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Alan Turing, the Inventor of Software
Roland Piquepaille writes "BusinessWeek celebrates its anniversary with a series of articles about the great thinkers and innovators from the past 75 years. The series stars with a profile of Alan Turing, "Thinking Up Computers." In case you forgot, Turing is the man who created the concept of a "universal machine" which would perform various and diverse actions when given various sets of instructions. In other words, he laid out in the 1920s the foundations of software. You'll find the introduction of Turing's profile, plus more details, photographs and references in this overview."
...or just a computer-generated one?
gay. This is a fact that much of the mainstream media glosses over in noting his accomplishments. (It is possible that there is an anti-gay bias in the history book authors' community... ;) )
:)
So, any time someone says gays are just a bunch of promiscuous, stupid sinners, ask them if they've ever heard of Alan Turing...
Honey, I shrunk the Cygwin
So now we know who to blame for the whole mess!
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he died suddenly, almost certainly by suicide from eating a cyanide-laced apple.
Has anyone else heard the rumur that apple computers logo is a tribute to Turing? Rainbow colored apple with a bite taken out of it and all? I wish I could remember where I heard that.
Ansi's and stupid tricks!
"Turing is the man who created the concept of an "universal machine" which would perform various and diverse actions when given various sets of instructions. In other words, he laid out in the 1920s the foundations of software."
Actually the turing machine served as the basis of the first hardware, not software. Its really the theoretical basis for the entire computing model.
I don't mean to be picky, but I have my Automata Theory final in 5 hours and I just spent all night studying for it..
-ashot
I think Lawrence Waterhouse and Rudy von Hacklheber deserve some credit, too.
Equivalence to a turing machine is used in lots of CS proofs even today.
The turing test is also still considered one of the fundamental challenges of 'weak' Artificial Intelligence.
Well... Turing whas the inventor of turing machines. But Aristoteles provide the logic. So maybe a more accurate title can be "Alan Turing, the Inventor of Turing machine" or maybe "Alan Turing, the ''Inventor'' of Computers". Not true, but better title.
-Woof woof woof!
A hollow voice says, "Jacquard", whose NC looms were old long before Turing came along. Turing put a firm theoretical foundation under what others had been doing for some time.
I'd say his concepts defined the requirements or foundations of how the hardware would operate. Maybe I'm being pedantic as form follows function; software is dictated to a large degree by the base hardware.
I just finished Discrete Structures II. In this class we were to idealize a Turing machine, as a C program. We also went over Alan Turing's paper (the one linked in the article). My professor, who has been involved in cryptographic research for over 20 years, even he went so far as to say that Turing could be labeled a genius. Call me a dork, but I found the automatas to be one of the funnest parts of my CS education.
I always though Ada Lovelace was considered to be the first "programmer"
Not only was Turing gay, but his society "rewarded" him for his contributions by arresting and convicting him for a homosexual encounter. He was an honest man, and talked about it in court. And so then, the British government subjected him to chemical castration. His suicide followed that conviction. Please do your bit to stamp out anti-gay bias in your workplace and society. There are a lot of contributing, good people in computer science, and every other field. It's really a shame how most of the world mistreats them.
This page has a description of the machine.
Turing didn't invent the machine. The germans did.
I see that someone else already mentioned Charles Babbage, who designed a mechanical proccessing engine, in addition to mechanical calculating engines. But Lady Ada Byron, Countess of Lovelace, wrote the first computer program for Babbage's Analytical Engine... (and you folks may recall that there is today a programming language named in her honor).
Nice try, but Ada Lovelace and Charles Babbage are recognised as the inventors of modern computing and programming. I suggest reading a bit about the architecture of the analytical, difference and related "engines" that he designed: they should remarkable similarity to a von neumann / harvard architecture (i.e. central processing units, memory banks, ALUs, etc).
Not to undervalue Alan Turing's contribution though, but he was really breaking more substantial ground in the theory of computability; which really transcends software, hardware, and the trivial implementation details.
Alan Turing actually fits alongside Newton and Eistein and those others who developed great universal insights.
It's a bit sickening that already posts on this thread are making gay-bashing remarks about him. The history of how he was discarded by the British Government, believed to be partly at the instigation of the US government, is a sad story of how intolerance helped the British lose their early lead in computing. If he had been born forty years later, he'd probably be running an equivalent of Apple,Oracle, Sun or Microsoft, and no-one would care about what he did in his spare time.
