Coordination Amid Scarcity

There was an old warehouse on the edge of the town where anyone could walk in and use the tools. Saws went missing, drills broke, half-finished projects piled up in the corners, and people argued every other day about who left the mess. One afternoon they decided to change it. Each person claimed a workbench and their own set of tools. A simple sign went up, what's on your bench is yours. Jake took the woodworking corner. Sofia claimed the electronics table. A week later, Sofia's soldering iron burned out right in the middle of the project. She walked over to Jake and said, "Lend me yours for an hour and help me finish this circuit. I will cut and send the wooden case for the speaker you are building." Jake looked at his clean bench, then at her half-done work, and nodded. They spent the evening side by side. Both projects got finished. Soon others started doing the same, trading a rare tool for an extra pair of hands, or swapping skills instead of arguing. People kept their promises because the tools and the space were theirs. Nobody wanted to lose a useful neighbor. The warehouse stopped feeling like a battleground. It filled up with finished inventions instead. Owning their own little corner made cooperation the smartest move in the room.

The key insight is that private property is not about owning a patch of land, houses, or money. It can also be understood as a way of organising decisions about scarce resources, determining who gets to use them, who bears the consequences of their use, and who has the authority to decide what happens to them.

Imagine a small village with one hundred people, one well, a limited supply of farmland, and a limited supply of food. Everyone needs water, food, and shelter, but the village didn't have unlimited resources. Scarcity means the available quantity is insufficient to satisfy every possible desire. For example, water used to irrigate a field can't simultaneously be used to fill every household's storage tank; land used to construct a factory can't be simultaneously used to grow crops on the same land; time spent producing one good can't be spent producing another at that moment. Every resource therefore involves choice. Economists call the value of the best alternative forgone the opportunity cost.

Scarcity creates a coordination problem. When every villager wants to draw water from the well at the same time, it gets overcrowded. People wait, argue, and perhaps take more water than they need. Some households might receive too little, while others waste what they collect. The problem is not necessarily that the villagers are selfish or unintelligent. The problem is that their individual decisions must somehow fit together despite the limited supply of water that essentially creates the coordination problem. A society must discover ways to answer: Who may use a resource? For what purpose should it be used? How should competing uses be reconciled?

Private property is one institutional arrangement for addressing these questions.

Imagine a group of hunter-gatherers living in a forest. They obtain food by hunting animals, gathering fruits, and collecting other resources from their surroundings. Their survival depends heavily on what nature provides. The forest contains a finite number of animals. Its plants grow at particular rates. The group has only a limited area in which to find food; its tools allow it to obtain resources only at a limited rate. As the population grows, the pressure on these resources increases. Initially, a forest can sustain twenty hunter-gatherers comfortably. As more hunters enter the same area, they must share the available animals and other resources. If the population doubles but the amount of food available doesn't, each person may receive less food. Adding more people doesn't add more productive capacity.

The possible trap arises in which the community consumes the resources available to it without substantially improving its ability to replenish or produce them. When resources become insufficient, the group must find other new resources, develop better methods, or face declining living standards. The limited knowledge and relatively unchanging technology could have made it difficult for early communities to escape this situation. It might be plausible that some communities migrated when their surroundings could no longer sustain them. The challenge is not that nature contains limited resources, but that humans need better knowledge and better ways to organise them.

A major transformation occurred during the Neolithic revolution, when some human communities began practising agriculture and domesticating animals. People deliberately produce food rather than relying on nature. Agriculture didn't eliminate scarcity. Crops could fail, droughts may destroy harvests, and livestock could die. But it opened new possibilities for increasing production. A field could be prepared today to produce food in a future season. Irrigation could make previously unproductive land useful. Seeds could be selected, and cultivation methods improved. In other words, people began using resources not only for immediate consumption but also as inputs into future production.

Economists call resources used to produce other goods capital goods. The cultivated land and improvements to it are productive assets. These assets can create a continuing stream of future benefits rather than providing a one-time benefit. It changes the coordination problem. Once people invest time and effort in land, irrigation, houses, tools, and livestock, they have much to lose if someone else takes or damages those resources.

Private property becomes extremely important here. Imagine that two farmers cultivate neighboring plots. One farmer spends months clearing stones, improving the soil, building irrigation channels, and planting seeds. Farmer B makes no such investment. Suppose that anyone in the village can freely enter either field, change the irrigation channels, or take the tools wherever they want.

What incentives does farmer A have in improving the field?

The effort is costly, but someone else could take the benefit. This doesn't mean A will never invest. A might rely on family ties, standard customs, community agreements, or protection from others. But if control over the field is uncertain, investment becomes riskier. Private property offers one way to address this problem.

In the economic context, private property means that identifiable people or organisations have recognised rights to control particular resources, subject to relevant laws and rules. The rights commonly include:

Control: Deciding how a resource will be used.

Exclusion: Preventing unauthorised use by others.

Transfer: Selling, exchanging, gifting, or leasing it, where permitted.

Responsibilities: Bearing at least some consequences of decisions about the resources.

