Unexplainable

Despite what the title says, this is not a post about voodoo magic, or supposed UFO sightings. It's about some bizarre theories and calculations that challenge the very foundations of math and physics.

There are some weird postulates that don't make sense intuitively, but at the same time, cant be altogether disproved. Some of these are:

• Russell's paradox: suppose there is a barber who shaves men in a town and only those men who don't shave themselves. Now, if the barber doesn't shave himself, he must shave himself. But, by definition, he can only shave those who don't shave themselves. So this is a contradiction. Formulated by Bertrand Russell.
• The three body problem: If two large heavenly bodies come near each other, the gravitational pull between them can be mathematically determined. However, if just one more body is present in their vicinity, the physics is thrown into complete chaos.
• Cantor's theorem: it states that infinity as represented by mathematicians is not the highest object there is. There are, in fact, many levels of infinity, including the continuum. This is proved when Cantor demystified Hilbert's hotel paradox by explaining that the power set of a set is always bigger than the set itself. This is true for even something as huge as the set of all natural numbers(N). Explained by Georg Cantor.
• The Archer's paradox: This is a relatively less known paradox which states that even though arrows are not perfectly straight(and there are imperfections in the bow), when launched, they adjust themselves to the desired trajectory i.e. they follow the path the archer wants them to(ignoring any shortcomings in the archer's skill).
•  The transcendence of pi: Pi(the ratio of a circle's circumference to its diameter) is a transcendental number which means there is no way it can be converted into a natural number. There is no 'bridge', as they say it.
• The prosecutor's fallacy: When a prosecutor says, " The probability that the blood found at the site of the attack is the attacker's is 99%, so he or she is guilty, he or she is wrong. The statement itself is meaningless, because there is no more information available. Suppose the town where the crime is committed has a population of 5 million people. Taking into account the 1% margin of error, there could be 50 people who match the blood found. So the actual probability that the defender is guilty is 1/50 or 2%. However, a lot of juries don't pick up on  this fallacious reasoning and are misled. This is one of the cornerstones of Bayesian probability.
• The Poincare conjecture: This states that the only topological figure that does not contain any mathematical holes(those figures which cannot be shrunk smoothly to a point) is the sphere.
• The P/NP problem: A major unproved problem in math, it asks if those problems which can be checked quickly, can also be solved as quickly. A good example is the factorisation of large prime numbers.
• The sum of an infinite number of terms can be finite(for more, see Zeno's paradox)
• Euler's perfect cuboid: A perfect cuboid, with surfaces and body diagonals, as whole numbers, hasn't been found yet! The closest we have is a perfect parallelpiped and an Euler brick, with surface numbers as whole numbers.
• Hawking radiation: The process of evaporation of black holes(theoretical) has shown scientists that it is possible to have a free lunch i.e. it is possible to harness energy from a black hole. We are many thousands of years away from actually achieving this.
• Quantum entanglement: Scientists have been able to teleport particles such as photons using a process called 'entanglement' by which the information between particles can be manipulated by knowing the quantum information of one of them.
• Kaluza-Klein theory: this states that there are many more dimensions than previously anticipated. They explained this by saying the extra dimensions are hidden; much like a garden hose looks one dimensional from far away.

Please leave some other amazing items I may have skipped in the comment section.

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