On Randomness

I believe that randomness is the core of the universe.

Disclaimer: I’m not an expert on the topic. This is personal thought after watching some YouTube videos and reading some books about the origin of universe.

What is Randomness?

To start this post, there are two very insightful videos on YouTube about randomness and whatnot by Vsauce and Veritasium: “What Is Random” and “What Is Not Random“. They essentially said that:

• What is random: Be careful when one is saying “he/she is being random”, most likely that person is just doing things that are unrelated but predictable. By and large, a lot of things can be predicted if the precise initial state is known. Quantum mechanics utilizes random property of matter.
• What is not random: Information can be represented as things that are not random. This can be compressed to certain degree of randomness, i.e. entropy. Linking with 2nd law of thermodynamics, entropy will always increase, means that the amount of random & amount of information will increase over time.

Emergence of Randomness

When one observes the inputs and outputs of a system, given that the inputs are independent and the observer does not interact with the system, the outputs will result in a nice random distribution.

A probability distribution will emerge from non-random inputs. One of the most famous one is “Bell Curve” or “Gaussian function”, which is widely used for grading system, including in my university. My Engineering Mathematics tutor said that this grading system is so fascinating: everyone will try their best in the exams (not random), but yet the result will still be distributed normally (random), i.e. randomness arises from non-random actions.

However, this distribution does not show up if the inputs are not independent. As an example, there is a research about the comments section of Hacker News: when a submission initially have a positive comment, it tends to go more positive, and vice-versa. When a post about Airbnb was submitted to HN, the thread was filled with mostly negative comments, yet the company thrived. There are a few other examples given in the research, and concludes that since a person can read another person’s comment, one may tend to follow the sentiment that has more influence in the thread, hence the tendency of being very positive or very negative.

The random distribution also does not emerge if the intermediary process got interacted by observer. One famous example of this is the double-slit experiment whereby the interference pattern at the end of the screen was not observed if one observes which slit the electron passes through. This shows that the observer changes the “state” just by observing the intermediary process.

The Second Law of Thermodynamics

This law states that, in an isolated system (i.e. an environment uninterrupted by external factors) entropy (degree of randomness) can only increase. This is a fascinating law because this law is actually provable with math. A simple proof that I heard is that given some gas particles in a closed system, the particles are more likely to be found at “random” places in the system rather than in one corner of the system. For example, if there are only three atoms in a closed box, they are more likely to be found spread out (i.e. more entropy) rather than closely together in one corner (less entropy). It will take much effort (energy) to make them closely together (“non-random”). Therefore, it seems like an emergent property of universe over time is randomness.

Conclusion

In the end, I think that randomness is at the core of universe. A random distribution will emerge if one observes the inputs and outputs of a system, given that the inputs are independent and the observer does not interact with the system. This seems to also goes hand-in-hand with the second law of thermodynamics.

P.S. I started this post in February 2016 while I was still in university. I started to write some stuffs, but then stopped and this post has stuck at my drafts for a very long time as I struggle with how to conclude the post.

P.P.S. A good reading material about this topic is Stephen Hawking’s A Brief History of Time.