Property rights differ across societies and are not absolute. For example, a landowner may be restricted by environmental regulations, zoning rules, or the rights of neighbors.

If Farmer A can reliably control the field and retain the benefits of improving it, A has stronger reason to invest in better seeds, irrigation, and soil quality. If a person has clear and more secure property rights, then they have greater confidence in retaining future benefits. It encourages them to invest in and maintain resources that, in turn, raise productivity and more future goods. Investment also depends on security, access to tools, knowledge, credit, demand, and many other conditions. The transition to settled agriculture made property rights more important because resources become more durable, numerous, and valuable to maintain.

Suppose a village has a hundred plots of land. Each plot differs in soil quality, water availability, slope, and suitability for different crops. The villagers also have different abilities and preferences. One person knows how to grow wheat, another is skilled at fruit cultivation, and someone else understands irrigation. A single village leader might know some things, but it would be difficult for that person to know everything about every field, farmer, local condition, and every possible use. The farmer who works in the field may know the details that the leader doesn't.

Property rights help distribute decision-making authority. Rather than requiring one person to approve every small decision, they allow many people to make decisions about the resources they control. For example, a farmer decides which seeds to plant, a carpenter decides how to use the timber, a builder decides how to organize a construction project, and a household decides how to use its living space. Each decision maker can draw on local knowledge that might never reach a central authority. The difference is between having knowledge and having the authority to act on that knowledge. A farmer may know exactly how to improve a field, but if another person can arbitrarily take it away, the farmer's knowledge may not translate into action. Secure control can connect knowledge with the ability to put it to use.

Private property can be understood as a coordination mechanism: it assigns decision-making authority across many individuals instead of concentrating every decision in one place. However, private ownership is not the only way to distribute authority. Community-managed resources and public institutions can also delegate decisions to people with relevant knowledge.

Specialization becomes more important once property rights and settled production make long-term planning easier. Imagine a settlement with four people: a farmer produces grain and vegetables; a carpenter produces tables, doors, and tools; a potter produces storage vessels for food and water; a builder constructs and repairs houses. If everyone tries to grow food, make furniture, produce pottery, and build houses independently, each person must spend time learning and performing many tasks. Alternatively, they can specialise and exchange goods and services. This is called the division of labour.

Specialization raises productivity because people develop expertise, use suitable tools, and avoid repeatedly switching between unrelated tasks. But it creates interdependence. The carpenter needs food, the farmers need tools, the builder needs both food and equipment, and the potter needs materials. Nobody needs to produce everything alone, but everyone must find a way to obtain what others produce. Property rights with the development of this kind of cooperation: people can specialise in production and exchange the results of their work.

Ownership allows people to make decisions about transferring resources to others. Without clear rules about who controls a resource, exchange becomes difficult. If the carpenter can't establish whether the table is theirs to sell, or if another person can't claim the grain after the exchange, both parties face uncertainty. Recognised property rights can make these transactions more reliable. Ownership doesn't mean isolation. Private property is sometimes misunderstood as a system in which everyone looks after themselves and has no reason to cooperate.

In reality, ownership makes cooperation easier. The farmer doesn't need to know how to build a table; the carpenter doesn't need to grow all their food. Each can concentrate on a particular activity and obtain other goods through exchange. This creates a network of cooperation among people who may never meet. A person who buys a loaf of bread doesn't need to know the baker personally. The baker doesn't need to know the person who supplied the wheat. Yet a chain of production and exchange can connect them. Private property can help establish who controls the resources at each stage, while exchange coordinates how those resources move between people.

Suppose that a carpenter wants grain, but the farmer doesn't need a table. Perhaps the farmer wants a pair of shoes. Now the carpenter must find a shoemaker who wants a table, or find some other way to complete the exchange. This is the problem economists call the lack of a double coincidence of wants. Each person must possess something the other person wants to make the barter transaction work efficiently. As the number of specialists and goods increases, finding suitable trading partners becomes increasingly difficult.

Money helps overcome this difficulty. Instead of trading a table directly for grain, the carpenter can sell the table for money and use that money to buy grain. Money therefore builds on the coordination made possible by property and exchange. It provides a common medium through which people can trade with many different partners.

Private property can create incentives for investment and clarify decision-making, but doesn't solve every economic problem automatically. Private ownership can make it easier to decide what to plant, invest in irrigation, and retain the benefits of improving the soil. Community rules may be effective when many households depend on the same well. Clear access limits and shared maintenance responsibilities can prevent conflict and overuse. A factory may benefit from producing goods while imposing pollution costs on people who don't directly own or control it. Ownership alone doesn't ensure that these external costs are addressed.

Conclusion: The rules governing resources must take into account incentives, information, responsibilities, and the consequences for others. A resource may be privately owned or managed collectively. What matters for coordination is how effectively the institutional arrangement enables people to make informed decisions, resolve conflicts, and address the costs their actions impose on others.

If you have liked this post, please share it with others on WhatsApp, Twitter, and LinkedIn. Please share your feedback in the comment box.

