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The Liar’s Paradox

A paradox is something that may seem absurd or contradictory but yet can be true, or at least makes sense. For example,

Let’s say there is a bullet which can shoot through any barrier. Let’s also say there is an absolutely bullet-proof armor which no object can penetrate. What will happen if such a bullet hits such an armor?

Probably the most famous paradox is the Liar Paradox which simply states “I am lying.” You may recall the Liar Paradox from the Star Trek TOS “I, Mudd.”

[youtube https://www.youtube.com/watch?v=giOq3hcHGHs]

The reason the Liar Paradox is important is that it goes to the fundamental search for truth.

The great British mathematician Alan Turing was fascinated by the Liar Paradox and postulated a machine that could solve the Liar Paradox by being able to determine whether any possible statement was true or false. What Turing was able to show was that his fanciful “Turing Machine” would run forever (what we would call an ‘infinite loop’) and, hence, there were unsolvable mathematical problems in the universe.

However, if a problem was solvable, a Turing Machine could solve it which lead to the machine that was able to break the Enigma Code and eventually the modern computer.

There are many interesting aspects of the Turing Machine. For instance, Turing noticed that “programming” of a loom was done through punched cards and postulated that as the way to input instructions to his machine. So now you know where IBM punched cards came from.

Today we are faced with numerous situations of seeming paradoxes which form the basis of the arguments we have in society today such as:

  • If you like your doctor you can keep your doctor, but you can no longer afford your doctor.
  • This legal person is illegal.
  • The most important role of government is protecting life but abortion is legal.
  • Every citizen has a right to a gun but guns are used in mass shootings.

Computationally, the issue is that you can’t tell whether a computer is just taking a very long time working on the problem or whether the problem is unsolvable.

So does this help in understanding how we’re going to solve the issues of the day? Not one bit! But you learned something new and got to watch a classic Star Trek: TOS clip. And that’s really what we’re all about here at the Sparta Report!

 

 
Mark Rosneck

Written by Mark Rosneck

Site owner and bilagáana

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