Panurge has posted for the last time. Thanks for the positive moderations.
it seems like some countries *cough* *cough* go to war mostly for the economy
Name one war that was not fought for economic reasons. Even the so-called Crusades, nominally fought for religion, were an excuse to keep increasinly powerful nobility in check by making them incur such a large expense as trying to invade the middle east. Every war I can think of has economic motives despite frequent facades of other purposes. Not that there's anything wrong with that; large scale human social activity comes down to economics.
Here is a nice clickable overview:
History of computers
Don't forget Turing's Bombes, which ran at Bletchley park deciphering intercepted German signals (see http://www.turing.org.uk/turing/scrapbook/ww2.html ).
Of course, the real father of programmable computing was Tommy Flowers, who seems to have been largely forgotten.
Dunstan
The last scintilla of doubt just rode out of town
"... he laid out in the 1920s the foundations of software"
Actually it was the 30's (especially given that he was born in 1913, so even at the end of the 20's he was still a teenager).
But at that same time in the thirties, the German Conrad Zuse wasn't just 'thinking it up' but doing it. Unfortunately, by being in the wrong country at the wrong time, he still is rarely credited.
Turing was an amateur chemist in addition to being a world-class mathematician. His choice of suicide method was intended to lessen the impact it would have on other members of his family, in particular his mother. By eating a cyanide laced apple, it has been speculated that he wanted to make his death look like an accident. His mother would think that he had been performing some chemistry experiment, and then forgot to thoroughly wash his hands before eating the apple. Having one's son die is bad enough, but for it to be a suicide is doubly worse.
On the more dramatic side, if one were so inclined, it could be said that his method of suicide was rather symbolic. Turing had partook in what was in his day forbidden. For this, he had been "cast out" of his chosen profession and what he loved to do -- in some sense, his Eden. As a final gesture before leaving this world, he ate a piece of forbidden fruit that was symbolic of this fact.
It's a tragedy that the ignorance and intolerance of first half of the 20th century could have driven such a brilliant man to suicide. If it weren't for Turing, much of what we take for granted today may be a lot different or may not even exist at all. Hopefully the world has wisened over the last 50 years.
Actually, according to what he wrote in his letters and the memories of his friends, it was not so much the surveillance per se, as the overall inability to get work done or have a satisfying life that left him feeling so hopeless. The hormones did awful things to his body, from reduction in sex drive to growing breasts, the police bullied a street kid into faking the confession that led to Turing's conviction, the funding in England was getting routed around him and his travel was impaired by government restrictions. (This, keep in mind, while the Americans were surging ahead in computer design and would have been delighted to have Turing join them.)
Oh, it was death by a thousand cuts while the nation that owed so much to him mostly looked on and let him be humiliated and kept from his work.
Also keep in mind folks, that Turing, while thought of a theoretician, was arguably even more important as an operations guy. He led the effort to confront Churchill with the initial absurdly low levels of funding at Bletchley Park (the British code-breaking center), he played a key role in getting the staffing figured out and codes to the right places, and so on. IIRC, he was not averse to picking up a soldering iron and stepping into the physical work of *building* the computers.
Of course, this isn't even getting into his late in life interest in things like how to use a computer to replicate patterns in nature like the spots on the side of a cow. Work that was leading him decades ahead of anybody else to the concepts we now know as fractals and chaotic phenomena.
We'll never know what we've lost, but at least we're getting better at admitting who people like him were.
But then, when we've still got stuff like A Beautiful Mind not even mentioning that Nash was mostly gay (the real reason he lost his clearance was not for mental illness but because he was found in bed with a young man) we've clearly got a long way to go.
Rustin
Data is the lever, rigor the fulcrum, brains the force that drives it all.
Athletic Scholarships to universities make as much sense as academic scholarships to sports teams.
An excellent biography is "Alan Turing, the Enigma" by Andrew Hodges, 1983, updated American edition 2000: http://www.turing.org.uk/book/
Derek Jacobi starred in a 1986 play about Alan Turing and also the excellent 1996 television adaptation. Videos can be purchased.
The site linked by the slashdot article incorrectly identifies a photograph of an Enigma machine. It shows the cryptographic device manufactured by the Germans to encode and decode messages. This is not a device invented by Turing. He had a key role in the development of the programmable computing systems used by the British to crack intercepted German messages.
The game of Go (Igo, Weiqi, Baduk) has the simplest concept and the deepest play.