Photo by Vitaly Gariev on Unsplash

Life's Hidden Laws

A young scientist named John walked through a forest after the rain. He saw a tree branch divide into smaller branches, and those branches divided again. In the soil, roots followed the same pattern. Nearby, a river split into streams, while veins spread through a fallen leaf. "How can unrelated things resemble one another?" John wondered. His teacher explained that they faced similar problems: distributing water, nutrients, or energy across a large area while using as little material as possible. Branching solved the problem efficiently, so nature repeated the same pattern in trees, rivers, roots, lungs, and blood vessels. The tree was not copying the river, and the river was not copying the leaf. Each had arrived at a similar design because the same physical pressures favored similar solutions. John smiled. Nature had many inventions, but when a problem was repeated, the pattern often returned.

We see enormous diversity around us, yet broad scaling patterns appear across many species. It suggests that underneath biological diversity are powerful constraints imposed by physics and geometry. Evolution creates diversity, but physics constrains it. At the smallest scale, physics describes particles such as quarks and electrons. They combine to form atoms; atoms combine into molecules; and molecules form complicated structures. Eventually, something qualitatively different appears: Life. A cell is not simply a large molecule. It's a highly organised system containing thousands of interacting molecular components. A whale, for example, contains trillions of cells, yet those cells are coordinated into one functioning organism.

Reductionism is one approach to solving problems. Suppose you want to understand a car. You can take it apart: engine, transmission, wheels, brakes, and electrical system. Then study each component individually. Physics often works the same way. To understand matter, we can ask: What is an atom made of? Eventually, we reach elementary particles such as quarks. The reductionist approach has been enormously successful, but it has one limitation. Knowing all the components doesn't necessarily tell you how the system behaves.

Sometimes the whole behaves differently from its parts. Imagine you know everything about water molecules, like hydrogen atoms, oxygen atoms, chemical bonds, and molecular interactions. This knowledge is insufficient to explain everything about a river. It has properties such as flowing turbulence, waves, currents, and whirlpools. These aren't properties of one isolated water molecule. They emerge from interactions among an enormous number of molecules. This is called emergence.

A cell contains an enormous number of molecular interactions. A cell consists of DNA, RNA, proteins, membranes, enzymes, mitochondria, signalling systems, and metabolic networks. Each component follows relatively simple chemical and physical rules. But their interactions produce something extraordinarily complicated: a living cell.

The cell can consume energy, repair itself, reproduce, respond to its environment, maintain internal conditions, and communicate with other cells. None of these abilities belongs to a single molecule. They emerge from the organization of many interacting molecules. Living systems aren't just a collection of components. They are networks. For example, arteries branch into arterioles and eventually capillaries; airways branch into smaller airways and eventually alveoli. Similarly, renal blood vessels branch into smaller vessels and eventually reach the filtration structures.

These networks solve the resource distribution problem. The resources can be oxygen, nutrients, water, hormones, heat, and information. The organism has to transport resources from relatively few entry points to an enormous number of cells. Life depends upon networks that distribute resources throughout the organism.

Consider a tiny organism such as a bacterium. It's so small that molecules can travel relatively short distances through diffusion. Now imagine making the bacterium a thousand times larger. Its volume increases significantly more than its surface area. The large organism can't depend on its outer surface area to exchange nutrients and gases.

Now diffusion becomes far too slow. A cell deep inside the organism would be extremely far from the external environment. Therefore, size increase creates a fundamental transportation problem. Evolution solves it through transportation networks. That is why large organisms evolved systems such as circulatory systems, vascular systems, and nervous systems. The appearance of these networks is not accidental. Size itself creates the need for them.

The next major transition is from single cells to a collection of cells. A multicellular organism contains an enormous number of cells. But simply adding cells together doesn't create a functioning organism. The cells have to coordinate. For example, the heart pumps blood, muscles coordinate movement, kidneys perform filtration, and the immune system provides defense. The organism therefore develops specialization. Complexity increases because different components become specialized while remaining interconnected.

Metabolism is the set of biochemical processes through which organisms acquire energy, transform energy, build biological structures, maintain themselves, and perform work.

According to Kleiber's law, metabolic rate∝(Body mass)3/4.

Dividing metabolic rate by mass, metabolic rate/mass∝(Body mass)−1/4.

Metabolism increases sublinearly with size. Large organisms use energy more economically per unit of body mass. That doesn't mean evolution keeps on making animals efficient forever. It has to balance energy acquisition with energy expenditure(growth, maintenance, and reproduction).

Different levels of organization have different effective descriptions. Atoms obey quantum mechanical rules. When atoms combine into molecules, we talk about chemical bonds, acidity, molecular shape, and reaction pathways. When molecules organise into cells, we think in terms of metabolism, replication, membranes, and cellular signalling. When cells organise into organisms, we talk about circulation, respiration, growth, and behavior.

The higher levels emerge from lower-level interactions, but we don't normally understand them by calculating every elementary particle. That would be practically impossible. Instead, we search for higher-level regularities.

