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I'm a professor at Rawl Holloway.

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I'm going to shift the level of discourse

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away from how the individual programs work.

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Can you hear me now?

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>> Yes.

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>> How the individual programs work and indeed how the individual machines work.

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Because my interest is in, really, how the machines came to be.

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How were those individual designs captured and

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marshalled together into these very complex objects.

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So my main goal is to

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help you get some insight into the diagram that is behind the figure wheel there.

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Which captures a description of the causal chain within the printer, which

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was designed both the analytical engine and for difference engine number two.

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And that physical printer you can go and view in the science museum.

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Now because I stand between you and

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lunch, and we're clearly over-running, I'm gonna show my last slide first.

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>> [LAUGH] >> Because it contains an invitation.

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>> Elizabeth Scott and

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I have a table set up outside which has got this device on it.

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And you're very welcome to come and play with it,

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because it will add together your two favorite numbers,

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as long as they are single digit numbers, >> [LAUGH]

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>> And it is a direct representation

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of the atom mechanism from difference engine number two.

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Which is related to the kinds of adding mechanisms that would have been used in

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the analytical engine, and we can explain to you how it works and

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you can have a play with it.

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So why don't you come and talk to us, we'll be there in the breaks both today

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and tomorrow, there's plenty of opportunity.

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If I'm allowed I'll even bring it along and

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have it on the table at dinner this evening.

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Okay, so now, let me get on to what I really wanna talk about.

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Now I'll leave this up for you to read while I'm speaking.

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I study formal languages.

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That means languages which are more or less mathematically specified,

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both the syntax and the semantics.

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In practice, that means programming languages.

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It means mathematical symbolism, it means some aspects of network protocols, and

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it means in particular, a curious byway in the field of formal languages,

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which are hardware description languages.

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Now hardware description languages are little known,

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but are incredibly important.

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Because our modern technology really rests on the achievement

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of hardware description languages.

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A modern high end integrated circuit has on it one transistor for

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every person on this planet.

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Now anybody who hears that for the first time and

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is not shocked is not paying attention.

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How on earth could you possibly marshal the geometry and the inter connections

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in a structure which is as complex as the population of the planet?

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How do you do that?

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And hardware description languages are how you do it.

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You use techniques from software engineering, where we use hierarchy and

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abstraction to enable the designer to focus on a particular part of the machine,

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a particular level of the machine at any one time.

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And, you also use new ideas.

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Idea's which I call faceting.

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What we do is bring together multiple descriptions of the same piece of

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hardware, its interconnectivity, its geometry.

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The intent of its behavior.

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And we have these things in parallel.

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And hardware description language works so

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as to enable you to check the internal consistency of those descriptions.

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Now the use of hardware description languages is quite recent.

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When I started as a young academic in the mid-1980s.

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It was still something that you had to persuade

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hardcore electronic engineers to do.

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Because they could still just about cope with the complexity of

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the systems they were designing by drawing pictures.

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But that battle was won.

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And these days, I think almost nobody designs high end hardware without

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using hardware description language.

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As an aside, one of the two dominant hardware description languages

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called VHDL, is derived from the language called ADA,

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which you'll hear about this afteroon, it's just a little historical accident.

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So, the thing that is interesting is that Charles Babbage,

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as well as well as being the pioneer of computing, as well as being an embryonic

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figure in economics, as well as all the other strange rocks that you lift and

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there is Babbage smiling at you, this anachronistic figure.

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>> [LAUGH] >> He invented hardware

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description languages.

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And I don't think this is widely known fact, which is great for

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me because it enabled me to extract a very large amount of information from

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the trust to run a research project on this topic.

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It is clear that Babbage was fixated on notation throughout his life.

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We don't have time to do biographies of Babbage here but Dubby has it here.

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The Leibnizian notation that we use for

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differential calculus essentially is in our current usage, because

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Babbage went to war with the authorities at Cambridge as an undergraduate.

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And that battle was won very quickly.

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So notation was always central to Babbage's ideas.

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Now, writing 80 or 90 years after this picture of Babbage was taken,

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Bertrand Russell said something quite interesting.

