### From Correlation to Causation through stories and math

Correlation and causation are two concepts that people often mixup in their minds. I must admit that I myself have been guilty about this, and it unlikely that I would ever entirely grow out of it as it is wired deeply into our psychology. Let me use this article to briefly emphasise what the concepts of correlation and causation means, some interesting stories that have emerged from people misunderstanding these concepts and an algorithm that attempts to find causal relationship using correlation information. Here is a story that I heard a professor of mine, Prof. Dr. Ernst-Jan Camiel Wit, tell us during a lecture. There was a school that was involved in a study to see if providing free mid-day meals to students, which they could choose to be subscribed to this or not. At the end of the study, both the students who subscribed to it and did not where tested for different health indicators. It was observed that the students who chose to have meals from the programme had poorer health

### Programming bouncing ball in JavaScript

While studying Newton's laws of motion during my schooldays, I found some of the questions related to bouncing ball quite fascinating. The sheer number of different kinds of questions that one could come up with just a ball bouncing on the ground is quite a lot.

My attempt is to create the example as simple as possible. I would not be defining additional classes; I would be using the position value which is already present in the DOM Element and adding velocity as a parameter to the DOM Element.

First, let us define the HTML and CSS to get the visual appearance of the ball and the floor right.

<html>
<style>
#ball{
position: absolute;
left: 50%;
top: 0;
width: 50px;
height: 50px;
background: #005eff;
}
#floor{
position: absolute;
bottom: 2px;
background: #000;
width: 100%;
height: 20px;
}
</style>
<body>
<div id="ball"></div>
<div id="floor"></div>
</body>
</html>
Now, let the fun begin! Let's start with gravity as a global variable (just in case I feel like adding more balls in the future).

Let us tackle the problem statement at hand in a discrete time way. Let us observe how smooth this is going to be. Adding the following JavaScript to the HTML/CSS shown above.

<script>
// Globals
var gravity = 0.01;
var deltaT = 1; // Updated at every time step
var restitutionCoefficient = 0.8;
var ball = document.getElementById("ball");
var floor = document.getElementById("floor")
ball.v = 0; // Initial velocity
setInterval(function(){
ball.style.top = ball.offsetTop + ball.v * deltaT + 0.5 * gravity * deltaT * deltaT;
ball.v = ball.v + gravity * deltaT;
if(ball.offsetTop + ball.offsetHeight > floor.offsetTop){
ball.v = - ball.v * restitutionCoefficient;
}
}, deltaT);
</script>

Well, the ball does bounce with this, but it just does not look smooth for some reason. Well, let's try something else.

The issue may be caused by too much computation involved at such a short time step. First of all, the half accelleration times time squared term is insignificant. Let us remove that. After that, divide gravity by a factor of 10 and multiply deltaT by a factor of 10. Observe how things smoothen up.

If you understand this post, it is not very far fetched to think that you can create your own JavaScript game using a few keyboard callbacks. Enjoy!