Definitely one of the handful of brightest minds of the 20th Century and one of the people most individually responsible for the victory of the Allies after WWII. His subsequent treatment was vile and deplorable, but hey, how is that new in the military? Check out those prisoners... mmm, mmm, mmm... that's some good stuff. Considering the hypocrisy involved in the British Military going after a homosexual for being a security risk, well, I'll just leave off here.
Turing's work on AI was so revolutionary that the entire field pretty much languished for a couple decades after his death until people finally started to pick up where he left off.
Turings universal machine was implemented in the Colossus machine (the worlds first general purpose programmable computer). It was dismanteled and the whole thing classified after the war.
After the war the british sold captured Enigma machines to their colonies but kept it secret that they had broken Enigma. Nice touch.
The initial breaks into Enigma was done by the polish before the german invasion and the british work build upon their work.
TCAP-Abort
The turing test only works in terms of 'weak' AI - that is that actions determine intelligence, and internal state doesn't matter.
Strong AI on the other hand, says that to be intelligent, you must not only act intelligent, but also be intelligent internally.
On the other hand, the self-preservation requirement doesn't really strike me as a facet of intelligence. A suicidal person might still have the intelligence to write a thoughtful note...
It requires human perception, which is fallible and inconsistent, to validate the quality of AI.
Worse, it requires the AI to fake human fallible and inconsistent human perception. Any test that requires an AI to wait for a bit before giving the answer to a hard numerical problem is a daft test.
The Turing test tests humanness, not intelligence. There is no reason for (artificial) intelligence to be similar to a human's at all.
I believe posters are recognized by their sig. So I made one.
Alan invented Enigma, a machine to decode encrypted messages from the Germans. Uh, No. Turing invented the Bombe, which was used to decode the Enigma transmissions made by the germans. It was the germans who invented the Enigma machine. Given that the Enigma machine when properly setup could encode over 15 million million million combinations, cracking it was no mean feat. If you're in the UK I can recommend a visit to Bletchley Park which these days is a fascinating museum. And if you're knowledge of Enigma is based on Hollywood schlock like U-571 i'd suggest you read up on the truth! Also, kind of fittingly a park in Manchester is dedicated to Alan Turing with a statue of him. It sits between the UMIST institute of science and technology and the gay village.
If you're interested in Turing, you might like the Turing Archive. This site has scans of a lot of his personal papers and research notes. You can read all his unpublished stuff too :)
Starring Halle Barry as his love interest, Lady Ada Lovelace. Famous for its one-liners used during gun battles with Enigma Nazis: "Code This!" and *BLAM!* BLAM!* "You failed the Turing Test.". Directed by Jerry Bruckheimer, it features Enigma machines that blow up like the Hindenburg whenever the wrong code is entered.
Negotiations are underway with Barry Sonnenfeld's production company to bring back the giant robot spider from "Wild Wild West" to make an appearance as the very first computer bug.
Don't blame Durga. I voted for Centauri.
Jacquard developed looms that could be controlled by using punched cards, but this wasn't really
"programming" as such. What Turing created was the concept of algorithm execution, which until then nobody had come up with.
Algorithm execution is where the data and the sequence of instructions for manipulating that data are all part of your input. Jacquard's loom was more along the lines of just the data being in his punched cards, while the sequence of events that occurred was built into the loom, and only dependant upon the punched cards for specific info about position and such.
- Give a man a fire and he's warm for a day, but set him on fire and he's warm for the rest of his life.
Not to take anything from Turing but wasn't she recognized as the first programmer by coding a virtual program for a virtual (now working) computer conceived by Charles Babbage in 1843?
m
http://www.agnesscott.edu/lriddle/women/love.ht
"When inspired Ada could be very focused and a mathematical taskmaster. Ada suggested to Babbage writing a plan for how the engine might calculate Bernoulli numbers. This plan, is now regarded as the first "computer program.""
What you have understand is that Turing didn't know about push down automata (PDA) when he developed the Turing machine (TM). Turing formulated the TM as a way to show that our formal axiomatic system for mathematics was undecidable (that is, there are statements whose truth values cannot be determined algorithmically). When he designed it, the states of the machine were compared to human states of mind. Finite automata (FA) and PDAs are things that logicians and theoretical computer scientists have developed over the years as simpler models of computation. By teaching about them in an automata theory class, students are more prepared for the concepts of the TM. If I just plopped the general definition of a TM down in front of a person, they'd probably run screaming from the room or at least be horribly confused until examples of simpler devices were presented. (Also, FAs and PDAs have the nice property of recognizing regular and context-free languages, respectively, which allows a discussion of formal languages and their recognition to progress in a natural manner.)