There is a common misunderstanding about emergence. If something is emergent, then it must be unpredictable. A system can be extremely complicated at the microscopic level while exhibiting simple large-scale patterns. For example, a single molecule doesn't have a meaningful temperature. But billions of molecules collectively produce a measurable temperature. Similarly, individual molecules inside a cell can behave in complicated ways, yet an organism can exhibit a remarkably regular relationship between body size, metabolism, growth, life span, and heart rate. Complexity at one level generates simplicity at another level.

When an organism enlarges, its volume increases significantly more than its surface area. They are not geometrically scaled versions of each other but exhibit allometric scaling. This means that one biological quantity changes with another according to a mathematical power law.

The general equation is Y = a × Mᵇ, where Y is the biological quantity, M is the body mass, a is the scaling constant, and b is the scaling exponent. According to Klieber's law, metabolic rate∝(Body mass)3/4. The metabolism follows a three-quarters power law because of transport networks. For example, the heart branches into large arteries. They further branch into smaller arteries, then into arterioles, then into capillaries, and finally transport oxygen to cells.

The organism's metabolism is partly constrained by the architecture of its resource distribution network. In essence, the transportation network constrains the organism's overall physiological space. The same self-similar structure is found in trees. A structure is self-similar when similar patterns repeat at different scales. For example, in a tree, a trunk is divided into branches, branches into twigs, and twigs into smaller twigs. The branching pattern repeats. A small branch is a miniature version of the large branching structure. For example, rₖ represents the radius of the vessel at level k. In a self-similar structure, rₖ₊₁ / rₖ is equal to a constant.

A biological organism isn't a perfect fractal. For instance, a large artery is not a scaled-up version of a capillary. They have different diameters, wall thickness functions, pressures, and flow characteristics. Animals are not perfect fractals. They are an approximately self-similar organization of branching networks. The approximate self-similarity helps generate mathematical regularities.

Before moving forward, let's spend some time to understand the underlying idea of fractals.

Imagine you want to measure the length of a coastline. You traced the length of a coastline using a 100km ruler and found it to be 2000km. You did it again using a 10km ruler and, surprisingly, the length turns out to be 3000km. You did it again with a 1km ruler, and this time it became 5000km.

If we keep measuring it with smaller and smaller rulers, does the length of the coastline keep increasing?

The surprising answer is yes. In the mathematical idealization of a fractal boundary, the measured length can increase without approaching a conventional finite value.

A fractal is a structure that exhibits complicated geometric patterns across different scales. Zooming in reveals more structure rather than revealing a completely smooth object. This is also called self-similarity. Natural objects are usually approximately self-similar rather than mathematically identical at every scale. Let's understand it with an example of a Koch curve.

Koch Curve

Start with a straight line. Now replace the middle portion with two segments that create a triangular bump. Repeat the process on every segment. Eventually, you obtain a huge irregular boundary. Suppose the original line has length L₀.

At every iteration, each segment is replaced by four segments, each one of which is one third as long. Therefore, L₁ = L₀(4/3).

Next iteration, L₂ = L₀ × (4/3)².

After n iterations, Lₙ = L₀ × (4/3)ⁿ

Since 4/3 > 1, the length continues increasing. As n approaches infinity, the length tends towards infinity. Yet the overall curve occupies a finite region of space. Two observers can measure the same object and obtain different results because they are looking at different scales. Therefore, L(ε), the measured length, is a function of the measuring scale ε and can increase as ε decreases.

In ordinary geometry, a line has one dimension, a surface has 2, and a volume has 3 dimensions. But fractals don't always fit into these integer dimensions. A fractal can have a dimension such as D = 1.26, D = 1.5, etc. Imagine the fractal dimension as how complicated the object is across scales. A perfectly smooth line has D = 1, and a filled surface has D = 2. A complicated fractal boundary might have 1 < D < 2. So it is geometrically more complicated than an ordinary line but doesn't fill a two-dimensional space.

Mathematically, L(ε ) ~ ε⁽¹⁻ᴰ⁾, where L(ε ) = measured length, ε = size of the measuring unit, and D = fractal dimension.

For an ordinary smooth line, D = 1. Therefore, L(ε) is constant. The measured length doesn't depend on the measuring scale. But if D > 1, then (1 - D) < 0. Therefore, L(ε) = 1 /ε⁽¹⁻ᴰ⁾. As ε becomes smaller, the measured length increases. That is why the coastline keeps on increasing when the ruler's length changes.

A mathematical fractal can theoretically continue indefinitely. Larger systems branch into smaller components. The smaller components branch into even smaller components. Real biological systems can't. Eventually, we reach cells, molecules, atoms, and physical limits. Similarly, a coastline doesn't literally have infinite length in the physical world. At sufficiently small scales, molecular structure becomes relevant. Therefore, natural fractals are fractals over a finite range.

