PREDICTING THE UNPREDICTABLE

Look at the above image. It is artistic and intriguing but what if I told you that this image was made by the plotting of one simple equation.

The above equation is called the Mandelbrot's set equation and this is responsible for the pattern you saw earlier. The American-French-Polish mathematician who had broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life" actually sought after something that most of the mathematicians shied away from, i.e., "subtle randomness in Natural structures". We can't say that a Mountain is a Cone and Clouds are Spheres and the jagged edges of a Seashore as Triangles.

So, Is there an equation for the intricate snowflakes and other natural random phenomena? And the answer is Yes. Even though we cannot accurately do it, the equation has the power to approximate it.

This powerful equation has been used to model a populations on a controlled environment, explain the dripping of water from a water tap and also used to generate random numbers which becomes pseudo-random only if the starting point of the series is known.

So now the real question is CAN THIS EQUATION BE USED TO PREDICT THE ABSOLUTE TIMESTAMPS OF WRONG DECISIONS TAKEN BY AN ML MODEL?

If Yes, wouldn't it be fascinating to study these datapoints and use it to further benefit our model? Yes I do know that Machine Learning model must make mistakes at certain points because it is only an approximation of a bigger picture, but what if I tell you to model an ML model that keeps on predicting consecutive Prime Numbers from a sequence of training Primes. Let us take a closer look at this problem in a graphical way shall we?

The x-axis denotes Natural Numbers and the y-axis the Primes. Note that for every primes there is a spike in the graph resulting in this step function. Now what if we try to model a Machine Learning Model to estimate the subsequent primes upto infinity. What will be your go to model to solve this fundamental problem? A simple Linear Regression? or a Lasso Regression? or a Ridge Regression? or totally something else. Yes all the above mentioned problems can solve the problem effectively but will it be accurate? Of course No.

Now let's look at a more mathematical solution called Dirichelet's Prime Theorem where the Red Line represents Dirichelet's Primes.

END NOTES:

Even though Machine Learning/AI is a major technological breakthrough, there are certain limitations which cannot be broken at least for now since we are only estimating things as just spheres and cones. But the real-time scenario is even more complex with a pinch of randomness in the mix. My recent venture into Chaos Theory and Mandelbrot set Equation made me wonder what if we apply Chaos Theory into ML algorithms so that it is able to adapt and learn infinite different possibilities that a random variable can impose as an obstacle for the ML model to make the right decision.

Anyways that's all I have got for you today. I Hope that I was able to convey my arguments to you in a clear way and kindle a new spark in you some Math related to ML. Thank You for your time.