I guess that my point is that the way we are taught mathematics (and that's what the theory of computation is) does not always coincide with the order in which the ideas were developed, no matter how natural the order they are taught in might seem. (For another example, consider that most calculus texts develop differentiation before integration, which is historically backward. The only text that I know of that presents calculus in the historically-correct order is Tom M. Apostol's Calculus. However, in his Mathematical Analysis, he follows the traditional order of differentiation first.)
"You will only be remembered for two things: the problems you solve or the ones you create." Mike Murdock
Turing left a bunch of still new ideas unexplored. Just look at his 48's paper Intelligent Machinery> .
Recurrent connectionism was the starting point, and P machines have not even been explored.
What's in a sig?
What's in a sig?
IMHO, he invented the first programming language.
Details here
there are 3 kinds of people:
* those who can count
* those who can't
I think you are referring to the "Young Turing" movie "biography" starring Yahoo Serious. This details Turing's life growing up in Australia where he rassles crocodiles and invents shoelaces and joins a rock and roll band. Later, when he grows up, he invents computing when he figures out how to crack RIAA encryption in order to download the latest "Wyld Stallyns" tunes.
Don't blame Durga. I voted for Centauri.
The idea of identifying gender, rather than human or not human, is actually much more subtle than might be at first realised. He of course meant this to be extended as we all nowadays quote the test, but the original idea is subtly elegant... He was tackling the problem from the other direction: forget a computer pretending to be "intelligent", but what do we mean by "thinking" - If a man can "pretend" to be a woman, as per his test, what does that prove? That he is a woman?! Of course not... Thus was does it mean to be a woman, etc etc - Turing was a genius with amazing insight and perception.
What a loss.
Actually the turing machine served as the basis of the first hardware, not software.
:) The important thing is to acknowledge which contributions they each made and try to do it correctly without letting the labels get in the way. And for that, I turn you to the expert:
:)
It's usually John von Neumann who is given credit for inventing the modern concept of the "stored program" in the mid 40's. So if I had to pick a single person to label the inventor of software, I think I would probably choose him. Turing could perhaps be labelled a father of computing.
But then again, those are all just subjective labels.
Alan Turing
John von Neumann
I don't mean to be picky, but I have my Automata Theory final in 5 hours
Good luck.
Alan invented Enigma, a machine to decode encrypted messages from the Germans
The Germans used the Enigma to encrypt messages and it was a polish mathematician, Marian Rejewski,who worked out the first attack on the Enigma cipher.He actually designed a machine to automate the process of figuring out the scrambler setting,which is known as a Bombe.Turing refined and improved these machines but he wasnt ,by any stretch of imagination,the originator of cracking up Enigma.
Wanted : A Signature.
If he had been black/female/whatever, and accomplished what he did, and in the end was imprisoned and eventually driven to suicide as a direct result of his ethnicity, he would be constantly brought up as a grim example of racism.
Children in school would learn about how the man who cracked Enigma and might have literally saved WW2 was eventually driven to commit suicide....
While no gay person I know has even heard of Turing. I never heard about him until college.
I think its another case of people not giving a damn about geeks...
My point here is that simply in and of itself anyones sexuality is pretty irrelivant, but the prejudice surrounding homosexuality directly impacted Turing's life. Because fo that failing to mention that he was gay would be similar to failing to mention that Beethoven was deaf. You'll notice that you don't often see articles about Motzart talking about how he was able to hear either. These facts were important to their lives, in a way that, say, Albert Einstein's hetrosexuality wasn't. Streightness is not mentioned much because it is assumed that a person is streight unless its otherwise specified, and due to its wide acceptance hetrosexuality simply doesn't affect a person much. However other sexual specifics are mentioned when its important (JFK's affairs, St. Francis' chastity, etc).
"Mission Accomplished" -- George W. Bush May 1, 2003
Who cares? Aside from the fact that Turing's sexuality is not ignored, it would be a good thing if it was. Let me guess: if it was something that the mainstream media obsessed about, you'd post comments about how homophobia in mainstream media glosses over Turing's accomplishments in favor of irrelevant discussion of his sexual preferences.
Go read Cryptonomicon if you need to obsess about what everybody's sexuality is.
perl -e 'print $i=pack(c5, (41*2), sqrt(7056), (unpack(c,H)-2), oct(115), 10)'
I like how the poster complains that it wasn't explicitly made clear he was gay - as if that was relevant at all. This reminds me of an Onion spoof :
Alan Mathison Turing was one of the great, gay pioneers of the computer field.
