Alan Turing: Crash Course Computer Science #15

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In this section, we introduce Alan Turing, the father of computer science, and his contributions to the field.

Alan Turing's Early Education and Introduction to Computer Science

• Alan Turing was born in London in 1912 and showed an aptitude for maths and science from a young age.

• In 1935, while studying at King's College in Cambridge, he encountered the Entscheidungsproblem or decision problem posed by David Hilbert.

• The decision problem asked if there is an algorithm that can accurately answer any question written in formal logic with a "yes" or "no" response.

• Alonzo Church presented a solution using Lambda Calculus, but Turing developed his own approach using a hypothetical computing machine called a Turing Machine.

The Concept of Turing Machines

• A Turing Machine is a theoretical computing device equipped with an infinitely long memory tape and a read/write head.

• It has a state variable and a set of rules that describe its behavior.

• Given a state and the current symbol on the tape, the machine can write symbols, change states, or move the head left or right based on its rules.

Example of a Turing Machine

• We explore an example of a Turing Machine that determines whether there is an even number of ones in a string ending with zero.

• The machine has different states and rules for each state based on the current symbol being read.

• By following these rules, it can compute whether there is an even number of ones.

Significance of Turing Machines

• Turing Machines demonstrate that simple hypothetical machines can perform any computation given enough time and memory.

• They serve as general-purpose computers capable of executing various programs.

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In this section, we discuss the simplicity and computational power of Turing Machines.

Turing Machines as General-Purpose Computers

• Turing Machines can perform any computation if given enough time and memory.

• They are considered general-purpose computers capable of executing various programs.

Computational Power of Turing Machines

• Despite using different mathematics, Turing Machines and Lambda Calculus are functionally equivalent in terms of computational power.

• However, Turing Machines gained popularity due to their relative simplicity compared to Lambda Calculus.

The Components of a Turing Machine

• A Turing Machine consists of an infinitely long memory tape, a read/write head, a state variable, and a set of rules.

• The machine can read and write symbols on the tape, change states, and move the head based on its rules.

Example Application of a Turing Machine

• We demonstrate how a Turing Machine can determine whether there is an even number of ones in a string ending with zero.

• By following specific rules based on the current state and symbol being read, the machine computes the result.

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In this section, we continue exploring the example application of a Turing Machine.

Step-by-step Execution of the Example Turing Machine

1. The initial state is "even" and the first symbol on the tape is "1".

2. Following the rules for an "even" state with a current symbol "1", the machine updates its state to "odd" and moves the head to the right.

3. With an "odd" state and another symbol "1", the machine returns to an "even" state and moves right again.

4. When encountering a symbol "0" while in an "even" state, the machine writes "1" on the tape and changes its state to "halt", indicating the computation is complete.

Significance of Turing Machines

• Turing Machines demonstrate that simple hypothetical machines can perform any computation if given enough time and memory.

• They serve as general-purpose computers capable of executing various programs.

New Section

In this section, we discuss the significance of Turing Machines and their computational capabilities.

The Power of Turing Machines

• Turing Machines show that even a simple hypothetical machine can perform any computation with sufficient time and memory.

• This demonstrates the concept of a general-purpose computer capable of executing various programs.

The Power of Turing Machines

This section discusses the power and efficiency of Turing machines as a model of computing.

Turing Machines and Computing Power

• A Turing machine is a powerful idea in computing, despite being inefficient.

• In terms of computation capabilities, there is no computer more powerful than a Turing machine.

• All modern computing systems, such as laptops, smartphones, microwaves, and thermostats, are Turing complete.

The Halting Problem

• The halting problem is a computational puzzle that asks whether an algorithm can determine if a program will run forever or halt.

• Some programs may take years to run, so it would be useful to know if they will halt before executing them.

• Unfortunately, Alan Turing proved that the halting problem is unsolvable through a logical contradiction.

Bizzaro Machine Paradox

• Turing designed a hypothetical machine called "H" that determines if programs halt or not.

• He then created another machine called "Bizzaro" that contradicts the output of H.

