Samuel Korenberg

Setting Up Hermes, My Always-On AI Agent

Sat, 26 Sep 2026 00:00:00 GMT

This summer I built a live sweepstake tracker for the World Cup in an evening: a Cloudflare site with a Worker backend, push notifications and an installable app. A year ago that would have taken me several weekends, and I probably wouldn't have finished it. The difference wasn't that I'd become a much faster programmer. It was that since the spring I've had an AI agent running for me, and I can hand it a project the way you'd hand one to a capable friend.

That agent is Hermes. This post is about how I set it up, what I use it for, and what isn't perfect about it.

What Hermes is

Hermes Agent is an open-source AI agent made by Nous Research. The easiest way to explain it is by comparison with a chatbot. A chatbot waits in a browser tab, answers, and forgets. Hermes runs continuously on a machine I control, and it can:

use tools: a terminal, the web, files and APIs, so it can act rather than just advise;
remember: it keeps notes on me, my projects and my preferences across conversations;
learn procedures: after a complex task it writes itself a "skill", a step-by-step recipe it reuses the next time something similar comes up;
run on a schedule: it has a built-in scheduler, so jobs can run without me asking.

I talk to it through Telegram, so it is in my pocket like any other chat: I send it a message, and it replies when the job is done.

How I set it up

The basic install is short, which is part of why I tried it:

curl -fsSL https://hermes-agent.nousresearch.com/install.sh | bash
hermes setup

The setup wizard asks which model provider to use, and hermes model changes it later without touching any code.

To reach it from my phone, I made a Telegram bot:

Message @BotFather on Telegram, send /newbot, and keep the token it gives you secret.
Run hermes gateway setup, choose Telegram, and paste in the token along with your numeric Telegram user ID. The allow-list matters: without it, anyone who finds the bot could talk to your agent.
Start it with hermes gateway.

The delegation ladder

Running an agent all day means a lot of model calls, and paying top prices for every one would be expensive and wasteful. So Hermes works down a ladder of models:

An OpenCode Go subscription as the main rung: a flat monthly plan covering a set of capable open models.
Free models when that allowance runs low.
Paid models through OpenRouter as a last resort, so it never simply stops.

Most work never leaves the first rung. When I'm building something substantial, like the World Cup tracker, the heavy coding goes to Claude Code, which also deploys to Cloudflare for me.

Laptop, with a VPS as backup

Hermes normally runs on my laptop. When the laptop is shut or unreachable, a VPS picks up so I can still reach it on Telegram. I'd be lying if I said I could explain exactly how the handover works, because I didn't build it. I asked Hermes to make itself reachable when my laptop was off, and it set the whole thing up, and it has worked since. That is probably the best illustration of what it is like to use: I describe the outcome, and it deals with the details.

What I actually use it for

Building things. Planning, writing and shipping projects like the sweepstake tracker. I decide what to build and how it should be shaped; it does most of the implementation.
My calendar and errands. Adding and moving things in my calendar, and chasing the small jobs I'd otherwise forget.
Scheduled jobs. Tasks that run on their own and message me the result on Telegram, so information comes to me rather than me going to look for it.
Research and summaries. Reading around a topic and giving me the short version, with sources to check.
Study and admin. Revision, organising deadlines, and getting ready to start at Cambridge.
Planning explores. Before visiting an abandoned site or a cave, I use it for open-source research: old maps, historical records and accounts from other people, what condition a place is likely to be in, and whether access is allowed. The explores themselves are written up on cesspool.uk.
Odds and ends, like keeping my Nuvio media library and add-ons organised.

Keeping it on a leash

An agent that can run commands, and has access to my Cloudflare account, needs limits. Mine are:

Approval prompts. Before anything potentially destructive, it stops and asks on Telegram, and nothing happens until I reply yes.
Scoped API tokens. Each service gets a token with only the permissions it needs, rather than full access to my accounts.
Spending limits on every model provider, so a runaway loop can't cost much.
A customised SOUL.md. Hermes reads a file called SOUL.md at the start of everything it does, which sets its personality and ground rules. I've rewritten mine, along with some other prompts, to make it more careful about acting outside what I've asked for.

What isn't perfect

Hermes is an open-source project that is updated constantly, not a polished consumer product, and it shows in maintenance. Over time, hidden bloat builds up: leftover files, overlapping skills, configuration that no longer does anything. Every so often I point Claude Code at the installation to find it all and clean it out, which keeps Hermes running smoothly.

It has also made a real mistake. I once had my travel plans in a Google Doc, and Hermes decided to tidy it up by reformatting it. The new version looked better, but it contained wrong information. With the calibre of models I have available now I see that problem as solved, but it was a useful early lesson in what handing over control means.

What it's changed

The biggest change isn't any single task. Things I used to only talk about building, I now build, because the gap between having an idea and having something working has shrunk to an evening. The skill that matters has shifted too: less about knowing every API by heart, more about knowing what to build, how to split it into the right pieces, and how to direct something capable enough to build it.

If you're curious, Hermes is free and open source. Start with something small you'd like done every day, and see how quickly you start handing it bigger things.

Building a World Cup Sweepstake Tracker

Thu, 02 Jul 2026 00:00:00 GMT

Every World Cup, a group of us runs a sweepstake. Everyone gets a team drawn at random, and whoever's team goes furthest wins. Normally that means someone manually updating a spreadsheet after every match. This year I built a proper live tracker instead: a Cloudflare Pages site with a Worker backend, push notifications, and a PWA you can add to your home screen.

What it does

The site shows the live bracket, everyone's team, and how they're doing, and sends a push notification when your team plays or gets knocked out. It's a Progressive Web App, so it installs like a real app rather than living as a browser tab, and a cookie remembers which manager you are so it can personalise what you see.

How I built it

I want to be upfront about how this actually got made, because I think it's the more interesting part of the project: I didn't write the code by hand. I planned the feature set and picked the general shape of it (the bracket logic, the push notification flow, which APIs to pull fixture data from), and then built the whole thing through Hermes, the AI agent I run (more on that setup here), working with Claude Code.

That's not a small caveat, it's the actual point of the project. I described what I wanted, worked through the architecture and trade-offs with Claude, and it wrote and shipped the code: the Cloudflare Worker backend, the push notification system using VAPID keys, the PWA manifest and service worker, the whole thing. Claude also has direct access to my Cloudflare account, so it deploys changes itself rather than me copy-pasting commands. What used to be a multi-weekend side project became something I could build and iterate on in an evening.

I think this is honestly the more useful skill going forward than knowing every API by heart: knowing what to build, how to break it into the right pieces, and how to steer a tool capable enough to build it properly. It's also why I've been able to take on more projects like this one recently instead of just talking about wanting to build them.

The stack

Cloudflare Pages for the frontend, deployed straight from the repo
Cloudflare Worker as the backend, handling fixture data and push subscriptions
Web Push / VAPID for the "your team just played" notifications
PWA manifest + service worker so it installs properly on a phone

It's a small project compared to some of the physics and research stuff on this site, but it's the one that's actually being used by a group of people every few days during the tournament, which is its own kind of satisfying.

Why Eight? Unpacking the Octet

Thu, 10 Jul 2025 00:00:00 GMT

As we approached the end of the school year, our chemistry department gave us the chance to research and present on a topic of our choice. I wanted something I was genuinely curious about and could blend with some physics, so I picked a question that had bothered me since GCSE: why do atoms obey the octet rule?

Every chemistry student learns that atoms react to end up with eight electrons in their outer shell. It is one of the most useful rules in the subject, and almost nobody explains it. Why eight? Why not six, or twelve, or five?

