I (Ed Thelen) continued with word-by-word examination/correction, correcting as many technical terms, historical names and the like as I could in a "reasonable" time.

In July 2005, Mark Brader of Toronto sent a list of 32 suggested corrections. These have been incorporated into the text.

Doron Swade Stanford Talk - Babbage
[Dr. Swade was introduced by Len Schustek, Computer History Museum]

Thanks very much.

I understand from the orientation from the people present that they may be more interested in the technicalities of the engine than in the actual historical context of Babbage's efforts. I'm afraid there's some medicine that I'm going to have to administer and that is some history. Because if there is a message about Babbage's efforts at all, it's something that might be familiar to you but is perhaps worth repeating.

And that's that the face of innovation depends on issues that are other than the technical merits of the invention. And if there is a lesson from Babbage at all, it has to do with that. So I'm afraid the unpleasant aspects of medicine and history need to be administered because, actually, why his engines are the way they are and not otherwise and that is unfinished, is inseparable from the context of his time -- who he was, who he knew, his personality, the vendettas, the personal conflicts -- were actually an inseparable part of the story, why it is he failed.

In other words, there is no technological determinist specific answers as to why he failed. What we'll do in the course of the afternoon is to actually explore some of those issues. So much for preliminaries. So I apologize for the history, and I will continue to do so, but it's a necessary element in the story.

Babbage is celebrated as the great ancestral figure in the history of computing, and almost every lecture about Babbage starts with a statement of that kind. He's famous equally for two things -- for the genius of inventions, and his failure to build any of them. His name is inseparable from failure.

Babbage and failure, genius and invention are all sort of one package. It's one scrambled egg. He committed everything, he staked everything -- his reputation, his self-esteem, civil honors, money -- on one single gamble. And that is he said, "Judge me by my engines". And he failed to build them. He failed to communicate a vision he had. He failed to communicate a vision of what automatic computation he was capable of. He failed to communicate it to his peers. He was deeply embittered by absence of recognition, the failure of civil honors.

And you will see we got some inkling in the process of building this machine as to just how extreme that disappointment must have been because it's only through the process of building the machine and actually witnessing it -- and you'll have an opportunity of seeing the video -- that you begin to understand the frustration and the despair he must have felt in his inability actually to speak to anyone about what it is he was doing.

He was unable to communicate this vision, and therefore he was the first inhabitant of a completely foreign country. The reasons for his failure -- every book on the history of computing will have a chapter or a passage on Babbage. Almost without exception, you will read the same thing. Babbage failed because of limitations of Victorian machine tool technology. Almost without exception that is a received perception.

When people go further, they say -- and often they don't. There's just the -- either the implication or the explicit suggestion -- the reason the limitations of Victorian machine tool technology entails that he could not make parts with sufficient precision that when the machine was built it would work. So people either implied that or they specifically state it.

Now, there's something very comforting in this thesis of limitations of technology. From the high ground of microelectronics, it's easy to patronize Babbage. Babbage had to wait for us, the children of the Silicon age to rescue him from his world of cogs and levers and wheels. E.B. Thompson, the historian warned -- you see, he warned against the enormous condescension of posterity, this tendency actually to regard all that was past as somehow inferior. And I think that through the -- so credible as this thesis is and attractive as it is to us, he failed limitations of technology.

It's like the causes in science. It's a single cause has a direct effect of failure. Credible as this thesis is and attractive as it is to us and as self congratulative as it is to us, Silicon is in fact is the legacy of the life of Babbage. The fact of it is there is absolutely no contemporary evidence that limitations of technology was in fact a limiting factor if limitations of technology is equated with limitations of precision. Measurements done on contemporary machines show that they were capable of the repeatability of one and a half thousandths of an inch. That is to say, he gave Joseph Clement, the engineer, a part of an intricate, they could make other parts within one half thousandths of an inch. The issue is, is one half thousandth of an inch enough?

That's a highly precise thing. This was England, the workshop of the world. And what we were looking into one of the issues we had an opportunity to evaluate is the extent to which precision was or wasn't an issue. The fact is that the circumstances surrounding the collapse of Babbage's major efforts to build his engine. He conceived of the engine in 1821, and he spent over a decade of design and development building this machine.

The circumstances surrounding the collapse of his efforts in 1833 do not owe anything implicitly or explicitly to limitations of technology. The circumstance are complex -- he had a dispute with his engineer, Joseph Clement, over compensation for moving the workshop from Lambeth to a special fire proof workshop on the ground of Babbage's house. So the circumstance are complex -- so when you remove the technological *? * When you say, okay, if it is not the limitations of engineering, what was it? You come up with a very, very complex rich historical story. And there are many elements to this story.

One of them is personal vendettas that they in fact were advising the government -- George Airy, the Royal Astronomer, persistently and consistently was opposed and hostile to the utility of these engines.

In other words, experts would disagree whether these engines had any fundamental utility. Other experts disagreed *, Sweeden said why do you need engines that could calculate 30 or 50 decimal places? One of his machines has double precision arithmetic, multiplying a 50 digit number by another 50 digit number, a hundred-digit result. Why did you need precision of this kind when you could only measure to three or four digits of accuracy? So experts would disagree about fundamental utilities. It wasn't as though there was a universally accepted problem to which there was a solution that was needed.

Personal vendettas.
Babbage was convinced that Airy's hostile advocacy of his engines and his advice to government that the engines were worthless was based on a personal hostility of jealousy, and a particular court case court case in which Babbage acted as an expert witness against the party that was being advised by Airy.

And Babbage makes these allegations public, the specifics of it don't matter. The point about it is that there are all these broad and peculiar factors involving personalities, vested interests, that affected the fate of the engines other than the specific merits of the technology.

Runaway costs.
There was little credible progress. After 11 years he manufactured about 10,000 parts of the 25,000 needed. He had nothing to show. The government invested large sums of money. This money was unmanaged. There was no ceiling. There was no budget. There was no delivery date. There were no staging posts. There were no phrasing of stage payments. He was just wonderfully muddled and terribly English. [some laughter]

It's inconceivable in this day and age with this obsession about cost efficiency and all the other management gobbeldy gook that this gentlemen's arrangement about funding a project to completion on the good-faith basis could ever come about. But it did.

So the fact of the matter is that the limitations of technology -- attractive as that thesis is to us -- is not a specific feature that feature in the contemporary circumstances that resulted in the collapse of this work. Clement downed tools after complaining about compensation, and the work was never resumed in 1833, after about 10, 11 years of design and development.

The question that becomes very tantalizing to historians is did the complex circumstances surrounding the collapse of the project to build the machine mask the technical or logical possibility - feasibility, of this machine? In other words, had people been distracted by either -- the question is: If people accepted that limitation that technology was the reason and it turns out it is not the reason, did circumstances surrounding the collapse mask the fact that these engines could not have been built? In short, the question is: Could the machines have been built in Babbage's day? And, secondly, if they had been built, would they have worked? And that is the issue we actually set out to address.

I promised that you would have some medicine before we get onto the technology -- onto the actual specifics of the machine. And so because the fate of the engine is inseparable from the context of Babbage's times, I'll just give you a quick thumbnail sketch of Babbage's his life. Who was he? What was the context? What were the circumstances? Why did he wish to build these machines? It's very quick, and it's sort of -- without doing violence to the riches of any man's life -- just sort of caricature a thumbnail sketch of the man's life if you like.