Let's get back to the biological structures. Suppose one vessel branches into 2. Then each of these branches divides again. After several generations, 1 becomes 2, 2 becomes 4, 4 becomes 8, and so on. The number of vessels increases rapidly. Meanwhile, the diameter decreases. Eventually, the network becomes extremely dense. This allows a relatively small number of large vessels to distribute resources throughout a huge organism.

The biological structures can't be designed arbitrarily. It has to satisfy several competing requirements:

1. It must reach all cells. Almost every cell must receive resources. The network must fill three-dimensional space and should fit inside the body. It also has physical space constraints.

2. It must minimize energy expenditure. Pumping blood through vessels requires energy.

3. It must keep transport distances manageable. Oxygen can't simply diffuse indefinitely through tissues. Therefore, the hierarchical and the terminal units are invariant.

4. It must operate reliably. The organism must survive damage, variations, and changing demands.

These constraints force the network into particular mathematical forms. The smallest unit of networks, such as capillaries, has relatively constrained properties. For example, capillary dimensions can't change arbitrarily because they must service cells. The smallest unit remains relatively similar even as the overall organism changes dramatically in size. A mouse and an elephant are vastly different animals, and their microscopic transport systems operate under many of the same physical constraints.

The large organism needs more terminal units rather than simply making each terminal unit enormously larger. Similarly, plants also have a transportation network. They use xylem to transport water and minerals and use phloem to transport sugar and other resources.

Geoffrey West and his colleagues developed a theoretical framework based on fractal-like transport networks and the constraints required to distribute resources throughout organisms. The basic idea is that the geometry of the network, its branching structure, and the requirement of efficient distribution combine to produce an exponent close to 3/4. The precise derivation involves assumptions about network geometry, branching, conservation of flow, terminal units, space filling, optimization of transport, and physical constraints. So, 3/4 is not a statistical coincidence but emerges from the architecture and physics of biological networks.

A dog, an elephant, a whale, and a human are different organisms. Yet their heart rate, metabolic rate, blood vessel dimensions, lifespan, and growth show remarkably similar mathematical relationships with body size. This is also known as universality.

Heart Rate ∝ M⁻¹ᐟ⁴

Lifespan ∝ M¹ᐟ⁴.

Multiplying both of them, we get

Heart Rate * Lifespan = M⁰(Constant)

This suggests that the total number of heartbeats over an organism's lifetime can be roughly similar across mammals. However, empirical relationships have important exceptions and should not be treated as a universal fixed number. A faster biological clock tends to be associated with a shorter lifetime, while a slower biological clock is associated with a longer lifetime.

The quarter power laws emerge from the physical and mathematical constraints imposed by the hierarchical networks that transport resources through living organisms. The network combines three-dimensional space and one-dimensional transport pathways that lead to the fourth-power dependence. The flow of energy is one of the fundamental constraints that shapes biological organisation.

Life looks extraordinarily organised. Yet organisms constantly produce entropy and dissipate energy. Living systems maintain their internal organisation by continuously taking in energy and exporting waste and heat. So, life doesn't escape the laws of thermodynamics. It has to abide by the physical laws.

Conclusion: Life may appear infinitely diverse, but beneath that diversity lie simple physical principles. From branching trees and rivers to blood vessels and cellular networks, similar problems repeatedly produce similar solutions. Emergence, scaling laws, fractal-like organization, and transport constraints show how complex biological systems can arise from simpler interactions governed by physics. Evolution creates remarkable variety, but physics sets the boundaries within which that variety can exist. Ultimately, life is not separate from the laws of nature. In fact, it is one of their most intricate expressions.

If you have liked this post, please share it with others on WhatsApp, Twitter, and LinkedIn. Please share your feedback in the comment box. 

Photo by Y on Unsplash

From Problems to Possibilities: How Intelligence Creates Knowledge

In 1854, London was in the grip of a deadly cholera outbreak. Hundreds of people were dying, and doctors believed the disease was carried through the air. One physician, John Snow, was not convinced. He noticed something strange: many of the victims lived near the same public water pump on Broad Street. Instead of accepting the prevailing explanation, Snow treated the outbreak itself as a problem to be investigated. He carefully mapped the deaths and found that they clustered around the pump. Snow persuaded the local authorities to remove the pump handle. The outbreak soon declined. Years later, scientists confirmed that cholera could indeed spread through contaminated water. The problem that had seemed like a catastrophe forced Snow to ask a better question, and that question helped transform understanding of the issue.

We feel discomfort and irritation when we face problems, yet it's only because of the problems that we make profound discoveries. Problems force us to think in ways that have not been thought of before. Sometimes a problem is not merely an obstacle. It is a signal pointing toward something we have yet to understand. Programming languages like C, C++, Python, etc., are developed to solve certain kinds of problems. It's a way to explain computing.

We often think computing is equal to calculating. For example, 7 * 8 = 56. We might say that a computer is computing because it is calculating. But it's too narrow. Computation is about representation. Suppose you want to remember the number 5. You can either write it or use your fingers. The physical fingers are being used to represent an abstract idea, the number 5. So we have the physical object that represents an abstract object. This is the idea behind computation. A computer does something similar, but at an enormous level of complexity.