The answer turned out to be more involved than I expected, running through thermodynamics and quantum mechanics before it gets back to chemistry. Rather than narrowing the topic, I tried to build it up from simple analogies so my classmates could follow it. This is the write-up of that presentation.

What does "stable" actually mean?

In general, something is stable if it tends to stay in the state it is in. Picture a ball in a valley: nudge it and it rolls back to the bottom. A ball balanced on top of a hill is unstable, because the smallest push sends it rolling down and converts its energy from one store to another. Stability, in other words, is about sitting at low potential energy.

At A-level, a stable species is defined as one that tends not to react, one that stays at the bottom of its valley. But at the fundamental level, a chemical reaction is a rearrangement of electrons: they are transferred or shared. That gives a more useful definition. A stable species is one that holds on to its own electrons and doesn't take on anyone else's.

To describe why some atoms seem "generous" with their electrons and others "greedy", we need two properties:

Ionisation energy: the energy needed to remove an electron from an atom.
Electron affinity: the energy released when an atom gains an electron.

Reactive metals like sodium have low ionisation energies and give electrons away easily. Reactive non-metals like chlorine have high electron affinities and take them readily. A species that has neither tendency, that is hard to strip and gains nothing from an extra electron, is stable.

Why does anything favour stability?

The energy balance

A reaction is favourable when it releases more energy than it absorbs, leaving the products lower in potential energy than the reactants. That difference is the enthalpy change, $\Delta H$.

It is tempting to say this just means electron affinity has to beat ionisation energy, but the numbers show it is more subtle. Taking an electron from sodium costs $496\text{ kJ/mol}$, and giving it to chlorine only releases $349\text{ kJ/mol}$, so on its own the transfer loses energy. What pays for it is the attraction between the ions once they have formed: packing $\text{Na}^+$ and $\text{Cl}^-$ into a lattice releases about $787\text{ kJ/mol}$, many times more than the shortfall. The same logic applies to covalent bonds, where the energy comes from both nuclei attracting a shared pair.

Entropy: the real driving force

But why should the universe favour losing energy at all? The answer is the Second Law of Thermodynamics: in any real process, the total entropy of the universe increases.

Entropy is best understood as a measure of how spread out energy is, which comes down to counting arrangements. There are thousands of ways for a room to be messy and only one way for it to be perfectly tidy, so a room left alone drifts towards mess. Energy behaves the same way. (I've written more about this in Why Must Time Flow Forward.)

When a reaction moves to a lower energy state, the energy it releases escapes as heat, and heat is the most disordered form energy can take. That heat raises the entropy of the surroundings by

$$ \Delta S_{\text{surroundings}} = -\frac{\Delta H}{T} $$

so an exothermic reaction (negative $\Delta H$) increases the entropy of everything around it. The "drive for stability", including the drive to reach an octet, is really the universe maximising its entropy by releasing and spreading out energy.

That explains why atoms settle into low energy arrangements. It doesn't yet explain why the lowest energy arrangement so often involves exactly eight electrons. For that we need to look at orbitals.

Rethinking orbitals

An orbital isn't a little track the electron runs around. It is a wavefunction: a description of the electron as a wave, whose intensity at each point gives the probability of finding the electron there. A node is a place where that wave has zero amplitude, so the electron is never found there.

The best way I found to picture this is a standing wave on a string. The simplest standing wave has no nodes between the ends; the next one up has one node in the middle; the next has two. Each extra node squeezes the wave into a shorter wavelength, and a shorter wavelength means more energy. Electron waves follow the same pattern: more nodes means more energy.

This gives a simple rule. An orbital in energy level $n$ has exactly $n - 1$ nodes. Those nodes come in two kinds:

A radial node is a sphere around the nucleus where the electron can't be.
An angular node is a flat plane through the nucleus where the electron can't be.

Now count how many different orbitals each level allows.

Level 1 has zero nodes. There is only one way to have no nodes: a plain sphere, the 1s orbital.

Level 2 must have exactly one node, and there are only two ways to add it:

Make it a sphere. A sphere around the nucleus has only one possible orientation, which gives the single 2s orbital.
Make it a plane. A plane through the nucleus can face along the $x$, $y$ or $z$ axis, giving three separate orbitals: the three 2p orbitals.

That makes four orbitals in the second level, and nothing else is allowed.

Bringing it all together

The last ingredient is the Pauli Exclusion Principle: no two electrons in an atom can have exactly the same set of quantum numbers. Electrons have only two spin states, "up" and "down", so each orbital can hold at most two electrons, one of each spin.

Four orbitals, two electrons each:

$$ (1 + 3) \times 2 = 8 $$

That is where the eight comes from. It isn't a coincidence or a rule of thumb; it is the capacity of the second energy level, set by the geometry of standing waves and the Pauli principle.

An atom with its 2s and 2p orbitals completely full, like neon, is exceptionally stable:

Removing an electron takes a huge amount of energy. Neon's first ionisation energy is $2081\text{ kJ/mol}$, compared with $496\text{ kJ/mol}$ for sodium, the very next element.
Adding an electron gains nothing. The level is full, so an extra electron would have to go into level 3, which is higher in energy.

Other atoms react because gaining, losing or sharing electrons moves them towards that same filled arrangement, releasing energy and increasing the entropy of the universe as they do.

The same counting works for every level:

Level ($n$)	Nodes	Orbitals	Capacity
1	0	1s	2
2	1	2s, three 2p	8
3	2	3s, three 3p, five 3d	18

Where eight stops working

Seeing where the number comes from also explains its exceptions, which is how you can tell an explanation is doing real work.

Hydrogen and helium only have level 1, which holds two electrons. That is why hydrogen is happy with two (a "duet"), not eight.
Period 3 can in principle hold 18, but the 3d orbitals sit higher in energy than 4s. After 3s and 3p fill there is still a big energy gap, so eight remains the magic number for elements like chlorine and argon.
Transition metals do use their d orbitals: one s, three p and five d make nine orbitals, or 18 electrons. Chemists use exactly this as the 18-electron rule for transition metal complexes.
"Expanded octets" like $\text{SF}_6$ and $\text{PCl}_5$ are often explained at A-level by using d orbitals, but most chemists now think the d orbitals contribute very little and the bonding is better described in other ways.
Noble gases aren't completely inert. In 1962 Neil Bartlett made the first noble gas compound, and xenon forms stable fluorides like $\text{XeF}_2$. A full shell makes reacting very hard, not impossible.

How it went

I found the approach mostly successful. The analogies let me get the ideas across without leaning on equations, and afterwards I was able to clear up the points people had found confusing.

What I liked most about the project is that a rule I had been using for years without questioning turns out to rest on physics I only met much later: thermodynamics explains why atoms settle into low energy states, and quantum mechanics explains why those states so often hold exactly eight electrons.

Echoes of Gdańsk: A Personal Journey

Wed, 25 Jun 2025 00:00:00 GMT

The apartments that were reclaimed by my family after the fall of the Soviet union after a tedious legal process

Introduction

In the summer of 2024, my Opa (grandad) proposed that I should join him for a trip into Gdansk. While the city is now a site of historic beauty, that attracts millions of tourists a year, hidden beyond the architecturally stunning streets lies a dark tragic history. One that I have a deep connection to.

History of Jews in Gdańsk

Stutthof, one of the deadliest and most notorious Nazi concentration camps, the site where tens of thousands of Jews met their fates - of which my family were likely amongst

The history of the Jewish community in Gdańsk, or Danzig, began in the 15th century, though for centuries, their presence was tenuous and heavily restricted, a story all to familiar for the Jewish Diaspora. Initially prohibited from settling within the city walls, Jewish merchants and families established organized communities in outlying suburbs, navigating persistent limitations imposed by the city's semi-autonomous authorities.

