Learning a University Through Its Equations

I have been trying to learn more about physics, chemistry, and mathematics, but I keep running into the same problem. Equations are difficult to remember when they arrive without context.

A formula written on a whiteboard can feel detached from reality. It contains letters, symbols, subscripts, and Greek characters, but no obvious reason for existing. Even when I understand it in the moment, the meaning often disappears from memory soon afterward.

So I began thinking about a different way to learn. Instead of studying mathematics as an isolated subject, I could use an entire university as the structure.

I studied at National Cheng Kung University in Tainan. NCKU contains departments of engineering, medicine, architecture, computer science, chemistry, biology, planning, design, economics, psychology, literature, and many other fields. Almost every department has its own set of equations.

Civil engineers calculate whether buildings will stand. Doctors estimate blood flow and drug dosage. Urban planners measure density and accessibility. Computer scientists calculate complexity. Economists model growth and incentives. Psychologists study how quickly people make decisions. Designers measure usability. Physicists describe light, motion, energy, and black holes.

Together, these equations form a mathematical map of the university.

A university is divided into departments because knowledge has become too large for any one person to master. Each department looks at reality through a particular lens. Mechanical engineering studies forces, movement, heat, stress, and machines. Medicine studies cells, organs, blood, disease, treatment, and survival. Architecture studies space, structure, light, sound, temperature, and human scale. Computer science studies algorithms, information, probability, memory, and computation. Urban planning studies population, transportation, land, access, and concentration. Business studies revenue, cost, risk, growth, and value.

These departments sometimes study the same phenomenon while describing it in completely different ways. A physicist might describe a human body as mass moving through space. A biomechanical engineer might describe it as a system of forces and joints. A doctor might describe it through circulation, respiration, and metabolism. A psychologist might describe it through attention, memory, and perception. An interaction designer might describe it through goals, actions, feedback, and experience.

The equations reveal these different perspectives.

An equation is often treated as a calculation, but it is also a compressed story. Newton's second law is written as:

F = ma

Force equals mass multiplied by acceleration. The equation says that heavier objects require more force to accelerate, and that greater acceleration requires greater force. It can describe a rocket, a car, a dancer, a runner, a falling object, or the tiny motors stabilizing a smartphone camera. The equation is short, but the story behind it is enormous.

The fundamental equation of traffic flow is:

q = kv

Traffic flow equals vehicle density multiplied by average speed. A road can move many vehicles when cars travel at a reasonable speed and remain sufficiently spaced apart. When density becomes too high, speed collapses, and the total flow can decrease. The equation helps explain why adding more cars to a road can eventually result in fewer people moving through it.

In medicine, cardiac output is often represented as:

CO = HR × SV

Cardiac output equals heart rate multiplied by stroke volume. The heart can pump more blood by beating faster, by pumping more blood with each beat, or through a combination of both. An abstract equation becomes a story about a living system trying to deliver oxygen throughout the body.

I began imagining an equation atlas covering all the departments at NCKU. The goal would not be to memorize every formula taught at the university. That would mean thousands of equations, many of them highly specialized. The goal would be to find the equations that represent the central ideas of each field.

Architecture might be represented by the equation:

Q̇ = UAΔT

Heat loss depends on thermal transmittance, surface area, and the temperature difference between inside and outside. This helps explain why large windows, poor insulation, and extreme temperatures increase the energy needed to heat or cool a building.

Urban planning might begin with:

D = P / A

Population density equals population divided by land area. The equation is simple, but density affects transportation, housing, energy use, street life, services, and the economics of a city.

Electrical engineering might begin with Ohm's law:

V = IR

Voltage equals current multiplied by resistance. This relationship appears throughout electrical systems, from sensors and batteries to appliances, computers, and power grids.

Computer science might use:

T(n) = O(n log n)

This describes a class of algorithms whose running time grows slightly faster than linearly. It helps explain why some software remains fast when processing millions of items while other software becomes unusable as the amount of data increases.

