Two worlds, same three letters. WTF, slope. WTF.
Imagine an ancient Sumerian farmer in 3000 BCE. He needs to irrigate his crops. He digs a ditch from the river to his field. Here is the drama: if the slope is too steep, the water will rush down with violent kinetic energy, eroding the earth and flooding the field. If the slope is too shallow, the water will stagnate, refusing to fight the friction of the dirt, becoming a breeding ground for mosquitoes and failure.
When scientists study how a virus spreads, they look at the slope of the infection curve. A steep positive slope means panic; a negative slope means recovery. Economists look at the slope of a stock curve to predict a crash. In the real world, we don't care about the destination (the y-intercept); we care about the direction (the slope). We care if things are getting better or getting worse. Slope is the mathematical definition of hope and despair. slope wtf
To understand why the "wtf" occurs, we can look at the difference between a (predictable) and an exponential slope (the "wtf" zone).
so steep they scrape the soul (and the bumper) off your car. Two worlds, same three letters
It’s just how much one thing changes compared to another (like miles per hour).
When you stand on flat ground, the slope is zero. Gravity pulls you down, and the ground pushes you up. You are in equilibrium. But step onto a ramp or a icy hill, and the "normal force" is no longer normal. It is angled. Imagine an ancient Sumerian farmer in 3000 BCE
Are you struggling with a or just venting about a steep hill in your neighborhood?