Six of the Best Thought Experiments of All Time

"The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."

-Plutarch

One of the oldest thought experiments and most famous is the paradox known as the Ship of Theseus. It was first mentioned in the writings of Plutarch. Basically, it describes a ship that remained seaworthy for hundreds of years of use due to to constant repairs and the constant replacement of parts. Once as one plank became old and no longer stable, it would be replaced immediately, until every working part of the ship was no longer original to it.

Gregory S. Kavka created this thought puzzle which has everything to do with intention and inaction. In his own words (in 1983):

An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is. . . intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

The most familiar real world example of the Kavka's Toxin puzzle is the Political Manifesto. Before an important election takes place, a political representative can release a document detailing his or her policies and plans should he or she win. Many of these promises may be difficult or impossible to keep, but having won, he or she is no longer obligated to follow the manifesto even if her or she would have lost without releasing it.

Searles thought experiment begins with this hypothetical premise: suppose that artificial intelligence research has succeeded in constructing a computer that behaves as if it understands Chinese. It takes Chinese characters as input and, through following the instructions of a computer program, produces other Chinese characters, which it presents as output. Suppose, says Searle, that this computer performs its task so convincingly that it comfortably passes the Turing test: it convinces a human Chinese speaker that the program is itself a human Chinese speaker. To all of the questions that the human asks, it makes appropriate responses, such that Chinese speaker would be convinced that he or she is talking to another Chinese-speaking human being.

Searle then supposes that he is in a closed room and has a book with an English version of the computer program, along with sufficient paper, pencils, erasers and filing cabinets. Searle could receive Chinese characters through a slot in the door, process them according to the programs instructions, as well as make Chinese characters as output. As the computer had passed the Turing test this way, it is fair, says Searle, to deduce that he would be able to do so as well, simply through running the program manually.

Searle argues that without "understanding" (what philosophers call "intentionality"), we cannot describe what the machine is doing as "thinking". Because it does not think, it does not have a "mind" in anything like the normal sense of the word, according to Searle. Therefore, he concludes, "strong AI" is mistaken.

Two suspects are arrested by the police, but they don't have enough evidence for a conviction. They then separated the prisoners, and visit each of them to offer the same deal. If one rats out the other (defects) and the other remains silent (cooperates), the defector gets to go free and the silent accomplice receives the maximum sentence of 10 years. If both of them remain silent, then both prisoners get only a six month jail sentence. If they each betray the other, then each receives a 5 year sentence. Each prisoner can either choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation.

Two generals, each leading an army, are preparing to attack a fully fortified city. The armies are camped out near the city, each on its own hill, with a valley separating the two hills. The only way for the two generals to communicate with each other is to send messengers through the valley to the other hill. But, the valley is occupied by the citys defenders and because of that, there is a chance that the messenger sent through the valley might be captured. So while the two generals have agreed that they definitely will attack, they haven't yet agreed upon a time for attack, but they need to have their armies attack the city at the same time in order to succeed.

They need to communicate with each other to decide when to attack, and each general needs to know that the other general knows that he has agreed to the attack plan. Because acknowledgement of message receipt can be lost as easily as the original message, a potentially infinite series of messages is required to come to consensus.

The thought experiment involves considering how they might go about coming to consensus. In its simplest form one general (referred to as the "first general" below) is known to be the leader, decides on the time of attack, as well as need to communicate this time to the other general. The requirement that causes the "problem" is that both generals need to attack at the agreed upon time to succeed. Having a solitary general attack is considered a disastrous failure. The problem is to come up with algorithms that the generals can use, including sending messages and processing received messages, that can permit them to correctly conclude:

Yes, we will both attack at the agreed upon time.

Note that it is somewhat simple for the generals to come to an agreement on the time to attack. One successful message with a successful acknowledgement suffices for that. The subtlety of the Two Generals Problem is in the impossibility of designing algorithms for the generals to use to safely agree to the above statement.

In philosophy, the brain in a vat is an element used in a variety of thought experiments intended to draw out certain features of our ideas of knowledge, reality, truth, mind, as well as meaning. It is drawn from the idea, common to lots of science fiction stories, that a mad scientist, machine or other entity might remove a people brain from the body, suspend it in a vat of life-sustaining liquid, as well as link its neurons via wires to a supercomputer which would provide it with electrical impulses identical to those the brain normally receives. According to such stories, the computer would then be simulating reality (including appropriate responses to the brains own output) and the person with the "disembodied" brain would continue to have perfectly average conscious experiences without these being related to objects or events in the real world.