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The Zeta Function Derivation of the Ramanujan’s Summation

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Please note that the famous Ramanujan Summation has three derivations: Heuristic (Infinity Manipulation), Zeta Function Regularisation and the Cutoff Regularisation. This article presents represents the  Zeta Function Regularisation proof  of the summation. To read more on the other methods of summation,  click on this . Moving on to the article: In one of my previous articles , I talked about the Ramanujan’s summation and its derivation with countable Heuristics method, infinity manipulation. It was an interesting approach, however, the hypothesis that 1+2+3+4+5+… = -1/12 is a viable hypothesis in many perspectives. For the purpose of this article, I will be talking about the Riemann Zeta Function, a complex analysis method, and how it is used to prove the Ramanujan Summation through a different perspective. The Riemann Zeta Function is defined as follows: This function is interesting as it always converges into a fraction including a power of Pi for even integers (Bernoulli Numbers
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The Future of Humanity – The Fourth Industrial Revolution!!!!

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  We, the human race, are creatures who solve problems. We, as a community, are smart and have lead humanity from the stone age until the information era. After the rise of agriculture, life has become better and has led to more technological revolutions, making humanity a powerful race. What defines a scientific revolution is a drastic improvement in all the three key resources responsible for productivity: Transport, Communication, Energy. The first industrial revolution occurred in the 19 th century. The steam engine, radio and coal boosted Brittan’s economy, making them one of the superpowers of their time. The second industrial revolution came only a few decades later in the 20 th century. Personal vehicles, telephones and oil-powered electricity changed the world and has defined the current technology of our time. Recently, the third revolution has come with the dawn of the 21 st century. The internet has provided a new means of communication. Hybrid cars have changed th
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Quantum Communication

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  In the contemporary world, the internet has revolutionised communication technology. With a click of a button, you can talk to people anywhere in the world. For the current age, this is an ideal way of communication, and its efficiency can only be improved with better bandwidth speeds like 5G. However, as humans tend towards colonising planets in our solar system, the distance travelled by information will be so large that a single text message may take minutes to send with our current technology. Current communications are based on electromagnetic waves. These waves transfer information at a maximum speed of 299,792 kilometres per second. The Earth’s equatorial circumference is around 40,000 km, leading to a communication time of milliseconds. However, the distance between Earth and Mars is around 66,000,000 kilometres, making the communications time consuming (approximately 220 seconds on a good orbital path). As humans expand further than mars, the time taken to transmit a bit o
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The Monty Hall Problem

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  Have you ever seen the game show “Let’s make a deal” hosted by Monty Hall? My guess is that your answer is “Yes” for the show but a firm “NO” for the host. This show aired in the 1960s, making it one of the oldest game shows presented on tv. On this show, a participant was asked to choose between three doors. Two doors having a goat behind it, while the remaining one having a brand-new car. If you are a participant, you would want to be smart because between the choice of a goat and a car, you would probably want a car. Mathematically, the probability of choosing a car  is 1/3 , and with no information pointing to which door is ideal, a blind guess is inevitable. So, you choose door “1”. After your choice, you are told that behind door 3, there is a goat. Then, the host asks if you want to switch your answer to door 2 or stay with door 1? What should you do? The probability of getting a car is now 1/2 as there is now one goat and one car. At first glance, it does appear as a blin
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Proof of why 0! Is Equal to 1!

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Proof of why 0! Is Equal to 1! If you are a high school student taking probability and statistics, you would have encountered the topic of permutations and combinations. Within this topic, the use of factorials are prevalent. A factorial – represented by ‘!’ or exclamation mark- is a function that represents a descending multiplication of a number until 1. For example, 4! is 4 x 3 x 2 x 1 = 24. However,  there is something called ‘0!’. According to the principal established above, a factorial descends until 1 but 0 is less than 1. Yet, it is taught that the answer is 1. At first, this seems illogical, but if the perspective of how the factorial is defined is changed, 0! does, in fact, equate to 1. Look at the factorial table here: As the factorials (n!) move up the table, the previous term ((n-1)!) is multiplied by n. This is the conventional representation of multiplication. However, what if the perspective of division is taken? As the magnitude (n) of the fac
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How Hard Do You Have to Slap A Piece of Chicken to Cook It?