And in order to qualify -- students were ranked according to ability by a preliminary set of prestigious called The Acts in which you have to defend, sometimes in Latin, a proposition against opponents. And he chose to defend the thesis that God was an ethereal agent. And this was regarded as blasphemous, and he was disqualified. He was thrown out.

He didn't leave Cambridge, but he qualified without honors. The reason I mention that tale is first, between these students, they ought to be aware that principles sometimes have consequences that are politically damaging to their futures. This stopped any prospect -- I'm not suggesting they compromise but they ought to be aware of the consequences. This stopped any prospect Babbage having an academic career. He couldn't get a fellowship, he left with an ordinary degree. He was a top mathematician, so you know he was going for the degree.

He later became Lucasian professor of mathematics, so it wasn't a disastrous thing for him in career terms. The point about it is that it set a pattern because that was not the only time Babbage damaged his personal political interests by public protest and sometimes ill considered -- and it's not as though he was alone in the radical views he held. John Herschel, George Valerie held similar views. One of the views was that they resented and resisted the notion that education was dominated by the church, university education was dominated by the church.

None of them wanted to take orders. In order to take a fellowship, you had to become a member of the church, take orders. Babbage was hostile to this but so was Airy and so was Herschel. Both became hugely successful contemporaries in science. I mean, Herschel was a model ambassador for science. They shared Babbage's view, but they were slightly more prudent in their public expression.

And this pattern that Babbage set repeated later far more damagingly and actually affected the fate of the engine. So here I come again with this horrible medicine looping back. We cannot separate the fate of these engines from who Babbage was and this proclivity he has for public protest. Most of these writings are written really more to protest than to persuade. He was indignant, he was highly principled, uncompromising in principle.

And if there is a lesson there, it is that there is a personal cost to high principle, especially if you're politically inept. [Much laughter]

Golly, at this rate, we're never going to get out of here. So that's back in 1813. Georgiana, his wife, married in 1814 just after he graduated in defiance of his father he ran away and got married. He didn't get along with his father at all. Georgiana tragically died in 1827, and Babbage was quite bereft, never really recovered, never remarried.

[image]
This is Babbage Lucasian professor of mathematics. So this is an engraving by Roaf. Babbage occupied the Lucasian professorship from 1828 to 1839. This is around 1830, 32. And it's a highly idealized -- it doesn't look like that you'll see from the images I'll show you presently.

And the point about it is that he said that he was deeply resentful of the fact that his peers did not acknowledge him. He was not recognized for what he did. It's perfectly clear he had a very clear conviction he had discovered something fundamental about the machine behavior, the stepwise algorithmic procedure. He knew he had seen something. And he was unable to communicate it with others. He was deeply resentful of the fact that this was not acknowledged. And he said of his appointment of Lucasian professor that this was the only honor his country had bestowed upon him. And he said this without bitterness. He was deeply gratified for the chair. He didn't do anything, he never gave any lectures while at Cambridge. That was a loophole in the regulations, which have since been closed. [Laughter]

In 1830 he published a critique of science in England. This was an absolutely vicious, vituperous, sarcastic attack on the royal society on the side of establishment. This was the same establishment that was to support him three times in securing government funding for his engines. So he had a fantastic habit alienating the people of whose support he needed. He somehow though that being right entitled him to be rude.

He personally attacked the officers of the society, accused them of fiddling the minutes, of misappropriating -- of rigging the rules by which awards were given. He accused Davey of personally profiting from publications. It was a thoroughly indiscreet -- it was not settled over brandy and cigars as a gentlemen would. This was a public broadside, a broadside of outrage and indignation about the deficiencies of the society. So, again, we go back to the resonance of what happened in Cambridge. So that's -- now in 1832 -- 1830 he published the client of science around the time of this thing.

1832
He published the "Economy of Machinery Manufactures". This was an absolutely ground breaking book in political economy and one of his most successful books. He was established as an elder statesman of the industrial movement. It's an extraordinary volume and did much as it were to repair the damage that he had done with the scientific establishment. After the publication of decline he never -- he was a member of the royal society from 1816 -- after that, he never went to the royal society, never attended any meetings. In a sense he excluded himself from the power base upon which science was operating.

[image of Babbage] That's Babbage. And that's an oil painting by Samuel Lawrence of the national portrait gallery. That's Babbage in his early 50's, about 1843. This is Babbage as a man of science in letters esteemed by his peers. He was very well known. He was a celebrity. He was well published. He published half a dozen very credible, not acclaimed but well regarded, mathematical papers. He published in all six monographs and 86 papers miscellaneous scientific and mathematical.

So that's Babbage if you like at his height, very credible figure, socialite of the London society, and esteemed by his peers. That's very intriguing. That's * by *Clowday and why it's significant for us is because this was taken at the time he was designing difference engine II, which is the machine we'll spend if there is any time left on. And there you can see he's still sort of combative, but he's weary. He's been through a lot, but he's still up there designing. He had by that time almost given up the prospect of building an engine, but he was carrying on designing them. So that's about 1849, 1850. So he's in his early fifties there.

Okay. That brief, thumbnail sketch sort of traces Babbage from an idealistic student into an esteemed man of science into a venerable grump. And that is a very brief account of his life. His father died 1827. 1827 was a staggeringly tragic personal tragic year for him. His father, two of his children and his wife died all in the same year. He effectively had a breakdown -- I don't think they used those words and know quite what the word means, but he went on a continental tour for over a year with one of his workmen and stopped working the engines.

He inherited a hundred thousand pounds which was a staggering amount of money in those days. If you think that -- a steam engine by Stephenson shipped to the States in 1830, the * cost off-shelf, brand new steam locomotive cost 784,000 shillings. He inherited a hundred thousand pounds in modern day terms you here to multiply that out 30 to 150. So he was sort of near a millionaire. He was well able to afford to fund the projects of his engines from his own pocket. To a large extent, he did bankroll the projects despite government money.

Okay. That's enough of Babbage. The medicine's been taken. Thank you for being so gracious. And I hope that it has the appropriate anxiety effect or be cured of your obsession of technology. I meant that facetiously.

Okay. Why did Babbage design engines? What were they for? What was the whole movement about? That's a page of mathematical tables from *Vega -- a lot of tables from *Vega, 1794, typical of mathematical tables at the time. And the point is how were these produced?

These tables are produced by hand. I mean, clearly being typeset, but there were four stages in the process of production of mathematical tables. Mathematical tables are highly important. There were no devices that you could produce -- do instant calculation at the time and place of need. So almost anyone in need of tables -- and that's insurers, journeymen, tradesmen, scientists, engineers -- whatever they needed to do any calculation beyond anything trivial, including * for fractions, multiples, squares, cubes and all that. Absolutely relied to put them into immediate communications paper and print. And it's perhaps necessary to remind ourselves of that.

There was one particular application of tables which was absolutely paramount and that was astronomical navigation. Ships were reliant on tables for determining their position at sea, capital and life was at risk, England was a major seafaring nation, the navy and merchant navy depended on accurate navigation. Shipwrecks were a very serious fear, and these were reported with graphic detail in public media, illustrated London news, for instance. And the number of gismos and gadgets to prolong life at sea off the ship is astonishing. It's like America has endless devices for keeping people vertical, for bringing fish biting you, for doing all sorts of things. And clearly there was a lot of public fear. So there was a deep insecurity about shipwrecks.

