Babbage's Puzzle - Computerphile

Charles Babbage was a pioneer in the field of computer science, and his ideas about building machines to perform calculations were well ahead of his time. However, as he went about trying to bring these ideas to life, he encountered numerous challenges and criticisms from those around him.

One of the critics of Babbage's work was Thomas Hughes, who wrote a book titled "Memoranda on the Analytical Engine". In his book, Hughes criticized Babbage for not delivering on some of the promises he made about his machine. However, instead of apologizing or admitting fault, Babbage would often respond by saying that he had a better idea and would build something even more impressive. For example, when critics pointed out that the Difference Engine was not yet complete, Babbage would say that he had a new and better design for it.

Babbage's approach to dealing with criticism has been described as arrogant and dismissive. He seemed to think that anyone who disagreed with him must be mistaken or incompetent, and that he knew better. This attitude made it difficult for him to work with others or receive constructive feedback on his ideas. Despite this, Babbage was able to build a significant amount of work on the Difference Engine, and he did eventually complete several versions of the machine.

One of the most interesting aspects of Babbage's work is the fact that he developed a system of mechanical notation that he used to describe the workings of his machines. This notation, known as "mechanical notation", consisted of a series of squiggles and symbols that were used to represent different parts of the machine. While this notation was useful for describing Babbage's designs, it was not well understood by others, and many people found it difficult to work with.

Despite these challenges, Babbage continued to work on his machines, and he eventually developed a new design called the Analytical Engine. This machine was capable of performing an infinitely wide range of calculations, and it was intended to be the ultimate solution to the problem of performing complex mathematical calculations by hand. However, building the Analytical Engine proved to be much more difficult than Babbage had anticipated.

One of the main challenges with the Analytical Engine was that it required a vast number of gears and other mechanical components. While Babbage estimated that he would need around 100 times the number of cogs as the Difference Engine, he ultimately ended up requiring many more. The machine also required a complex system of control mechanisms to operate it correctly.

In addition to these technical challenges, Babbage's work on the Analytical Engine was also hindered by his own personality and management style. He had a tendency to ignore criticism and feedback from others, and he often spent large amounts of money on projects that were never completed or didn't quite work as planned. Despite this, he continued to hold out hope that one day he would be able to build the Analytical Engine and prove his ideas to be correct.

Despite Babbage's many challenges and setbacks, his legacy continues to endure today. One of the most significant developments in recent years has been the construction of a replica of the Difference Engine by Charles Doran-Sued. This machine was built using modern materials and techniques, but it retained many of the original design features that made the Difference Engine so fascinating.

In fact, Doran-Sued's work on the Difference Engine was one of the first attempts to build a Babbage machine in over 200 years. The machine was built using traditional craftsmanship techniques, and it is now on display at the Science Museum in London. While the Difference Engine is an impressive piece of engineering, it is also a reminder that many of the technological challenges that Babbage faced are still relevant today.

Doran-Sued has since been working on other Babbage-related projects, including a replica of the Analytical Engine. However, building this machine has proven to be far more difficult than expected, and it remains to be seen whether it will ever be completed. One of the main challenges with the Analytical Engine is that it requires a sophisticated system of control mechanisms in order to operate correctly.

In recent years, there have been some attempts to use 3D printing technology to build replicas of Babbage's machines. While this approach has shown promise, it also raises many technical and practical challenges. For example, building a machine like the Analytical Engine requires an enormous number of precisely fitted parts, which can be difficult to replicate using 3D printing.

Despite these challenges, some researchers are exploring the use of 3D printing technology in order to build replicas of Babbage's machines. This approach has the potential to make it easier and more affordable to build these machines, but it also requires significant advances in materials science and manufacturing techniques. As a result, while the idea of building a Babbage machine using 3D printing is fascinating, it remains to be seen whether it will ever become a practical reality.

In conclusion, Charles Babbage's legacy continues to endure today, despite many of the challenges and setbacks that he faced during his lifetime. His work on the Difference Engine and the Analytical Engine was well ahead of its time, and it has had a profound impact on the development of computer science and engineering. While some of his ideas may seem quaint or even laughable to modern audiences, they also demonstrate a remarkable prescience and vision.