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It's a common place that ordinary language is too ambiguous to

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enable us to specify electronic and mathematical systems.

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Russell makes the very excellent point that only mathematicians, mathematics, and

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mathematical logic can say as little as a physicist needs to say.

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This idea that what we are going to do is strict, meaning out of symbols, so

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as to deliver precision and

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insight, Is absolutely at the heart of what we do in mathematics and

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in computing, and all other forms of it or other forms of engineering.

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Now for the folk in the audience who are not engineering and

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mathematically oriented, I want to make absolutely

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clear that this got nothing to do with linguistic relativism.

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Concepts which was satirized so ablely by Orwell in 1984.

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It's always seemed to me, that anybody that reads that paragraph,

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this is a quote from Simon in 1984, explaining what is.

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Anybody that reads that, and doesn't think it's nonsense, isn't paying attention.

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Because the with which humans create words and terminology is outstanding.

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I'm sure you can create a language where people won't say out loud anything

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that the thought police won't come after you for.

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But the idea that you could actually erase modes of thought,

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by restricting It was vocabulary, I think is bizarre.

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And functionally, I think, is not a common, not a commonly

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supported mode in natural linguistics at the moment.

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Orwell, himself, wrote a couple years previously, in almost opposite terms.

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I have to be very careful about saying things like this,

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because linguists are famous for their viciousness of their debates.

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>> [LAUGHTER] >> And I don't want,

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I do not wish to have any bricks thrown at my head.

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And as Pinker says here you wouldn't believe the kind of hate mail he

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gets just from his work on irregular verbs.

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So I'm keeping right off human linguistics.

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The only reason for putting this slide up, is to tell you that I am not

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talking about linguistic relativism, I'm talking about something different.

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Now the project that I mentioned earlier comprises these four folk here, and

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I want to give full acknowledgement to them.

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Doran Swade on the end there.

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I met Doran 25 years ago, when I turned up at the science museum to

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hear about efforts in the conservation of early computers.

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and he and I worked together on a variety of projects, and into earlier

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he showed me the difference engine which is under construction at that time and

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began to talk to me about Babbage's work.

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And for me the central questions was, What!?

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How can this possibly be?

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Anybody who encountered Babbage's work For

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the first time without perspective in the 21st century.

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And isn't shocked, isn't paying attention.

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And they should be shocked for two reasons.

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Firstly because the machinery exists and

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secondly because it does not connect through our technology.

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Doren has this glorious phrase which he calls Babbage

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the great uncle of computing.

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As this notion of something really important going on over there,

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but there is no dissident connection to the current generation of children.

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It is astonishing as much that Babbage's machines existed,

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it is astonishing the stuff disappeared again.

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And the study we're doing does throw a little bit of insight as to why that is

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so, so the people in the team, there's Doren at the end,

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there's some weird guy there in a sweatshirt.

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Professor Elizabeth Scott who you can meet outside, and Doctor Pierce Plumber who is

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a very fine mechanical electronic engine here,who has designed and built some of

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the alternate Babbagery systems that we're playing with us part of our project.

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Now I want to show you some timelines,

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and just skit it through some of the machines so you can get a feel for them.

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The reason that I like to put this slide up, is because it is a common

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place that Babbage is this anachronistic Victorian engineer.

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He's no such thing.

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He's an anachronistic Georgian engineer.

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This is not Victorian engineering.

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>> [LAUGH] >> This is Georgian engineering.

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By the time Victoria concedes to mount the throne,

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the whole difference engine one project has been and gone.

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Work on the analytical engine has begun.

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The concepts and

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the ideas that we've been talking about today are already well in place.

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The other thing I want to draw to you attention is that Babbage had a son.

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To whom, well he had several sons, we'll come to that in a moment.

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He bequeathed his equipment and much of his knowledge and Henry Prevost Babbage

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continued his work after Babbage's death, really right up to the first world war.

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So this is really a very, very long development program indeed

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that we're talking about, 50 years of Babbage, and then more years of the son.

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It's not clear that the son really moves thing forward any more,

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he did a few things that are important.