Finance might begin with compound growth:

FV = PV(1 + r)^t

Future value equals present value multiplied by growth over time. The equation describes investing, debt, savings, business growth, and the strange power of accumulation.

Environmental engineering might use:

CO₂e = Σᵢ Activityᵢ × EmissionFactorᵢ

A carbon footprint can be estimated by multiplying each activity by its corresponding emission factor and then adding the results together. This connects directly to the ideas behind Green Filter. A product's environmental impact can be understood as a collection of activities involving materials, production, transportation, usage, repair, and disposal.

One of the most interesting discoveries is that departments do not really possess separate mathematics. The same structures repeatedly appear in different fields.

A derivative measures change:

dy / dt

In physics, it can describe velocity or acceleration. In chemistry, it can describe reaction speed. In medicine, it can describe changing drug concentration. In business, it can describe revenue growth. In environmental science, it can describe the increase in atmospheric carbon dioxide. In product design, it can describe whether engagement is improving or declining.

A metric tells us where a system is. A derivative tells us where it is going.

An integral describes accumulation:

∫ f(x) dx

It can calculate distance from velocity, energy from power, blood volume from flow, total pollution from emissions, total revenue from transactions, or total exposure from changing risk. The integral is a mathematical way of saying that large outcomes are often made from many tiny events.

Exponential growth appears in the equation:

N(t) = N₀e^(rt)

The same structure can describe a population, an investment, bacteria, a chemical reaction, technological adoption, viral spread, or a rapidly growing company. The subject changes, but the mathematical shape remains.

Optimization appears in almost every college:

x* = arg minₓ f(x)

This means finding the choice that minimizes a cost, error, risk, or energy. Engineers optimize structures. AI systems minimize prediction error. Companies minimize cost or maximize profit. Transportation planners minimize travel time. Designers reduce friction. Doctors select treatments that balance benefit, risk, and side effects.

Optimization may be one of the deepest shared ideas across the university.

A good equation often reveals a relationship that intuition fails to notice. Poiseuille's law describes fluid flow through a narrow tube:

Q = (πr⁴ΔP) / (8μL)

The most important part is:

Q ∝ r⁴

Flow depends on the fourth power of the radius. If the radius doubles, the flow can increase by a factor of sixteen, assuming the other variables remain unchanged.

This relationship matters in blood vessels, medical devices, plumbing, microfluidics, and ventilation. A small change in width can create an enormous change in flow.

The dynamic power consumption of a digital circuit is often approximated as:

P = αCV²f

Power depends on the square of voltage. Reducing voltage slightly can therefore create a much larger reduction in power usage. This helps explain why chip designers care so much about voltage, heat, and energy efficiency.

Aeronautics provides another example:

L = ½ρv²SC_L

Lift depends on the square of velocity. Under otherwise identical conditions, doubling the speed contributes four times as much through the velocity term. Equations show which variables matter most.

Some equations describe physical laws, while others are conceptual models. A sustainability researcher might use:

Impact = Population × Affluence × Technology

This is known as the IPAT identity. It does not predict the future with perfect precision. It separates environmental impact into several major drivers and makes their relationships easier to examine.

A product designer might think in terms of:

Value = Benefit - Cost - Risk - Effort

This is not a physical law, but it helps explain why people adopt or reject a product.

A natural-hazard researcher might write:

Risk = Hazard × Exposure × Vulnerability

An earthquake in an uninhabited area may represent a large hazard but relatively low human risk. A smaller earthquake in a dense and poorly prepared city can be far more destructive. The equation forces us to distinguish the event itself from the conditions surrounding it.

Conceptual equations are useful because they make assumptions visible.

Design is often presented as a field driven by intuition, taste, empathy, and creativity. It is all of those things, but it also contains mathematical relationships.

Fitts's law predicts how long it takes to select a target:

MT = a + b log₂(1 + D/W)

A target takes longer to reach when it is farther away or smaller. This is why large buttons are easier to tap and why interface elements near screen edges can sometimes be easier to select.

