nominal dollar returns that make investors feel wealthy are an artifact of the signal they are measuring in. The BTC/gold ratio measures the relative signal quality of the two monetary systems. The structural direction of that ratio reflects the market gradually pricing in the information differential between a stronger signal and a weaker one.
The Drain
Jordi Visser has observed that all money flowing into Bitcoin flows from some other asset, because Bitcoin's supply is not inflated. This raises the question of whether Bitcoin's appreciation is simply portfolio reallocation rather than genuine information being priced in.
But portfolio reallocation IS how markets price in information. When a bondholder sells treasuries and buys Bitcoin, that transaction is the market expressing the judgment that the honest signal is more valuable than the degraded one. The flow of capital from degraded-signal assets to honest-signal assets is what pricing in the information advantage looks like mechanically.
Under current incentive structures, this flow is largely one-directional. Holders who move savings into Bitcoin tend not to move them back voluntarily, for the same reason that people hoard good money and spend bad money. This is Gresham's Law restated in signaling terms: rational actors store value in honest signals and transact in degraded ones. Over time, Bitcoin functions as a drain on the degraded-signal system, absorbing value that the inflationary system itself creates. The dollars printed since 2020, roughly forty percent more than previously existed, are in a meaningful sense funding the transition from degraded to honest signaling.
This drainage is durable under current conditions, but it is not inevitable under all possible conditions. Nation-states can introduce real friction: criminalizing mining hardware, restricting grid access, isolating network traffic at the ISP level. These actions cannot alter the protocol, but they can slow adoption and interrupt the flow in specific jurisdictions. The drain is a structural tendency, not a physical law. Its persistence depends on the incentive structures that currently make honest signals more attractive than degraded ones, and on the continued inability of governments to offer a competitive alternative.
What Happens Next
Honest signals do not persuade degraded systems to reform. They tend to make degraded systems less relevant over time.
Every institution optimized for degraded signals, from credit ratings agencies to the asset management industry to central banks themselves, faces the same structural challenge: their value proposition depends on navigating a system whose signals carry diminishing information. If money becomes an honest signal, the need for a multi-trillion-dollar financial intermediation layer to help you figure out whether your savings are growing or shrinking is substantially reduced.
This will not happen through persuasion. It will happen through drainage. The people who adopt Bitcoin early are making a scarcity trade: acquiring the honest signal while it is relatively cheap. The institutions that eventually engage are making a probability trade: the probability that the old signals continue to function is declining. The transition is asymmetric and non-linear, which is precisely what the power law describes. Bitcoin's price trajectory is not speculative mania. It is the market gradually pricing in the information advantage of an honest signal over a degraded one.
Regulatory action, political obstruction, exchange failures, bad actors: these are real forces that drive medium-term price volatility. They do not alter the difficulty adjustment, the supply schedule, or the energy cost of mining. The power law describes the signal. The noise around it is real, and for any individual holder the noise can be financially devastating in the short term. But the noise does not change the information content of the signal any more than a zoning dispute changes the scaling dynamics of a city. Over time, the physical constraints dominate and the noise averages out. That is what power laws describe.
One internal risk deserves acknowledgment. As the block subsidy halves toward zero over the coming decades, the fitness signal will depend increasingly on transaction fees sustaining sufficient hash rate. If fees fail to replace the subsidy, the energy expenditure securing the network drops and the signal weakens. This is the one scenario in which Bitcoin's fitness signal degrades from within rather than being disrupted from without. The timeline is long. The final meaningful subsidy halvings are decades away. But the question is real, and the framework presented here predicts that a significant decline in hash rate energy expenditure would weaken the power law fit.
The power law will hold for as long as Bitcoin remains an honest signal and fiat remains a degraded one. Given that the former is enforced by protocol and thermodynamics, and the latter is guaranteed by the incentive structures of sovereign debt issuance, both conditions appear durable.
The signal is the money. The money is the signal. This was once true of gold. For centuries, gold's physical scarcity and the cost of its extraction made those two statements functionally equivalent. But over time, institutions found ways to decouple the signal from the money: paper claims, fractional reserves, confiscation, revaluation. The signal degraded because nothing in gold's nature prevented it from being manipulated by the institutions built around it. Bitcoin's design as a protocol layer, enforced by thermodynamics rather than institutional trust, makes such manipulation prohibitively costly. For the first time in history, we have a form of money where the signal is very difficult to separate from the money, and those two statements will remain true for as long as the protocol runs and the energy expenditure sustains it.
This article draws on Jason Lowery's Softwar thesis (MIT, 2023) for the power projection framework, Geoffrey West's Scale (Penguin, 2017) for biological and urban power law dynamics, Giovanni Santostasi's original power law research and feedback loop theory, Matthew Mezinskis's power curve work at Porkopolis Economics, Robert Metcalfe's network valuation law, Michael Spence's signaling theory, Amotz Zahavi's handicap principle, Thorstein Veblen's Theory of the Leisure Class (1899), and Jeff Snider's eurodollar system analysis.
The connection between these frameworks emerged in conversation with Claude and has not, to my knowledge, been previously articulated. *This article was written with assistance from Claude."