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He constructed some small test pieces, much like the one that I can

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show you outside and let you play with, conceptually at least.

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And they were distributed to major institutions of learning.

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There's one in the Oxford history of the History of science.

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One went to Harvard.

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And one is sitting in fact at the moment in the Science Museum in London,

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where difference engine number one normally lives because DE1 is

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being moved upstairs for the Ada exhibition.

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So if you're in London you can go and have a look at one.

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[COUGH] The other thing I want to draw your attention to

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Is the relative timing of the pieces of work.

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Now Difference Engine Number One is a project that failed.

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It failed not because the engineering was impossible, but perhaps

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because the engineering organization was beyond what was possible for the time.

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Or possibly because Babbage was being ripped off.

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Discuss.

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Not my job.

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>> [LAUGH] >> It failed, but immediately thereafter,

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Babbage's vision expanded towards generalizations

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of the polynomial computation that the Difference Engine does.

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It's clear that Babbage was haunted by the failure of that early project.

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And towards the middle of the analytical engine development,

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Babbage re-implemented the same architecture.

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Probably the first example in history of a range of machines where an architecture

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has two physical manifestations.

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So Fred Brooks, move over.

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He reimplemented the Difference Engine architecture using the new ideas and

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technology that he developed whilst thinking about the analytical engine.

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And the heck line result is that the number of pulse goes down by the factor 3.

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So, the complete Difference Engine number One ran about 24 thousand pulse.

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Difference Engine number two, about 8,000 parts.

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The analytical engine, well put a wet finger in the air,

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how many registers do you want?

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Do you see these numbers are quite large?

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They're not as large as the population of the planet, but I don't know

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how good you are at holding the details of 24,000 things in your head at once.

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It's an extraordinary intellectual achievement at how it is done.

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Let's skip through some material very quickly.

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I wanna just, because I'm gonna talk about collaboration in a moment.

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I wanna talk briefly about Babbage's character.

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You see here the list of Babbage's children with their births and deaths.

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It's not a happy story.

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By 1827, five of Babbage's children and his wife were dead.

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That's gonna do something to a man.

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And I think having an enormous project to throw yourself into for decades,

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might possibly be a side effect of that kind of hand that fate has dealt you.

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We can talk very briefly about all the Difference Engine does.

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It kind of does that.

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There's an Excel sheet, and

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I've done a quadratic, actually a cubic fit to some data.

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It's the data from one of our research algorithms.

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You probably know that you can take

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equations which are made off of powers of X.

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And if you do it carefully enough,

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you can fit them to most other equations that you might be interested in.

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It's trigonometric functions and so on.

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And the way that these machines were used, was to get a competent mathematician to

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do a piece wise fit of polynomials to the function you actually wanted to compute.

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And then difference engine, using method of Newton's, enables you to tabulate

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the values of that polynomial, simply by performing repeated additions or

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subtractions, depending on how you care to think about it.

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And that's what the difference engines do.

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They are both very limited, and yet very, very useful.

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Because not so much of the utility polynomials but

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the fact that you can fit polynomials so easily to the functions that you want.

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[COUGH] Here's different engine 911 Derek Doren has already shown this.

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The reason I'm showing you these slides, is so

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that you can look at the progression in the physical manifestation of the parts.

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This Georgian engineering definitely Georgian engineering.

244
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All finished before Victoria came along.

245
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Rather beautiful rather Baroque and curvaceous in places.

246
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This is difference engine number two.

247
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Which is much more in your face.

248
00:13:59,745 --> 00:14:02,285
It's a lot bigger for a start.

249
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Remember, this has got a third as many parts as the earlier engine.

250
00:14:05,225 --> 00:14:06,575
The earlier engine is only a fragment,

251
00:14:06,575 --> 00:14:09,515
about a seventh of it, so you've got to do a bit of arithmetic in your head.

252
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But this is a much chunkier piece of kit.

253
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Just for your information, the section on the end here is the printer, and

254
00:14:17,155 --> 00:14:19,145
we're gonna talk about that again in a moment.