Now, the few court martials of ships going aground that I've looked at -- none of them specifically incriminate inaccuracy of tables. It's always to do with the practice of navigation or it's -- the fact was that there was this deep fear. So the fear was that the tables were riddled with errors. And the reason they were riddled with errors was -- well, * and they look at errata sheets. When errors were found, they printed errata sheets and you could tell by analyzing the errata sheets just how error riddled the tables were. And in a random of selection of 140 volumes of tables, * account 3,700 errors printed in errata sheets. He hoots with uncontainable glee to discover that some of the errata sheets had error themselves. And he's utterly uncontainable when it turns out that the second errata sheet also had errors. * errata, errata, errata.

It was quite a credible position to hold that these things were riddled with errors. Why they were riddled with errors? Because of the method in which they were produced. Tables were calculated by hand by people who were called computers. It's known people were computers, they weren't machines. Just as typewriters were people rather than machines.

And so firstly there was the risk of human error, the fallibility. We end up very bad at doing accurate calculations especially repeated, tedious things like repeated addition. From differences which is a technique for generating these things.

The second thing is you've got to write the answers down in the table to give to a printer. So there was a possible error of transcription, writing the results down.

Third source of error was typesetting. Each of these digits is represented by loose type, by compositor. It's possible to put them upside down, they fall out, you put them in the back around. There is no contextual thing to indicate -- it's no more likely that one number is a six or a seven. It's not like a word where somebody could recognize an error. So there's no contextual information to indicate to the compositor that it's wrong. So error of calculation, error of transcription, error of typesetting.

Fourthly proofreading. How do you know the stuff is correct? And anyone who's seen it, has seen the table some idea just -- I mean, you might say okay it's not so bad doing that. But you give some indication of (knock, knock) that's the volume that that page came out of.

What confidence could you conceivably have if two people tried to check tables of that kind? That's one volume of just logarithms and trig functions. So that's the problem. The problem was error in tables and the solution for Babbage was mechanization, engines, machines. So that's the entry point, if you like. And the genesis episode.

How did this happen? Did it come in a flash, you know, bolt of lightning, flash of thunder? What? Something like that. He's sitting with John Herschel, his good buddy, in 1821, checking tables from the astronomical society. And what you typically did you gave the same set of calculations to two separate computers who, without collaboration, computed the results separately, and you compared them. If they were the same, doesn't mean they were correct because there are a few instances that two people make the same mistake. You had a high degree of confidence that they were correct. And for Herschel and Babbage sitting there in 1821, the summer of 1821, in the rooms of the astronomical society, checking the two results from the sets of computers. And they were just amazed by the discrepancies. And Babbage, as it were, clasps his hand to his head and says, "I wish to God these calculations had been executed by steam."

Okay. That was it. That was the rest of his life. That phrase dominated the rest of his life. He spent the rest of his life in one way or another very intensively trying to calculate -- to produce mechanized * way of printing mathematical tables. Now steam was a method for mechanization. It wasn't that these things would be solely driven by steam. No where else in any of his writing have I found reference any of these machines being driven by steam engine.

So steam was a method for mechanization. It was the middle of the industrial revolution, England was the workshop of the world, and so steam was metaphorical in the literal uses of steam. So that was the start. He then became obsessed. He became so obsessed by these things that he actually became ill. And he was advised by his medical friend to stop thinking about engines, and he didn't.

Right. What was the state of play at the time? Just how revolutionary is his conception? Just how revolutionary is his conception of these things? Well, it's probably well known that the earliest known mechanical -- mechanical calculation received a huge emphasis in the 17th Century. Schickard in 1623 made his calculating clock, didn't survive. Earliest surviving calculator is Pascal's pascaline, 1642. Sorry. That's an arithmometer. Where's the pascaline? No. Sorry. It's not there. The point about the pascaline and likenesses -- and * calculator, 17th century. Is that that they are or basically ornate curiosity.

That's a calculator by Müller, 1784 to give you some indication it's based on likenesses of step wheel. And these were ornate curiosities. They were totally unsuited for routine or regular use. That's a *universal calculator, does addition, multiplication, does multiplication and repeat addition and so on. These were objects of course quite a stir. They were paraded through the salons of the elite, Aristocracies, stimulated huge discussions about mentalism and machines. But they were not work horses for daily calculation.

The arithmometer which we have there was the first commercially successful machine. It wasn't commercially successful much later. It was produced in 1820 from **Mr. Colmar. They were used in vast numbers, made by the tens of thousands later in the century, took many, many decades before they actually caught on. So they were introduced this 1820 's first commercially successful calculator, they were decades of development before they actually ironed the bugs out of them. So 1820 just before the point at which Babbage conceived this conception -- had this great revelation that the onset this invocation of steam to solve the problem of mathematical tables, this was -- and that's a later one. A cruder version of this was it. And the point about this is that it's manual. It relies on the continuous informed intervention of the operator to achieve useful results. You have to use push the sliders, you have to turn the handle a fixed number of times, you have to lift the carriage, multiply by tens, you lift the carriage, shift one indicator over. You could make a mistake and shift it two.

You had to write the results down. Transcription errors. So there's possibly operated and it's a manual calculator relies in formed intervention for getting useful results out of it. So that's the big first step, was automation, to embody the mathematical principal into the machine. And Babbage conceived this difference engine number one, his first difference engine, which is 1821. And that's what ultimately -- (inaudible) He spent 10, 11 years on design and development of this machine. That was one seventh of it. It's all that was assembled.

By 1832 he was losing credibility, he had nothing to show. He asked his engineer, Joseph Clement, to assemble something from the parts and this is what resulted. It's probably the most celebrated icon in the prehistory of computing. It has that position for several reasons. Firstly, it's a methodological standard. If you want to know how precisely you could machine parts, repeatability, accuracy, any kind of precision manufacture, you do measurements from this machine. It was made by Joseph Clement to the highest standards available at the time. So it's a methodological standard so it's a (inaudible) and historically (inaudible).

It is also the first automatic calculator that survived. There's a handle on top. You crank the handle, you set the initial values, you crank the handle, you get the results. Every time this machine goes through one cycle it produces the next value of the table by method of finite differences which I assume is completely familiar to you. And I think I've got a small trivial example to show you just in case it isn't. All it does is by repeated addition evaluate the polynomials, and we'll see how it does that. The point about it is that it's the first machine to successfully embody mathematical rule and mechanism.

The operator does not need to understand the mathematical principle in which it's based or how the machine works in order to get useful results. You exert physical energy and you achieve results which up to that point in time, you could only arrive at by mental effort, by thinking. And the implications of this were not lost by Babbage and his contemporaries. They called it the thinking machine. And the marvelous pulp and fiber of the brain had been substituted by brass and iron. He, Babbage, had taught wheel work to think. This was so said, **Harry Buxton, a junior colleague of Babbage's. And so the implications of this were not lost, I mean, the machine intelligence was not lost on Babbage's contemporaries. So that's difference engine number one.

Question from audience member -- inaudible. So high. About two-feet high. The full machine would be something like 11 feet high, 8-foot deep, and weighed many, many tons. Question from audience member -- inaudible. Many tons. We don't know. I can tell you that difference two [engine] specifically because we weighed it. And this would be vastly heavier. The difference two weighs five tons. And this was about three times the weight. And this is three times more parts. So we're talking about 10 to 15-tons when estimated.

Question from audience member: I guess this was the first technician for artificial intelligence? Yes, I would say that's one of the original artificial intelligence artifacts, yes.

Question from audience member: What was the effect of (inaudible - laughter) -- We've redefined them. We've defined it as the "Crick." And I'll come to the Crick, and I'll tell you exactly what a Crick is. Crick is the name of the engineer who cranked the handle. We know exactly how many cricks these machines can run. There is a conversion factor.