As researchers continue to explore the use of Babbage machines in modern applications, we can learn much from his approach to problem-solving and innovation. Despite many setbacks and challenges, Babbage remained committed to his vision and continued to work towards it, even when others doubted him or abandoned their efforts. This level of dedication and perseverance is essential for success in any field, and it remains an inspiration to researchers and engineers today.

In addition, Babbage's legacy also highlights the importance of collaboration and teamwork in scientific research. While some critics of Babbage have argued that his work was too individualistic and self-centered, others have pointed out that he was often forced to work alone due to a lack of support or resources. However, despite these challenges, Babbage was able to build a significant amount of work on his machines, and he remains one of the most fascinating figures in the history of computer science.

Overall, Charles Babbage's legacy continues to inspire and influence researchers and engineers today. While some of his ideas may seem outdated or even absurd to modern audiences, they also demonstrate a remarkable level of vision and innovation. As we continue to explore the use of Babbage machines in modern applications, we can learn much from his approach to problem-solving and innovation, and we are reminded of the importance of collaboration and teamwork in scientific research.

"WEBVTTKind: captionsLanguage: enlet's start by drawing a diagram of what we might call the Eternal Triangle really there Charles babage but then there's this other well-known person that we need to include in our story aah Lovel and in the end among Charles babbage's many proposed designs there was one for what really is the world's first stored program toing complete computer is the analytical engine only problem is it's totally mechanical let me link these with double-headed arrows and we'll move about this diagram sort of keep it in view most of the time the sources of material really I became aware of these when I went to an ad love lace Symposium last December and yes it's taken me almost a year to digest it all and and to prepare these talks let's begin at the beginning and let's begin at the top left of my diagram some of you may recall that actually I did mention Charles babage in a video I did on why binary trying to explain why the binary system came to dominate in computers large scale automation manufacturer wasn't quite there in babbage's time and he moaned like mad at the invoices the bills he had to pay to his talking about the 1820s roughly where this story starts and saying that um he was a very celebrated mathematician but his big Forte was that he wanted to actually be able to automate the production initially of log tables now those of you at the older end of the audience May well at high school have been taught before you know hand calculators even came in that the way to do multiplication was to turn them into additions by using things called logarithms so tabulating log tables was the most enormously important thing to do I've got here the log tables I used at school and Steven wol from in his blog says that even he who was rather younger than me uh did do multiplication by adding together logarithms and then taking the so-called antilog of them when he was at High School those are four figure Precision log tables here very ancient book I bought second hand ages ago these are seven figure log table so therefore yeah you looked up logs you added the logs you turned them backwards with things called anti- logs and that was the only way for years of doing complicated multiplications so Charles babage actually did supervise the production of log tables as it were by hand before he ever got interested in mechanizing it so a lot of the early Victorian log tables got Charles babbage's name on them but it drove him mad because first of all there was the problem of computing these log tables worst of all and he saw very clearly another big problem was getting them printed the mathematicians who drew them up might well have got them perfectly right but they handed them then over to the typ Setters for printing and the typ Setters of course tried their Darice couldn't read the handwriting and made typo mistakes all through and just checking them was a pain he uh came from a sort of gentlemanly background was not fabulously wealthy but well enough off to afford a good lifestyle during his career at Cambridge he eventually became the Lucasian professor of mathematics those of you into the history of math Keen followers of number five will know that perhaps the most famous Lucasian professor was Isaac Newton himself and more recently until very recently I think where he's given up Steven Hawking the Lucasian professor of mathematics at Cambridge Charles babage was not uh in my view as illustrious as as those two I mean Newton and Gaal and people were just at a level of Genius Way Beyond most Mortals but he you know he was a perfectly creditable appointment and like his predecessor Newton oh boy was he thin skinned he couldn't take criticism and what's more he if he was around today he would have been banned from email Facebook and Twitter already he loved flaming people people who were stupid not to realize the value of what he wanted to do and even more the stupid Grant givers because he did get grants to build these engines they were so penny pinching and stupid and lacking in foresight and when people said to him look babage you're your own word enemy why do you do this he had a bright idea he would continue to Flame but he would write anonymously and of course his writing style and the fact that nobody else would rant on immediately gave the game away yes it's babage again so this was the backdrop then but he did actually draw up designs for a general very general kind of hand cranked Engine That Could do more than just lock tables from mathematical point of view it could be set up to do any mathematical