How does a computer turn a photo into numbers?
A photo is millions of numbers, and almost everything AI does with it is multiply and add. Vectors, the dot product and matrices at three levels, with two widgets.
- Mathematics
- Artificial intelligence
Lessons
Every lesson is explained with three cards. Pick yours at the top and the site remembers it everywhere.
Why doesn't diamond turn into graphite?
Breaking bonds costs energy and making them pays it back, but almost no reaction starts without climbing a hill. Why diamond lasts and water works as a battery.
- Chemistry
- Energy
- Thermodynamics
What is a wall made of? Atoms and elements without fear
Protons, neutrons and electrons, elements and isotopes, diamond versus graphite and the mole, explained with building blocks, in three levels.
- Chemistry
- Physics
Can you make something from nothing? Conservation, no fear
Mass, energy and charge are never created or destroyed: they change form. Lavoisier, a slide, a balloon and E = mc², with two widgets, in three levels.
- Physics
- Energy
- Chemistry
Why does the computer say 0.1 + 0.2 isn't 0.3?
0.1 doesn't fit in binary, so the computer rounds it. What floating point is, why the error adds up and what AI and money use. In three levels, with a widget.
- Mathematics
- Artificial intelligence
How much is 7×10²⁷? Huge numbers without fear
Scientific notation, SI prefixes from kilo to quetta, orders of magnitude, log scales and Fermi estimates, explained with grains of sand, in three levels.
- Mathematics
- Physics
Joules, watts or calories? Energy and power without fear
Energy is how much; power is how fast. Joules, watts, kcal and kWh explained with a bathtub, why fast means hot and how to compare scales, in three levels.
- Physics
- Energy
- Thermodynamics
Logistic regression or neural network? Same neuron
A logistic regression is a neural network with a single neuron. What deep learning adds, when it pays off and when the classic model is enough, at three levels.
- Artificial intelligence
- Machine learning
- Deep learning
- Statistics
Symbol cheat sheets
Short sheets for reading the strange signs in the lessons: what they mean, how to say them and the usual trap. Secondary-school maths is enough.
What does Δ mean? Changes and tiny little letters
Δ means “how much it changed”, and the small letters underneath are labels. A short cheat sheet for reading ΔT, Eₐ or ΔᵣH° without fear, with a widget to try.
- Mathematics
What's that weird E? Σ, adding up a whole list
Σ is an order: add up everything in the list. A short cheat sheet for reading Σ, xᵢ, the mean x̄ and the product Π with secondary-school maths, plus a list to add up.
- Mathematics
≈, ≤, ≠: equal, nearly equal or not even close?
The comparison signs school skips: ≈, ~, ≤, ≥, ≠, ≪, ≫, ≡ and the absolute value |x|. A short cheat sheet, with a widget that tells you which ones hold.
- Mathematics
The dot and the arrow: ·, → and ⇒ without the mess
The dot · that multiplies (or is a dot product), the arrow → of reactions and of “tends to”, and the double ⇒. A cheat sheet with formulas that read themselves.
- Mathematics
10⁻³, mol⁻¹, e and log: powers going backwards
Negative exponents, units like J/(mol·K), the number e, logarithms, the floor ⌊x⌋ and superscripts that aren't powers. A short cheat sheet with a slider.
- Mathematics
σ, θ, λ: why does science speak Greek?
The Greek letters in the lessons, how to say them and what each means where it appears, because the same letter changes jobs. With a deck to practise.
- Mathematics
‖x‖, ᵀ, ∈ ℝⁿ: the symbols of vectors
The norm ‖x‖ (the length of an arrow), the transpose xᵀ, “belongs to” ∈ and the number sets ℝ and ℤ. A short cheat sheet with an arrow you can stretch.
- Mathematics
d/dt, ∂, ∫: change and adding up, without calculus
Derivatives and integrals with no sums to do: d/dt is the rate of change, ∂ changes one thing, ∇ points uphill and ∫ adds up slivers. With a car that speeds up.
- Mathematics