Signs of Improvement

The Great Synagogue, which was demolished in 1939 by the Nazis

Fortunately, the situation dramatically improved following the city's incorporation into Prussia in 1793. The 19th century ushered in an era of legal emancipation, growth, and assimilation into German culture. This period of stability and prosperity culminated in the official merger of the various suburban Jewish congregations in 1883, and was symbolized by the construction of the Great Synagogue in 1887, which stood as a marker of the community's civic integration and confidence.

The Holocaust in Gdańsk

This vibrant Jewish life was tragically extinguished in the 20th century. After Gdańsk became the Free City of Danzig post-World War I, the local Nazi party's rise to power in 1933 led to immediate and intensifying persecution. Faced with the systematic stripping of their rights and property, the community leadership made the difficult decision to organize the emigration of the majority of its members. This desperate act saved many lives, but the community itself was shattered. The Great Synagogue was demolished in 1939, and the approximately 1,700 Jews who remained were largely murdered during the Holocaust. After the war, Gdańsk became part of Poland, and while a small Jewish community was re-established, it consisted of new arrivals with few ties to the centuries-old Jewish heritage that had been so violently erased.

The Apartment Buildings

This history is also deeply personal. Tragically, all but one of my family members on the Polish side fell victim to the violent, Nazi-orchestrated persecution, and their fates remain unknown to this day. The lone survivor, my great-grandfather, fled to Israel just in time, on the advice of a friend in the military. Arriving penniless, he enlisted in the British Armed Forces, where he served as a POW officer, a role for which he was well-suited due to his incredible affinity for languages, speaking nine in total.

Following the fall of the Nazi regime and, much later, the collapse of Soviet influence in Poland, Gdańsk was once again declared safe for Jews. This eventually created an opportunity for my family to reclaim property that had been seized by the various regimes. After a series of complex legal processes, the housing complex that once belonged to them was finally returned.

The buildings now lie in a poor state but regeneration projects in the local area lend hope to the eventual restoration of the buildings to their former glory, while offers have been made to buy the estate, the sentimental value of the site far exceeds any potential offers with the buildings remaining as a symbolic reminder of what happened to the Jews of Gdańsk.

The Beauty of Gdańsk

Despite its dark past, Gdańsk now sits as one of the most beautiful towns in Europe with stunning Baroque architecture on every corner. Below are some of the photographs I successfully captured. I have intentionally kept this section brief as to not detract from the main message of this article.

Boats by the river Motlawa

Examples of the stunning Baroque architecture

Contrast between the old Gdansk and the new Gdańsk

Overlooking the clocktower of the town hall

Sun setting over one of the many beautiful buildings

View down the river at night with the bustling riverside restaurants

The beautiful stained glass and organ inside St Mary's

The figure head of Gdańsk: Żuraw or The Crane

The view from the hotel room in the morning

St Mary's Church; one of the largest in Europe

Looking down the river Motlawa as the sun sets

END

Why Must Time Flow Forward: Entropy

Fri, 06 Jun 2025 00:00:00 GMT

Introduction

Drop a glass on a tiled floor and it shatters into dozens of fragments. An ice cube left on a kitchen counter melts into a lukewarm puddle. We watch people grow older, never younger. This directional asymmetry is what Arthur Eddington termed the "arrow of time" - the intuitive, everyday reality that the past feels fundamentally different from the future.

The real puzzle appears when you look at the fundamental laws of physics. Newton's laws of motion, Maxwell's electrodynamics, Einstein's general relativity, and the Schrödinger equation are all time-symmetric. If you reverse the time variable (t -> -t) in any of these equations, the resulting motion remains physically valid. A video of two billiard balls colliding looks plausible whether played forwards or in reverse.

So what breaks this symmetry at macroscopic scales? What forces the universe along a one-way path? The answer is not built into the equations of motion themselves; it emerges from combinatorics and statistics through the concept of entropy.

What Entropy Actually Measures

Entropy is frequently introduced as a vague measure of "disorder" or "messiness," but this framing often obscures the real physics. A much more precise definition comes from Ludwig Boltzmann: entropy quantifies the number of microscopic arrangements (microstates) that correspond to a given macroscopic condition (macrostate).

$$ S = k_B \ln \Omega $$

Here, $S$ is entropy, $k_B$ is the Boltzmann constant, and $\Omega$ represents the number of accessible microstates.

Consider the shattered glass. There are only a very small number of ways to arrange all of its constituent molecules so that they form an intact, pristine wine glass with a smooth bowl and stem. That macrostate has a tiny $\Omega$, meaning very low entropy.

By contrast, once the glass breaks, the fragments can land in an astronomical number of positions, orientations, and scatter patterns while still fitting the description "broken glass on the floor." That macrostate corresponds to an enormous number of microstates.

The universe does not possess a mystical preference for destruction. Rather, systems evolve toward states of higher entropy simply because those states are overwhelmingly more probable. If a system continuously explores its accessible phase space at random, the odds of it spontaneously wandering into one of the handful of "intact glass" configurations are so small that you could wait many times the age of the universe without ever seeing it occur.

The Microstate Count

To see the mathematics on a small scale, imagine a container divided in half, containing just four gas molecules (A, B, C, D).

If we list every possible configuration:

All 4 on the left: Only 1 combination (ABCD on the left).
3 on the left, 1 on the right: 4 combinations (A, B, C, or D on the right).
2 on each side: 6 combinations (AB, AC, AD, BC, BD, CD).
1 on the left, 3 on the right: 4 combinations.
All 4 on the right: Only 1 combination.

Out of 16 total microstates, 6 (or 37.5%) have the molecules evenly split. If we scale this from 4 molecules to a mole of gas ($6.022 \times 10^{23}$ particles), the distribution becomes unimaginably sharp. The probability of finding all gas molecules grouped into one corner of a room by pure chance is effectively zero:

$$ P \approx \left(\frac{1}{2}\right)^{10^{23}} \approx 10^{-3 \times 10^{22}} $$

This is why gas expands to fill a vacuum. It is not being pushed outwards by a repulsive force; the particles are simply bouncing around independently, and the uniform state happens to represent the overwhelming majority of possible configurations.

The Second Law and Open Systems

The Second Law of Thermodynamics states that in any isolated system, total entropy cannot decrease over time:

$$ \Delta S_{\text{universe}} \ge 0 $$

A common point of confusion is whether localized decreases in entropy violate this rule. We freeze water into structured ice crystals; living cells build intricate DNA polymers out of scattered nutrients; humans assemble semiconductors and construct buildings.

None of these violate the Second Law because neither a freezer nor a living organism is an isolated system. They are open systems that exchange energy and matter with their surroundings.

When a refrigerator cools water into ice, the entropy of the water decreases ($\Delta S_{\text{water}} < 0$). However, the refrigerator's compressor consumes electricity and releases waste heat into the surrounding kitchen air. The thermal entropy generated in the room ($\Delta S_{\text{surroundings}} > 0$) strictly exceeds the entropy lost by the ice:

$$ \Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 $$

Living organisms survive by drawing in low-entropy energy (such as sunlight or chemical energy from food) and exporting higher-entropy thermal waste into their environment. Erwin Schrödinger described this in What is Life? by noting that organisms maintain their internal structure by continually drawing "negative entropy" from their environment.

The Past Hypothesis and the Ultimate Fate

If entropy always increases, it implies something profound about the origins of the universe: the early universe must have started in a state of extraordinarily low entropy.

