Robert McNees
@mcnees@mastodon.social  ·  activity timestamp 2 years ago

In 1936 Turing wrote "On Computable Numbers, with an Application to the Entscheidungsproblem," in which he addresses Hilbert's decidability problem, proves that the Halting Problem is unsolvable, and lays out the modern definition of computability.

Ref: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s2-42.1.230

ON COMPUTABLE NUMBERS. WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM By A. M. TURING. The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers. it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth.The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique.I hope shortly to give an account of the relations of the computable numbers, functions, and so forth to one another. This will include a development of the theory of functions of a real variable expressed in terms of computable numbers,According to my definition, a number is computable if its decimal can be written down by a machine.
ON COMPUTABLE NUMBERS. WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM By A. M. TURING. The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers. it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth.The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique.I hope shortly to give an account of the relations of the computable numbers, functions, and so forth to one another. This will include a development of the theory of functions of a real variable expressed in terms of computable numbers,According to my definition, a number is computable if its decimal can be written down by a machine.
ON COMPUTABLE NUMBERS. WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM By A. M. TURING. The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers. it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth.The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique.I hope shortly to give an account of the relations of the computable numbers, functions, and so forth to one another. This will include a development of the theory of functions of a real variable expressed in terms of computable numbers,According to my definition, a number is computable if its decimal can be written down by a machine.
Robert McNees
@mcnees@mastodon.social  ·  activity timestamp 2 years ago

Given the proliferation of bots on social media, and of LLMs [sweeps arm in revealing gesture] basically everywhere else, Turing's paper "Computing Machinery and Intelligence" may be of more current interest.

In this paper he proposes the "imitation game" for scrutinizing a machine's ability to emulate human intelligence. We now call it the Turing Test.

Ref: https://academic.oup.com/mind/article/LIX/236/433/986238?login=false

I. COMPUTING MACHINERY AND INTELLIGENCE BY A. M. TURING 1. The Imitation Game. I PROPOSE to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine' and 'think'. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words 'machine' and 'think' are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, 'Can machines think?' is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.
I. COMPUTING MACHINERY AND INTELLIGENCE BY A. M. TURING 1. The Imitation Game. I PROPOSE to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine' and 'think'. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words 'machine' and 'think' are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, 'Can machines think?' is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.
I. COMPUTING MACHINERY AND INTELLIGENCE BY A. M. TURING 1. The Imitation Game. I PROPOSE to consider the question, 'Can machines think?' This should begin with definitions of the meaning of the terms 'machine' and 'think'. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words 'machine' and 'think' are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, 'Can machines think?' is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.
Robert McNees
@mcnees@mastodon.social  ·  activity timestamp 2 years ago

Really, the test proposes to gauge a machine's ability to emulate a human trying to deceive another human.

This is perhaps even more relevant to the current moment, to the ways LLMS and related technologies are impacting social media, spam and email solicitations, legal filings citing unusual case law, and a zillion other things. You may have heard some things recently!
Robert McNees
@mcnees@mastodon.social  ·  activity timestamp 2 years ago

Turing initially describes the imitation game in terms of a man (A), a woman (B), and an interrogator.

The man and woman are in one room, the interrogator in another. The interrogator passes them questions and receives replies labeled "X" or "Y."

The interrogator's goal is to correctly assign "X is A and Y is B" or vice-versa. The man's goal is to trick the interrogator into making the wrong assignment. The woman's goal is to help the interrogator.
Robert McNees
@mcnees@mastodon.social  ·  activity timestamp 2 years ago

The Turing Test is now usually phrased in terms of a person and a machine, with the machine trying to convince the interrogator that it is a person, and the person trying to help the interrogator make the correct identification.

In informal usage, the Turing Test has come to refer to a person trying to decide, on the basis of replies to conversational questions or some sort of test, whether or not they are speaking to a machine or another person.

A still image of a scene from the beginning of the movie "Blade Runner," where a replicant named Leon is given a "Voight-Kampff test" by a Blade Runner named Dave Holden. The image is mostly blue and green tones and shadow. The image is seen from the side, with Leon and Dave sitting on opposite sides of a table with a CRT monitor in the middle. Leon sits on the left-hand side of the table wearing something that looks like a hospital gown. He is in a high-backed leather chair and his hands are conspicuously in his lap. Holden is on the right hand side, in a similar chair. He is hunched over the Voight-Kampff machine used to administer the test. There is a large ceiling fan above them with blades approximately five feet long. Light streams in through a high, rectangular window, giving the whole scene the appearance of something happening underwater.
A still image of a scene from the beginning of the movie "Blade Runner," where a replicant named Leon is given a "Voight-Kampff test" by a Blade Runner named Dave Holden. The image is mostly blue and green tones and shadow. The image is seen from the side, with Leon and Dave sitting on opposite sides of a table with a CRT monitor in the middle. Leon sits on the left-hand side of the table wearing something that looks like a hospital gown. He is in a high-backed leather chair and his hands are conspicuously in his lap. Holden is on the right hand side, in a similar chair. He is hunched over the Voight-Kampff machine used to administer the test. There is a large ceiling fan above them with blades approximately five feet long. Light streams in through a high, rectangular window, giving the whole scene the appearance of something happening underwater.
A still image of a scene from the beginning of the movie "Blade Runner," where a replicant named Leon is given a "Voight-Kampff test" by a Blade Runner named Dave Holden. The image is mostly blue and green tones and shadow. The image is seen from the side, with Leon and Dave sitting on opposite sides of a table with a CRT monitor in the middle. Leon sits on the left-hand side of the table wearing something that looks like a hospital gown. He is in a high-backed leather chair and his hands are conspicuously in his lap. Holden is on the right hand side, in a similar chair. He is hunched over the Voight-Kampff machine used to administer the test. There is a large ceiling fan above them with blades approximately five feet long. Light streams in through a high, rectangular window, giving the whole scene the appearance of something happening underwater.