The Turing test replaces the question whether a machine thinks with a question about what a judge can tell. Model the judge as an updater with two hypotheses, human and machine, show that a perfect mimic gives a Bayes factor of 1 on every answer, and compute what one tell does.
Core ideas
Behaviourism says that being in a mental state is a matter of behaving a certain way. The Turing test turns that into a procedure, and a procedure that yields evidence can be computed.
The judge begins with some belief that the party behind the screen is human, and each answer moves it by the Bayes factor, the probability of that answer if the party is human divided by its probability if not. This is the updating of Knowledge and Evidence.
If an answer is exactly as probable from the machine as from the human, it is no evidence either way. Ten such answers are ten factors of 1, and the belief ends where it began.
The test compares “human” with “machine”. It does not compare “thinks” with “does not think”. To connect them takes a further premise, and that premise is behaviourism.
The material
Behaviourism first, then the judge as an updater, then what the numbers can and cannot be made to say.
Behaviourism about the mind is the claim that to be in a mental state is to be disposed to behave in certain ways. On its strongest version nothing is left over: there is no inner fact about whether a thing thinks beyond what it would say and do.
Turing's proposal replaces the question. A judge converses in writing with two parties, one human and one machine, and must say which is which. If the judge cannot do better than chance, the machine has passed, and the question whether it thinks has been swapped for one that can be answered. Turing himself set the original question aside as too ill-defined to discuss. Read as a test of thought rather than of imitation, his game is behaviourism put to work, and that reading is the one this lesson examines.
The lab models the judge as what the judge is, an updater. There are two hypotheses about the party behind the screen, human and machine, and each answer is data. Each hypothesis assigns a probability to each kind of answer. Take the answers to be of two kinds, a plain answer and a tell, an answer the machine gives more often than a person would. A tell might be an arithmetic result too fast, or a reply too even in tone.
That is a machine with a tell. The Bayes factor of one tell for the hypothesis human is (1/10) / (9/10), which is 1/9: the answer is nine times as probable if the party is a machine. Starting from a prior of one half, the lab reports a posterior of 1/10 for human after the one tell.
Now the perfect mimic. Give the machine the human's row: a plain answer with probability 9/10 and a tell with probability 1/10, whichever party it is. Every answer, plain or tell, is exactly as probable under one hypothesis as under the other, so every answer has a Bayes factor of 1, and ten answers together have a factor of 1. The posterior is the prior. The judge has learned nothing about who is behind the screen, and that is all that a pass is.
Prior matters too. A judge who starts at 9/10 for human and meets one tell lands at one half: the factor of 1/9 exactly cancels the odds of nine to one. A judge who starts at one half lands at 1/10. The same tell is the same evidence, and it moves different judges to different places.
Two consequences for the claim that the test measures thought. A pass is not a proof: a factor of 1 says the judge could not tell the parties apart, which is a fact about how well the machine imitates, and a very good imitation of a thinking person need not think. A failure is not a disproof either: a tell shows that the parties differ in style, and a person with an odd manner of answering would show one too. The behaviourist closes the gap by definition, because for the behaviourist there is nothing for the test to miss. “The Chinese Room and the Lookup Table” shows what that costs.
The limit: the probabilities in the lab are numbers someone chose. The lab computes what a judge holding those numbers should believe. It cannot say whether a real answer is a tell.
Interactive
prior times likelihood, normalised; the Bayes factor is the weight of the data
Method
Five steps. The fourth is the one a quick reading skips.
State them as who is behind the screen: human and machine. Do not state them as thinks and does not think. Those are different hypotheses, and the test only reaches the first pair.
For each kind of answer, say how probable it is if the party is human and how probable if a machine. Each row must sum to 1.
The prior is how likely the judge thinks a human before any answer. The data are the answers, in order.
If every answer is equally probable under both hypotheses, the Bayes factor is 1 and the posterior is the prior whatever was heard.
A factor away from 1 means the parties can be told apart. It says nothing about thought until a premise about behaviour and mind is added, and you should say which.
A judge with a prior of one half for human, hearing a perfect mimic, and then a machine with a tell.
The mimic's ten answers are not weak evidence. They are no evidence, because the rows are the same. The tell is one answer and moves the odds on human from one to one down to one to nine, and the whole difference between the cases is a row of probabilities.
Given two likelihood rows and an answer, you should be able to compute the Bayes factor and the posterior, say whether the answer separates the parties, and state the premise that would carry the result from who is behind the screen to whether it thinks.
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