255
00:14:19,145 --> 00:14:22,145
I've thrown a picture of the Rosetta Stone in there as well,

256
00:14:22,145 --> 00:14:24,745
courtesy of Wikimedia Commons.

257
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The reason I've done that is because, for our project, this is our Rosetta Stone.

258
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Every time people talk about that, they should say, oh,

259
00:14:31,605 --> 00:14:32,840
of course he never finished anything.

260
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[LAUGH] Go to hell is my response.

261
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This man did incredible things.

262
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One thing he did finish was a design for de2.

263
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And he offered it to the government, and the government said, oh no thank you.

264
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Cuz they got burned pretty badly on de1.

265
00:14:48,645 --> 00:14:51,335
But the presence of the full design enabled Doran and

266
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his team in about 1990 to construct this physical machine.

267
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This is not a reconstruction, this is a first construction.

268
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But they did it purely by reference to the engineering diagrams.

269
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They didn't use the notational elements that I'm going to describe to you

270
00:15:05,575 --> 00:15:06,605
in a moment.

271
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As a result we have this physical artifact and we have these notations independently.

272
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And we can use the physical artifact to decode the notations.

273
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So this is kind of Linear B for early computing.

274
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Finally, we have the analytical engine, or one version of it.

275
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And this is much more likely constructed.

276
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It's a much smaller system.

277
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Apart from all the other things he did,

278
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Babbage became interested in manufacturing technology and took a tour of the country.

279
00:15:32,965 --> 00:15:37,425
And wrote a book on it, which was cited by Karl Marx in Das Capital,

280
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because it was one of the first studies of what was possible in manufactories.

281
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So what you see here, in fact, is a third generation of engineering hardware.

282
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It would be very interesting to see what the difference engine would look like if

283
00:15:52,525 --> 00:15:56,125
it was constructed using this style of hardware.

284
00:15:56,125 --> 00:15:59,195
Before I show you the notational stuff proper, I want to talk to you about

285
00:15:59,195 --> 00:16:03,645
a nature collaboration, because it's about the only thing I have to say about either.

286
00:16:03,645 --> 00:16:07,655
Now, the first thing you must understand, is that all engineering design is really

287
00:16:07,655 --> 00:16:11,835
a conversation between the designers, the artifacts and the users.

288
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Designers are always surprised by what their things actually do.

289
00:16:15,515 --> 00:16:18,455
Sometimes they do weird stuff because you made a mistake.

290
00:16:18,455 --> 00:16:21,485
Sometimes they do weird stuff because they've got capabilities that you

291
00:16:21,485 --> 00:16:22,875
haven't imagined.

292
00:16:22,875 --> 00:16:25,835
Never less true than of computing.

293
00:16:25,835 --> 00:16:27,415
Nearly all systems are unfinished.

294
00:16:27,415 --> 00:16:30,395
They're simply abandoned, because people moved on.

295
00:16:30,395 --> 00:16:33,475
And really, the only distinction between designers, implementors, and

296
00:16:33,475 --> 00:16:36,435
users, is about the level of abstraction that they're working in.

297
00:16:36,435 --> 00:16:40,885
Now, this is something I feel very keenly, because I work in various collaborative

298
00:16:40,885 --> 00:16:43,665
relationships, none of which are comfortable.

299
00:16:43,665 --> 00:16:46,625
They're all necessary to drive forward the ideas.

300
00:16:46,625 --> 00:16:48,395
But it's not a fun sport.

301
00:16:48,395 --> 00:16:50,455
Anybody who's got a very comfortable, cheerful,

302
00:16:50,455 --> 00:16:55,375
collaborative relationship probably needs somebody with a bit more grit in there.

303
00:16:55,375 --> 00:16:59,291
And I think one of the tragedies of Babbage, is that he didn't have any users.

304
00:16:59,291 --> 00:17:04,085
Apart from that brief supernova explosion, as Doran talks of it,

305
00:17:04,085 --> 00:17:08,155
maybe nine months, in one year, in the middle of a 50 year research program.