Inside a computer, there are physical things: electrical states, transistors, voltages, switches, memory cells, etc. But we interpret those physical states as numbers, characters, images, sounds, variables, objects, instructions, and relationships. So, the computer's physical memory is used to represent abstract things.

A computer program is essentially a set of instructions that causes a physical machine to behave in a particular way. Imagine a simple program that adds two numbers and stores the result. The program isn't just writing words. Those instructions ultimately cause the computer's physical components to undergo particular changes. For instance, an operation causes a transition from memory state A to memory state B. So, there are two levels:

Abstract level: Add 5 and 7.

Physical level: Electrical states inside the processor and memory change in a particular instance.

The program connects the abstract problem to physical changes inside the computer that lead to the desired result. Therefore, software engineers are physicists who cause physical matter to behave in ways that instantiate abstract relationships.

A Turing machine is a mathematical idea of computation associated with Alan Turing. The machine can read information from the tape, change it, and move along the tape according to the rules. A universal Turing machine has an extraordinary property. It can simulate other computational processes. Instead of building a machine for every task, you can build one sufficiently general machine and give it different instructions.

That's essentially the conceptual foundation of the modern programmable computer. Your laptop can play music, display photographs, run a game, edit a document, calculate mathematics, and browse the internet. The hardware is largely the same; only the program changes.

Programming begins because someone wants something to happen that isn't happening. A problem isn't terrible. It's a conflict between two or more ideas. Suppose we want accurate navigation tables. But the tables contain errors. There is a conflict. Desired accuracy is not equal to the actual accuracy. That is a problem, and someone needs to find a solution.

Before modern computers, people needed mathematical tables containing things such as logarithms, trigonometric values, and cosine values. These are useful for navigation and other calculations. But calculating huge tables manually was difficult. A large number of people were employed as computers to perform calculations. Computers were originally referred to a person, but humans make mistakes. An incorrect mathematical table could have serious consequences, particularly for navigation. So there was a problem: humans need accurate calculations, versus human inevitably make errors. The proposed solution is to build a machine that can perform the calculations automatically.

Charles Babbage conceived the Difference Engine, a mechanical calculating machine designed to automate the production of mathematical tables. Babbage was not simply fascinated by machines. A problem motivated him to build a machine that would reduce errors in mathematical tables.

Babbage later imagined something more ambitious: The Analytical Engine. The Difference Engine was designed for particular mathematical calculations. The Analytical Engine was much more general. It was conceived as a programmable machine. It generated the idea of a general-purpose computer.

Ada Lovelace recognised that Babbage's Analytical Engine could potentially manipulate symbols according to the rules, not merely perform ordinary numerical calculations. She wrote what is considered one of the first computer programs.

Technology begins with problems. Suppose you want instant communication. Before digital communication, sending information over long distances could take time. Messaging software solved the problem by sending instant messages. Similarly, facial recognition addresses the need for quick identification without using a username/password or manual identification. Computer security solved the accessibility problem without letting unauthorised people access confidential information.

Suppose you have a problem to sort 1 million pieces of data efficiently. You might write a program that successfully sorts them. But that doesn't necessarily mean you have written a good program. There are multiple solutions to a problem. Some are good while others are bad. So, solving the problem is not enough. You need a good solution.

A good solution is hard to vary and is one that is well adapted to the problem it solves. Imagine a puzzle, and your job is to find a configuration where every piece fits perfectly. If you randomly change one piece, the solution breaks. That is a sign that pieces are arranged for a reason. The same idea applies to programs. A good program has components that work together to solve a particular problem. If you arbitrarily change components, the program may become worse. Therefore, a good solution adapted to a problem is hard to vary.

There are many familiar software engineering principles that can be understood as special cases of being hard to vary. For example, modularity divides a large system into well-defined components, and reusability creates components that can be used appropriately in multiple contexts. These aren't just arbitrary rules programmers invented. Good engineering generally produces structures that are well adapted to their purposes.

Suppose a programmer needs to solve a difficult problem. Does the programmer magically know the correct program?

Usually not. He thinks of a possible solution. Try it and finds problems with it. Upon modification, he tries it again. He rejects unsuccessful approaches, keeps improving until a better solution may emerge. It's basically a trial-and-error approach.

Consider biological evolution. A population contains variation. Some variations are better adapted to particular environments. Those variations become more successful and generate better adaptations. Similarly, a programmer proposes different possible solutions. Some are bad, while others are better. The programmer rejects bad solutions and retains better ones. The creation of a good program is itself an evolutionary process of generating and eliminating candidate solutions.

Karl Popper described the knowledge creation using the ideas of conjecture and refutation. Conjecture is a guessed solution to a problem, and refutation means finding problems in the proposed solution. Then, a new conjecture is made, which is again criticised by refutation. This continues until we have a better explanation for a problem. Therefore, it is reasonable to place programming and scientific reasoning into the same framework.

