Chapter 3 Units and Dimensions
Units
Once you’ve tamed a number with scientific notation and balanced it with significant figures, there’s still one more charm to cast: units.
In our vast universe, numbers alone are like potions with no labels; mysterious at best, dangerous at worst. Is that “5” a length? A time? The weight of a standard unit dragon egg? Without units, we’re just guessing.
Units are the magical tags that anchor numbers to reality. A second tells us we’re measuring time. A meter marks distance. A kilogram weighs in with mass. These are three of the seven base units, the foundational runes of measurement used by scholars and spellcasters across the realms.
And just like combining spells, we can fuse base units into more complex ones:
- Speed - The SI units meters per second: m/s
- Force - The SI units are kilogram meter per second squared: kg·m/s²
- Energy - The SI units are kilogram meter squared per second squred: kg·m²/s²
If you forget a unit, your calculations will fall apart faster than a novice wizard’s first fireball. Include the wrong one, and you might mix healing potions with poison. Choose wisely.
Dimensions
Even deeper than units lie the dimensions, the ancient scaffolding of the universe itself. Where units name things, dimensions define what they are.
No matter where you are (on Earth, on Mars, or sailing the outer moons of Jupiter) the same fundamental dimensions form the basis of all physical quantities. Time, mass, and length may behave differently under extreme conditions, but they remain the core ingredients of the universe. The following are three of the seven fundamental dimensions:
- \([T]\) for time
- \([M]\) for mass
- \([L]\) for length
All physical quantities are built from the seven dimensions, combined and rearranged like alchemical ingredients:
- Speed has dimensions Length per Time: \([L][T]^{-1}\)
- Force has dimensions Mass multiplied by Length divided by Time squared: \([M][L][T]^{-2}\)
- Energy has dimensions Mass multiplied by Length squared divded by Time squared: \([M][L]^{2}[T]^{-2}\)
Units label your measurements. Dimensions reveal the nature of your measurements. Alone or together, they help keep your calculations from turning into chaos.
