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Twinkle twinkle little star is a short musical piece I composed and recorded last evening.

This piece consists of 56 measures. It is 1 minute 52 seconds long. The music is composed of four tracks. This is my second attempt at recording music with multiple tracks. The last such attempt was more than two years ago when I composed and recorded 'A few notes'.

The links to the audio files, sheet music, etc. are provided below. The files reside in my website. In case, my website is down, the YouTube link provided below should still work.

The four tracks in this piece are:

  1. Grand piano
  2. Slow strings
  3. Xenon pad
  4. Music box

This arrangement is based on the popular melody of the nursery rhyme called Twinkle, twinkle, little star. The melody is played with the treble notes of the piano. I wrote the bass notes for the piano and the strings, and the high notes for the pad and the music box to fill the music with emotions of love and happiness. I recorded this after about two hours of practice.

Random post

After a long meeting, I went to the cafeteria with a friend to have a cup of cappuccino, my favourite drink at office. In the dialogue below, P is my friend and colleague, and S is me.

S: Hey, they have a 'Silence Please' board here. We can't talk.
P: Rules are made to be broken.
S: So, your rule is to break rules?
P: Yes.
S: This implies that you should break your rule of breaking rules and thus not break rules and be silent.
P: Umm… My rule is to break rules made by others.
S: Ah! You avoided a self-reference there. It makes sense now.

I could have still trapped her by making a rule that P breaks rules made by others but this didn't occur to me in the cafeteria.

Such self references often set up paradoxes in logic. One of the simplest ones is the liar paradox.

This statement is false.

Now, is this statement true? Is it false? Is it both true and false, or is it neither? This is discussed pretty nicely in the Wikipedia page for this paradox.

How do we avoid such paradoxes? Yes, one way is to avoid self-references by restricting a statement from talking about itself. But does it really solve the problem? Let us have a look at this.

The next statement is true. The previous statement is false.

Is the first statement true or false? Yes, we have set up a paradox again despite avoiding self-reference here. The correct way to prevent these paradoxes from happening is to categorize the statements into various levels and allow a statement to talk about statements belonging to a lower level only.

So, if we categorize the first statement "The next statement is true" as a level 1 statement, then the next statement automatically becomes a level 2 statement as it is talking about level 1 statement. But wait! This implies that the level 1 statement is talking about level 2 statement which is illegal as per our new restriction of not allowing a statement to talk about another statement at the same or higher level. So, we see that we can avoid such paradoxes with this additional restriction.

A friend of mine, shown as W below, often claims something strange.

W: I only ask questions in a debate. I don't take sides.
S: Ok. Let us debate this. Side 1: You take sides. Side 2: You don't take sides. Which side do you take?

Comic by Randall Munroe:

Let me list down some of my favourite logical paradoxes.

Do go through Al Franken's advice.