So that's difference engine one. I don't think there's time. There's a wonderful -- I believe it's history so it's probably unpleasant for you. This machine featured in the development of the history of ideas in a way that is not specifically * technology but it had a huge impact. Babbage used it to demonstrate his theory of miracles -- and I know this is dangerous territory, especially in an environment like this. Religion was under increasing siege from science. Geology started producing in the 1830's, geology started producing evidence that the earth was older than theologists had actually liked to believe. So there were rifts and cracks appearing in the edifice of religion. And the problem is how do you reconcile rational science with theism?

How can you both be a scientist and believe in God? And Babbage used this machine in a very ingenious way, to try and reconcile those two positions. And you see the problem was with miracles, you see miracles are very good for religion. They have fantastic PR. Because you don't need -- science espouses the notion of physical cause. Right? If God causes everything, it isn't a problem because that's the explanation. Science says there's physical cause. The problem is miracles manifest the stress *(inaudible) science because they are events without physical cause.

So on this science addressed the issue of miracles, it was indeed trouble. And if you like doing this wrestling match with an explanatory receptor, they were competing with each other for the accepted view of the world. And Babbage had an absolutely ingenious way of showing that miracles -- the discontinuities in nature were not necessarily manifestations of the mind intervention. What he did was he set -- okay.

Babbage was a social liar. If you wanted to know what was going on in science, in literature, art religion, you went to Babbage swaray center. They were the social events of the week. Everyone was there, Darwin, McGreedy, anyone you can think of was there. And social intellectual League of London, the English Society, was at Babbage's. And Babbage used this thing as a party trick. It sat on his mantle piece and he cranked the handle. What he did was he set the machine up to do something very trivial like increment by two. So every time he turned the handle, a number moved to two. And he'd do this and very quickly people would become pretty inured to the expectation of incrementing by two. So he'd crank the handle, and he'd go by two, four, six, eight. And he'd ask, you know, what do you think the next result would be, and it would be there and by God. And he'd do this endlessly. He'd do this a hundred times. People began to get bored it was rather trivial. And suddenly, without any intervention on his account at all, the machine would form a discontinuity and suddenly he had 117.

And he would turn to his people and say, "You see, for you, the observers, that was a violation of law. It was a violation of the law of incrementing by two. But for me, the programmer, I programmed that machine. And after 150 integrations, it would do something discontinuous. And for me, the programmer, that is not a violation of law, but a manifestation of higher law, known to me but not to you. By analogy, miracles in nature, discontinuities in nature, are not violations of law, they're manifestations of higher law. God's law is yet unknown."

So for Babbage, God was a programmer, and those in the software industry may be very flattered to know that. Okay.

I apologize for the insulting triviality of this next example.

So the question is what special -- why is the difference principle so important? The answer is you can evaluate polynomials which ordinarily in the evaluation of the various coefficients, constants -- of the various coefficients, of the various powers, of the unknown. Ordinarily you need multiplication, division, subtraction, arithmetic -- and division to -- multiplication, subtraction, and addition to find the value of the coefficient of the multiplies. Now the point about -- now, doing direct multiplication and division in mechanics is monumentally difficult. It's something Babbage accomplished much later. The beauty of the method of finite differences is it allows you to find the value and tabulate values of polynomials using repeated addition. And this trivial example -- and I apologize again for the triviality.

Okay. Counting numbers. Oh, boy. X -- X squared is the familiar table. Now assume that we've generated up to 36. We want to generate the table of squares. That's the object. The exercise -- so I've got 1, 4, 9, 6, and 31. Say we've got up to 36. Well, I mean, I apologize if all of this is familiar, but -- All right. You take successive difference. 4 minus 1 is 3, 9 minus 4 is 5 and so on, and so on. The first column is the first difference. Second column predictably is constant 2 it's the second order of polynomials.

By working backwards, you add 2 to 11, 11 to 13, 13 to 13 -- you get 49. You get the next element of the table having performed no multiplication. Okay. That's a trick. Repeated addition you can find the polynomial. Trivial example. It's X squared, but the point is that Babbage's machines and the one we built calculates to seven orders of difference and 30 decimal places. Right? So each of these digits is 30 to 31 figures long and there's seven orders of difference. So you can calculate so that the difference in the two, for example, were designed to calculate and tabulate a seventh order of -- any seventh order polynomial, positive and negative coefficients, X plus or minus, any seventh order polynomial with all terms present to 30, 31 decimal figures of accuracy.

So that was the ambition, and that's no slouch even by modern standards. These were fixed point machines, but even a modern calculator is -- overpowers any, all these other things monumentally, you still can't get 31 digits of significant figures out of it.

So we shouldn't be back to E.B. Thompson's enormous condescension of (**). This was some no small accomplishment to conceive of an engine with that capacity. They didn't build them, of course. But we remedied that.

Okay. These are decimal digital machines. They use the digits in order to turn (***). He considered all numbers including binary. He considered duodecimal, X divisible, 8 bases of 5 -- he considered all kinds of bases. He chose this for reasons we can discuss presently. And the reason for this slide is really to show the intense -- why it was digital.

Okay. He only acknowledges discrete states, whole numbers. So wheel -- okay. Numbers are represented by figure wheels with engraved things on it and teeth on them. And a wheel between 2 and 3 does not represent 2.5. It represents an invalid state. The point about it, these are not bi-stables. They're not meta-stable things that flip automatically once a threshold is exceeded.

These are analog devices. The reason they're digital is the control system, and here's an example. You can see this roller tries to sandwich itself between two half-moons as it goes around. That is how it digitized. The roller locks and fixes it. Because it's a roll-on rather than a wedge, it doesn't flip over once it actually goes beyond a threshold. But you can begin to see why it's digital is because that is what actually makes it invalid. If that is obstructed by one of those half moons sitting on the apex, the machine jams. So the machine jamming is a form of error correction, and it's a specific part of the control mechanism. The discreetization of the state is through its controller, not inherent lack of stability as you wouldn't be saying in modern threshold, bi-stable, whatever. That's 1822.

Okay Babbage is not famous because of his difference engines. He's famous because he was the pioneer of computing. His difference engines are calculators. You put numbers in, it crunches numbers the only way it knows how is by repeated addition. So it takes a column and adds it to another column and so on. That's a calculator. It has specific functions. However elaborate, it can only do what it's programmed to do.

The analytical engine is why he really has his claim to fame as the first binary computing. And the analytical engine is simply stunning and shocking. I'll put that up there. It's not the analytical engine. It's the piece of the minimum analytical engine under construction at the time of his death.

Small, experimental model. The analytical engine, in its minimum configuration would have been 20 to 30 foot long, 15-foot high, 8-foot in diameter. It would have been impossible to turn by hand. He talks about the minimum configuration would have a hundred variables. He talks about variables. What he means is registers. A variable is a register which can take a different value. And the minimum configuration would be a hundred variables. That would give you a machine the size of a locomotive, 20 feet, 30 feet long. He talks about machines with a thousand variables and 50 digit registers with double precision arithmetic with a hundred digit results.

So we can see his machines just in conception and physical size are monumental leap, a quantum leap, in conception, in logical conception in relation to what the -- he was like a jack in the box. He pops up in history, as it were, without a clue. So the analytical engine, if I can just stun you with the respect in which it incorporates and embodies and almost -- I ought to be careful here I've given his present -- it embodies almost every single logical feature of the modern digital electronic computer. Hah. Right.

