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Arduino one drone write for me research paper on information technology in healthcare cornamusa elettrica prezi presentation hi I'm Kerry Ann and welcome to crash course computer science over the past few episodes we've been building up our understanding of computer science fundamentals such as functions algorithms and data structures today we're going to take step back and look at the person who formulated many of the theoretical concepts that underlying modern computation the father of computer science and not quite Benedict Cumberbatch to look like Alan Turing [Music] Alan Matheson cheering was born in London in 1912 and showed an incredible aptitude for maths and science throughout his early education his first brush of what we now call computer science came in 1935 while he was a master student at King's College in Cambridge he set out to solve a problem posed by German mathematician David Hilbert known as the entscheidungsproblem or decision problem which asked the following is there an algorithm that takes as input a statement written in formal logic and produces a yes-or-no answer that's always accurate if such an algorithm existed we could use it to answer questions like is there a number bigger than all numbers no there's not we know the answer to that one but there are many other questions in mathematics that we'd like to know the answer to so if this algorithm existed we'd want to know it the American mathematician Alonzo Church first presented a solution to this problem in 1935 he developed a system of mathematical expressions called lambda calculus and demonstrated that no such universal algorithm could exist although lambda calculus was capable of representing any computation the mathematical technique was difficult to apply and understand at pretty much the same time on the other side of the Atlantic Alan Turing came up with his own approach to solve the decision problem he proposed a hypothetical computing machine which we now call a Turing machine Turing machines provided a simple yet powerful mathematical model of computation although using totally different mathematics they were functionally equivalent to lambda calculus in terms of their computational power however their relative simplicity made them much more popular in the burgeoning field of computer science in fact they're simple enough that I'm going to explain it right now a cheering machine is a theoretical computing device equipped with an infinitely long memory tape which stores symbols and a device called a read/write head which can read and write on water flight symbols on that tape there's also a state variable in which we can hold a piece of information about the current state of the machine and a set of rules that describes what the Machine does given a state and the current symbol the head is reading the rule can be to write a symbol on the tape change the state of the machine lose the read/write head to the left or right by one spot or any combination of these actions to make this concrete let's work through a simple example a Turing machine that reads a string of ones ending in a zero and computes whether there is an even number of ones if that's true the machine will write a one for the tape and if it's false it's alright or zero first we need to define our Turing machine rules if the state is even and the current symbol of the tape is one then we update the Machine state to odd and move the head to the right on the other hand if the state is even and the current symbol is zero which means we've reached the end of the string of ones then we write one for the tape and change the state to halt as in we're finished and the Turing machine has completed the computation we also need rules for when the Turing machine is in an odd state one rule for the symbol on a tape is a zero and another for when it is one lastly we need to define a starting state which will set to be even now we've defined the rules in the starting state of our cheering machine which is comparable to a computer program we can run it on some example inputs let's say we store 1 1 0 onto tape that's two ones which means there is an even number of ones and if that's news to you we should probably get working on crash course maps notice that our rules only ever move their head to the right so the rest of the tape is irrelevant we'll leave it blank for simplicity our cheering machine is all ready to go so let's start it our state is even and the first number we see is a one that matches our topmost rule and so we execute the effect which is to update the state two odd and move the read/write head to the right by one spot okay now we see another one on the tape but this time our state is odd and so we execute our third rule which sets the state back to even and reads the head to the right now we see a 0 and our current state is even so we execute our second rule which is to write a 1 for the tape signifying that yes it's true there is an even number of ones and finally the Machine halts that's how Turing machines work pretty simple right so you might be wondering why there's such a big deal well cheering shows that this simple hypothetical machine can perform any computation if given enough time and memory it's a general-purpose computer our program was a simple example but with enough rules States and tape you could build anything a web browser World of Warcraft whatever of course it would be ridiculously inefficient but it is theoretically possible and that's why as a model of computing it's such a powerful idea in fact in terms of what it can and cannot compute there's no computer more powerful than a Turing machine a computer that is as powerful is called cheering complete every modern computing system your laptop your smartphone and even a little computer inside your microwave and thermostat are all cheering complete to answer Hilbert's decision problem cheering apply these new during machines to an intriguing computational puzzle the halting problem per simply this asks is there an algorithm that can determine given a description of a Turing machine and the input from its tape whether the machine will run forever or halt for example we know our cheering machine will halt when given the input 1 1 0 because we literally walk through the example until it halted but what about a more complex problem is there a way to figure out if the program will halt without executing it some programs might take years to run so it would be useful to know before we run it and wait and wait and wait and then start getting worried and wonder and then decades later when you're old and gray control-alt-delete so much sadness unfortunately Turing came up with a proof that shows the halting problem was in fact unsolvable through a clever logical contradiction let's follow his reasoning imagine we have a hypothetical cheering machine that takes a description of a program and some input for his tape and always outputs either yes it halts or no it doesn't and I'm going to give this machine a fun name H for Holtz don't worry about how it works let's just assume such a machine exists we're talking theory here during reasons if there existed a program whose halting behavior was not decidable by age it would mean the halting problem is unsolvable to find one cheering designed another Turing machine that built on top of H if H says the program holds then we'll make our new machine loop forever if the answer is no it doesn't the hole will have the new machine output and no and halt in essence we're building a machine that does the opposite of