The Hick-Hyman law describes the relationship between the number of choices and decision time:

T = a + b log₂(n + 1)

Increasing the number of choices tends to increase the time needed to decide. This applies to menus, navigation, onboarding flows, settings, product comparisons, and information architecture.

A design researcher might calculate a weighted score:

S = Σᵢ wᵢxᵢ

Different criteria receive different weights. This could be used to compare products according to sustainability, price, repairability, safety, accessibility, reliability, or any other set of values. It is also the underlying logic of many recommendation systems and decision-support tools.

Design becomes mathematical whenever it needs to move beyond opinion and describe relationships consistently.

The traditional university structure divides knowledge, but equations reconnect it. The wave equation:

v = fλ

appears in physics, photonics, telecommunications, medical imaging, acoustics, music, and wireless networking.

Diffusion equations appear in chemistry, biology, medicine, materials science, and environmental engineering. Probability appears in finance, epidemiology, artificial intelligence, psychology, law, and quality control. Network theory appears in computer science, transportation, social science, biology, and literature. Feedback appears in engineering, physiology, ecosystems, organizations, and product development.

Once these recurring patterns become visible, a university begins to look less like a collection of separate departments and more like a single system describing reality at different scales.

My original problem was memory. I wanted to understand physics, chemistry, and mathematics, but equations would not stay in my head. The mistake may have been trying to remember them as strings of symbols.

A better method is to attach every equation to a department, a phenomenon, a visual image, a real example, and one surprising consequence.

Consider the continuity equation:

Q = Av

This belongs to hydraulic engineering. It describes fluid moving through a pipe or channel. The visual image is water flowing through a narrowing tube. If the pipe becomes narrower, the water must move faster to maintain the same flow rate. The surprising consequence is that constricting a flow path can increase its velocity without increasing the total volume passing through each second.

This way of learning turns an equation into a place, an object, and a story.

I like the idea of imagining a walk through NCKU. At the College of Science, I encounter gravity, atoms, waves, entropy, and probability. At Engineering, I encounter forces, structures, aircraft, oceans, materials, energy, and machines. At Electrical Engineering and Computer Science, I encounter circuits, algorithms, information, chips, networks, and artificial intelligence.

At Medicine, I encounter blood flow, drug concentration, electrical signals, survival, and risk. At Planning and Design, I encounter cities, buildings, human movement, accessibility, value, and behavior. At Management, I encounter investment, queues, logistics, markets, and organizational decisions. At Social Sciences, I encounter voting, perception, learning, incentives, and collective behavior. At Bioscience, I encounter growth, genetics, ecosystems, enzymes, and microorganisms.

The campus becomes a memory palace. Each building contains a different family of equations.

It would be impossible to fully master every discipline at NCKU. It may still be possible to understand the central equations that shape how each department thinks.

Perhaps one hundred or one hundred and fifty equations could form a basic mathematical vocabulary of the university. That would not be enough to become a doctor, engineer, physicist, economist, or architect. It could be enough to recognize the ideas they use, understand the kinds of problems they are trying to solve, and move more easily between fields.

This feels increasingly relevant in a world where AI can perform specialized calculations, write code, simulate systems, and retrieve technical knowledge. The human advantage may come from recognizing which equation, model, department, or perspective is relevant to a problem.

The point of learning equations is not to become a calculator. It is to notice the hidden structure of the world.

A city has equations. A body has equations. A building has equations. A company has equations. A forest has equations. A computer has equations. Even a user interface has equations.

A university is one place where all of these structures coexist.

Learning its equations could become a way of learning the university itself.

AI authorship note

This essay grew from Kris Haamer's attempt to learn physics, chemistry, and mathematics by mapping memorable equations onto the departments of National Cheng Kung University. AI helped organize the university's disciplines, select representative equations, and edit the essay. Kris provided the personal framing, editorial direction, and final text.

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