A programmer guesses a program, runs it, finds bugs, and keeps modifying it until a good solution is found. Similarly, a scientist proposes a theory, tests it, finds contradictions, and keeps refining it until a better explanation is found. A common misunderstanding is that creative people simply have brilliant ideas. In fact, creativity involves generating possible solutions and using criticism to eliminate the bad ones. Therefore, creativity generates candidates and criticism selects them.

Imagine you have written a program that poorly solves a problem. There are multiple ways to improve it. You could change the algorithm, restructure the code, change the data representation, improve efficiency, and remove unnecessary components. This implementation is easy to vary. That suggests it hasn't reached a highly adapted solution. A good solution has few opportunities for improvement.

There are two ways to vary the program: Internal variation and External variation.

Internal Variation: The program solves a particular problem, but you could modify its internal components and make it substantially better. That means the implementation is not well adapted.

External Variation: The program isn't strongly adapted to any particular purpose. It might be capable of doing many things but doesn't solve a particular problem especially well. So, good implementation means the details are strongly connected to a particular purpose.

Programming isn't about producing useful tools. It is connected to the creation of knowledge. Imagine you discover an algorithm that solves a difficult problem. That knowledge can be embodied in the program. The program therefore becomes a kind of explanation. That is why software engineering has a deeper relationship with reasoning than we normally recognise.

If two ideas appear to contradict each other, reality can't contain the contradiction in the same way. For example, the program works correctly, but it fails every test. Both can't simultaneously describe the same program in the same respect. Therefore, when we encounter a problem, at least one assumption may be wrong, incomplete, or inadequate. Solving the problem means discovering what needs to change. For example, we believe objects fall towards Earth. You also discover that Earth is round. Now you can ask, why don't the objects on the other side of the Earth fall off into space?

There appears to be a conflict between your existing ideas. That conflict creates a problem. Your mind searches for an explanation that resolves the conflict. Eventually, Newtonian gravity provides a much deeper explanation.

Knowledge is not obtained by simply collecting observations. It is created through conjecture, criticism, and error correction. Imagine that you see the following: The sun rose yesterday; it rises today; and has risen every day of your life. Therefore, the sun will rise tomorrow. This is a wrong way to predict and generate knowledge. It's basically inductivism, which is the process of finding a pattern from many examples and generalising knowledge using those patterns. For example, you observe many swans and all of them are white. You may conclude that all swans are white. This seems logical, but then you discover a black swan that refutes your conclusion.

The problem is not that induction can sometimes make mistakes. It's about how to identify what observations and patterns to look for. Suppose one person studies birds with long necks. He notices swans, geese, cranes, etc., and suddenly your classification looks different. Another person studies animals whose beaks are approximately 5cm long. Now the relevant observations are different again. So there is no mechanical rule saying that if you look at these observations, a correct theory will automatically emerge. The observer always needs a problem and a conceptual framework.

If knowledge were simply extracted from observations, then creativity wouldn't be fundamental. A sufficiently powerful machine could collect data, process it, and obtain truth. But if knowledge requires new explanations, then something must generate those explanations. That's creativity. Suppose Newton sees an apple fall. The observations itself doesn't contain F = m * a or universal gravitation inside them. The physical event is one thing, and the explanation is another. Someone has to invent the explanation.

It doesn't mean observations don't matter. They matter enormously to criticise theories. For instance, all metals expand when heated. We perform experiments. If we found a counterexample, we have a problem. We must modify or abandon the theory. So experiments are powerful because they allow reality to criticise our ideas.

It's good to think that we could be wrong. It's actually not a weakness but a strength. Suppose someone says my theory is certain and can't possibly be wrong. There is no room for criticism and therefore no mechanism for improvement. But a scientist says This is my best explanation. Show me where it fails. Now other people can attack it, find an error, and knowledge improves. If they can't, the theory remains. Therefore, fallibility is essential to knowledge growth.

If a system can predict correctly, doesn't that mean it knows?

The production of successful outputs and possession of explanatory knowledge are different things. Suppose I give you a complicated formula that predicts tomorrow's weather. You ask, why does this formula work? I say, I don't know. I just discovered that it usually gives the right answers. That's different from understanding the physical mechanism of weather. A good explanation doesn't produce a correct answer. It tells us why the answer is correct and how different phenomena are related.

Is intelligence simply the ability to process data?

An intelligent system must be capable of encountering problems, generating possible solutions, criticising those explanations, detecting errors, creating improved explanations, and applying knowledge to new problems. This is more demanding than simply recognising patterns. A good explanation should not merely fit one observation. It should explain many things at once. Suppose two theories explain why a ball falls:

Theory A: Balls fall because they want to fall.

Theory B: There is a universal gravitational attraction between masses.

Both might be compatible with the observation that balls fall, but Theory B has more explanatory power. It explains why the moon orbits Earth, why planets orbit the Sun, why objects have weight, and why projectiles follow predictable trajectories. So, Theory B has greater explanatory power and is better than Theory A.

