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Riemann Zeta Function

Imagine a sum that keeps getting bigger: 1 + 2 + 3 + 4 + ... but somehow, its "value" is said to be  \[1+2+3+4+5… = -\frac{1}{12}\] This equation isn’t a joke. It isn’t a typo. And it definitely isn’t like one of those internet tricks that try to prove that 2 = 3. But how? Doesn’t calculus dictate that the sum should diverge? How can an infinite sum of positive integers result in a negative fraction? This equation is one of the paradoxical results of the famed Riemann Zeta function: \[\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}\] First Encounters My first encounter of the Riemann Zeta function was in a problem introduced to me in Math circle India:\(\newline\)               What is the probability that two random numbers x & y are coprime i.e. gcd(x,y) = 1 for \(  x,y \in \mathbb N\) At first glance, it seems like an impossible question to compute. We’re picking 2 numbers at random — how do you even define a probability over an...

Cloning, Biological and Physical.

 If you are a science fiction lover, you must have dreamt of cloning, but have you ever wondered how does cloning work and what are its dangers? Believe it or not, cloning was real, but not the cloning you would imagine, but biological cloning.

In 1996, dolly the sheep was successfully cloned by fusing the nucleus from a mammary-gland cell of a Finn Dorset ewe into an enucleated egg cell taken from a Scottish Blackface ewe. Biological cloning is almost like passing down of genes from parents but is performed in laboratories.

 Recent studies have shown that genetic engineering, which is recent technology can remove the child is prone to inherit from the parent thus making a "perfect child" it seems cool and nice for sometime after you hear it, but it is an horror as it takes away all your individuality and personality and leaves you as a child shaped robot.
Wait, that's getting too much into biological cloning, let's  discuss physical cloning, which means everything same to the subatomic level, the charge, the spin, the position, etc. The method best candidate for physical cloning is a machine that measures all the features of the main body you want to clone and arrange some raw materials in the very same way. 

Even though it sounds so, it is not so easy as there are some problems and the major one is lies in the Heisenberg uncertainty principle-                                               
 

The Heisenberg uncertainty principle states that at the subatomic level, the more the certainty in the speed of the particle, atom, or molecule, the more uncertain the position the object, vice versa. There is but one solution to this problem that we take a number of the same thing, all identical even to the subatomic level, and then we measure different attributes of the object on individual objects eg. Measure height in one, weight in one, position in one and speed in one, etc.
 

 

But don't get your hopes up for physical cloning as getting these completely identical objects is impossible in today's understanding, and don't try any type of cloning as it is very dangerous and certainly don't try to alter personalities as it destroys the value of human individuality.

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