And I challenge you to -- [ Inaudible comments from the audience. ] I'll now list some of the features. Separation of store and mill. The memory and the center process is separated, physically separated -- and realize for the same reasons that the modern computer engineers as to why this was necessary. The capital investment in processing was too high to distribute. They centralize and then ship the results in and out and then ship them back. Separation of store and mill.

Second thing is conditional branching. "If then" statements. If a particular condition were satisfied, it would take one other action automatically.

It was programmable using punch cards. There are four kinds of cards --

The variable cards told the addresses and the store where it must go to. The operational cards had what instruction it could do. It had a fundamental repertoire -- a number card was a beta card. And a commentarial card told you how many durations to do. So it was all programmable in this way. Internal repertoire of instructions -- it had automatic multiplication, automatic division, subtraction and addition. It was user programmable.

You could screen listed instructions in any sequence you like, you could even rate them. So it had conditional branching integration. It had multiple processing. So it's about multiple processes. It had card punch output, printed output, (**) output.

These are specific designs. This is not wishful thinking. This is not retrospective projection from the modern age. These are explicitly and specifically embodied in his mechanical designs. This is not the coded vagueness of Nostradamus. This is engineering. So when we say he was the first pioneer of computing, this is not a casual tribute. All these features are specifically embodied in his machines. There's pipelining -- and I'll explain the (**) of pipelining.

Microprogramming. You give it a single macro instruction, say do this, and it automatically executes the lower level instructions. These are specific embodied instructions. So that's the analytical engine.

I can show you some punch cards and operational cards and variable cards. These are the face board cards. The large ones are the operation cards, small ones are the variable cards. You can tell it when -- store to find the material. The cards were based on the (**) as is well known. Which was used to control patents of weaves, automatic control of patented -- the patent of the textiles.

That's one of the very earliest computer graphics. That is a portrait of Jacquard, the man that devised and developed that thing. And that is not an etching, it is not an engraving. It's woven in silk using 20,000 cards in ****. And this, again, had an interesting influence in the development of ideas. What it did -- shaving was regarded as an aesthetic quality which was peculiar to craft and art.

What this proved -- because you can mechanize this and produce other copies of this -- you can show that the industrial arts were capable of subtlety which was easy to consider the province only of craft and art.

Now this had huge influence at the time. It showed that such subtlety was still within the province of mechanization at a time when mass production was actually beginning to compete in cross technology. And he had this hanging on his wall, and Prince Albert saw it, and it was a very well known celebrated piece. And precisely that because it was mechanical and it embodied features that could easily be regarded as -- the outside a province of a dirty old engineering.

[Inaudible question by audience member. ] Yes, there's one hanging in Science Museum in the Babbage Gallery. You peer at it. I cannot tell, even with glasses, the resolution of the weave. It is so fine that you cannot tell -- I cannot tell it's woven.

Okay. So that's Babbage's -- when am I supposed to stop? 25 minutes? Fine. Okay. We'll do more history then. Okay. Babbage failed to build any of his engines. He failed to build any of his engines. And the reasons for that are still hotly debated. And his life in a sense has become kind of a modern parable.

[Inaudible question from audience member. ] He never completed engines. He completed designs. He never completed any of his engines in the metal. He built partial assemblies and experimental pieces. And the biggest piece we saw was the difference engine, that two-foot thing. I would say that the fate of the rest of the parts -- he made 11 to 12,000 parts of the 25,000 needed. The rest went to the melting pot used partly by somebody who was at Harvard University, in fact, small assembly pieces. But the rest went into a melting pot, and all that was the most substantial piece he ever accomplished was that piece I showed at the beginning, number one. It works impeccably to this day. All the control mechanisms are intact, and it's one of the most cogent arguments against Babbage's detractors. They had the ****whole thing removed would work and. But there was always this uncertainty given that he never completed one. And that is the sort of doubt that has always hung over Babbage's reputation.

Was he, in fact, a dreamer? Was he an engineer of the highest caliber? And I hope we will have some answers within the next 25 minutes.

Right. This is difference engine number 2. That's the next thing he built. It was designed between 1847 and 1849. That is after Babbage had completed his major work on the analytical engine. So he had already gone way, way beyond methods of differences and repeated addition. He had already managed to get machines to multiply and divide directly, which is a strongly difficult thing to do. And he -- during the course of the refinement of his ideas, in the needs and demands of the analytical engine, he realized he could build a difference engine vastly with (inaudible).

This is like a master work. He produced no experimental pieces for it. It was like Mozart. He conceived of it and just produced the design. It is also the only complete set of drawings that was ever left, for reasons which I'll elaborate on presently.

So that's difference engine number 2. It's 11-foot long, 7 feet high, 18 inches deep. It weighs 2.6-tons in its present form. What's missing is the printer. What I didn't say after the business about the tables was -- and Babbage's conception was simply to eliminate all sources of error -- that's calculation; transcription; typesetting, compositing; and proofreading -- in one go through mechanization. And the idea was that the unerring certainty of mechanism would ensure that there were no errors in calculation.

If you could incorporate a printer integral with the machine, mechanically coupled to it -- that is, to eliminate the human from the information loop completely -- you set the initial values, you turn the handle, what comes out is printed results. Then you not only solve the issue of transcription, but the (**) of typesetting. And because of the method of finite differences, you will also solve the problem of proofreading. With each result, depending on the previous results, if the last result is correct, you have a high degree of confidence that everything else is.

So you only need to check one value. So by using method of differences and using automatic computation --

[Inaudible question by audience member.] Great. Absolutely. Having one copy is pointless because the whole point is to have a medium of communication. The machine does not only print a checking record in hardcopy on a print roll. What it does is impress the results on stereotype plates of soft metal from which printing plates could be produced. Now the bit that is missing over there is the printer. Integral to the concept of this engine is the notion of an automatic integral printer. And the bit that's missing there, for political reasons -- we couldn't raise the money in time for the anniversary -- is there.

And I will show you presently the first -- we're now building the printer through kind benefactual (***). We're also building an entire replica of this engine and printer for his house. And we have just done the trial assembly in the last few weeks before I came of the printer, and I will show you first images ever of the printer -- of the trial assembly of the printing maker. It's massive. It's more complex. It's more interesting than the engine in many respects. And the answer is it not only produces a hard copy but allowed you to produce a stereotype plate which using the conventional printing press, you could replicate results.

Okay. I haven't quite finished saying what this is (**) about. Okay. That's the machine. It has 8 columns of finger wheels. Numbers are represented on -- numbers are stored and operated upon (***) figure wheels. And I'll show you picture one presently. It's operated by turning a handle. That operates through a cam stack. There's your microprogram.

You turn the handle and say calculate the next value. The cam stack translates. That's 14 conjugate cams -- the geometric inversion of each other -- 14 conjugate cams translates circular motion into lifting and turning motions. They intermate in lifting and turning signal the motions required for the method (***) of differences allow you to add a number from the right-hand column to the next column, to the next column, so on.

So you're into the initial values from a table that you calculate by hand. And every time you turn the handle after that, you get the next result which appears in the last column. So the information progresses from right to left.

Now, at any given time -- so the units on the bottom, the 30-digit numbers represented in the column, that's a register -- the units at the bottom tens, hundreds, so on all have top 31 digits. So the constant difference, the last difference -- if you're using a set of polynomials on the last one -- that keeps its own value. It adds that number to the next one, next column, next column, next column, so on without a given line. Now, at any given time you've only got two columns that are effective. If you've got want eight columns in the machine, you've got only two columns working.

