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I use this blog to post some interesting facts and experiences from my forays into science. They may include anything ranging from  interesting results of my homemade experiments or important (or unimportant) discoveries made in interesting ways.

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Probability and it's probability!

This post seeks to find a free meeting room in my office floor. The shores of Dirac Sea has an interesting puzzle about probabilities which also inspired the results of my findings. Let us say that someone gives you a lopsided bet. Say that with probability \(r\) one gets heads, and with probability \(1 - r\) one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let's say after the first toss it came out heads. What is the probability that \(r > 1/2\)? The question seems redundant, the outcome of a bet is determined by another event's probability, basically what we are dealing with is - the probability, of a probability ! One day when going to one of the meeting rooms in my office floor for our daily meeting, none of the meeting rooms were vacant, since this had happened a number of times before as well I thought how would I know if any of the meeting rooms is empty or not. It immediately made me wonder how I could calcul...
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The noise inside your head

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Have you ever felt that your head was full and you couldn't think more? To my surprise, that was not just a metaphor, it was quite literally true! For an ever-growing, learning brain, and to keep in-taking information, there is a big price humans have to pay! Not delving into the biology of our brain, I'll try explaining things in a computer scientist friendly way; every-time our brain intakes new information/data, we make stronger synapses (connections) between nerve cells. The strength of these synapses determines how easily we can retrieve information from our brain, and consequently, some synapses become stronger/larger when we repeatedly intake the same information (thus when we want to memorize something, we find revision helpful for later retrieval.) In a single waking day, synapses continuously strengthen/enlarge as we absorb all kinds of experiences, but this process can't happen indefinitely as synapses reach a saturation point - hence 'our head becomes...
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Probability of success: False uniqueness bias

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It's very ideal to see that the path we choose, be it for success or anything else we try to achieve is unique, our own to follow. An extreme example I see is when a person models their own idea/business on someone else's yet have a false uniqueness bias . It made me wonder to what extent such a thing can be actually be true. This blog post is a naive mathematical approach I have adopted to dispel the fact that even our ways to success are in fact not as unique as we may feel they may be,such that at-least one other person apart from us is following it; thus, trying to prove the false uniqueness bias. Assuming the maximum number of unique path-ways to be successful is equal to the number of people in the world ,~7 billion (1 way to success for each person): \(\mu=7,000,000,000\) Let's take another assumption, that the path chosen is uniformly distributed across the \(\mu\) number of ways. Let \(success_i\) be the path of success the \(i^{th}\) person chooses,...
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