Cosmologists call this the Past Hypothesis. Roughly 13.8 billion years ago, matter and energy were distributed almost uniformly throughout space at immense density and temperature. In a system dominated by gravity, a smooth distribution of matter actually represents extremely low entropy, because gravity naturally tends to clump matter together into stars, galaxies, and black holes (which possess astronomical amounts of Bekenstein-Hawking entropy).

The expansion of space and the condensation of matter into stars has allowed the universe to spend billions of years gradually climbing the entropy ladder. Every star burning hydrogen, every geological process, and every biological metabolic cycle is another step along this statistical gradient.

Eventually, on timescales of $10^{100}$ years and beyond, all stars will burn out, matter will decay or fall into black holes, and those black holes will gradually evaporate via Hawking radiation. The universe will approach thermodynamic equilibrium, often called the "heat death." At that point, with no free energy gradients left and entropy maximized everywhere, macroscopic change ceases, and the thermodynamic arrow of time effectively runs out of track.

Room Temperature Ionic Liquids Research Project

Thu, 05 Jun 2025 00:00:00 GMT

As part of a research project in collaboration with Queen's University Belfast, select students in our school were given the opportunity to synthesise and analyse a novel protic room temperature ionic liquid (RTIL). The project's goal was to first create the ionic liquid, triethylammonium hydrogen sulfate ([TEA][HSO₄]), and then demonstrate its viability as a greener catalyst for producing a biodegradable polyester, poly(ethylene succinate) (PES).

This article details the various processes our cohort undertook, from the initial synthesis of the ionic liquid to its final application in polymer chemistry.

Synthesis of the Protic Ionic Liquid ([TEA][HSO₄])

Synthesising the ionic liquid started with safety: the whole process was done in a fume hood. Triethylamine was placed into a small round-bottomed flask with a magnetic stirrer bar, then the flask was set in an ice bath to manage the heat generated during the reaction.

Concentrated sulfuric acid was then added dropwise to the chilled, rapidly stirring triethylamine. Adding it slowly was essential to control the exothermic reaction. Once added, the mixture was stirred in the ice bath for another hour.

After that, the ice bath was removed and the flask left to stir overnight at room temperature to complete the reaction. The next day, the resulting viscous ionic liquid was stoppered, labelled, and stored at room temperature, ready to use in the catalytic studies without further purification.

Confirming Catalytic Viability: Qualitative Esterification Test

Before trying to make a polymer, we needed to confirm [TEA][HSO₄] could actually catalyse a reaction. We needed something that would only proceed with a catalyst present, while staying within what the school's science department could actually run, so we went with an esterification of iso-amyl alcohol and ethanoic acid, which we could judge by smell. The human nose is a surprisingly good chemical detector (it can outperform specialised e-noses on some tasks, if not on raw ppm sensitivity), so it was a reasonable way to check whether the reaction had worked.

We prepared three test tubes. The first, a negative control with just the alcohol and acid, stayed colourless with no notable scent. The second, a positive control using concentrated sulfuric acid, turned yellow with a strong pear-drop smell, as expected from the ester, isoamyl acetate. The third, with our [TEA][HSO₄], also turned yellow and produced the same pear-drop smell, confirming the ionic liquid had catalysed the reaction. That gave us the confidence to move on to making a polymer.

From Monomers to Polymer: Synthesising Poly(ethylene succinate) with [TEA][HSO₄]

The ionic liquid that we would use for the polymerisation

Building on the successful catalytic test, we used our [TEA][HSO₄] to synthesise the biodegradable polymer poly(ethylene succinate) (PES). The monomers, succinic acid and ethane-1,2-diol, were combined with a catalytic amount (approx. 12 mol%) of our ionic liquid. The mixture was heated under reflux for one hour, during which all solids dissolved to form a clear, pale yellow, and slightly viscous liquid.

To encourage the formation of higher molecular weight polymer chains, the reaction was subjected to a second, longer reflux period. A drying tube containing silica gel was fitted to the condenser to remove water (a byproduct of the reaction) and drive the polymerisation forward. After four hours of this second reflux and subsequent cooling, a large amount of a flocculent white solid precipitated from the pale brown solution. This solid was the target poly(ethylene succinate), and its appearance confirmed that our RTIL had successfully facilitated the formation of long-chain polyester molecules.

Conclusion

This covered a full research cycle, from synthesising a new catalyst to actually using it. We made the ionic liquid [TEA][HSO₄], confirmed it worked as a catalyst with the esterification test, and then used it to make the biodegradable polymer poly(ethylene succinate).

It's a decent demonstration that protic ionic liquids could be a less corrosive, greener alternative to catalysts like sulfuric acid. And watching the polymer actually precipitate out at the end made the whole thing feel a lot more real than most of what we do in a normal chemistry lesson.

The Four Equations that Redefined Light: Maxwell's Equations

Tue, 03 Jun 2025 00:00:00 GMT

Maxwell's equations are the cornerstone of classical electromagnetism, unifying the previously distinct fields of electricity, magnetism, and light into a single, simple set of four equations. This unassuming set of equations stands as arguably the most important physics discovery of the 19th century, providing engineers across the globe with the theoretical basis for understanding the behavior of electromagnetic waves. Consequently, nearly all electronic devices we use today, from antennas and electric cars to the humble toaster, have almost certainly been designed and optimised using principles laid out by Maxwell's equations.

My goal for this project is to gain an intuitive and mathematical understanding of the fundamental principles that govern our modern world of electronics and communication, which is not provided by the A level course (at the time of writing I have completed only first year content). The article will go law by law providing an explanation for what each equation states and deriving them not using calculus but rather through more conceptual and intuitive explanations of the divergence and curl of electric and magnetic fields.

Gauss's Electric Law

To understand Gauss's Law in its differential form, it is helpful to conceptualize the electric field, E, as a vector flow field in space. The mathematical operation known as divergence, denoted ∇, defines the behavior of this field (E) at any specific point in the field. A positive divergence at a point signifies a source, indicating a net outflow from an infinitesimal region surrounding the point. Conversely, a negative divergence signifies a sink, indicating a net inflow into such a region. If the divergence is zero, there is no net origination or termination of field lines within the region; the flow merely passes through.

The sources or sinks of this electric field are identified as electric charges in Gauss's first law. By convention positive electric charges function as sources, from which electric field lines originate and extend outward. The magnitude of this source effect is proportional to the charge density, ρ, within a given region. Negative electric charges, conversely, function as sinks, towards which electric field lines converge. Similarly, the magnitude of this sink effect is determined by the density of negative charge.

This local relationship between field divergence and charge distribution is precisely formulated by Gauss's Law in its differential form:

$$ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} $$

This equation states that the divergence of the electric field (∇⋅E) at any point is directly proportional to the electric charge density (ρ) at that same point. The constant $\epsilon_0$, the permittivity of free space, is a fundamental physical constant that ensures both dimensional consistency and quantifies that if electric fields travel through mediums of high "resistance" to electric fields the magnitude of the vectors must decreases.

Gauss's Magnetic Law

The magnetic field, denoted as B in Maxwell's equations, can also be conceptualised as a vector flow field in space. Its divergence, ∇⋅B, quantifies any net outflow or inflow from a point. Gauss's Law for Magnetism, a fundamental principle of electromagnetism and one of Maxwell's equations, states that this divergence is universally zero:

$$ \nabla \cdot \mathbf{B} = 0 $$

This means that the net magnetic flow is always zero and magnetic fields must form closed loops, with all field vectors eventually returning to their origin. Consequently, distinct absence of origination and termination points cannot exist under Gauss's second law meaning that magnetic monopoles are physically impossible - in contrast to the electric field.