If you're adding one to one -- the first column to the second, second to the third. So during the cycle, column one will add to column two. And then column two will add to column three and so on. At any given time, only 25 percent of the machine is working.

What do you use with pipelining? He adds columns 1, 3, 5, and 7 to columns 2, 4, 6, 8 in the first half cycle and columns 2, 4, 6, 8 to the odd columns in the second half cycle. You can then extend the machine to 14 differences and the cycle time is independent of the number of differences. And as long as you offset the initial values, you have an (**) of pipelining. 1847.

[ Applause by the audience. ] I trust that applause is for Babbage and not for me. So we've got microprogramming, we've got pipelining. Okay. The mechanics of it, I'll go into presently. And I assume you're perhaps more interested in that than in the history. But, sorry. Tough. You're going to have to live with the history. What else about it?

Okay. That's one of the figure wheels. It has four **decades. The reason is he needs big wheels. He needs big wheels because he has to have security. They are a very secured mechanism. The whole thing is premised on the fact this machine cannot error. Now, Babbage -- he has three separate security mechanisms -- he challenges you. He says you can walk up to this machine, and it will calculate correctly. It will jam, it will break, but it will never deceive. And he's challenging you during an operation to walk up to the machine and try and derange those wheels.

Now that's a rather startling thing because if you've got a wheel, whether or not it moves depends on whether it's added to. It can be added to in two ways. From the wheel on the right of it on the column on the right, giving off a number to it. Or it can receive a carry from below. And because -- whether this wheel moves or not is data dependent. The wheel cannot know. You cannot know in advance whether to free it up. So what you have to do is free it up for the window in which can either accept the number from the right or the number from below.

You would think that during that window you could derange it, but you can't. It is designed only to accept information from legitimate sources. And we didn't actually fully understand the mechanism by which that happened. But because of the historical integrity -- which is something I haven't spoken about -- of this construction was such that we replicated even things that we didn't understand. And it was only through the course of assembling this machine that actually we understood the monumental subtlety of the way he had accomplished that. And I'll show you the part that actually allows that to happen.

So the answer to the question that it (**) unknown, why did Babbage build so big, the other machines that are smaller that were built subsequently -- the reason is security mechanism. Okay. That's to give you some physical scale. That's Rich Crick, and I'll explain about the mega-flop presently. Well, I'll do it now. You turn the handle. That's a construction in public view. The public could speak to the engineers as they did it.

That's Rich Crick; that's Barry Holloway, the two engineers who had a major role in doing it. Okay. When you turn the handle, the machine performs in one cycle seven 31-digit additions. Right? It performs six calculations a minute. So one calculation takes ten seconds. So one crick is ten -- one crick is seven 31-digit additions in a minute. And that's the -- you need a multiplying factor to get that in the mega-flops.

Okay. What was the informational data from which we -- which we started this to life? Babbage left a complete set of drawings. There were twenty drawings and four tracings. That is the one that is, perhaps, most evocative of the shape of the machine. It's BAB A-163.

One thing you may notice is that the handle comes out from a vision slightly below the main shaft of the bevel. You look at the next drawing, you can see the handle comes out directly from the main shaft. (**inaudible** we could afford **) When engineers first looked at that -- people who weren't Babbage freaks -- looked at that drawing, they didn't actually understand how it worked. In fact, neither did we at that stage. And they looked at all these numbers of (**) and said it would be impossible to turn the handle. These were people who he brought in for advice, so he had to take the advice. None of the Babbage zealots could possibly conceive that their hero could have made a mistake of such fundamental -- you know, such a fundamental mistake. So they abided by the advice ***and we could afford introduction hearing.

It turned out the engineers were right but for totally unforeseen circumstances. If we built the engine as Babbage had designed, we would not have been able to turn the handle. But nothing to do with friction. I'll explain that presently. So the displacement of the handle -- you can see it comes out one below -- is to do with the form of introduction given. Now, one of the principles of the whole issue is that any variation in the design, any modification of the original design, had to be reversible. Otherwise, we would invalidate the historical -- we had to resist the charge: You built Babbage's engine, but Babbage could not have. It would have defeated the purpose of doing so. And as we could say Babbage could have done this but possibly by other means.

So the machine was built out of bronze cast -- gunmetal, cast-iron, and steel. We did composition analysis on 1832 metals to find the best match. And there's only one instance we used a metal of steel -- a spring steel of a grade that Babbage did not have. And that doesn't affect whether or not the machine works. It only affects how fast you can drive it. It's an impact tooth that takes quite a hammering.

So the -- we went -- the historical integrity was extended to the point of actual -- of any materials. Now, the point about this drawing is that you can see that it, in a sense, it logically completely defines the machine. Not this particular drawing, but a set of drawings. The shapes of the parts are known. The intention is known, but there is insufficient information. You can't give a drawing like that to a workshop and expect them to make it. There is insufficient information. There are several categories that are missing.

Firstly, choice of materials. He doesn't tell you what the stuff is made of. He doesn't tell you anything about power and sync, the precision with 25 which parts are to be made. He doesn't tell you anything about finishing or methods of manufacture. Now, so these had to be provided by knowledge of nonessential machine practice. Tolerancing is a complete red herring. Tolerancing only has meaning if there is standardization. Right?

The fundamental notion of tolerancing -- I mean, you cannot make a nut in Manchester and a bolt in London and expect them to fit unless there's some method of standardization. Now, there was no standardation in those times. Two lathes in the same workshop would have different master screws. You couldn't cut the same thread a nut in one and a bolt in the other which is why he was confined to one component manufacturer. We used 46 separate subcontractors.

Babbage used one subcontractor, Joseph Clement. Joseph Clement made 11,000 parts in ten years. We made 4,000 parts in six months using 46 separate specialized subcontractors.

We unashamedly did not use contemporary tooling. We used modern manufacturing techniques. We used numerically controlled machines and computer controlled machines to produce the repeat parts. But everywhere we were absolutely scrupulous to ensure that no part was made with more precision than 25 we know from measurements Babbage was capable of achieving but possibly by other means. So that's our defense.

We welded where Babbage would have forged, and we dressed the welds to make it look like a (**). Not to deceive but to give the visual and the authenticity of the appearance of the machine.

We could have cast the figure wheels instead of machining it, and we did so to get the bright finish. We paid 25 extra pounds to do that so that when the machine was looked at -- because 90 percent of the message of this machine when people view it is not to do with the specifics of the technicalities, it's actually what does a 19th Century machine look like? What was it the Victorians never saw?

Okay. Now, there are several interesting things about the drawings. One is there are errors in them, and there's a serious curatorial dilemma. If you make a deviation from the design, then in what respect can we claim we built Babbage's engine? If you do not make any deviation from the design, in full knowledge, the engine is not going to work. Why build a piece of sculpture?

And there are various categories of error. There are redundant assemblies. There are assemblies which are exquisitely beautiful and perform -- do absolutely nothing. There are (**) assemblies. These are all to do with boundary conditions. All the errors usually occur on the boundaries. For instance, I'll get into that later.

I'll show you the most obvious one. There are inconsistencies in dimensioning. There are the same part depicted in different dimensions on two drawings. You have to resolve that. You cannot say we're going to make it the way Babbage intended. If the same part is -- what do you do? You make it half way between? You may do the same kind and try to -- I mean, you have to resolve that.

