The Smoothest Ride


So everyone knows the smoothest ride is one
where you’re just cruising along at some fixed speed, there’s no action in the speedometer,
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 accelleration
or decelleration too, like, when you’re getting up to speed on the highway you might
hit the gas which doesn’t feel so smooth but then you can accellerate 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 accelleration, what is a change in accelleration called? Or as we’d say in mathematics: what is the
third derivative of position? Y’know, sometimes mathematicians come up
with really terrible confusing names for things, like “Real Numbers” instead of Decimal
Placey Numbers and “Calculus” instead of “lookin 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, if you’re in the middle of a steady accelleration there’s no jerk, but when
you change the accelleration 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 accelleration. You’ll feel some amount of jerk during that
change from no accelleration to positive accelleration, and then if you suddenly stop accellerating
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 decellerate aka negatively accellerate 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 lookin 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 into reverse is
a negative jerk that jerks us out of our 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 then finally when we come to a full stop we get jerked out of our seat
again. So that’s lookin 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, y’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 apart 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 kinda do. I don’t know what’s up with that but I
do know that 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 hear its 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 forevermore! 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! It’s lookin’ at slopes! Look at the slopes! it’s calculuuuus! (lookin’
at slopes)

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