Curiosity On Rails

Many of us have seen the spokes of the wheels of super-fast cars revolve backwards. Why doesn't it simply go forward? Our eyes have millions of receptors called rods and cones. The color vision is mostly thought to involve a comparison of the signals received from different types of cones -photoreceptor cells in the eye that are sensitive to color. Rods, a different type of photoreceptor cell, that are thought to be used only for colorless vision in very dim light. The optic nerve, a cable–like grouping of nerve fibers, connects and transmits visual information from the eye to the brain; and finally, humans can see objects in three-dimension which is the courtesy of the crossing over of optic nerve fibers at the  optic chiasm . So  if we have all the correct connections in place and the images we perceive are at the speed of light , why are we affected by such an optical illusion? The answer is rather simple (though it got me perplexed for quite s...

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...

I was learning about Markov chains while reading about Hidden Markov Models (HMMs), they are used in understanding and decoding the meaning behind speech. Working on system design and architecture concepts, I saw an analogy of this concept, for using them for finding an optimal number of servers for your micro-service. This post has been long overdue though, since July 16 to be precise, the day ' Amazon Prime-Day ' took place this year ; the post is inspired by that busy day for servers, where multiple customer requests hop from one server to another, sporadically sky-rocketing the read/write load on the them. For lucidity and ease of understanding, consider that there are only 5 categories and data for each category is in a separate server, and each server can serve \(100k\) customers. The most important problem for Amazon is optimizing the number of servers for each category. Let's say that through deep-learning algorithms and yada-yada we can predict the total numbe...

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,...

The following question was dubbed the hardest logic puzzle, published in 1996, written by the renowned founder of theoretical computer science, Raymond Smullyan. One of the reasons I took it up in this blog was because after reading many articles explaining the answer, they were more of a reverse engineered solution and none of them, in my opinion,worked up-to the solution such that I could solve any question of this form posed(reason why I was not content with such explanations). Here's the Hardest Logic Puzzle Ever  : Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for “yes” and “no”...

Is it possible that the dice (singular form: die) that we get with our monopoly game/other games is not within the rules of it being called an unbiased die ? Maybe not. Hypothesis : Die is unbiased To test this hypothesis, the first question that arises (due to sheer lassitude) is - what will be the minimum number of tests/throws to get enough data of statistical importance? According to Pearson's \(\chi^2\) test   , the rule of thumb is to atleast have 5 times the total sample space of a single die. The die has 6 sides, so we need atleast 30 tests . To get more significant results, this will be repeated 3 times to give better results. In the first test, we threw the die  40 times  and its values are: 6,4,3,1,2,5,3,1,4,2,5,3,1,1,3,2,5,3,1,2,3,5,4,2,3,6,1,4,2,3,4,2,5,6,2,3,1,2,6,4 : \(sum=127\) Throw methodology: All throws were made with the right hand pivoted at a point and arc length of the throw was marked such that the same distance was covere...