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How Hard Do You Have to Slap A Piece of Chicken to Cook It? I don’t think  this question can answer by looking at how hard a piece of chicken must slap, but how fast to slap it? To solve this, let two assumptions be made: The law of conservation of momentum and a total elastic collision where all energy is transferred to the chicken from kinetic to thermal energy. Let us take the following into consideration: Specific heat capacity of chicken: 1.77 kJ/kg K = 1770 J/kg K Mass of Chicken = 1 kg Mass of an average hand (male): 0.65 kg Standard temperature: 25 C Internal Temperature to Cook a Chicken: 74 C Now, with all the variables in hand, the answer to the question can be found. (0.5) (Mass hand ) (speed squared) = (Mass Chicken ) (Specific heat Capacity Chicken ) (Change in Temperature) Speed squared = [(1) (1770) (74-25)]/ [(0.5) (0.65)] Speed = 516 m/s Or Speed = 1857.6 kmph or Speed = 1176.63 mph So, theoretically, if you mo
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Time Travel - How to make a time machine!

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Time Travel - How to make a time machine! Have you seen the movie Interstellar? If you have, the temporal continuance conveyed in the movie is theoretically true. Time travel is possible! However, a one-way ticket to the future can be bought and not to the past. According to Einstein’s theory of relativity, time dilation can occur in two forms: Velocity or Gravity. Suppose an individual moves at the speed of light. That individual bends the space-time curve by a factor of x. Let us take another individual who is stationary in space. He bends the space-time curve by a factor of y. The more the space-time curve bends, slower the flow of time. In this instance, x > y so, time moves slower for the person moving at the speed of light relative to the stationary observer. This is what you can call time travel as 1 minute for speed of light can be 1 year for the stationary person. Another possibility is gravity which is seen in interstellar. The higher gravitation you exp
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The Sum of All Positive Numbers Is A Negative Number- Heuristic (Infinity Manipulation) Method of Deriving the Ramanujan Summation!

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Please note that the famous Ramanujan Summation has three derivations: Heuristic (Infinity Manipulation), Zeta Function Regularisation and the Cutoff Regularisation. This article presents represents the  Heuristic (Infinity Manipulation)  of the summation and is simplified for understanding the power of infinity. To read more on the other methods of summation,  click on this . Moreover, this method of divergent summation proves to be an interesting approach.
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Controlled Unproductivity Can Lead To Increased Productivity!

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Controlled Unproductivity Can Lead To Increased Productivity! Has anyone questioned why the work time is from 9-5? Well, that stems back to when labour rights came into the picture. When the rights came into practice, it was understood that there should be a balance between leisure, work, and sleep. Therefore, the 24-hour day was divided into 3 equals 8-hour segments. To achieve maximum efficiency, 9-5 was chosen to be the optimal period to ensure the highest level of productivity. However, this division of time has become outdated. Working 8 hours a day is not suffice and with the advent of social media, people have extended their leisure time by cutting down on sleep. Countless teenagers claim that they sleep close to 4-6 hours a day as they spend most of their time on social media platforms and are bound by midnight texting. Similar is the case with millennials but the problem is not as abysmal. Netflix, working from home and better transport, as well as improved human ri
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Teleportation – The Truth Behind The Conventional Idea!

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Teleportation – The Truth Behind The Conventional Idea! When one thinks about teleportation, they think that we will disassemble from their location and reassembled at their destination. This is theoretically possible through the concept of quantum entanglement. Quantum entanglement is a spooky unexplained force that shows that two particles of matter are interrelated and can interact with each other instantly, regardless of the distance. Suppose we change one particle’s composition to that of one atom of a human body, its corresponding entangled particle will also change to that particle. Therefore, if we do this for each atom in the human body, we can conceptually, clone an individual anywhere in the observable universe. All that is left is to kill one of the clones and voila, we have teleportation. As said by Sheldon in Big Bang theory, I will not be stepping inside of that machine as it will just be a method of glorified suicide. A more realistic way of teleportation wh
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