• When Bizzaro evaluates itself using H, it leads to a paradox where neither halting nor non-halting can be determined correctly.

Limits of Computation and Turing's Contributions

This section explores the limits of computation and highlights Alan Turing's contributions during his early career.

Limits to Computation

• Church and Turing demonstrated that there are problems that cannot be solved by computation alone.

• Regardless of time or memory resources, some problems remain unsolvable.

Alan Turing's Early Career

• In 1936 at the age of 24, Alan Turing began his career in computing.

• He completed his PhD at Princeton University under the guidance of Church from 1936 to 1938.

• After graduating, he returned to Cambridge University for further research.

Turing's Contribution to World War II

• In 1939, Britain entered World War II, and Turing's genius was applied to the war effort.

• He worked part-time at the UK's government code and cypher school based in Bletchley Park.

• One of his main tasks was decrypting German communications, particularly those encrypted using the Enigma machine.

Decrypting German Communications with the Enigma Machine

This section focuses on Alan Turing's efforts to decrypt German communications during World War II using the Enigma machine.

Encryption with the Enigma Machine

• The Enigma machine scrambled text by using rotors and a plug board.

• Each rotor had 26 possible rotational positions, and there were billions of possible settings.

• If one knew the correct rotor and plug board settings, they could decrypt messages.

Alan Turing's Role

• Alan Turing played a crucial role in figuring out how to decrypt German communications encrypted with the Enigma machine.

• His work at Bletchley Park involved breaking complex codes and developing methods for decryption.

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This section discusses the flaws in the encryption process of the Enigma machine and how Alan Turing designed a special-purpose computer called the Bombe to exploit these flaws.

Flaws in Enigma Encryption

• The letter "h" was never encrypted as an "h" in the Enigma machine.

• Turing built on earlier work by Polish code breakers to design the Bombe.

• The Bombe tried various combinations of Enigma settings for a given encrypted message.

• If the Bombe found a setting that led to a letter being encoded as itself, it discarded that combination and moved on to try another one.

Narrowing Down Possible Settings

• Bombes were used to greatly reduce the number of possible Enigma settings.

• This allowed human code breakers to focus their efforts on the most probable solutions.

• They looked for common German words in fragments of decoded text.

Upgrades and Efforts during War

• The Germans periodically upgraded the Enigma machine, adding more rotors and creating many more combinations.

• Turing and his colleagues at Bletchley Park worked tirelessly throughout the war to defeat these mechanisms.

• Decrypted German communications provided valuable intelligence to the Allies, giving them an edge in many theaters and potentially shortening the war by years.

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This section highlights Turing's contributions after World War II, including his work on early electronic computing efforts and his famous post-war contribution to artificial intelligence.

Post-War Contributions

• After World War II, Turing contributed to early electronic computing efforts, such as the Manchester Mark 1.

• His most famous post-war contribution was in the field of artificial intelligence.

• Turing envisioned a future where computers could exhibit human-like intelligence and proposed the Turing test as a measure of machine intelligence.

The Turing Test

• The Turing test involves having a conversation with two different entities, one being a computer. If you cannot distinguish which one is human and which one is a computer, then the computer passes the test.

• A modern version of this test is called CAPTCHA, used to differentiate between humans and automated systems on the internet.

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This section briefly mentions Turing's personal life and tragic end.

Tragedy in Turing's Life

• Turing was gay at a time when homosexuality was illegal in the United Kingdom and many other parts of the world.

• An investigation into a burglary at his home revealed his sexual orientation, leading to charges of gross indecency against him.

• Given a choice between imprisonment or hormonal treatments to suppress his sexuality, he chose the latter but experienced negative effects on his mood and personality.

• Alan Turing tragically took his own life by poison in 1954 at the age of 41.

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This section highlights some recognitions for Alan Turing's contributions despite his life being cut short.

Recognition for Contributions

• Many things have been named in recognition of Alan Turing's contributions to theoretical computer science.

• The most prestigious among them is the Turing Award, considered the highest distinction in the field of computer science.

• Despite his life being cut short, Turing inspired the first generation of computer scientists and laid key groundwork for the digital era we enjoy today.