306
00:17:08,155 --> 00:17:10,405
Basically, you can see Babbage working alone,

307
00:17:10,405 --> 00:17:13,000
with a team of technicians to implement his ideas.

308
00:17:13,000 --> 00:17:15,525
[COUGH] Essentially in isolation.

309
00:17:15,525 --> 00:17:17,905
Not lecturing about what he's doing, and

310
00:17:17,905 --> 00:17:22,755
really somewhat resistant even to getting the stuff published and out the door.

311
00:17:22,755 --> 00:17:24,135
He's independently wealthy.

312
00:17:24,135 --> 00:17:25,055
Why does he care?

313
00:17:25,055 --> 00:17:27,715
He's not sitting in a modern university with a ref coming up

314
00:17:27,715 --> 00:17:32,255
to bite his back side in five minutes time.

315
00:17:32,255 --> 00:17:35,035
So now, I'm gonna get into the actual technical core of what I'm gonna do, but

316
00:17:35,035 --> 00:17:37,475
very briefly, because there's very little time.

317
00:17:37,475 --> 00:17:39,435
But you can come and talk to me afterwards.

318
00:17:39,435 --> 00:17:42,025
Here's a close up of the printer mechanism.

319
00:17:42,025 --> 00:17:45,875
The printer, in many ways, is the most complex part of the machine.

320
00:17:45,875 --> 00:17:50,765
It does different with columns, for instance.

321
00:17:50,765 --> 00:17:54,795
And one feature that I can draw to your attention, is that as you're printing

322
00:17:54,795 --> 00:17:58,075
a set of tables, the man on the other end is turning the handle.

323
00:17:58,075 --> 00:18:00,035
Sort of, probably a man.

324
00:18:00,035 --> 00:18:01,795
The person on the other hand is turning the handle.

325
00:18:01,795 --> 00:18:03,965
You can see this in the video.

326
00:18:03,965 --> 00:18:06,995
They don't know when you've got to the very bottom of a table.

327
00:18:06,995 --> 00:18:11,355
So there's actually a mechanism whereby a trip is thrown by the printer and

328
00:18:11,355 --> 00:18:15,505
there is a cat gut chord, which runs across the machine and

329
00:18:15,505 --> 00:18:20,045
disengages a drive dog in the handle, at which point you're running free and

330
00:18:20,045 --> 00:18:21,405
the machine itself is stopped.

331
00:18:21,405 --> 00:18:22,685
So this is glorious.

332
00:18:22,685 --> 00:18:25,615
Synchronization mechanism in there.

333
00:18:25,615 --> 00:18:28,465
I understand that the West Coast version has a bit of trouble here,

334
00:18:28,465 --> 00:18:31,065
because cat gut is hygroscopic I was told this morning.

335
00:18:31,065 --> 00:18:32,000
So it stretches.

336
00:18:32,000 --> 00:18:34,185
>> [LAUGH] >> Thank you for the anecdote.

337
00:18:34,185 --> 00:18:38,165
Now then, if you go and look at the engineering diagrams for the printer,

338
00:18:38,165 --> 00:18:42,525
you see a traditional side on view of the gears.

339
00:18:42,525 --> 00:18:47,855
As you've got at the back, but it's also heavily populated with strange symbols.

340
00:18:47,855 --> 00:18:52,115
And here are some in close up, you can see that there are letters in different fonts,

341
00:18:52,115 --> 00:18:55,005
and they have a variety of subscripts and superscripts.

342
00:18:55,005 --> 00:18:57,625
This is the core of Babbage's notation, and

343
00:18:57,625 --> 00:19:01,955
it is how he managed to make sense of the complexity of his system.

344
00:19:01,955 --> 00:19:06,085
This is what it looks like in total.

345
00:19:06,085 --> 00:19:07,935
This is a trains diagram,

346
00:19:07,935 --> 00:19:11,215
one of three facets of Babbage's hardware description language.

347
00:19:11,215 --> 00:19:16,335
And it captures the causal chains throughout the printer.

348
00:19:16,335 --> 00:19:19,605
You can't see it terribly well, so I'm gonna zoom it up a little bit on

349
00:19:19,605 --> 00:19:22,835
one of the central features, and you'll begin to see what's going on.

