SubjectsSee how it really works
Every subject has layers.
Physics, biology, chemistry, space, data, AI. Every subject explains the world from what you notice down to the mathematics underneath. Layerfall falls through those layers one question at a time, and the same ideas keep turning up.
- Your headphones
- The ear cup
- The speaker
- The air
- The wave
One descent
Five steps down, in any subject.
What you notice: something you can see, hear or feel. The parts: what it is made of. What moves: energy, matter, signals or information. The principle: the idea that explains it. The maths: the principle, written exactly.
- What you notice
- The parts
- What moves
- The principle
- The maths
Complex systems are built in layers. In Herbert Simon's parable, a watchmaker who builds from stable parts finishes about 4,000 times faster than one who must start over after every interruption.
Simon, 1962In Powers of Ten, Charles and Ray Eames move the camera ten times further every ten seconds, from a picnic to the edge of the known universe, then down into the nucleus of a carbon atom.
Eames, 1977
Six questions, six subjects
The same five steps. Six different worlds.
- Physics
How can headphones make silence with more sound?
- What you noticeThe engine hum fades the moment you switch them on.
- The partsTiny microphones, a fast chip and a speaker in each ear cup.
- What movesSound is a pressure wave in the air. The chip makes the same wave, flipped.
- The principleSuperposition: waves add up. Where a crest meets a trough, they cancel.
- The mathssin(x) + sin(x + π) = 0
- Biology
How can your watch measure your heartbeat using green light?
- What you noticeYour pulse appears on your wrist with nothing round your chest.
- The partsGreen lights and a light sensor on the back of the watch.
- What movesBlood absorbs green light. Each beat pushes more blood through your wrist, so less light comes back.
- The principleAbsorption: the more blood in the light's path, the less light returns.
- The mathsbeats per minute = peaks per second × 60
- Chemistry
How can a battery store something you can't see and give it back hours later?
- What you noticeYour phone runs all day on a thin, flat block.
- The partsTwo electrodes, an electrolyte between them, and a thin separator.
- What movesLithium ions cross inside the battery while electrons take the long way, through your phone.
- The principleA chemical reaction moves electrons from one material to another, and that flow does the work.
- The mathsenergy = voltage × charge
- Astronomy
How can a satellite keep falling for years without hitting Earth?
- What you noticeSatellites circle Earth for years and never come down.
- The partsA satellite, Earth's gravity, and a lot of sideways speed.
- What movesIt falls toward Earth all the time, but moves sideways so fast that the ground curves away beneath it.
- The principleAn orbit is falling and missing: gravity bends a straight path into a curve.
- The mathsv = √(GM ÷ r)
- Mathematics
How does Google Maps know there's a traffic jam before you reach it?
- What you noticeA road turns red on the map before you see a single brake light.
- The partsPhones in cars, sharing anonymous location and speed.
- What movesThousands of small speed readings flow in, road by road, minute by minute.
- The principleSampling: many small measurements reveal what no single one can.
- The mathsaverage speed = sum of speeds ÷ number of readings
- Computer science
How can AI look at a photograph and know what's in it?
- What you noticeYour phone finds every photo of a dog in seconds.
- The partsA grid of pixels, and a neural network trained on labelled pictures.
- What movesEvery pixel becomes numbers. Layer by layer, the network turns them into edges, shapes, then things.
- The principleLearning from examples: the network adjusts itself, a little at a time, to make fewer mistakes.
- The mathsoutput = f(weights × input + bias)
Where else does this happen?
The ideas that run through everything.
Learn a principle once and you start to see it everywhere. These are some of the threads that tie every subject together.
Waves
A wave carries energy and information without carrying the stuff it travels through.
- Noise-cancelling headphonesPhysics
- Wi-FiElectrical engineering
- An ultrasound scanMedicine
- A fibre-optic cableMaterials science
Fields
A changing magnetic field makes electricity flow in metal nearby.
- Wireless phone chargingElectrical engineering
- An induction stovePhysics
- Tapping a card to payEconomics
- An electric guitar pickupPhysics
Energy
Energy is never made or destroyed. It moves, and it changes form.
- A speakerPhysics
- A batteryChemistry
- A heat pumpEnergy
- Your musclesBiology
Feedback
Measure, compare, correct, repeat. It is how systems hold steady.
- A thermostatMechanical engineering
- Your body temperatureBiology
- A robot holding an eggComputer engineering
- Headphones checking what's leftComputer engineering
Information
Information is a pattern. It can be copied, squeezed smaller, and checked for mistakes.
- A damaged QR codeMathematics
- DNABiology
- A photo that shrinks 20 timesComputer science
- Shazam's song fingerprintComputer science
Scale
The same world works differently at every power of ten.
- Billions of switches on a memory cardComputer engineering
- Your phone's motion sensorMechanical engineering
- A satellite's orbitAstronomy
- An MRI scanMedicine
Science education agrees
Real things to explain. Big ideas across subjects.
Teachers and curriculum makers have reached the same idea from the other side: start from something real, and follow the ideas that cut across every science.
- Patterns
- Cause and effect
- Scale
- Systems
- Energy and matter
- Structure and function
- Stability and change
The US Framework for K–12 Science Education names seven ideas that cut across every science: patterns; cause and effect; scale, proportion and quantity; systems and system models; energy and matter; structure and function; stability and change.
National Research Council, 2012Science lessons there start from something real to explain, so the focus shifts from learning about a topic to figuring out why or how something happens.
Achieve, 2016Finland asks every school, every year, to run at least one theme or project that combines several subjects.
Finnish National Agency for Education, 2014Experts sort problems by the principle underneath. Beginners sort them by what they look like.
Chi, Feltovich & Glaser, 1981
Two maps
Questions on top. Knowledge underneath.
Every How question links to the concepts it teaches, and every concept knows the questions that lead to it. You follow your curiosity; Layerfall keeps track of the subject you are building.
- Mathematics
- Physics
- Chemistry
- Biology
- Medicine
- Computer science
- Computer engineering
- Electrical engineering
- Mechanical engineering
- Materials science
- Energy
- Economics
- Astronomy
- Earth science
Every fact, checked
Don't trust us. Check it.
Every number on this page comes from one of these studies.
Simon, H. A. (1962). The architecture of complexity. Proceedings of the American Philosophical Society, 106(6), 467–482.
jstor.org/stable/985254Eames, C., & Eames, R. (1977). Powers of Ten (film). Added to the US National Film Registry in 1998.
National Research Council (2012). A Framework for K–12 Science Education. National Academies Press.
doi.org/10.17226/13165Achieve (2016). Using Phenomena in NGSS-Designed Lessons and Units. NGSS.
nextgenscience.org/resources/phenomenaFinnish National Agency for Education (2014). National Core Curriculum for Basic Education.
oph.fi/en/education-and-qualifications/national-core-curriculum-basic-educationChi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5(2), 121–152.
doi.org/10.1207/s15516709cog0502_2