He inspired the now common terms of "The Turing Machine" and "Turing's Test.", and preferred the company of men to women. As a mathematician he applied the concept of the algorithm to digital computers, and liked to kiss and hold other men.
The homosexual's research into the relationships between machines and nature created the field of artificial intelligence. His intelligence and foresight made him one of the first to step into the information age. His sexual preference was for men.
Ada is credited with being the first programmer
That's a lie. Ada was rich, and to keep her paying for Babbage's project, he had to make her feel like she was accomplishing something. He figured out the Bernoulli program himself, explained it to her, and let her write it out.
Then in the 20th century, that lie was reinvigorated by educators wanting to supply girls with technical role-models.
Turing developed a model for computers (the Turing machine). He developed the proof of the Halting problem. That is, given a program and a input to that program, you cannot generally determine if the program will terminate execution.
As you're probably already aware, Turing was arrested and imprisoned for homosexuality. After he was released, he undertook a multi-month project to extract cyanide from the pits of apples. After he had sufficient quantities, he drank it and died (aged early 40s).
Kurt Godel was responsible for developing the mathematical proof of undecidability. Given a system with the capabilities of "simple" arithmetic, he showed that there are propositions (i.e. statements) you can make within the system which can be neither proven nor disproven. This is equivalent to Turing's "halting problem".
Godel was paranoid, and believed that people were trying to poison him. He only ate what his wife cooked. When she died, he stopped eating and starved himself to death.
Emil Post was an American mathematician (Columbia Ph.D., i think) who developed a proof of undecidability many years before Godel. In addition, he developed a model for computation which is similar to Turing's machine (it uses a pre-loaded queue to both hold the input string, and to hold the results of intermediate computations). He developed a proof of undeciability based upon his machine model (the "Post Correspondence Problem").
Post was a manic-depressive for most of his life. He lost an arm in an accident as a child. He had a hard time holding jobs after receiving his Ph.D. due to his depression. In the 50's he was treated for depression using Electro-Shock therapy (for interested readers... for a real shock go look up the 1948 or 1949 Nobel prize for Medicine :-). After one of his "treatments", he suffered a heart attack and died.
So, in conclusion, it's rather interesting to reflect upon the fact that the foundations of computer science comes from three individuals who suffered clear psychological problems. (And they wonder why nerds work in the dark :-)
Did Turing's affectional orientation effect his contribution to computer science? Certainly, even if only because his life was cut short by cruelty. But there are more important lessons to be learned as well. The permanent state of exception (extra-legal state of emergency, think Patriot Act) and the selection of a single group for sacrifice to the "good" of all (think not of gay marriage but of the response, several states have stripped LGBT individuals of even basic protection under civil law) exactly mirror the conditions of the democratically elected government of 1930's Germany. Several theoriticians like Giorgio Agamben have studing the juridical conditions that brought about the Nazi's Reich. Technology may be exactly the tool that prevents these things from ever happening again.
While Jacqard certainly has a major place in the history of computers, his looms can not be said to been computers in the sence we use today as they could "solve" only one problem - how to make fabrik.
No, the true inventor, if such a word can be used, of the true programable, mulitpurpose computer is one of Great Britans great geniuses from the early 1800s - Charles Babbage. In 1835 he presented a design for a programable, mechanical computer - the Analytical engine. It was to be powered by steam, and would been 30 meters long (roughtly 100') and 10 meters wide (roughtly 30'). It would use cards simular to those invented by Jacqard for input, while output was via a mecanical printer (rather simular to the printingpresses employed by newspapers), a curveplotter and a bell. Unlike modern, binary machines it would use base 10 in it's calculations.
Ada Lovelace, as someone else pointed out, was the first programmer for the analytical engine. It would have employed a launguage very simular in most respects to modern assembler, including the possibility to branch and loop.
More on his analytcal engine can be found here.
Everything in the world is controlled by a small, evil group to which, unfortunately, no one you know belongs.
Play with that a while, and you'll see why that was such a bitch to crack.
Now, come on. How does a computer scientist (for lack of a term broad enough to cover Turing) accidentally eat an apple laced with KCN? AFAIK cyanide isn't a common fixture of most computer/math research labs, and Turing as a (dabbling but competent) chemist would certainly have the common sense to not let a cyanide spill go uncleaned.
