Learn the tools
Learn all the mathematical formulas, terminology, and history behind the questions we explore.
What if Earth were as dense as a neutron star?
Density
P = M/V
P is density, M is mass, and V is volume. This helps us understand how all three of these variable relate.
Force of Gravity
F = GM1M2/R²
F is force of gravity, G is Newton’s gravitational constant, M1 is mass one, M2 is mass two, and R is radius of object. This equation determines the force of gravity that two objects feel as a result of each other, though some describe it as the force of attraction between two objects. Even though that is not technically true because of relativity, the result is the same anyways.
Schwarzschild Radius
R = 2GM/C²
R is Schwarzschild Radius (Radius an object must be compressed to in order to become a black hole), G is Newton’s gravitational constant, C is the speed of light.
Volume of a Sphere
V = 4/3πr³
V is volume and r is the radius of the sphere. This equation is very often used in density equations, but the volume of a cylinder is used quite a lot as well. And that is πr²h.
Newton’s Gravitational Constant
G = 6.67 × 10^-11
Despite its name, G was not calculated by Newton himself. Instead, it was Henry Cavendish in 1798 through his experiment using lead balls twisting a suspended apparatus. Measuring that twist allowed the strength of gravity, and therefore G, to be determined. We know for certain what the value of G is, though we don’t currently know why it is that value in particular.
The Speed of Light
C = 299,792,458 m/s or 3 × 10^8 m/s
Fun fact, the speed of light is this exact number with no decimals! This is because the meter was redefined around the speed of light, being the distance light travels in 1/299,792,458s of a second, or 3.34 nanoseconds. This value was established in 1983 by the international body responsible for measurement standards.
What if humans could photosynthesize?
Plant efficiency
Typical plants convert around 0.2-2% of sunlight into energy.
If you take a square meter of leaves, it is producing about 3-4 Joules of energy per second, or about 3-4 watts. That’s about the same energy that a phone charger produces.
Mosteller body surface area formula
BSA = √(( Height (cm) x Weight (kg)) / 3600)
This equation is commonly used in medicine for calculating certain medication doses, but as it related to this question it was used alongside the BMI formula to calculate how much a human’s proportions would change if their surface area increased.
Formula for BMI (Body Mass Index)
BMI = Weight (Kilograms) / (Height (m))²
This formula came from a Belgian mathematician in the 1830s, who noticed that people’s body weight roughly scaled with their heigh squared. It is still commonly used today and is found by dividing weight in kg by height in meters squared.
What if ants had human-like intelligence?
Calories to joules
1 calorie = 4184 Joules
If you assume the average human in general needs about 2,200 calories (kcal) a day, then this totals out to 9,204,800 Joules per day. That is about the same energy is takes to toast 184 slices of bread, in case you wanted to know.
Global Population of Ants
Population = 20 quadrillion
That is 20,000,000,000,000,000 ants. With a human population of roughly 8 billion people, that is 2.5 million ants per person. If you jumbled all those ants into one big mass, they would be about the size of a large watermelon. Spread out, they cover the area of the average bedroom.
Human Military Capabilities
27,000,000 active duty soldiers
Alongside this vast amount of soldiers, we spend almost 3 trillion dollars per year as a species on military expenditures. That is about 0.33% of all humans, so being in the military is actually quite rare!
What if humans’ hands and feet switched?
Primary Somatosensory Cortex
This section of your brain is responsible for receiving and processing fine touch, pressure, pain, temperature, and body position. Within this area of tissue are the motor and sensory homunculi, which is responsible for your brain’s “map” of your body. Essentially, it is how your brain sees your body, which is based on how sensitive each part is.
Neuroplasticity
This is your brain’s physical and structural capacity to adapt, learn, and reorganize its neural connections in response to new experiences, learning, or injury.
What if we harnessed the power of all lightning?
Average amount of energy per strike
E = 1 × 10^9 J
That is 1 billion joules of energy! That is enough to power an average home for a little over a week, and if you were wondering how many pieces of toast you could make, it would be around 20,000 pieces.
How often lightning strikes
100 times every second
That is about 8 million strikes per minute, and nearly 3 billion strikes in a year! Most lightning strikes occur near the equator, where all the hot air meets. There is a lake in Venezuela called Lake Maracaibo that can see up to 22,000 strikes on an active day!
Global consumption of energy per year
E = 6 × 10^20 J
That is 600 quintillion joules of energy per year. It is also known as 600 exajoules, which is a pretty cool name in my opinion. Among this massive amount of energy, 86 percent of it comes from oil, coal, and natural gas.
Equation for power
P = E/Δt
P is power, E is energy, and Δt is change in time. This equation helps relate energy and time, and it also helps explain why lightning looks so impressive yet actually supplies not as much energy as people would expect.