problem that could be represented as a function of polom uh those you've done this stuff will know Taylor series mcclan series all this kind of stuff yes a big class of problems including producing s tables or cosign tables or lots of others so you could say that this these So-Cal difference engines of bages were if you like special purpose computers um people at the time thought they were totally wonderful but do remember their special purpose they can do calculations but only things that can be expressive for sums of polom think if you like for those who watch The Bletchley Park series a bit like programming the bomb for whatever is the settings on Enigma today that electromechanical calculator the bomb is a special purpose computer it can do wonderful things but they have to be related to the settings for enigma machines the difference engines could do wonderful things but only to things that could in the end be reduced to the method of differences so don't think these are general purpose computers they're not there you were in the 1820s which was before Precision Machinery became available driven by electricity that couldn't happen till the end of the 19th century and yet you needed not a few dozen Cog wheels that you might need for a clock you know typical clock maybe a dozen two dozen Cog Wheels highly carefully done by Precision engineers and all this kind of stuff you needed hundreds and thousands of these wretched things and so the bills from the gear cutting technicians to babage sent him into a rage he then passed these on to the government who were funding him and despite all of this only little bits of difference engines Mar one and to were built which he kept to give people demos and the yells came from the funders when are we ever going to see this with these machines realized you want more money babage you're joking we have now given you at the end of Difference Engine two first stage we've given you £17,000 babage that is enough to build two battleships two of Lord Nelson's victories could be built for £1 17,000 babage had not delivered but like every bad software supplier you've ever known bage had the perfect answer to these critics whenever they said but you haven't delivered it was always tell you what let's forget about the mark one it was not good anyway I've had a far better idea here's my set of plans for Mark 2 and of course they bought it Between Difference Engine one difference engine two maybe a little bit more money would cause it to happen um but when he started getting a whole load of flak about not being able to deliver difference engin two he had an even better idea let's forget Difference Engine two I had a far better idea from machine that will far transcend only what can be done by sums of polom and method of differences this will be able to do basically an infinitely wide range of computations not just different variants on the same thing it's wonderful I'm going to call it the analytical engine of course it will need at least 10 or 100 times the number of cogs the the ones I haven't built but never mind it would be silly to waste more money on Difference Engine 2 when I've had this great vision for the analytical engine did Difference Engine 2 ever get built yes it did in the early 1990s his drawings and his technology were absolutely spot-on and the curator one of the heroes of our story here is a guy called Doran sued he got the difference engine built at the science museum once you built one of them for the science museum which you can see after a request from Bill Gates and Nathan mold respectively of course CEO and chief technical officer of Microsoft at the time they built another Difference Engine shipped out to Microsoft headquarters in Seattle then I think sent out to the Museum of computing history in Mountain View but the last I heard is it's migrated back to Seattle whether back to Microsoft or somewhere else I don't know maybe to some other Museum so anyway it did get built um and what Doran suede proved was that the tolerances that babage set on those Gear wheels how far far the teeth were apart all that were perfectly doable and he I think it was built in the Precision workshops down the base of the science museum but basically here's the wonderful thing you know what did you need to do this properly answer a computer control GE cutting machine in order to get this early technology working which really wasn't the technology of choice for doing this kind of thing I've just been wondering if it's possible maybe to do that with 3D printing now I you probably could you know I I never thought of that wonder if people could 3D print 3D print yeah so anyway there's a change to the viewers yeah so here we are then here is somebody who could never finish things the next release would always solve it the next release would always cost 10 times more to develop than the present one which was already way over budget he did have the vision and his massive number of drawings diagrams and so on were vital and they did work however reverting back to the guru Doran sued again let's just finish with the following observations Charles babage adorned his drawings with all sorts of his own Shand it was called a mechanical notation he never wrote a user manual for it so you had to more or less work out from the circumstances what these little squiggles meant and as Doran explained to me it didn't matter too much when he was building Difference Engine 2 because that that was so close to other calculators which go all the way back to blaze Pascal in 1642 you didn't need to understand every single squiggle you just could get the idea straight away of what to do not so with the analytical engine Which is far more complicated is there going to be an attempt to rebuild the analytical engine yes and it's underway and Doran sued is in charge of a BCS specialist little group looking at this and if it ever gets built it'll be built at lley Park I think is the current idea so I asked Doran I said well if I understand rightly analytical engine got so