350
00:19:22,835 --> 00:19:27,055
There are these rather strange looking formulae.

351
00:19:27,055 --> 00:19:33,545
We see here these labels, with actually up to six, suffixes.

352
00:19:33,545 --> 00:19:35,725
We see these braces, and

353
00:19:35,725 --> 00:19:41,655
we see arrows, and we see parentheses, and they all mean something.

354
00:19:41,655 --> 00:19:48,295
Now here's the kicker, Babbage was, by his own words, most proud of the notation.

355
00:19:48,295 --> 00:19:52,275
He saw it as his greatest achievement, and of course, he was correct.

356
00:19:52,275 --> 00:19:53,625
Because this is not a machine.

357
00:19:53,625 --> 00:19:56,435
This is not a program running on a machine.

358
00:19:56,435 --> 00:20:00,225
This is a way of thinking which enables you to design machines.

359
00:20:00,225 --> 00:20:01,135
This is not the thing.

360
00:20:01,135 --> 00:20:05,545
This is the meta-thing, and the meta-thing is always more interesting than the thing.

361
00:20:05,545 --> 00:20:08,615
And Babbage was absolutely correct, I think, in saying that

362
00:20:08,615 --> 00:20:12,365
his hardware description language was the pinnacle of his intellectual achievement,

363
00:20:12,365 --> 00:20:16,005
not least of all, because it enabled everything else.

364
00:20:16,005 --> 00:20:17,195
And it went nowhere.

365
00:20:17,195 --> 00:20:19,695
As far as anyone can see, apart from a few of his technicians and

366
00:20:19,695 --> 00:20:23,595
his son, nobody really used this notation in anger.

367
00:20:23,595 --> 00:20:25,115
Now why would that be?

368
00:20:25,115 --> 00:20:27,735
Well, I think the answer is very simple.

369
00:20:27,735 --> 00:20:32,775
Babbage was so far out of his time, in terms of the state

370
00:20:32,775 --> 00:20:35,745
space of the machinery that he was building, but no one else needed it.

371
00:20:35,745 --> 00:20:39,295
If you look at the steam engine, which I build in my copious free time.

372
00:20:39,295 --> 00:20:43,305
Or even an internal combustion engine, there is stake, there are cycles,

373
00:20:43,305 --> 00:20:46,205
there is a rotation, but there's nothing that you can't figure out by

374
00:20:46,205 --> 00:20:49,555
just looking at side elevation and imagine the bits moving around.

375
00:20:49,555 --> 00:20:51,715
It's only when you introduce memory into a system,

376
00:20:51,715 --> 00:20:57,195
it's only when you introduce state that things get too hard.

377
00:20:57,195 --> 00:21:02,685
And essentially you don't find machines with true state appearing until its

378
00:21:02,685 --> 00:21:07,435
use perhaps in the 30s, and certainly the post World War II flowering in computers.

379
00:21:07,435 --> 00:21:11,165
And I think it's exactly how big is the state space of your machine, and

380
00:21:11,165 --> 00:21:14,435
if it isn't too big to fit in your head, you might have a go at this.

381
00:21:14,435 --> 00:21:18,160
Anybody else is gonna run screaming from this, and they did.

382
00:21:18,160 --> 00:21:21,805
Babbage tried to push this as a notation that should be taught in the mechanical

383
00:21:21,805 --> 00:21:24,685
schools, and in fact, at the time of the great exhibition,

384
00:21:24,685 --> 00:21:29,535
he made a desultory attempt to contact people who might be interested in it.

385
00:21:29,535 --> 00:21:32,435
And try and generalize his notation in a certain way

386
00:21:32,435 --> 00:21:33,845
to give it wider applicability.

387
00:21:33,845 --> 00:21:37,775
It's one of the few instances that one can see of Babbage reaching out

388
00:21:37,775 --> 00:21:41,855
to other folks and saying, come and join with me.

389
00:21:41,855 --> 00:21:42,813
>> Seems lucky for you.

