So everyone knows the smoothest right is one where you're just cruising along at a fixed speed. There's no action in this pedometer. The only movement is in your position, which changes every second and moves the same amount forward every second. I mean, you can have a nice smooth acceleration or deceleration too, like when you're getting up to speed on the highway, you might hit the gas, which it doesn't feel so smooth, but then you can accelerate smoothly so that your speed increases the same amount every second. The speedometer climbing steadily. So if a change in position is called speed and a change in speed is called acceleration, what is a change in acceleration called? Or as we'd say in mathematics, what is the third derivative of position? You know, sometimes mathematicians come up with really terrible confusing names for things like real numbers instead of decimal-placing numbers and calculus instead of looking at slopes, but every once in a while someone gets it right, which is why the third derivative of position over time is called jerk. And that's really how you measure a smooth ride. If you're at a steady speed, there's no jerk. And if you're in the middle of a steady acceleration, there's no jerk, but when you change the acceleration, there is jerk. Like say you're driving at a steady constant 20 miles per hour through town, and then you hit the highway and suddenly floor it into a smooth acceleration. You'll feel some amount of jerk during that change from no acceleration to positive acceleration, and then if you suddenly stop accelerating because you're up to highway speed, there will be another little jerk. Or technically it's a negative jerk. See, when you hit the gas, you get jerked back into your seat. But when you suddenly let off the gas, you get jerked towards the windshield a little. So then you're going a constant 60 miles an hour, but you see way up ahead, there's a family of deer on the road. So you hit the brakes and feel a jerk towards the windshield, and then you smoothly slow down for a bit, aka decelerate, aka negatively accelerate, until you reach a full stop. And at that point you feel one last jerk that pushes you back into your seat. Everyone knows that slamming on the brakes can throw you forward, so it's interesting that when you actually reach a full stop, you feel jerked backwards, but it's an effect you can feel when you drive, and to see why it happens, you can just look at slopes. And looking at slopes is very helpful, if say you're filming an action scene with a car chase, and you have to pretend to get thrown around, and you want to do it in the right direction, like say after you stop for the deer, you go into reverse as hard as you can. So you're decreasing your speed into the negative, and then you slam the brakes until you stop again. Which way do you feel pulled? Well, this negative slope means negative acceleration, so when we're on the gas, we get pulled away from our seat, and then when we hit the brakes, the speed is sloping up from negative back to zero, so positive acceleration means we get slammed into our seat. Slamming on the gas to get in reverse is a negative jerk that jerks us out of the seat, and when we let off the gas and move to the brakes, we get double jerked into our seat. First when we let off the gas, and then again when we hit the brakes, and we're glued to the back of our seat while we're braking in reverse, and finally when we come to a full stop, we get jerked out of our seat again. So that's looking at slopes, and you might have to think through it if you want to act out a car chase, but the reason you should bother is because people have an intuition for calculus, and they can recognize bad acting when they see it, even if they can't pinpoint exactly why. Brains are weird like that. Like you know how I'm talking using language, and most of you listening can understand that I am speaking English sentences without thinking, hey, that was a verb! Let's see if I can figure out what object it applies to. It's possible to pick a part grammar and use terminology to analyze language, and that's amazing, but what's even more amazing is that we don't need to do that to understand language, we just kind of do. I don't know what's up with that, but I do know there's a similar thing going on where people communicate with calculus all the time, without thinking about the terminology or writing out an analysis. Like say you're driving so close to the car in front of you that at maximum, deceleration your speed would reach zero at a distance greater than the distance between you and that car. This is called tailgating, and some people do it on purpose as a method of communication, because when you're on the road in the oppressive mass of humanity all wrapped up in our individual bubbles of isolation, the only way we have of reaching out through the void to connect with our fellow human beings is with these mathematical signals. We broadcast our rate of change to the drivers around us trusting that. From mere observations of our position through time, they will take the first and second derivatives and predict our collision course, and here it's intended message, you too can change. Indeed, you must change, change or perish for that is the common fate of all living things. How sweet the moment when we see they have received our message, and indeed change lanes, and though we may accelerate away until reaching a new constant speed, leaving them further and further behind with linearly increasing distance, the bond of calculus will hold these two human souls together forever more. I know that somewhere, someday, that very same driver may bring themselves close to my projected position once more, and as they cut me off, I will understand their calculus communication and shout what a third derivative of position. Calculus is looking at slopes. Look at those slopes. It's calculus looking at slopes.