Construction Physics author Brian Potter: Technological invention is a search problem; modularity makes the impossible search space feasible
Brian Potter, author of Construction Physics, proposes the PTOP model to argue that technological creation is essentially a process of searching for viable combinations within a high-dimensional design space. Through simulation, he demonstrates how modularity, scientific knowledge, and performance trade-offs compress an astronomical search space into an operable range.
In Construction Physics, Brian Potter presents the view that creating new technology is essentially a search for viable combinations within a high-dimensional "design space." This space is unimaginably vast. He cites economist Matt Clancy's estimate: Wikipedia lists 272 "named equations" describing various natural laws. If each law can be either used or not used, the possible combinations amount to 2^272, which exceeds the common estimate of the number of atoms in the observable universe (approximately 10^80, or roughly 2^265). This is likely an undercount, as the same principles can be orchestrated in different ways or applied at different scales. Potter argues that there are likely at least thousands of natural laws that could actually be harnessed.
Faced with such scale, how do humans find technology? Potter's answer is information. Each bit of information halves the search space, so even a small amount of knowledge can turn an seemingly impossible search into an operable problem. Inventing technology is about gathering information: determining what works and what doesn't, what is promising and what is not, thereby narrowing down from vast possibilities to solutions that achieve specific goals. He uses the Wright brothers as an example: physical laws and the existence proof of birds had already narrowed the search space for aircraft, but the specific construction still offered countless variations. The Wright brothers' advantage lay in their exceptional ability to gather information, allowing them to converge on a viable design much faster than their competitors.
To turn this intuition into a simulatable model, Potter proposes PTOP: Phenomena Triggered by Objects with Properties. The model is inspired by Brian Arthur's book The Nature of Technology. Arthur views technology as a set of phenomena captured and utilized: a radio receiver is not just a collection of parts, but an orchestration of phenomena such as electromagnetic induction, electron attraction and repulsion, electron emission, voltage drop across resistance, and frequency resonance. A lightbulb utilizes Joule heating, incandescence, and transparency. Arthur and Wolfgang Polak also noted that when constructing logic circuits using only NAND gates and the values 0 and 1, an 8-bit adder is merely one of over 10^177,554 possible phenotypes with 16 inputs and 9 outputs. In Potter's model, objects have attributes like type and size; when the correct objects are arranged properly, phenomena are automatically triggered, altering other object attributes or generating new objects. Linking the correct chain of phenomena yields the desired result.
In a Level 1 model, with 10 object types, 10 sizes, and 5 objects arranged in a line, there are 10^10 arrangements; expanding to 100 object types, 100 sizes, and 10 phenomenon levels results in a search space of 10^40. Potter's simulations show that random blind search requires an average of one billion attempts to hit a design of that scale. However, modular search—adding one object at a time and adjusting its size until the next phenomenon is triggered, then locking in the successful module—requires only about 1,300 attempts on average. Crucially, the degree of modularity matters: if the model expands to 100 phenomenon levels, reaching a search space of 10^200, modular search finds the solution in about 10,000 attempts because 100 small steps can be locked in. Conversely, if the search space is equally large but only 10 steps can be locked, even modularity makes finding the solution nearly impossible.
The model also demonstrates the value of scientific knowledge lies in how many possibilities it excludes. Potter cites economic historian Joel Mokyr: if a searcher does not know natural principles, the range of experimentation would be far larger. In PTOP, knowledge acts as constraints, such as "phenomenon X cannot work with object Y" or "the two objects for phenomenon Z must be of equal size." The more possibilities excluded, the more information gained, and the faster the search. Real-world technological invention often relies on such "must" conditions: Marconi knew what was needed to generate electromagnetic waves, Edison knew what was needed for filament incandescence, and Manhattan Project scientists knew roughly what was needed to trigger a nuclear chain reaction.
A Level 2 model adds two complexities: a phenomenon can have multiple input objects (e.g., combustion in a gasoline engine requires fuel, oxidizer, and spark), and multiple phenomena at the same level can achieve the same goal (e.g., electric motors, hydraulic motors, and internal combustion engines all produce mechanical motion). Thus, while viable designs increase, non-viable combinations remain vastly larger. Potter uses a search method similar to Arthur's "encapsulation": once a group of objects triggers a phenomenon, that combination is packaged as a new object and randomly combined with others, allowing the system to accumulate partial solutions. He also simulates a "population" of technologies: 1,000 random technologies undergo asexual reproduction (one mutation per generation) or sexual reproduction (crossing branches of two parents). At 5 phenomenon levels, asexual reproduction failed to reach the highest level after 2,000 generations, while sexual reproduction achieved it in about 100 generations. This result is used to analogize biological evolution's avoidance of clonal interference to accelerate information accumulation.
A Level 3 model introduces performance tuning. Triggered attributes are no longer binary (on/off) but take values from 1 to 10, depending on input object size and previous phenomenon values; some phenomena maximize when prior values and sizes are equal, others when they differ maximally. Finding a working technology becomes easier, but pushing performance to the maximum requires repeated adjustment. Potter uses the lightbulb as an example: incandescent bulbs were demonstrated in the early 19th century but suffered from short life, blackening, and high power consumption. Edison took a largely defined basic configuration and improved performance by adjusting vacuum levels, filament size, and carbon type. The model also allows different phenomena to have different performance ceilings and includes parallel phenomena: the same condition may affect multiple results simultaneously, and optimizing one metric does not necessarily optimize another.
This leads to design trade-offs. Potter's simulations show that the optimal implementation of the same basic technology differs depending on the goal: a design maximizing a single metric is fundamentally different from one maximizing two metrics simultaneously. He gives real-world examples: carbon filaments had a performance ceiling, leading to tungsten filaments, which in turn required new processes for producing ductile tungsten wire; Formula 1 cars need pneumatic spring valves, whereas ordinary sedans suffice with steel wire springs. Potter concludes that technological progress can be understood as a search process, whose speed depends on how information is acquired, how modules are locked in, and how performance goals are traded off.
Boundaries must be retained: PTOP is a simplified simulation proposed by the author, not an empirical validation of real technological history. It assumes technology has a hierarchical modular structure, whereas real technology may involve non-hierarchical coupling, emergent properties, organizational coordination, regulatory hurdles, and social acceptance bottlenecks. Therefore, it serves better as a mental model for explaining the speed of invention rather than a tool for predicting when a specific technology will appear.