390
00:21:42,813 --> 00:21:44,095
>> [LAUGH] >> Doesn't it?

391
00:21:44,095 --> 00:21:45,720
Remember what happened to APL?

392
00:21:45,720 --> 00:21:46,425
[LAUGH] A very,

393
00:21:46,425 --> 00:21:51,265
very fine notation which is not broadly used outside of certain shops.

394
00:21:51,265 --> 00:21:53,565
Here's some detail on how it works.

395
00:21:53,565 --> 00:21:55,505
Names comprise a letter.

396
00:21:55,505 --> 00:21:59,795
And the font and whether it's in italics or not are significant.

397
00:21:59,795 --> 00:22:03,345
Above it there's a little icon which is called the index of form.

398
00:22:03,345 --> 00:22:07,105
That particular one is Iraq, I'll show you some other ones in a moment.

399
00:22:07,105 --> 00:22:10,385
Down the bottom there's an icon indicating the kind of movement that

400
00:22:10,385 --> 00:22:13,425
the element named by this name performed.

401
00:22:13,425 --> 00:22:17,205
So that motion there is actually the motion of something that is

402
00:22:17,205 --> 00:22:19,495
turning if your looking down the x axis.

403
00:22:19,495 --> 00:22:22,025
So actually that's the motion of the handle

404
00:22:22,025 --> 00:22:25,065
on the end of difference engine number two.

405
00:22:25,065 --> 00:22:28,775
The index of identity is set to be the same for

406
00:22:28,775 --> 00:22:31,345
all elements that are originally connected.

407
00:22:31,345 --> 00:22:34,577
The index of alphabet is used when you've run out of letters.

408
00:22:34,577 --> 00:22:35,735
[LAUGH] >> [LAUGH]

409
00:22:35,735 --> 00:22:37,555
>> And doesn't fit.

410
00:22:37,555 --> 00:22:41,855
So six was enough for a long time, and then it wasn't enough.

411
00:22:41,855 --> 00:22:45,455
The linear index is used to generate arrays.

412
00:22:45,455 --> 00:22:49,325
You will have seen in the example that Dorin showed this morning a sigma and

413
00:22:49,325 --> 00:22:52,645
something that looks suspiciously like an indexed expression from a software

414
00:22:52,645 --> 00:22:53,275
programming language.

415
00:22:53,275 --> 00:22:54,765
That's exactly what it is and

416
00:22:54,765 --> 00:22:58,195
it refers to the columns in the difference engine number two.

417
00:22:58,195 --> 00:23:01,605
And the angular index does the same thing, but it's used for rotation.

418
00:23:01,605 --> 00:23:04,085
Any of you that have seen the difference engine in action,

419
00:23:04,085 --> 00:23:08,895
will know that it has a spiral of levers behind it.

420
00:23:08,895 --> 00:23:11,145
So each element both goes up and

421
00:23:11,145 --> 00:23:16,045
rotates by a certain angle and that's the angular index.

422
00:23:16,045 --> 00:23:20,105
[COUGH] Not used very often, because those structures don't appear very much.

423
00:23:20,105 --> 00:23:25,495
Here are some, I love these, here are some of the icons that Babbage constructed,

424
00:23:25,495 --> 00:23:27,495
my favorite one is the escapement.

425
00:23:27,495 --> 00:23:30,475
He gave an example, the clock written in the notation,

426
00:23:30,475 --> 00:23:33,915
you know how the escapement works, and there's a little pendulum.

427
00:23:33,915 --> 00:23:36,515
And what I said earlier that run about time the great exhibition,

428
00:23:36,515 --> 00:23:38,225
the attention to reach out to other people.

429
00:23:38,225 --> 00:23:39,435
What they actually did was say to people,

430
00:23:39,435 --> 00:23:43,285
what other icons do I need, what other kinds of mechanisms are there?

431
00:23:43,285 --> 00:23:47,465
And there are that 70 or 80 of these little pictures.

432
00:23:47,465 --> 00:23:48,395
This ones a rack.

