Category Archives: Science

The Grandfather Paradox with a Markov Chain

The YouTube video “Solution to the Grandfather Paradox” does a great job discussing the Grandfather Paradox. Interestingly, at a point, the narrator states: “And a similar paradox-free solution can be obtained by viewing the problem as a steady-state solution to a Markov … Continue reading

Posted in Science

Visualizing eight elementary vector fields

I used Wolfram Alpha to draw eight vector fields that fascinate me, albeit or because of their simplicity. In Wolfram Alpha, I entered (x,y) and the engine plotted the integral curves for the corresponding vector field. Then I entered (x,-y) … Continue reading

Posted in Science

How jectivity corresponds to morphisms

“Jectivity” may or may not be a real word in the dictionary and my command of the English language is not adequate for me to make such a discussion. But “jectivity” is indeed a valid mathematical word and it concerns … Continue reading

Posted in Science

Venn diagrams vs. Euler diagrams

In Venn diagrams, all areas (subsets) are shown. Areas that contain no elements (empty subsets) are filled with black color. In Euler diagrams, only areas that contain elements (non-empty subsets) are shown. If we want to depict all areas, irrespectively … Continue reading

Posted in Science

Creating beats with Excel

Many years ago, a friend who is also a physicist like me, visited me and we talked about a few matters. When he told me that he began learning Excel, I knew I could impress him. I told him that … Continue reading

Posted in Science

The sad state of YouTube’s moderation

What good is it if you have obtained knowledge and you are not using it to offer the world some good out of it? Well, I feel obligated to use my knowledge to help mankind progress, no matter how small … Continue reading

Posted in Science

Why GPS needs at least four satellites

I found that whenever Global Positioning System (GPS) is explained, is is mentioned that a GPS receiver needs to be able to “see” at least four GPS satellites. And that is that. The explanations continue on to other GPS related … Continue reading

Posted in Science