And so one of the big learning issues of this project was you cannot regard these drawings as some kind of sacrosanct ideal of perfection that -- from which any deviation would impugn the historical integrity of the thing. You have to -- what became very clear to us is we were resuming a project that had been intimate a hundred and 40 years later. This was the continuation. If Babbage had taken these drawings of the drawing board and gone to the workshop, he would have hit exactly what we hit.

So the issue was not what are we violating by making any design alterations. The question is, what would Babbage have done when he found this? And we applied no solution that we had not found Babbage had used elsewhere. He never uses slotted holes. He never uses grub screws for adjustment. These are monolithic machines. There is no possibility of debugging this machine. You cannot isolate the drive from the calculating section.

If you wanted movement, it makes a fixed link -- if you wanted to another movement, you make another link. There is absolutely no adjustment -- splitting them up is a total nightmare.

They had never done it. They had never thought of (**). So when the machine jammed solid, which part of its error detection. So if it's jammed solid, you don't know where to start. There are no test points. You cannot isolate the drive. You go with a screwdriver somewhere and you fiddle and you hope for some play. If there's no play, you go further down the machine. When you find some play, you work backwards until there's no play and you then look. It's absolutely hair raising.

There is no method -- they had never built a machine of this complexity. I absolutely believe if they had done so, they would have used the modular construction of some kind. So we were breaking new ground. And what became very evident is we were actually continuing in intimate process. We were not actually building -- we were not actually -- there was an absolute interaction between what we were doing. This was not the distance of history working through, as it were, Diachronical kid gloves.

Okay. Just to give you some example of one of the issues we had to resolve. Okay. The printer that's being built is this huge section on the right here which is part of the control mechanism of the machine. This is a digression. I know there isn't time for it. I say the printer is part of the control mechanism. If you're turning the thing -- you set the initial values up -- everything -- from the moment you've turned the handle, the machine no longer in the state you've set it up. It is now in an unknown state.

If you overrun -- the printer gets to the end of the page -- if you overrun, you have it. You have to redo the whole thing because the machine will then be set up to produce the first wrong result in the beginning of the next page. Now, you're at this end of the machine; the printer's at that end of the machine. You cannot counting -- you have no index card. The machine has an index card. It knows how many calculations. But the printer knows when it's got to the end of the page. What it does is drop a ball into a scoop which moves, pulls a lever as if he's a catgut which runs along under some pulleys which goes up into a scoop cam. And all you do is turn. And when it gets to the end of the (**) suddenly the hand becomes free, the drive is broken through a scoop clutch and the machine freezes in precisely the state it's needed to change the plate and resume for next time.

[Inaudible question from audience member. ] Is that a reference to Microsoft again? Okay. Just to give you some idea of some of the informational issues we had to resolve. You can see that the pitch, that's a separation of those columns is all the same (microphone off speaker, inaudible) second and the third. Excuse me. The separation between the second and third column is different. Is that significant?

We're building Babbage's engines, are we going to build with that space there? We think, well, hang on a minute there's no coupling. Is there some special significance to the first two columns? Well, there isn't if we understand that these are just differences. They replicate the mechanism. Well, we think, okay. If you see a planned view of this thing -- if you look down from the top would this resolve the issue? And, indeed, you look at the planned view -- why is there no planned view? There. There's the planned view.

You can see how monstrous the printer is. It weighs another three tons, estimated, which brings it up to the five. If you look at that, you can see that there is a discontinuity in precisely the same place. That's looking at the engine from the top. We're looking between column 2 and column 3. And you can see there's a discontinuity there. There's a little (**) there.

Well, we puzzled long and hard. We didn't want to violate it unnecessarily. But equally, we didn't want to build something we didn't understand. We puzzled over this and the conclusion we came to is that the draftsman had started on the left on, say, Monday, and he'd worked all the way and he started on the right on Thursday and he got to the middle and said, the hell with this, I'm not doing this over. And he got the pitch wrong. And there was no more significance than layout area than a drafting error. There's no other conceivable explanation for this.

But those were angles. We took this very seriously. Was there some deep significance to the separation? Okay. That's one of the more obvious ones, but more there are vastly more subtle ones of the kinds of --

Okay. That's the cam stack when you check the wheel. That is another drawing that indicates the kind of absence of information. There is no -- it describes the drawing, you can logically understand it. But there is no information of choice of materials, method of manufacture, finish and tolerancing. Tolerancing is the red herring as I mentioned.

Okay. Now one of the security mechanisms I should mention -- because it has sort of another analogy to electronic computing -- is the way the machines lock. I don't even see there's a wedge. There's a wedge which drives it. Actually, there's a better drawing of that so I can expand it in the next one, I believe. Yes. That is the guts of the engine. That is what's clever about it. Now, the calculators up to that time had six to eight digits in them. Okay.

The problem is carriage of tens. How do you do that? That's the actual guts of the machine, and why it's so elegant, why you could extend registers to 30, 50, and a hundred digits is because it solved the principle of successive carry. All the calculators up to that day had six, eight digits, maybe up to twelve. And the reason for that is -- the worst case is if you have a row of nines and you add a one, you have to propagate the carry, ripple through domino carry it's called.

Now, if you were running with dials, and you've got 99999 and you turn the last one, you have to actually drive those wheels from the force derived from the last turn. They didn't have the materials. They couldn't do it. There was no success for progression way to. What he did was, he separated the addition cycle from the carry cycle by using memory. He used latches. I mean, he talks about one-unit memories.

And he did this entirely mechanically. Now what's clever about this machine is once you separate addition from carriage, you've actually solved the problem of force. But you've distributed in time bites. You don't apply all the force in one go at one point. You're distributing time and that's -- the most visually dramatic and attractive feature of this engine as you will see on the video is the this progression, this dancing D. N. A. of this rippling helices that you will see.

Now, this is the mechanism. That's the -- you can see that's the planned view of the helix, that little fairground thing with the **loggans on the end. And one of the security mechanisms is -- that's a figure wheel. The way you lock it is you have a wedge. It's like a sword blade which runs up the column and jams itself between the figure wheels, and it locks them. That's the wedge here, plan of the wedge. You can see the wedge. The wedge would drive it. So the wheel is only freed within the window in which it can receive information from a long side of below, and it comes and it's free to move. It's locked in other respects during the window which it's able to move. And that thing drives its way.

And the reason the machine couldn't be turned is because the pressure angle of a cam that drives that thing -- because it comes in and goes out very quickly -- so that's the steepness of the side. But the thing to follow it was too steep, and you actually couldn't drive the handle past this thing. And I'll show you a picture of that.

The point about this is that one of the security mechanisms is this lock. Now if the machine -- if a wheel deranges very slightly and the wedge can still go in, you've got a pulse shaper. It restores the slight derangement. If it goes up to two and a quarter degrees out, it's going to come in onto a cog, and it will jam. And that says this wheel is in indeterminate state. It's no longer a digital machine, it's an indeterminate state. And that is how the controller -- we saw the half moons with the roller that sandwiched on the first difference engine. The weights through the wedges and controls. And that slapping sound you'll hear is actually the locks coming in and out.

The reason for that drawing is to show you the difference between the Babbage specification of that part -- which is that part up there, which is a carry lever -- and the amount of information you need to specify a modern piece pod. That's the most complex piece. There are 210 of those, left and right handed. And that's the amount of information you need to specify to the modern machine tool shop. You can see the sparseness -- the richness of Babbage's drawing metals -- the sparseness of manufacturing information.

Now we had to produce these takings to drawings and produce piece pod drawings for all 4,000 parts of this thing. And that took another 50 drawings to do, and every one had to be specified. That's -- again, that's a modern drawing. That's the part up there on top right. And that's the technical of the 50 drawings that were made. That's 50 just for the calculating and another 50 drawings for the printer.

