A thought experiment is a proposal for an experiment that would test or illuminate a hypothesis, theory, or principle. Given the structure of the proposed experiment, it may or may not be possible to actually perform the experiment and, in the case that it is possible for the experiment to be performed, no intention of any kind to actually perform the experiment in question may exist. The common goal of a thought experiment is to explore the potential consequences of the principle in question.

## 10. Simulated Reality

Simulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from “true” reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation. In its strongest form, the “simulation hypothesis” claims it is entirely possible and even probable that we are living in a simulated reality. This is quite different from the current, technologically achievable concept of virtual reality. Virtual reality is easily distinguished from the experience of “true” reality; participants are never in doubt about the nature of what they experience. Simulated reality, by contrast, would be hard or impossible to separate from “true” reality. In brain-computer interface simulations, each participant enters from outside, directly connecting their brain to the simulation computer. The computer transmits sensory data to the participant, reads and responds to their desires and actions in return; in this manner they interact with the simulated world and receive feedback from it. The participant may be induced by any number of possible means to forget, temporarily or otherwise, that they are inside a virtual realm (e.g. “passing through the veil”). While inside the simulation, the participant’s consciousness is represented by an avatar, which can look very different from the participant’s actual appearance. A dream could be considered a type of simulation capable of fooling someone who is asleep. As a result the “dream hypothesis” cannot be ruled out, although it has been argued that common sense and considerations of simplicity rule against it. One of the first philosophers to question the distinction between reality and dreams was Zhuangzi, a Chinese philosopher from the 4th Century BC.

## 9. Bell’s Spaceship Paradox

Bell’s spaceship paradox is a thought experiment in special relativity involving accelerated spaceships and strings. In Bell’s version of the this thought experiment, two spaceships, which are initially at rest in some common inertial reference frame, are connected by a taut string. At time zero in the common inertial frame, both spaceships start to accelerate, such that they remain a fixed distance apart as viewed from the rest frame. Question: Does the string break (i.e. does the distance between the two spaceships increase)? According to discussions by Dewan & Beran and also Bell, in the spaceship launcher’s reference frame the distance between the ships will remain constant while the elastic limit of the string is length contracted, so that at a certain point in time the string should break. Objections and counter-objections have been published to the above analysis. For example, Paul Nawrocki suggests that the string should not break. However we know the theory of relativity by Einstein which states if speed approaches near to that of light, distance should increase i.e it should break. According to Bell, a “clear consensus” of the CERN theory division arrived at the answer that the string would not break. Bell goes on to add, “Of course, many people who get the wrong answer at first get the right answer on further reflection”. Later, Matsuda and Kinoshita reported receiving much criticism after publishing an article on their independently rediscovered version of the paradox in a Japanese journal.

## 8. Infinite Monkey Theorem

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In this context, “almost surely” is a mathematical term with a precise meaning, and the “monkey” is not an actual monkey, but a metaphor for an abstract device that produces a random sequence of letters *ad infinitum*. The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa. The probability of a monkey exactly typing a complete work such as Shakespeare’s *Hamlet* is so tiny that the chance of it occurring during a period of time of the order of the age of the universe is minuscule, but not zero. Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. Popular interest in the typing monkeys is sustained by numerous appearances in literature, television, radio, music, and the Internet. In 2003, an experiment was performed with six Celebes Crested Macaques. Their literary contribution was five pages consisting largely of the letter ‘S’. There is a straightforward proof of this theorem. If two events are statistically independent, then the probability of both happening equals the product of the probabilities of each one happening independently.

Suppose the typewriter has 50 keys, and the word to be typed is *banana*. If we assume that the keys are pressed randomly and independently, then the chance that the first letter typed is ‘b’ is 1/50, and the chance that the second letter typed is *a* is also 1/50, and so on, because events are independent. Therefore, the chance of the first six letters matching *banana* is (1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)^{6}, less than one in 15 billion.

## 7. Galileo’s Balls

Contrary to what your teachers told you, Galileo Galilei likely did not drop balls from the Tower of Pisa; he conducted the gravity experiment in the laboratory of his mind. His 16th-century peers believed heavier objects fell faster than light ones. So Galileo imagined a heavy ball attached by a string to a light ball. According to Aristotelian logic, if a light object and a heavy object were tied together and dropped off a tower, then the heavier object would fall faster, and the rope between the two would become taut. This would allow the lighter object to create drag and slow the heavy one down. But Galileo reasoned that once this occurs, the weight of the two objects together should be heavier than the weight of either one by itself. Would the light ball create drag and slow the heavy one down? Nope, he concluded, they would hit the ground simultaneously.

## 6. Halting Problem

In computability theory, the halting problem is a decision problem which can be stated as follows: given a description of a program, decide whether the program finishes running or will run forever. This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for *all* possible program-input pairs cannot exist. We say that the halting problem is *undecidable* over Turing machines. B. Jack Copeland (2004) attributes the actual term *halting problem* to Martin Davis.

Excellent article:

Similar to Galileo’s thought experiment, one great thought experiment in history to settle a scientific controversy was by Alhazen (Ibn-al-Haytham in arabic, circa 1000 AD), who settled a 1000-year old controversy of which direction light traveled in. It was not understood whether light came from object to the eye, or whether eye shot out some rays which interacted with the objects. Alhazen argued that it couldn’t be the latter, since we are able to see distant stars the moment we open our eyes, and also since eye suffers from looking at a very bright light. See the section of ‘Vision’ on this page: http://en.wikipedia.org/wiki/Alhazen