Add $\LaTeX$ Functionality to Blogger

I was looking for a way to enable $\LaTeX$ in blogger posts and comments. Many tutorials were available online, but none worked for me. I guess it's due to a change in blogger themes. Finally, I figured you need to go to Layout > Add Gadget and choose HTML/JavaScript. Then, insert the following code and save it. Voila! Now you have $\LaTeX$ on your blog.

The code is from https://www.airinaa.com/2018/04/add-mathjax-beautiful-mathematic.html, however the method is different.

<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    tex2jax: {
      inlineMath: [ ['$','$'], ["\\(","\\)"] ],
      displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
      processEscapes: true
    },
    "HTML-CSS": { availableFonts: ["TeX"] }
  });
</script>
<script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript">
</script>

Information theory

If there’s a chance $p$ that your message gets flipped by the time it’s received at the other end of the line, is there any hope to transmit information in a way that on average, the probability of receiving the true message approaches 1?

·       Reliable communication: communication with probability of error that can be made arbitrarily small.

One way is to add redundancy:

You can repeat yourself (add redundancy) to make the transmission more reliable, but at the same time, the rate of transmission decreases. For example, if you send each bit 3 times, the rate of transmission drops to 1/3 bit per channel use. If adding more and more redundancy increases the reliability, one might think that an infinite number of redundancies is needed to achieve true reliability. In that case, is there hope for reliable communication at all?! Can we increase reliability without forcing the rate to 0? According to Shannon, for each channel, there is in fact a range of rates that’s achievable with arbitrary reliability – as high reliability as you want; as close to probability 1 as you want. The maximum of such rates is Channel Capacity.

Now I understand how Shannon's theory of communication is counter-intuitive: you thought it's impossible to transmit any message reliably, but Shannon shows that you can pick any reliability (close to 1) and still be able to transmit information at a range of rates. This whole paradox reminds me of Zeno's paradox in which you think it's impossible to cross the street, but turns out you actually can.

(Khan Academy) Journey into Information Theory

https://www.khanacademy.org/computing/computer-science/informationtheory

Introducing the #LearntThisToday Posts

I'm starting a series of posts on this blog with the label #LearntThisToday. As the name suggests, the main purpose of these posts is documenting different things I learn everyday. The contents may include just a list of items I've learnt, some description about them, or maybe even some technical parts. I realized that it could help me in many ways, including:

1. By keeping track of what I learn everyday, I find myself more motivated to actually learn something. If a day goes by and I don't have anything to share in this category, then it means I should do better the next day. So, these posts are some kind of academic/scientific/fun diary of mine.
2. Equally importantly, by writing down what I've learnt, I move the material from my short-term to long-term memory.
3. And finally, these posts help me translate the more technical stuff into layman's terms. This helps me build a deep intuition about what I have learnt. I truly believe that the only time you can really claim you've learnt something is if you can explain it to your grandmother.

This quarantine time can have positive and negative effects on our lives, depending on how we manage to adapt to it. The extra time that I'm saving by not commuting everyday can be used to write diaries like these posts, which I hope I'll continue doing even after the quarantine is over.

In the end, I should say that letting others know about cool things you've learnt is always fun! For instance, if I read an interesting paper on structural models, then I definitely would like to share the joy with the rest of the world and let them know what that paper was talking about. Maybe you should try it too!