Okay. That's the same -- that's the plan. That's the -- okay. There is a major error. There is a major, major error in the design. It is not a logical error, although we didn't know that at the time. I'll go back to this mechanism. That is the guts of the engine. This figure wheel column adds to that figure which is an intermediate sector wheel so you don't get a nondestructive transfer. To have a wheel and you rotate it to zero, it will transfer its number to the next wheel but you've lost the numbers so you have to restore it. But the intermediate wheel it stores the number, uncouples from the other one, and then restores it. And you'll see that cycle on the --

There's a fundamental error. We don't have a pointer. You can see that curved nook over there on the wheel just up there. That nook is what is nudged when a wheel goes above ten. This is a successful carry mechanism. So when a wheel goes above ten, a nook knocks that curved nook and it latches through an indent. I'll show you a computer animation of it presently. The point about it is that that mechanism can only work if the wheel turns, for you, anticlockwise.

The staggering thing in the designs is that the wheels go the wrong way. The mechanism won't work. It is absolutely fundamental. This created a terrible crisis. But the issue is was he using some (**) form of arithmetic that we didn't understand? Was this a method of preventing industrial espionage? Was the error deliberate? And we wracked our brains about what the solution was.

There are three solutions. You can lengthen the cycle. [Interruption by moderator re time.] Let's snap along. What was I talking about? Wheels going the wrong direction. Okay. There are several ways you can do this. You can make the wheels go the other way by changing the control mechanism. You can insert an intermediate wheel and reverse the direction. Or you can mirror image each alternative access. You can see the thing is biased to the right. Each alternative access you can bias to the left. The implication of biasing it is -- mirror imaging it is -- it introduces a 2 and a quarter degree shift. And the reason for that is peculiar, one is something Babbage never foresaw. If you join the center line of that thing to that thing, you'll find that the center line does not go through the middle of the tooth. It goes to the right of the tooth. So if you mirror image it, you get a tooth where there should be a gap. The result of that is you have to turn the thing 2 and a quarter degrees and the problem is how do you know the damn thing would work?

And so that was the -- the problem was a major design. It's not a logical error; it's a layout error. Second thing is what is the solution? The solution is mirror imaging. So we actually had to redesign the whole thing and take account of the 2 and a quarter shift all the way through.

[Question by audience member: Do you have a 3-D model? ] I'll show you. We built a trial piece to verify the fundamental mechanism. Sorry, it's a back to front slide. It adds a two-digit number and takes account of carry. Now, it's not automatic. You manipulate the rods and levers from the top to actually execute -- the cycle has 11 separate stages in it. And this is what we built which is the first -- it's actually the engine that we built to verify this new configuration.

We learned something very fundamental about the psychology. Okay. We were also trying to get funds that I haven't spoken anything about the politics and what we're going to do. I mean, this is a bunch of lunatics in a back room trying to do this stuff. And the question is how do you attract attention? And we discovered something fundamental about the psychology of what we were doing. We found that if you want to convince somebody that something is made accurately and precisely, you make it shiny. And that's a legacy of instrument making. Where precise things get polished.

Now, we got practically no attention for this project. We put in for the trustees, and they were sort of dutifully respectful of us. So we polished the top plate. We got on television. They ran credits passed it, they put on the (**). Trustees wanted to give us money. So -- okay. There the beautiful -- the beautiful --

okay. This is the helical mechanism that I showed you, (inaudible). It's an object of beautiful elegance in this machine. That's the helical mechanism which does successive carry. The (**) is very interesting so I'm going to tell you about it. What happens is, the thing in its addition cycle adds all in one go. All the 31 wheels are meshed to 31 (**) and the addition is done all at once. If a wheel in any decade exceeds ten, it latches -- the thing using an indent. What happens is that each of the positions need to be pulled -- right? -- in succession. And how it pulls it is, tipping the thing that -- as the thing -- as the wheel turns, it knocks the latch. The latch has a lever. The lever puts it in a particular position. What happens with this thing, as it rotates, it pulls each position in turn. It is placed in the fixed angular position, and pulls each lever. The way it pulls it is it sweeps the position. If the lever is set, that's (**), it's intersects and the locaters of the two intersections nudge it and it goes into the next wheel up. If it's not set, it misses it completely. So there's a conditional pulling which does successive carry. It's a ripple through carry so bottom carry can progress all the way up, and it can handle secondary carries, carries that are (**) carries because it rotates twice.

So that's how the carry mechanism works. Now, the force on that thing at any given time is never more than it takes to move one wheel. That's how you can extend these things. Okay. I think what we should do -- let me just check to see what's there, and I think we should run the video. That's another piece of (inaudible) -- okay. Just -- back of the -- that's the carry mechanism assemble, the back of the machine. And if you think that's impressive, have a look at that. And if you think that's impressive, have a look at that. And if you think that's impressive -- that's the (**) version. That's the back of the machine with the double helices which you'll see. Okay. I'll -- I suggest what we should do now is probably run the video, and you'll see the machine running.

[Video running now. ]

[ Inaudible question from audience member. ] Setup. Setup, ten minutes.

Sorry. There was a question which I didn't finish answering. [Question from audience member: How often did you run it? ] We ran it twice a day as a matter of routine during the anniversary year of the exhibition, and now we run it to anyone who expresses interest. [Brief inaudible conversation with audience member. ] Sunday is difficult because we have explainers who do this on weekends. Any weekday, either myself or my assistant will demonstrate the machine to you, even if you're an individual. You don't need to be a group or by arrangement. If we're there, we'll do it. We're going to change that. Now that we're building the printer, we're going to actually -- I'll show you the slides of the printer -- we were planning on having the printer run and printouts using conventional 1838 printing press and get results out. And we tend to do that as fixed demonstrations. There well be fixed demonstration times.

So I think that's the end of the -- is that the end of the televised proceedings? Seems so. Do we need a decision about whether you want any more? Do you want to hear about the printer or not?

[ The audience: Yeah. ] Okay. Right. We can relax now.

We can talk dirty. Okay. This is to give you some idea of some of the information density. The photographs -- the images I've shown you before are some of the best ones. They're the ones that are most evocative in shape and ones that are most meaningful in terms of internal mechanism. But not all of them are so immaculate.

That's an example where they didn't have automatic ways of producing tracings. So what they do is draw one view over another view and over another view and rely on dotted lines to present hidden edges. And that's if you like -- the point is, the thing becomes impenetrably dense. And there were some issues which we actually could not resolve.

The question from that drawing is whether the framework is one piece, is one cast bed, or that it's made up of multiple things. And, actually, we did not -- we were not able to resolve that. So we had to make decisions based on knowledge of 19th century machine (**). We were fortune in having (**) with Michael Right, who steps right out the 19th century. Instead of phoning Babbage, we would just go talk with this guy, and he knows everything there is to know about 19th century machines.

When we walk into his basement, it's like I can see Clement. So we relied on him very heavily on what parts, what materials Babbage would have used, what's the composition of gunmetal and all that stuff. And, you know, what size castings would they be capable of making. You see, they didn't have planing machines. They didn't have long bit planing machines. Now you just make something very rough and plane it and get the precision that way. But the casting techniques were vastly more evolved than ours. Because they didn't have planing techniques, their casting was vastly better. So the question is, we may not be able to cast beds that precisely. But what we do is plane them. So what we do is we make them out of separate sections. Off the air.