Knowledge is closely related to what a program can do. So instead of asking, " What information is stored inside the computer?" We should ask what that information enables the computer to do. You can describe a hammer physically: a metal head, wooden handle, certain weight and dimensions. But none of these descriptions explains what a hammer is for. Its function is to drive nails. Similarly, we should not understand computer knowledge just by looking at its bits, memory locations, and symbols. A program uses the knowledge embedded in it to solve real-world problems.

Computers are machines that represent physical abstractions. Suppose we want a computer to understand the concept of a dog. It doesn't contain a dog. Instead, physical states inside the computer represent abstract objects. The physical computer manipulates electrical states, but those states can represent abstract relationships. Software connects physical processes with abstract ideas. The computer's physical machinery is not itself the knowledge. Rather, its physical states instantiate representations of knowledge.

Suppose there are two programs. Program A contains 10 million facts but requires enormous changes when it encounters a new situation. Program B contains a smaller number of principles that allow it to deal with many different situations. Program B is more powerful than Program A because its knowledge has greater explanatory power. It captures something deeper that explains many cases.

A good program has a well-defined structure to solve a problem. The structure represents relationships about the problem. Those relationships allow the program to produce solutions. Therefore, the program embodies knowledge of how to solve the problem. Specialised knowledge is the one adapted to a particular problem, but general intelligence is the ability to create or discover knowledge that allows you to solve new kinds of problems.

We can make machines that are excellent at games, image classification, language generation, medical prediction, and pattern recognition. But artificial general intelligence requires something broader: the ability to create useful knowledge about problems that were not anticipated by its designers. It means the system must somehow go beyond merely applying predefined knowledge. It must be able to discover new explanations.

A universal system is one that can, in principle, perform or solve everything that belongs to its domain. For example, a basic calculator can add, subtract, multiply, or divide. But it can't be used to write a novel, run a weather simulation, control a robot, or play a video game. A general-purpose computer, however, can potentially do all these things. It's not restricted to one task, but can be programmed to implement many different processes. Human intelligence appears to be extraordinarily general-purpose.

A universal computer is powerful not because of its physical structure. But because it can represent and execute many different solutions. Suppose I want to study a planetary system. I could either build a physical miniature solar system or write software that represents mass, velocity, gravity, and time. The computer can then calculate how the planets would move. The computer doesn't literally become the solar system. It simulates its behaviour. A physical computer represents an abstract system that executes rules to simulate behaviour.

A computer can be universally programmable without being intelligent. For example, a universal computer can run many programs doesn't mean a universal computer understands what problems matter, creates explanations, and invents new knowledge. Intelligence is the system capable of creating explanations across multiple domains. The universal machine moves much of the complexity from hardware into software.

Universality is always relative to a domain. In classical mechanics, Newton's theory can explain an enormous range of phenomena involving motion, falling objects, projectiles, planets, and moons. So, within its domain, it has enormous reach. When an explanation can solve all problems in a domain, it has universal reach in that domain.

Before Newton, people often treated Earthly motion and celestial motion as different things. An apple falling from a tree seemed like one phenomenon, and the moon orbiting Earth was another. Newton showed that the same underlying principle can explain both. That is an enormous increase in explanatory reach. Universality is connected to unification. A good universal explanation can replace many disconnected explanations.

Technologies move from stone tools to specific machines. The specialised machines then transitioned to programmable machines that eventually created the universal computer. At some point, capability doesn't increase quantitatively. There would be a qualitative transition. A machine that can perform one task is fundamentally different from a machine that can perform an enormous variety of tasks. The same idea appears in the history of computation. Universal Turing machines are important precisely because one machine can simulate other machines rather than being dedicated to one computation.

Imagine an animal has an instinct: when a predator appears, run. It can be extremely sophisticated, but it is relatively specific. Now imagine a human encounters a completely new threat. They can potentially reason: what exactly is happening? What could cause it? What experiments could distinguish these possibilities? What new technology could solve it?

The ability to generate new solutions to new problems is the ultimate expression of intelligence. Universality doesn't mean omniscience. In fact, it has the ability to solve problems across broad domains. A universal program doesn't contain the set of all programs. It has the capability of running programs that can be supplied to it. Likewise, an intelligent person doesn't know every scientific fact. They have the ability to create knowledge when confronted with something unknown.

Conclusion: Problems drive discovery and innovation by forcing us to question assumptions and create new explanations. Programming is a form of problem-solving that connects abstract ideas to physical processes in computers. Good programs are well-adapted solutions: they evolve through trial, error, criticism, and refinement. The same process underlies scientific knowledge. As Karl Popper argued, knowledge grows through conjectures and refutations rather than simply collecting observations. Intelligence therefore involves more than processing data: it requires creating, testing, and improving explanations. Universal computers can perform many tasks, but true general intelligence requires the ability to generate new knowledge and solve unfamiliar problems.

If you have liked this post, please share it with others on WhatsApp, Twitter, and LinkedIn. Please share your feedback in the comment box. 

Photo by Vitaly Gariev on Unsplash