It is noteworthy that no fundamental principle actually forbids magnetic monopoles, and some advanced theories like string theory even predict their existence. These theories suggest their predicted properties, such as extreme mass and high-energy formation requirements, could explain their current elusiveness. Consequently, the search for magnetic monopoles remains an active area of physics.

Faraday's law

Next, we turn to Faraday's Law of Induction, which showed that magnetism and electricity aren't just static partners: a changing one can induce the other. This is the principle behind the generator, used throughout the national grid.

Michael Faraday, through meticulous experimentation, demonstrated that a changing magnetic environment could induce an electromotive force (EMF), a force that drives current through a conductor. The core concept in the induction of EMF revolves around "magnetic flux" (Φ), which quantifies the amount of magnetic field lines piercing a given area. Faraday's Law states that the induced EMF (ε) in any closed circuit is proportional to the rate of change of the magnetic flux through that circuit or how many magnetic field lines are piercing area per second:

$$ \mathcal{E} = -\frac{d\Phi_B}{dt} $$

The minus sign, a crucial addition known as Lenz's Law, signifies that the induced EMF (and any resulting current) will always act to oppose the change in magnetic flux that produced it – to adhere to the conservation of energy stopping an otherwise infinite propagation of electric and magnetic fields.

Feynman further clarifies that this change in magnetic flux can occur in several ways: the strength of the magnetic field (B) itself can vary over time, the area (A) of the loop through which the field passes can change, or the orientation of the loop relative to the field can alter. Regardless of the specific mechanism, if the total magnetic flux is changing, an electric field must be generated. This electric field differs from the divergent electric fields produced by static charges (as described by Gauss's Law); rather, as Feynman notes, it's an electric field that forms closed loops, a "curly" electric field. This "induced" electric field is what exerts a force on charges within a conductor, giving rise to the EMF.

Maxwell translated Faraday's integral law into its more local, differential form:

$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} $$

This compact equation elegantly states that a time-varying magnetic field (∂B/∂t) will always be accompanied by a spatially varying, circulating electric field (realised through the mathematical operator ∇ × E, which represents the "curl" of E). It was no longer just about wires and magnets; but rather a fundamental property of the fields themselves. This equation, paired with Ampère's Law (which we'll explore next, along with Maxwell's crucial addition to it), reveals how changing electric and magnetic fields can generate each other, paving the way for the understanding of electromagnetic waves, and ultimately, light itself.

Ampere-Maxwell law

A fisherman using the Ampere-Maxwell law (electromagnetism) to retrieve an old car

The fourth and final law is the Ampere-Maxwell Law, describing how magnetic fields are produced by electric currents. It's essential to speakers, motors, and electromagnets, some of the most common technology around.

The original Ampere law stated that magnetic fields (denoted as B) would "circulate" or "curl" around electric currents producing a magnetic field. Mathematically, in its differential form, this was expressed as;

$$ \nabla \times \mathbf{B} = \mu_0\mathbf{J} $$

where J is the electric current density and μ₀ is the permeability of free space.

This law worked beautifully for steady currents, such as those flowing continuously in wires. However, James Clerk Maxwell identified a critical flaw when applying it to situations with changing electric fields. A key example is the space between the plates of a charging capacitor, where the capacitor is charged through the charging of plates with no actual current flow. Despite no current passing through the capacitor, a magnetic field is still observed around this gap - a phenomenon Ampere's original law was unequipped to explain and suggesting the electric field between the charges may induce a magnetic field.

To address this inconsistency Maxwell proposed an additional source term for magnetic fields: a changing electric field. He introduced what he called the "displacement current" density

$$ \mathbf{J}_D = \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} $$

, where ε₀ is the permittivity of free space and ∂E/∂t is the rate of change of the electric field (relative to time).

As Feynman clarifies, this new term; "displacement current" is crucially not a flow of charge in the traditional sense, but it acts just like a real current in its ability to produce a magnetic field. By adding this term, Maxwell not only resolved the inconsistency seen in the capacitor example but also completed the symmetry between electricity and magnetism. If a changing magnetic field could induce an electric field (by Faraday's Law), then a changing electric field should, in turn, induce a magnetic field.

Thus, the complete Ampere-Maxwell Law became:

$$ \nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial t} $$

This equation now states that a magnetic field can be generated by two means: by actual electric currents (μ₀J) or by a time-varying electric field (μ₀ε₀∂E/∂t).

While this addition may just seem like a simple correction it was the key that transformed our understanding. With Faraday's Law showing that changing magnetic fields create electric fields, and the Ampere-Maxwell Law now showing that changing electric fields create magnetic fields, the stage was set for a brilliant realisation. Faraday's Law proves that a time-varying magnetic field induces a circulating electric field, while the Ampère-Maxwell Law proves that a time-varying electric field induces a circulating magnetic field. Couplings between these orthogonal vector fields yield a self-propagating electromagnetic wave equation with phase velocity $c = 1/\sqrt{\mu_0 \varepsilon_0}$. Maxwell had found the mechanism for light.

Conclusion

Working through Maxwell's equations beyond A-level, from Gauss's laws on field sources, through Faraday's induction, to Maxwell's completion of Ampere's law, was one of the more satisfying things I've done this year. The best part was seeing how the four laws link together: changing electric and magnetic fields sustaining each other, which is what light actually is. It's given me a much better sense of why these four equations matter as much as they do.

Glimpses of Vienna

Fri, 30 May 2025 00:00:00 GMT

Vienna was the heart of the Habsburg Empire for centuries, and it's a city that takes both the magnificent and the morbid seriously. It is famous for its balls as much as for its elaborate "schöne Leich" (beautiful funerals). Mozart wrote music there; Freud developed psychoanalysis there. Both drew on the same city.

Alongside the palaces are the social housing projects of "Red Vienna," built in the early 20th century, and architects like Otto Wagner pushing the city toward modernism. It's a place that holds onto its past without being stuck in it.

Vienna's Karlskirche (St Charles Church), known for its turquoise dome, is a major example of late Baroque architecture. Emperor Charles VI vowed to build it during the 1713 plague, dedicating it to St. Charles Borromeo. Mostly designed by Johann Bernhard Fischer von Erlach and finished in 1737, it mixes styles: the dome, a classical portico, and two triumphal columns modelled on Roman ones, carved with spiral reliefs telling the story of the saint's life.

In Maria-Theresien-Platz stands the monument to Empress Maria Theresa (1717–1780), the only woman to rule the Habsburg lands in her own right, pictured here with an uninvited bird on her head. Unveiled in 1888, mostly the work of sculptor Kaspar von Zumbusch, the bronze shows her enthroned holding the Pragmatic Sanction that secured her succession, surrounded by statues of the military, political, and cultural figures from her reign.

The first thing I did after landing in Vienna was go for a late-night run. About 3km in, I spotted something huge and dark up ahead and went to look. It turned out to be a massive, windowless concrete structure that looked completely out of place next to the old city. I had no idea what it was, so I just took a photo.

Turns out it was one of Vienna's Flak towers. Nazi Germany built three pairs of these during WWII (six in total), each pair made up of a "G-Tower" (Gefechtsturm) for anti-aircraft guns and an "L-Tower" (Leitturm) for command and radar, both able to shelter thousands of people from air raids. They were built to be almost impossible to demolish, and mostly still stand today. They are too costly to take down, so some now carry graffiti or get used as art spaces instead.

The Haas Haus, with its curved glass front, sits in deliberate contrast to St. Stephen's Cathedral next door, and you can see the cathedral's spire reflected in the facade here. Architect Hans Hollein's postmodern design was finished in 1990 on the historic Stephansplatz and caused a lot of debate at the time, but the reflections do tie it back to its surroundings rather than just ignoring them.

