Think “all other things remain equal.”

As an example: supply, demand and price are very related but there are a lot of other factors that affect both. So in order to make a simple to understand point about how they are related, you could say “rising prices lead to less demand, *ceteris parabus*.” That means the example is true as long as no other factors change.

Like in a science experiment. You want to control something so only one factor is changing so you can measure how changing that one thing alters everything else.

So for instance if you drop an apple out a second story window, and nothing changes, gravity says the apple will fall down if you’re on the surface of the earth, because the force of gravity is F=mass of the falling object × 9.8meters/second^2.

But that’s not the real equation for gravity, that’s holding the mass of the earth, and the radius of the earth constant, ceteris paribus, as a simplification.

The actual equation for gravity between two objects is

F = G × m1×m2/r^2

G is the gravitational constant, and we multiply it by the mass of both objects, and the distance between their centers of mass. When we hold m1 and r constant, as the mass of the earth and radius of the earth at sea level, the equation simplifies to mass×9.8, because that’s just what the mass of earth times G divided by the radius of earth squared happens to be.

But if we had a way to change the mass of the earth, then we could get different results than the apple falling. If the mass of earth suddenly dropped to 0, then the apple would just hang in midair and would not fall. If the distance between them grew so vast it approached infinity, the apple would also remain still and not be drawn towards the earth.

The simplification to F=m×9.8 is useful in daily life for engineers and scientists because the mass of the earth and it’s radius is so vast that climbing to the top of mount everest or riding in an airplane has such a small effect on the force of gravity that it’s still effectively m×9.8.

“assuming everything else stays the same”

It’s a common phrase when talking about real world scenarios, because real life can be complex.

It’s typically used when you want to emphasize that only certain things are changing.

“If this changes, cet.par., what happens” is like saying “if this changes, and ABSOLUTELY NOTHING ELSE, YOU DINGUS… what happens?”

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