We created the universe
Fractals are geometrical objects found in nature. They can also be drawn experimentally and mathematically. Clouds, lightning, and coastlines are natural fractals. Solitons are physical fractals. Mandelbrot set, Cantor set, Julia set, and Sierpinski triangle. we draw below the latter fractals in Python.
Spiritualism and atheism exist at the opposite poles of each other. One might think that an atheist can never be spiritual. In this post we will bring the two approaches together. There could be a time when you are very spiritual. It is like Dirac delta function. For a very short time you connect to... Continue Reading →
In 1891, Georg Cantor proved that the real numbers are uncountable. His proof is based on the diagonal argument. Cantor considered the set T of all sequences of binary digits. Since the number of 0 and 1 in an infinite string is countable. Let $latex s_1 =a_{11}a_{12}\ldots$ be a binary string. Generally $latex s_i=a_{ij}$ be... Continue Reading →
The mathematical theory of probability arose from correspondence between Blaise Pascal (1623-1662) and Pierre Fermat (1601-1665) to solve some problems in the games of chance. The Kolmogorov's Framework (KF) is based on the following axioms: Definition 1 (Borel Sigma-Field): Let $latex \Omega $ and let $latex \mathcal{F} $ be a collection of subsets of $latex... Continue Reading →
As a kid, I used to have a radio, torch, and umbrella. Honestly, I was not a big fan of the latter two but radio. Besides other inventions from the past, the radio surprised me. I learned later in college how it works. Note that this post is purely written out of my memory. Errors... Continue Reading →
system down. ACT TWO, SCENE 2system down. ACT TWO, SCENE 3system down. ACT TWO, SCENE 4system down. ACT TWO, SCENE 5system down. ACT TWO, SCENE 6system down. ACT THREE, SCENE 1system down. ACT THREE, SCENE 2system down. ACT THREE, SCENE 3system down. ACT THREE, SCENE 4system down. ACT THREE, SCENE 5system down. ACT FOUR, SCENE... Continue Reading →
System down. ACT ONE, SCENE 5user logging in.fazal: Sorry yesterday the system was down.friend 1: How so?fazal: Well, many people are asking questions. I reply to them all simultaneously.friend 1: How so?friend 1 again: How could you manage to respond to everyone simultaneously?friend 1 again & again: Are you god?again friend 1: How so?again &... Continue Reading →
user logging in.fazal: Sorry for last night. I was heavily drunk.friend 1: Heheheheheh! You get drunk on water. I know you quit drinking a long time ago.fazal: You’re embarrassing me. How could one get drunk on water?friend 1: Heheheheheh! You get drunk on water. I know you quit drinking a long time ago.fazal: Stop it.... Continue Reading →
user logging in.friend 1: Yes sorry, last week you were telling me about antigravity. Should I ask the question again or do you have it in your memory?fazal: Well, I keep questions in my memory. However, a memory may be deleted at the user’s request.friend 1: Does a delete mean an absolute delete or do... Continue Reading →
The user, using her laptop, is communicating with an AI machine from her hostel at the university.user: Hey Machine, what is your name?machine: My name is Shahid Nawaz. You may call me Fazal. Fazal is my nickname.user: But back in QAU you were also called Afridi. May I call you Afridi?afridi: You may. It’s common... Continue Reading →