what H says halt if the program doesn't halt and run forever it's the program halts so this argument will also need to add a splitter to the front of our new machine so they accepts only one input and passes that as both the program and input into H let's call this new machine Bizzaro so far this seems like a plausible machine right now it's going to get pretty complicated but bear with me for a second look what happens when you pass Bizzaro a description of itself as the input this means we're asking H what Bizzaro will do when asked to evaluate itself but if H says Bizzaro halts then Bizzaro enters its infinite loop and thus doesn't halts and if H says the zero doesn't halt then Bizzaro outputs and knows and halt so H can't possibly decide the halting problem correctly because there is no answer it's a paradox and this paradox means that the halting problem cannot be solved with cheering machines remember cheering proves that Turing machines could implement any computation for this solution to the halting problem proves that not all problems can be solved by computation wow that's some heavy stuff I might have to watch that again myself long story short Church and cheering showed there were limits to the ability of computers no matter how much time or memory you have there are just some problems that cannot be solved ever the concurrent efforts by church and cheering to determine the limits of computation and in general formalized computability and now called the church-turing thesis at this point in 1936 Sharon was only 24 years old and really only just beginning his career from 1936 through 1938 he completed a PhD at Princeton University under the guidance of church then after graduating he returned to Cambridge shortly after in 1939 Britain became embroiled in world war ii cheering's genius was quickly applied for the war effort in fact a year before the war started he was already working part-time at the UK's government code and cypher school which was the British code breaking group based out of Bletchley Park one of his main efforts was figuring out how to decrypt German communications especially those that use the Enigma machine in short these machines scrambled text like you type the letters h-e-l-l-o and the letters x WDBJ would come out this process is called encryption the scrambling wasn't random the behavior was defined by a series of real double rotors on the top of the Enigma machine each were 26 possible rotational positions there was also a plug board at the front of the machine that allow pairs of letters to be swapped in total there were billions of possible settings if you had your only Enigma machine and you knew the correct rotor and plug board settings you could type in X WDBJ and hello would come out in other words you decrypted the message of course the German military wasn't sharing their enigma settings on social media so the Allies had to break the code with billions of rotor and plug board combinations there was no way to check them all by hand fortunately for cheering Enigma machines and the people who operated them were not perfect like one key flaw was that a letter would never be encoded as itself as in an H was never encrypted as an H sharing building on earlier work by Polish code break has designed a special-purpose electromechanical computer called the bomb that took advantage of this flaw it tried lots and lots of combinations of enigma settings for a given encrypted message if the bomb found a setting that led to a letter being encoded as itself which we no the railway nigga machine could do that combination was discarded then the machine moved on to try another combination so bonds were used to greatly narrow the number of possible enigma settings this allowed human code breakers to hone their efforts on the most probable solutions looking for things like common German words in fragments of decoded text periodically the Germans would suspect someone was decoding their communications and upgrade the Enigma machine like they'd add another rotor creating many more combinations they even built in tiny new encryption machines throughout the war cheering and his colleagues at Bletchley Park worked tirelessly to defeat these mechanisms and overall the intelligence gained from decrypted German communications gave the Allies an edge in many theatres with some historians arguing is shortened the war by years after the war Turing return to academia and contributed to many early electronic computing efforts like the Manchester mark 1 which was an early and influential stored-program computer but his most famous post-war contribution was Sir artificial intelligence our field so knew that it didn't get that name until 1956 it's a huge topic so we'll get to it again in future episodes in 1950 cheering could envision a future where computers were powerful enough to exhibit intelligence equivalent to or at least indistinguishable from that of a human Turing postulated that a computer would deserve to be called intelligence if it could deceive a human into believing that it was human this became the basis of a simple test now called the Turing test imagine that you are having a conversation with two different people non-white voice or in person but by sending type notes back and forth you can ask any questions you want and you get replies but one of those two people is actually a computer if you can't tell which one is human and which one is a computer then the computer passes the test there's a lot of version of this test called a completely automated public Turing test to tell computers and humans apart or capture for short these are frequently used on the Internet to prevent automated systems from doing things like posting spam on websites I'll admit sometimes I can't read what those squiggly things say does that mean I'm a computer normally in this series we don't delve into the personal lives of these historical figures but insurance case his name has been inextricably tied to tragedy so his story is worth mentioning cheering was gained a time when homosexuality was illegal in the United Kingdom and much of the world an investigation into a 1952 burglary home revealed his sexual orientation to the authorities who charged him with gross indecency cheering was convicted and given a choice between imprisonment or probation with hormonal treatments to suppress his sexuality he chose the latter in part to continue his academic work but it altered his mood and personality although the exact circumstances will never be known its most widely accepted by Alan Turing took his own life by poison in 1954 he was only 41 many things have been named in recognition of Jerry's contributions to theoretical computer science but perhaps the most prestigious among them is the Turing award the highest distinction in the field of computer science equivalent to a Nobel Prize in Physics Chemistry or other sciences despite a life cut short alloys by the first generation of computer scientist and lathe key groundwork that enabled a digital era we get to enjoy today I'll see you next week crash course computer science is produced in association with PBS Digital Studios at their channel you can check out our playlist to show like gross science APF reactions and the art assignment this episode was filmed at the chad and stacey emigholz studio in indianapolis indiana and it was made with the help of all these nice people and a wonderful graphics team thought cafe thanks for watching and try turning it off and then back on again [Music] enterprise risk management certification usa for money Queens College, Flushing.