The Palais Equitable, on the left here, was my favourite building to photograph in Vienna. Completed in 1891 at Stock-im-Eisen-Platz as the local headquarters for The Equitable Life Assurance Society, it has an elaborate facade and a green copper roof. At street level, on the corner, it's also home to the "Stock im Eisen", a medieval tree trunk studded with nails, which is where the square gets its name.

The trip itself was thrown together over the phone at short notice, and it turned into one of my favourite cities I've been to. It started on a low note (Bayern Munich lost to Inter Milan the night we arrived), but the city, and good company from my Opa, made up for it fast.

Rethinking Refraction: Feynman's way

Thu, 29 May 2025 00:00:00 GMT

Introduction

Understanding why light bends or slows when it enters a new material (due to its different refractive index) is a common question in physics classes. However, it's surprisingly tricky to explain satisfyingly using only introductory concepts. This very challenge sparked my fascination with light and prompted me to explore deeper into how it interacts with the media it travels through.

A Few Common (and not so physically sound) Explanations...

To begin, we will examine some commonly taught models for explaining the laws of refraction, and then demonstrate why these models are physically incorrect.

Absorption and Remission

A common idea you might hear, even from some teachers, to explain why light appears to slow down when the photons travel from one medium to the next is that the photons in the ray are absorbed by the atoms in the medium. After a brief moment, these atoms then eject the photons back out, in a slightly different direction. This constant absorption and reemission cycle, in combination with the indirect path the photons take, give the light the emergent property of travelling at different speeds in different mediums.

However, this idea doesn't quite hold up physically (as I myself realised while learning). If photons were truly absorbed and then re-emitted in random directions, then water wouldn't be transparent as the light would be scattered in all directions making the water appear cloudy or opaque which is not what we see in the real world.

Tank Track Model

Another common way teachers attempt to explain refraction is with the "tank tracks" model. This analogy explains that when light moves from one medium to another, it slows down and changes direction. Like a tank going from pavement to mud: when one of its tracks enters a more optically dense boundary first, that track slows, causing the entire tank to gradually turn and slow. A more detailed diagram is available from the BBC.

This explanation proved extremely unsatisfactory to me for one simple reason - a single photon is simply not a tank and does not have tracks and yet a single photon still refracts despite not having two tracks. It is rare that a simple classical model can be used to satisfactorily explain quantum phenomena. Indeed this is not the case here.

Below I will explore the underlying reasons why light changes speed in a medium, why the change in speed depends on the frequency of the light, why light changes direction during refraction and an explanation of the principle of least action.

Why does light slow down in a medium?

The apparent slowing of light when passing through a medium can be understood by considering the interaction of light, as an electromagnetic wave, with the charged particles within the material, primarily electrons. Light, composed of photons, is characterised by oscillating perpendicular electric and magnetic fields.

As this incident electromagnetic field propagates through the material, its oscillating electric component exerts a force on the electrons, causing them to oscillate. These oscillating electrons, in turn, become sources of secondary electromagnetic waves of the same frequency as the incident light.

These secondary waves are coherent with the incident light. While the precise phase relationship can be complex and depend on the material and frequency, they are generally out of phase by π/2, the electrons interfere (or superpose) with the original incident wave. In the forward direction of propagation, this superposition generally results in a combined wave whose phase is behind compared to what it would be if the light were propagating in a vacuum over the same distance.

Although the phase shift resulting from interaction with a single layer of atoms is very small, light interacts with numerous layers of atoms as it traverses the material. The cumulative effect of these continuous interactions and the resulting phase retardation of the total electromagnetic field leads to a wave with a shorter wavelength within the medium for the same frequency. Since wave speed is the product of frequency and wavelength (v=fλ), this reduction in wavelength at a constant frequency means the overall wave propagates at a reduced phase velocity. This results in a wave within the material that appears to be a wave of light that is effectively slowed down in a medium.

While this answers many question it raises just as many. Why do different colour of light have different refractive indexes? Why does light bend and not simply travel in a straight line?

Why do different colours of light have different refractive indices?

The variation of the refractive index with the colour (or frequency) of light, a phenomenon known as dispersion, is directly linked to the way light interacts with electrons in a medium, as described in the previous paragraph. Electrons within a material have natural (or resonant) frequencies at which they oscillate most readily. These resonant frequencies are intrinsic properties of the material, determined by the electromagnetic binding forces on the electrons (much like a driven harmonic oscillator), giving them a resonant frequency at which they responds most strongly.

Now that we have established exactly why light slows down in a medium, we need to explore what causes the change in direction as described by Snell's Law. To try to find out the reasoning behind why this is the case I turned to 3Blue1Brown's excellent video on the topic here, however I found this explanation unsatisfactory as it could not explain why a single photon will still undergo refraction and felt analogous to the previous tank explanation.

To resolve this quandary I turned to Fermat's principle of least time, which states that when light travels between two points it takes the path of least time not necessarily the shortest distance which explains why light bends and its adherence to Snell's law - which can be simplified to light finding the most time efficient path to get from one point to another. However, simply stating that light bends in order to minimise the travel time is an incomplete explanation and does not explain why light takes the path of least time or how light even knows what the fastest path is, to offer no explanation to these phenomena would leave the important part of physics - the question “why”? - incomplete.

The fascinating reason light adheres to Fermat's principle isn't because individual photons are somehow clairvoyant, pre-calculating the quickest route. The deeper answer, which gets to the heart of this "why" and "how," comes from Richard Feynman's quantum "sum over paths" (or path integral) formulation. This theory suggests that a photon doesn't just pick one neat line to get from point A to point B. Instead, it explores every conceivable path simultaneously. One can imagine infinite possibilities, some straight, some looping the photon considers them all.

Position of arrows represents the phase

Each of these potential paths that light might explore between two points has a value associated with it, often visualised as a little spinning arrow, with the direction of this arrow determining its phase. The final orientation of this arrow for each path is determined by the total “action” accumulated along that path, divided by Planck’s constant. For light, this action is directly related to the travel time.

The next question we must ask is: how does this flurry of infinite paths, each with its own arrow, result in the single, well-behaved path of least time that is actually observed?

For most imaginable paths, particularly those deviating significantly from the quickest route, their associated 'arrows' end up pointing in seemingly random directions. This high sensitivity occurs because the phase, which dictates each arrow’s final orientation, varies greatly even with slight changes to the path. A path’s ‘action’ value is typically so large compared to Planck’s constant that the arrow's final direction becomes acutely dependent on the precise path taken. Due to this randomness in their final orientations, when the contributions from these numerous paths are combined, they effectively cancel each other out. This is destructive interference; these 'inefficient' paths are eliminated as their differently pointing arrows result in a superposition effectively of zero.

At the parabola's minimum (or least action), the curve is nearly flat. This illustrates that small sideways steps (variations) near the minimum result in very little change in height (action), unlike on the steeper slopes where the same step causes a much larger change

Conversely, for paths very close to the path of least time, the situation is different. For this path and its immediate neighbors, a slight variation in the path geometry results in almost no difference to the total travel time and thus action. This is due to the mathematical nature of an extremum, where the value is 'flat' around such a point. Consequently, the arrows for these nearby paths all end up pointing in almost exactly the same direction. Instead of cancelling, their contributions add up and reinforce each other. This is constructive interference, leading to a significant final amplitude.

Therefore, it is this strong, coherent contribution from paths clustered around the path of least time that overwhelmingly dominates. All other paths, with their widely varying phases, have effectively cancelled themselves out. The principle of least time thus emerges not as a prescribed rule, but as the natural consequence of this wave-like interference across all possibilities.