I mean, think about it. What would you do if your government arrested you and said, "Hey bub, you read too much porn and we think porn-reading is a mental illness, so we're putting you on estrogen to kill your sex drive. For life, probably, since nobody can really cure porn-reading. Oh, and you'll grow boobies. If you don't like it, you can take prison instead, where people will ass-rape you daily for being a porn-reading sicko. Have a nice day!"? (On the odd chance that you're a woman, instead imagine some mythical hormone that withers up your breasts, kills your libido, and turns you into a tomboy.) I'm not sure that I know any people, regardless of gender or sexual orientation, that wouldn't be demeaned and degraded by such a radical forced change to their identity.
Range Voting: preference intensity matters
He would have been delighted with a 1GHz / 1GB RAM machine and now it is just taken for granted.
http://stephan.sugarmotor.org
actually, that in fact does make Ada the first programmer, Babbage would be a 'systems architect' :) She was just a lowly coder...
MP3 Search Engine
Just to clarify, the Halting Problem is undecidable, not impossible.
i.e. There are many cases wherein one machine can compute whether another machine will halt.
While Troy will be noticeably lacking in Orlando Bloom-on-boy action (much to the fangirls' dismay), the upcoming movie Alexander has no such problem.
"Jared Leto has recently been cast to play the role of Hephaestion, Alexander the Great's best friend and homosexual lover in Oliver Stone's latest movie, "Alexander". The role was originally offered to Brad Pitt but was turned down due to pressure from his wife, Jennifer Aniston. Alexander is to be played by Colin Farrell."
Mmm...
Tommy Flowers in my verdict was more important to the development of the first electronic computer than Turin. Tommy built Colossus under Turin's direction during the Second World War and is often overlooked as he turned Turin's ideas into a reality.
Tommy died quite recently in comparative obscurity. After the war he tried to encourage the Post Office (whom he worked for) to develop a digitally controlled automatic telephone exchange. The Post Office (now BT) didn't understand what he was suggesting, so digital telephone exchanges were not developed until the late 1970's, some 30 years later.
It takes a genius to come up with an idea, but it takes another genius from an engineering background to turn them into something that will work.
Not quite. Kurt Godel demonstrated that mathematics (or any sufficiently powerful "formal system") was either complete (all valid statements are decidable) or inconsistent.
Turing demonstrated that -- assuming you want your system to be consistent -- there is no finite, deterministic method for determining whether a given statement in that system is decidable or not.
I.e., not only is mathematics "sullied" by these undecidable statements, but there is no way to neatly characterize them.
This was the last nail in the coffin of the Hilbert Program. (David Hilbert was a leading German mathematician of the early 20th century). Hilbert asserted that mathematics can be characterized as "an inventory of provable formulas", without possibility of inconsistency (i.e., it was not possible for 'A' and 'Not A' to be true at the same time). Godel proved that not all formulas are proveable. Turing destroyed any remaining hope by proving that there was no way cordone off the unprovable formulas.
In the annotations, which were called "Notes", Ada Lovelace described how the Analytical Engine could be programmed and gave what many consider to be the first ever computer program.
:-)
She described the Analytical Engine in the following way [6]:
The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs. It is in this that the distinction between the two engines lies. Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
She also wrote in the Notes [6]:
Again, [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine . . .
Ada Lovelace born 1815; Alan Turing born 1912
The sexy chic wins! Too bad that the Ada programming language was named after her - way to formal, I think she would have liked something kool like perl - a love^^^^necklace of perls
You want a signature? You can't handle a signature!!
Although I see no problem paying respect to an underappreciated mathematician, I'm always a little weary of how we seem to forget the contributions of others. For instance, Martin Davis in his book "Computability and Unsolvability" refers to Turing machines as a Turing-Post machine (perhaps a nod to his former undergraduate advisor). Also, Kleene invented the notion of a "primitive recursive functions". This was shown by Alonzo Church to be equally as powerful as Turing's Universal Computer. In other words, there were alot of guys involved in developing the foundations of computer science. How often do you hear of Emil Post, Stephen Kleene, and Alonzo Church? Heck, it was quite 'en vogue' to create fundemental models of computation|mathematics. I've seen models bearing the names of Markov, Godel, etc. "Computability: An Introduction to Recursive Function Theory" by Nigel Cutland has a chapter devoted to the subject.
What do you mean my sig is repetitive? What do you mean my sig is repetitive? What do you mean....