“Power! Unlimited power!” – Supreme Chancellor Palpatine

A core challenge of cyber security is the notable absence of the phenomenon that society uses to secure its rules-based systems in every other domain: brute-force physical power. Without having access to brute-force physical power to impose a real-world, physically-prohibitive cost on belligerent actions, people and programs acting in cyberspace are quite literally powerless do defend themselves against systemic abuse. This has made cyber security a notoriously difficult challenge. Software engineers must design specialized security software to protect their programs, but the security software is equally as powerless to defend itself against systemic abuse. The result of this negatively-reinforcing dynamic is increased complexity and bloatware as engineers continually chase down and patch the exploited systemic design flaws of their previous patching attempts.

Bitcoin appears to be the first operationally successful software protocol to harness brute-force physical power as a cyber defensive mechanism. Instead of relying exclusively on software patches to protect it against systemic abuse, the Bitcoin protocol uses a much different cyber security strategy. It digitizes brute-force physical power and then leverages its own power digitization process to impose a real-world, physically prohibitive cost on systemic abuse of its intermediation protocol.

Like all software, the Bitcoin protocol has physically non-intuitive properties that are not possible outside of the digital domain. One of the most difficult to conceptualize properties is the manner in which it partitions its supply of digitized brute-force physical power. For example, as the supply of real-world physical power backing Bitcoin increases, this does not correspond to an increasing supply of digitized power units. The protocol is designed to treat its digitized supply of power as a fixed and finite volume regardless of how many real-world watts are pumped into it. A simple way to envisage this counter-intuitive behavior is to consider two different geometrical shapes: a sphere and a horn. People are metacognitively wired by their experiences in the real world to perceive the growing supply of any matter as a growing sphere. For example, a supply of water in zero gravity naturally takes the shape of a sphere. If that sphere were to be injected with an increased supply of water, the volume of the sphere would increase (who doesn’t enjoy watching videos of astronauts demonstrating this behavior?).

Now imagine a different and far more bizarre scenario: an astronaut squirts a supply of water into zero gravity, but instead of taking the shape of a sphere, it takes the shape of a horn. Moreover, as the astronaut injects more water into the horn, the volume of the horn remains fixed but its surface area continues to grow. This mythical shape is what’s known as Gabriel’s Horn (see Figure below). While Gabriel’s Horn is a mathematically legitimate geometrical shape, physical limitations prevent it from existing in the real world because no known matter can be stretched to the point where it can have infinitely large surface area while retaining finite volume. But the things we metacognitively perceive as abstract digital objects in the software we engineer have no such limitations. Thus, it is trivial to design an abstract digital object to behave like Gabriel’s Horn. What is not trivial is our capacity to intuit it.

The supply of digitized brute-force physical power instantiated by the Bitcoin protocol behaves like Gabriel’s Horn, not a sphere. As volunteers inject an increasing supply of real-world physical power (i.e. electricity) into the horn, its volume remains fixed while the proportionate surface area stretches towards infinity. The surface area of that digital horn is then arbitrarily partitioned into 2,100 trillion equal segments colloquially referred to as “satoshis,” in much the same way that the surface area of the floating sphere we call Earth was arbitrarily partitioned into 5,100 trillion equal segments colloquially referred to as “square meters.” Note how that surface area can be further partitioned to any scale, big or small. 100 million Satoshis is called a bitcoin, in the same way that 2.6 million square meters is called a square mile.

Digitally converting real-world brute-force physical power into equally-partitioned surface area on the expanding surface area of Gabriel’s Horn is not only revolutionary from a cyber security perspective, it’s also extraordinary from a security dynamics perspective. As more users volunteer to increase the protocol’s real-world supply of physical power, the surface area of the horn increases. Since there is virtually no limit to the supply of real-world physical power that can be added to the network, there is virtually no limit to the surface area of the horn. This means there is no limit to the total size of each equally-partitioned segment of surface area, either. Since every infinitesimally small portion of surface area is equally capable of stretching towards infinite surface area, so too can any infinitesimally small portion of digital power stretch to represent an infinitely growing proportion of real-world physical power.

The result of this dynamic is something few people seem to appreciate: Every fragment of bitcoin represents unlimited real-world, brute-force physical power: all the power expended to defend it in the past, and all the power to be expended to defend it in the future. Thus, not only does the Bitcoin protocol empower people and programs to wield digital power as a mechanism to impose real-world, physically prohibitive costs on belligerent actions in cyberspace, there is virtually no limit to the amount of power that any Bitcoin user can wield, regardless of how few bits of bitcoin they personally control.