All images used on this page are used under the Free Use Act falling under both the education/research category, many thanks to Veritasium, 3Blue1Brown and Fermilab for visuals

The Beautiful World of Fermi Problems

Wed, 28 May 2025 00:00:00 GMT

Fermi problems are a unique type of challenge that set out to do one thing: answer the unanswerable. By using logic and estimated sums, you can approximate the value to questions which would be either impossible or unfeasible to measure. It's precisely this intriguing nature that led me to take them up as a fun exercise to test my application of physics.

Fermi, a renowned physicist, would pose such problems to his students to teach them the power of estimation and logical reasoning. For the piano tuner problem, he wouldn't expect anyone to know the exact figure. Instead, he would guide them to break down the large, seemingly intractable question into a series of smaller, more manageable estimations. This involved considering factors such as:

The population of Chicago: A reasonable estimate for the city's population at the time.
The average number of people per household: To estimate the number of households.
The percentage of households that own a piano: A guess based on general observation.
How often a piano needs tuning: Perhaps once a year, or every few years.
How long it takes a piano tuner to tune one piano: A few hours, for example.
The number of hours a piano tuner works in a year: Standard working days and hours.

By multiplying and dividing these estimated quantities, one could arrive at a surprisingly close approximation. While the exact figure isn't the point, the process of logical breakdown and estimation is. Fermi himself, known for his quick calculations, reportedly arrived at an estimate in the low hundreds, demonstrating that even without precise data, a reasonable answer can be found through structured thinking.

Personally I have found the value of Fermi problems to be the application of what I am taught in school to real-life problems, which solidifies the concepts and allows me to see the utility of what we have been taught, tying concepts together. Fermi problems also often encourage out-of-the-box thinking which is particularly important for the tougher a level physics problems, physics olympiads (which I received Gold in) and various other problems I come across online. These unique problems allow for a further final benefit and that is that they are simply a lot of fun to solve!

Below are some of my favourite Fermi problems that I've created, completed and verified.

What is total kinetic energy of all the rivers in the world in one year assuming no friction?

Rainfall on land: We need to work out the total amount of rainfall on land, as this feeds rivers. We take an average estimate of 1,000 mm (1 m) of rain falling on land each year.
Total water volume: Using the surface area of the Earth from its approximate radius ($r \approx 6{,}400\text{ km}$), $A = 4\pi r^2 = 4\pi (6.4 \times 10^6)^2 \approx 5.15 \times 10^{14}\text{ m}^2$, so a metre of rain over it is about $5.15 \times 10^{14}\text{ m}^3$ of water.
Total mass on land: Multiplying by the density of water ($1{,}000\text{ kg/m}^3$) gives $5.15 \times 10^{17}\text{ kg}$. Since only roughly 30% of the Earth is land, the mass falling on land is approximately $1.55 \times 10^{17}\text{ kg}$.
Runoff losses: Not all water reaches rivers; much is lost to evaporation, transpiration, plant uptake, and isolated endorheic basins. Reservoirs that don't feed back into the sea and agriculture take their share too. We assume this happens to around 60% of the water.
Effective distance factor: The water that is lost still flows partway before it goes, so it still carries some kinetic energy. We count it at half weight, assuming on average it travels half as far as the rest. That makes the multiplier $0.4 + 0.6/2 = 0.7$, giving an effective flowing mass of $0.7 \times 1.55 \times 10^{17} \approx 1.0 \times 10^{17}\text{ kg}$.
Gravitational Potential Energy: The mean elevation of land above sea level is approximately 840 m. Using $\text{GPE} = mgh$: $$ \text{GPE} = (1.0 \times 10^{17}\text{ kg}) \times (9.81\text{ m/s}^2) \times (840\text{ m}) \approx 8.24 \times 10^{19}\text{ J} $$
Total Kinetic Energy: Assuming negligible frictional dissipation in this idealised estimate, all GPE converts to kinetic energy before discharging into the sea: roughly $8.24 \times 10^{19}\text{ J}$ per year. For context, that is roughly one-seventh of humanity's annual energy consumption, or 390 of the most powerful bombs ever detonated.

How many photons are emitted in one night by all the Lamp posts in London?

Total road network length: Estimate London's road network at roughly 15,000 km.
Lamp post count: Assuming 70% of roads are lit with an average spacing of 30 m between columns: $$ N = \frac{0.70 \times 15{,}000{,}000\text{ m}}{30\text{ m}} = 350{,}000\text{ lamp posts} $$
Luminous flux to photon rate: A typical high-pressure sodium or LED street luminaire produces around 15,000 lumens. Using the optical conversion factor of $\approx 1.12 \times 10^{16}\text{ photons}/(\text{lumen}\cdot\text{s})$, each luminaire emits: $$ 15{,}000 \times 1.12 \times 10^{16} \approx 1.68 \times 10^{20}\text{ photons/second} $$
Nightly duration: Standard UK annual burning hours are approximately 4,000 hours/year, which averages to $\approx 11\text{ hours/night}$ (39,600 seconds).
Photons per lamp post per night: $$ 39{,}600\text{ s} \times 1.68 \times 10^{20}\text{ s}^{-1} \approx 6.65 \times 10^{24}\text{ photons} $$
City-wide total per night: $$ 350{,}000 \times 6.65 \times 10^{24} \approx 2.33 \times 10^{30}\text{ photons} $$

This astronomical value, if converted into energy (using green light for simplicity), would be equal to only the mass of a single large mosquito. In other words, each night London's streetlights output enough energy in the form of light to create a mosquito by nuclear fusion.

Two Weeks Inside the NHS

Sun, 25 May 2025 00:00:00 GMT

At 16, near the end of my GCSEs, I was trying to decide between two things: physics, which had always been part of my life, and a newer interest in biotechnology and where medicine might be headed.

To get a better sense of which way to go, my friend Jai and I arranged a two-week placement at Whittington Health to see how a hospital actually runs, and how research findings turn into patient care.

We were based in the Whittington Education Centre (WEC) with our supervisor Pov, and rotated through a wide range of departments: shadowing Security, sitting in on Research and Communications, watching the Emergency Room and Intensive Care Unit at work, sitting in on patient consultations, learning front-of-house processes, helping with fire safety checks, and even working a community outreach roadshow. It gave us a much better sense of how much has to happen behind the scenes to keep a hospital running.

It wasn't all easy going, though. Opening the WEC by 7:30 AM meant a 5:40 AM alarm most days, a big change from an 8:30 AM school start that used to feel early enough. It gave me a better sense of how demanding NHS work actually is, especially in A&E and ICU, where the staff stayed calm and made fast decisions under a lot of pressure.

We also saw the harder side of frontline healthcare: critical care, surgery, and patients and families in real distress, which takes a level of resilience and empathy I hadn't fully appreciated before. A briefing from the Security team was a bit of a wake-up call too: they told us that dealing with weapons, including knives and occasionally firearms, wasn't a rare occurrence for them.

We also picked up some practical skills along the way. I got certified in CPR and defibrillation, did some risk assessment training, learned about patient confidentiality and data protection, and helped out with more random tasks like equipment repairs, social media, and video editing.

What stuck with me most was how much bigger the NHS is than just doctors and nurses. It's closer to running a small city, with hundreds of interlocking parts that all have to work at once. We got good feedback and were even asked to stay longer, which was nice to hear. Seeing biotech and research up close made me more interested in it, but by the time I started my A-levels, physics had won out as what I wanted to focus on. Still, the two weeks changed how I think about the NHS and gave me a much better sense of what "real-world" work actually looks like.

