First Principles — Science, Maths & Invention
The other sections tell you what to build. This one tells you why it works — so when you have no plan, no parts, and no internet, you can reason your way to a working solution from the ground up. The periodic table, the physics and chemistry that run the world, the equations worth memorising, and a repeatable method for inventing your own tools.
1. The Periodic Table
Every material in the world is built from these. The ★ marks elements you can realistically source, use, or must respect in a grid-down world. Tap any element for its survival relevance.
2. Constants, Units & Conversions
The numbers you can't derive and shouldn't have to remember wrong.
| Quantity | Value | Why it matters |
|---|---|---|
| g (gravity) | 9.81 m/s² | Falling, pendulums, water pressure, ballistics |
| Water density | 1000 kg/m³ (1 kg/L) | 1 litre = 1 kg. Sizing tanks, rafts, counterweights |
| Water freeze / boil | 0 °C / 100 °C (at sea level) | Boiling point drops ~1 °C per 285 m altitude |
| Atmospheric pressure | 101 kPa ≈ 14.7 psi ≈ 1 bar | Siphons, pumps, pressure cooking, diving |
| Speed of sound (air) | 343 m/s (≈ 1 km / 3 s) | Count seconds after a flash: distance to lightning/blast |
| Energy to heat water | 4.18 kJ per kg per °C | Fuel needed to boil/pasteurise; solar heater sizing |
| Human daily energy | ~2000–2800 kcal (8–12 MJ) | Food planning. 1 kcal = 4.18 kJ |
| 1 horsepower | 746 W | A fit human sustains ~75–100 W; sprints ~300 W |
| Convert | Multiply by | Convert | Multiply by |
|---|---|---|---|
| inches → cm | 2.54 | miles → km | 1.609 |
| lb → kg | 0.454 | gallons (US) → L | 3.785 |
| °F → °C | (F−32) × 5/9 | °C → °F | C × 9/5 + 32 |
| psi → kPa | 6.895 | acres → m² | 4047 |
3. Equations That Matter
Not a textbook — the handful that solve real grid-down problems.
Ohm's Law
V = I × RMechanical Advantage (lever)
Load × a = Effort × bWater Pressure / Head
P = ρ × g × hPythagoras (right angles)
a² + b² = c²Heat Energy
Q = m × c × ΔTGear / Pulley Ratio
ratio = teeth_out / teeth_inProjectile Range (flat ground)
R = v² × sin(2θ) / gBattery Runtime
hours ≈ (Ah × V × 0.8) / W4. Physics First Principles
Energy is never created or destroyed — only moved or converted
Everything you build is a way of routing energy: fire (chemical→heat), a water wheel (gravity→rotation→electricity), a bow (muscle→stored spring→motion). Ask of any problem: where is the energy coming from, and where do I want it to go?
Heat always flows hot → cold, three ways
Conduction (touch — metal steals body heat fast), convection (moving air/water — wind chill, chimney draft), radiation (line-of-sight infrared — a fire warms your front, a foil blanket reflects you back).
Pressure differences move fluids — and you can make them
Fluids flow from high to low pressure. Heat air and it rises (rocket stove, solar chimney). Lift water and gravity gives it pressure. Suck air out and atmosphere pushes water up a straw — that's a siphon and a pump.
Mechanical advantage trades distance for force
Levers, pulleys, screws, gears, and inclined planes all let a weak input move a heavy load — by moving the input further. You never get something for nothing; you get force in exchange for distance.
5. Chemistry First Principles
Acids and bases neutralise each other (the pH scale, 0–14)
0–6 acid (vinegar ~3, stomach ~2), 7 neutral (pure water), 8–14 base (ash/lye ~12, baking soda ~9). An acid + a base → salt + water, releasing heat.
Oxidation: things combine with oxygen and release energy
Fire, rust, and metabolism are the same reaction at different speeds. Fast = flame; slow = rust and rot; controlled = your body burning food. Starve it of oxygen (smother) or fuel and it stops.
Salt, sugar, acid, smoke, and cold all stop microbes
Microbes need water, warmth, and a near-neutral pH. Remove water (drying, salting, sugaring), drop the pH (fermenting, pickling), add antimicrobial smoke, or remove warmth (cellar/ice) and food keeps for months.
States change at fixed points — exploit them to separate mixtures
Different substances boil and freeze at different temperatures. Boil salt water and only the water leaves as steam — catch it and you have distilled water (and salt left behind). Freeze cider and the water ices first.
6. Field Mathematics
Estimation and geometry you can do with a stick, a string, and your own body.
| Need | Method |
|---|---|
| Measure length | Know your body: hand span (~22 cm), forearm/cubit (~45 cm), pace (~75 cm), arm-span ≈ your height. Pace-count a known 100 m once and remember it. |
| Right angle | 3-4-5 rule: measure 3 units along one line, 4 along the other; when the diagonal is exactly 5, the corner is 90°. |
| Height of a tree/wall | Stand back until you can sight the top over a stick held at arm's length; or measure your shadow vs. the object's shadow — heights are in the same ratio as shadows. |
| Width of a river | Pick an object on the far bank. Walk a right-angle baseline along your side; use similar triangles (walk a known distance, sight the angle) to scale the crossing. |
| Estimate big numbers | Count a small sample, measure the area/volume it filled, multiply up. Good for seed counts, herd size, crowd size, storage. |
| Area of a circle | A ≈ 3.14 × r². Circumference ≈ 3.14 × diameter. For tanks, wheels, fields. |
| Volume of a tank | Cylinder: 3.14 × r² × height. In litres if you measure in metres × 1000. A 1 m × 1 m × 1 m cube = 1000 L = 1 tonne of water. |
| Angles without a protractor | A fist at arm's length ≈ 10°. The horizon to overhead = 90° = ~9 fists. Useful for sun height, latitude (Polaris angle ≈ your latitude), and slopes. |
7. The Invention Method
When no section has your exact answer, you invent one. This is a repeatable loop, not a flash of genius.
Step 1 — State the function, not the object
Write the job as a verb + outcome: "keep food below 10 °C," "cut wood faster," "signal 2 km." Banish brand names and specific parts. The looser the wording, the wider your options.
Step 2 — Find the governing principle
Match the function to a first principle above. Cooling? → heat flows hot-to-cold + evaporation cools (a wet cloth pot, a zeer fridge). Lifting? → mechanical advantage. Each principle hands you a family of known solutions to copy.
Step 3 — Inventory what you actually have
List materials by property, not name: rigid, flexible, waterproof, conductive, springy, heat-resistant, absorbent. A bicycle is a frame + bearings + chain + wheels + a spring saddle — five subsystems you can harvest. Salvage beats fabrication every time.
Step 4 — Substitute and analogise
Ask "what in nature or history did this job?" before electricity existed. Refrigeration → evaporation and cellars. Glue → hide, pine pitch, starch. Bearings → smooth stone, hardwood, glass. The pre-industrial world solved every survival problem at least once; copy it.
Step 5 — Build the ugliest version that could work
Prototype with cardboard, mud, scrap — anything fast. The goal is to learn, not to finish. A failed 20-minute mock-up teaches you more than a perfect plan. Expect 3–5 iterations.
Step 6 — Test to failure, then add margin
Load it until it breaks; now you know the real limit. Build the keeper at half that load (a 2× safety factor — 3× for anything overhead or over a person). Write down what failed and why — that note is the actual invention.