many cogs you can't hand crank it out the question bage was going to drive it by steam I do hope if you ever build a replica he face when like then he said you can forget any idea if we ever get this thing build built and we're talking decades not single years right we are not going to drive it by steam um and also we really cannot make progress until we understand babbage's notation so that's the state of the art at the moment they're trying to understand some of the really obscure things in the analytic design which just have to be understood before they can make real progress there are other things in here called variable cards those really were to stipulate where things might be stored you might have a read a number card but you would thenlet's start by drawing a diagram of what we might call the Eternal Triangle really there Charles babage but then there's this other well-known person that we need to include in our story aah Lovel and in the end among Charles babbage's many proposed designs there was one for what really is the world's first stored program toing complete computer is the analytical engine only problem is it's totally mechanical let me link these with double-headed arrows and we'll move about this diagram sort of keep it in view most of the time the sources of material really I became aware of these when I went to an ad love lace Symposium last December and yes it's taken me almost a year to digest it all and and to prepare these talks let's begin at the beginning and let's begin at the top left of my diagram some of you may recall that actually I did mention Charles babage in a video I did on why binary trying to explain why the binary system came to dominate in computers large scale automation manufacturer wasn't quite there in babbage's time and he moaned like mad at the invoices the bills he had to pay to his talking about the 1820s roughly where this story starts and saying that um he was a very celebrated mathematician but his big Forte was that he wanted to actually be able to automate the production initially of log tables now those of you at the older end of the audience May well at high school have been taught before you know hand calculators even came in that the way to do multiplication was to turn them into additions by using things called logarithms so tabulating log tables was the most enormously important thing to do I've got here the log tables I used at school and Steven wol from in his blog says that even he who was rather younger than me uh did do multiplication by adding together logarithms and then taking the so-called antilog of them when he was at High School those are four figure Precision log tables here very ancient book I bought second hand ages ago these are seven figure log table so therefore yeah you looked up logs you added the logs you turned them backwards with things called anti- logs and that was the only way for years of doing complicated multiplications so Charles babage actually did supervise the production of log tables as it were by hand before he ever got interested in mechanizing it so a lot of the early Victorian log tables got Charles babbage's name on them but it drove him mad because first of all there was the problem of computing these log tables worst of all and he saw very clearly another big problem was getting them printed the mathematicians who drew them up might well have got them perfectly right but they handed them then over to the typ Setters for printing and the typ Setters of course tried their Darice couldn't read the handwriting and made typo mistakes all through and just checking them was a pain he uh came from a sort of gentlemanly background was not fabulously wealthy but well enough off to afford a good lifestyle during his career at Cambridge he eventually became the Lucasian professor of mathematics those of you into the history of math Keen followers of number five will know that perhaps the most famous Lucasian professor was Isaac Newton himself and more recently until very recently I think where he's given up Steven Hawking the Lucasian professor of mathematics at Cambridge Charles babage was not uh in my view as illustrious as as those two I mean Newton and Gaal and people were just at a level of Genius Way Beyond most Mortals but he you know he was a perfectly creditable appointment and like his predecessor Newton oh boy was he thin skinned he couldn't take criticism and what's more he if he was around today he would have been banned from email Facebook and Twitter already he loved flaming people people who were stupid not to realize the value of what he wanted to do and even more the stupid Grant givers because he did get grants to build these engines they were so penny pinching and stupid and lacking in foresight and when people said to him look babage you're your own word enemy why do you do this he had a bright idea he would continue to Flame but he would write anonymously and of course his writing style and the fact that nobody else would rant on immediately gave the game away yes it's babage again so this was the backdrop then but he did actually draw up designs for a general very general kind of hand cranked Engine That Could do more than just lock tables from mathematical point of view it could be set up to do any mathematical problem that could be represented as a function of polom uh those you've done this stuff will know Taylor series mcclan series all this kind of stuff yes a big class of problems including producing s tables or cosign tables or lots of others so you could say that this these So-Cal difference engines of bages were if you like special purpose computers um people at the time thought they were totally wonderful but do remember their special purpose they can do calculations but only things that can be expressive for sums of polom think if you like for those who watch The Bletchley Park series a bit like programming the bomb for whatever is the settings on Enigma today that electromechanical calculator the bomb is a special purpose computer it can do