Beyond Voice Commands: Power of Siri Shortcuts

Sun, 30 Mar 2025 00:00:00 GMT

Introduction

Most people only use Siri for basic voice commands, but Shortcuts lets you go a lot further, chaining actions together across different apps into custom workflows. I've used it for years now, mostly to automate small annoying tasks, and it's also taught me to break problems down into logical steps.

I've built up a fairly large library of shortcuts over the years. Here are five of my favourites.

Climbing Capacity

I prefer climbing when the gym's quiet, so I built a shortcut that checks my local climbing gym's occupancy for me. It sends an HTTP GET request to their capacity page and parses the result with regex, instead of me having to open the site and check manually.

Get the shortcut here

Fun Facts for the Group Chat

This one's less about utility and more about practising with APIs, the OpenAI API, and prompt engineering. It runs automatically every day at 12:30: it calls an API for a fun fact, asks an LLM to come up with a relevant GIF search term, pulls the top Giphy result, and sends the whole thing as a message to the group chat.

Get the shortcut here

Managing Homework

I used to miss deadlines because I wasn't tracking assignments properly, so I built a shortcut for it: pick a subject from a dropdown, get a prompt tailored to that subject, and it links straight to the right Google Classroom page. It's made actually starting my homework a lot less friction-y.

Get the shortcut here

Corbett Maths Questions

Concentration for GCSE maths revision was hard for me with ADHD, so I wanted a way to start practising with as little friction as possible. Corbett Maths has well-structured daily resources, so I built a shortcut that takes the current (or a chosen) date, generates the right URL with regex, and pulls up the question and answer PDFs directly for annotation on screen, with no need to go hunting through the site each time.

Get the shortcut here

Water Eject

Everyone knows that muffled sound a phone speaker makes after it's been in water. Before this shortcut, the only fix was waiting for it to dry out or switching to headphones. This one clears the water out in a few seconds instead.

It's not magic, just audio engineering. The shortcut plays a low-frequency sound file (embedded in the shortcut as Base64) that vibrates the water out of the speaker cavity.

Get the shortcut here

My Journey into Web Development

Fri, 28 Mar 2025 00:00:00 GMT

In the summer of 2023, when I was sixteen, I spent a chunk of the holidays building two WordPress sites. One was my own space, samuelkorenberg.com; the other was a professional site for my mum's therapy practice in London, capucinekorenberg.com, built together with her.

My site

Building my own site (the first version of the one you're reading now; it has since moved off WordPress) was mostly about having somewhere to put projects and interests I've picked up over the years. I went for a clean, fairly minimal WordPress design, and it doubled as practice for the bigger job: helping my mum with hers.

Therapy site

The site for my mum, capucinekorenberg.com, was a different kind of project: more collaborative, and built around what she actually needed rather than what I wanted to build. We talked through the structure and content together, set up professional email accounts on the domain, and aimed for something that read as professional and welcoming without being cold.

For the design, we drew on Hokusai's "The Great Wave off Kanagawa". That was not a random choice, since my mum knows Japanese art well from her work at the British Museum. We worked it into the WordPress theme carefully, so it felt personal to her without looking out of place for a therapy site.

We also built in PayPal-based booking and payments, but launched with them switched off. The site went live and started getting visibility first, and we turned bookings on once my mum had finished her training and was ready to actually take clients through it.

Once bookings were on, it worked: her schedule filled up steadily, which was genuinely satisfying to watch happen. The site also picked up a few unexpected messages from people who knew her through her Hokusai and Japanese art work at the British Museum, using the contact form to get in touch about that instead.

Running both projects at once that summer was a lot, but it taught me more than either one would have alone about requirements, design, actually building the thing in WordPress, and the decision-making around a phased rollout. It also gave me a better sense of how different a site needs to be depending on who it's actually for.

Designing a Sustainable Lamp and Power Bank for Blackouts

Thu, 20 Mar 2025 00:00:00 GMT

For my GCSE DT coursework, the brief was to build a product in the context of climate change. What started as a normal school project ended up being the thing I spent most of my year on. Below is what came out of it: a lot of research, designing, pitching, and building.

Initial spark

I'd already been interested in lighting for a while, so I knew early on I wanted to build something focused on illumination.

Looking into the effects of climate change, I found that extreme weather is responsible for around 83% of power outages, as the grid comes under more strain. So I decided to focus the product on power outages specifically.

It needed to do two things: charge essential devices, and put out enough light to actually illuminate a room.

Diving into research

Main hall at the design museum

Good design starts with good research. Between visiting the Design Museum and taking apart a high-end torch, the product slowly started to take shape. From that research I settled on two main design decisions to match the two functions: Bauhausian design, and ceiling bouncing.

Most emergency products are designed to look tough and rugged rather than nice. My theory was that making it stylish instead might actually make it more effective. If it looks good, people are more likely to keep it out in the open rather than shoved in a drawer, which means it's easier to find in an actual blackout. So I leaned into Bauhausian design elements, which also fit the modern-home aesthetic and nodded to my client's German heritage.

I also came across "ceiling bouncing" in my research, which ended up being my favourite part of the whole design. Instead of diffusing light through a translucent material, you shine it at the ceiling and let it reflect back down. It's a technique borrowed from photography, and it gave me an even, diffuse light with the source itself hidden.

Shaping the design

Screen grab of my design process

Design is mostly iteration. My first concepts looked more like rugged fortresses than the sleek, minimal thing I was going for. It took a few rounds of sketching, prototyping, and refining to get from there to a design worth taking further.

The final design was a rounded wooden cube with box joints for a clean, strong build, and detachable magnetic legs so it could be used a few different ways. At the centre is an acrylic structure that houses the light and also breaks up what would otherwise be a fairly plain cube.

Sustainability shaped a lot of the design too. I used a press-fit base instead of glue so it stays repairable, and made a digital repair guide, accessed via a laser-cut QR code, instead of a printed manual.

Building: Triumphs and Trials

The manufacturing side had a steep learning curve, especially the woodwork. Cutting the box joints by hand was much harder than I expected, and my first attempts were pretty rough. It got better with practice; I filed each joint by hand for a tight fit and only used wood filler where I really had to.

The legs went through a few iterations too. The first pin-and-box mechanism was repairable but left visible gaps, so I switched to a friction-fit and magnetic system instead, which needed a lot of careful sanding to get the tolerances right. They turned out better than I expected.

Neon Orange Acrylic Centre-piece

The acrylic centrepiece was its own challenge, as the geometry needed a fair amount of maths to make sure everything lined up properly. The result is one of my favourite parts of the final design.

The electronics had their own set of problems. Power comes from standard 21700 batteries in a parallel case, wired with repurposed cable. I machined a brass pill and copper spacer on a lathe to hold the Nichia 519A LEDs in place, and laser-etched a QR code onto the device linking to the repair guide, to keep it out of landfill for as long as possible.

For finishing, I sanded the wood to a 240-grit finish for a smooth surface, then applied three coats of teak oil to bring out the grain and protect it.

Reflection

Looking back at the whole process, from initial concept to finished product, I'm pretty proud of it. There's plenty I'd still improve, but it came out close to what I set out to build.

What mattered more than the object itself was what I picked up along the way: new woodworking techniques, working through the acrylic geometry, and getting my head around the electronics. Each stage pushed me to figure something out I hadn't done before.

Mostly, it showed me what can come out of actually sticking with a project for a long stretch of time, something I don't usually manage. This was one of the more useful things I've done at school.

The coursework scored 94/100, which came out as the highest GCSE DT score the school's had on record (189/200).

All photos by me, capturing the journey from sketch to shine.