wonderful things but they have to be related to the settings for enigma machines the difference engines could do wonderful things but only to things that could in the end be reduced to the method of differences so don't think these are general purpose computers they're not there you were in the 1820s which was before Precision Machinery became available driven by electricity that couldn't happen till the end of the 19th century and yet you needed not a few dozen Cog wheels that you might need for a clock you know typical clock maybe a dozen two dozen Cog Wheels highly carefully done by Precision engineers and all this kind of stuff you needed hundreds and thousands of these wretched things and so the bills from the gear cutting technicians to babage sent him into a rage he then passed these on to the government who were funding him and despite all of this only little bits of difference engines Mar one and to were built which he kept to give people demos and the yells came from the funders when are we ever going to see this with these machines realized you want more money babage you're joking we have now given you at the end of Difference Engine two first stage we've given you £17,000 babage that is enough to build two battleships two of Lord Nelson's victories could be built for £1 17,000 babage had not delivered but like every bad software supplier you've ever known bage had the perfect answer to these critics whenever they said but you haven't delivered it was always tell you what let's forget about the mark one it was not good anyway I've had a far better idea here's my set of plans for Mark 2 and of course they bought it Between Difference Engine one difference engine two maybe a little bit more money would cause it to happen um but when he started getting a whole load of flak about not being able to deliver difference engin two he had an even better idea let's forget Difference Engine two I had a far better idea from machine that will far transcend only what can be done by sums of polom and method of differences this will be able to do basically an infinitely wide range of computations not just different variants on the same thing it's wonderful I'm going to call it the analytical engine of course it will need at least 10 or 100 times the number of cogs the the ones I haven't built but never mind it would be silly to waste more money on Difference Engine 2 when I've had this great vision for the analytical engine did Difference Engine 2 ever get built yes it did in the early 1990s his drawings and his technology were absolutely spot-on and the curator one of the heroes of our story here is a guy called Doran sued he got the difference engine built at the science museum once you built one of them for the science museum which you can see after a request from Bill Gates and Nathan mold respectively of course CEO and chief technical officer of Microsoft at the time they built another Difference Engine shipped out to Microsoft headquarters in Seattle then I think sent out to the Museum of computing history in Mountain View but the last I heard is it's migrated back to Seattle whether back to Microsoft or somewhere else I don't know maybe to some other Museum so anyway it did get built um and what Doran suede proved was that the tolerances that babage set on those Gear wheels how far far the teeth were apart all that were perfectly doable and he I think it was built in the Precision workshops down the base of the science museum but basically here's the wonderful thing you know what did you need to do this properly answer a computer control GE cutting machine in order to get this early technology working which really wasn't the technology of choice for doing this kind of thing I've just been wondering if it's possible maybe to do that with 3D printing now I you probably could you know I I never thought of that wonder if people could 3D print 3D print yeah so anyway there's a change to the viewers yeah so here we are then here is somebody who could never finish things the next release would always solve it the next release would always cost 10 times more to develop than the present one which was already way over budget he did have the vision and his massive number of drawings diagrams and so on were vital and they did work however reverting back to the guru Doran sued again let's just finish with the following observations Charles babage adorned his drawings with all sorts of his own Shand it was called a mechanical notation he never wrote a user manual for it so you had to more or less work out from the circumstances what these little squiggles meant and as Doran explained to me it didn't matter too much when he was building Difference Engine 2 because that that was so close to other calculators which go all the way back to blaze Pascal in 1642 you didn't need to understand every single squiggle you just could get the idea straight away of what to do not so with the analytical engine Which is far more complicated is there going to be an attempt to rebuild the analytical engine yes and it's underway and Doran sued is in charge of a BCS specialist little group looking at this and if it ever gets built it'll be built at lley Park I think is the current idea so I asked Doran I said well if I understand rightly analytical engine got so many cogs you can't hand crank it out the question bage was going to drive it by steam I do hope if you ever build a replica he face when like then he said you can forget any idea if we ever get this thing build built and we're talking decades not single years right we are not going to drive it by steam um and also we really cannot make progress until we understand babbage's notation so that's the state of the art at the moment they're trying to understand some of the really obscure things in the analytic design which just have to be understood before they can make real progress there are other things in here called variable cards those really were to stipulate where things might be stored you might have a read a number card but you would then\n"