433
00:23:48,395 --> 00:23:52,685
When you get the idea, they're all meant to be kind of pnemonic value and

434
00:23:52,685 --> 00:23:55,835
emotions too have some pnemonic value.

435
00:23:55,835 --> 00:23:57,205
Coming from modern perspective,

436
00:23:57,205 --> 00:24:01,181
when you look at it, you'll find there are obvious gaps all over the place.

437
00:24:01,181 --> 00:24:05,515
Some motions down some axis have an icon and some don't.

438
00:24:05,515 --> 00:24:10,135
So to a modern mathematician, a modern, someone who is interested in modern formal

439
00:24:10,135 --> 00:24:13,155
languages, one of the very interesting things is that Babbage just seems to

440
00:24:13,155 --> 00:24:16,075
use what he needed, and not bothered to define the rest of it.

441
00:24:16,075 --> 00:24:18,495
But I guess from a mathematicians perspective makes sense, but

442
00:24:18,495 --> 00:24:21,515
from an engineer's perspective it's confusing.

443
00:24:21,515 --> 00:24:25,145
There's some information on the naming conventions, and whether we're upright,

444
00:24:25,145 --> 00:24:26,715
or slanted letters.

445
00:24:26,715 --> 00:24:30,055
You can read about all this stuff and how long have I got?

446
00:24:30,055 --> 00:24:31,265
Have I run out of time completely?

447
00:24:31,265 --> 00:24:34,125
Oh you're waving your hands, you have a sign saying stop in front of you,

448
00:24:34,125 --> 00:24:37,330
but I cannot tell whether it's active or not.

449
00:24:37,330 --> 00:24:41,165
[LAUGH] You'll wave it at me, but I can keep going for a bit, okay.

450
00:24:41,165 --> 00:24:44,315
[LAUGH] So here are some of the conventions.

451
00:24:44,315 --> 00:24:46,815
Some of the conventions are desperately unhelpful.

452
00:24:46,815 --> 00:24:52,485
On a particular drawing the lettering of parts is such that,

453
00:24:52,485 --> 00:24:58,045
where does it say here, letter names are used to indicate depth into the diagram.

454
00:24:58,045 --> 00:25:01,555
So a distant part has a letter closest to the beginning of the alphabet,

455
00:25:01,555 --> 00:25:04,765
which is really great right up until the point when you've got the same part on

456
00:25:04,765 --> 00:25:07,515
two different diagrams, from two different angles.

457
00:25:07,515 --> 00:25:12,635
So these names are with respect to a particular diagram to some extent.

458
00:25:12,635 --> 00:25:14,215
There is cross referencing to some extent.

459
00:25:14,215 --> 00:25:16,075
I don't want to underestimate that, but

460
00:25:16,075 --> 00:25:18,515
again from a modern perspective we would think of

461
00:25:18,515 --> 00:25:21,825
the part having a name which popped up with the same name in various places.

462
00:25:21,825 --> 00:25:26,335
And here life is not so simple necessarily.

463
00:25:26,335 --> 00:25:29,535
One of the things that Babbage does which though is absolutely core and

464
00:25:29,535 --> 00:25:34,515
really important, is that he distinguishes between working parts and working points.

465
00:25:34,515 --> 00:25:38,305
Now he calls them working points, but in general they might be a surface.

466
00:25:38,305 --> 00:25:43,145
So a cam is a part and a cam follower is a part.

467
00:25:43,145 --> 00:25:45,075
The place where they contact each other,

468
00:25:45,075 --> 00:25:47,835
which in general is the surface, that's a working point.

469
00:25:47,835 --> 00:25:51,855
And for the computer scientist in the audience, essentially what Babbage is

470
00:25:51,855 --> 00:25:57,435
doing is constructing a directed graph of the hardware interactions.

471
00:25:57,435 --> 00:26:01,705
So we can think of the trains diagram as a description of a connected directed graph

472
00:26:01,705 --> 00:26:07,365
whose nodes form two classes, paces those of the physical objects and action point.

473
00:26:07,365 --> 00:26:09,265
And edges are also in two classes.

474
00:26:09,265 --> 00:26:15,375
There are ownership edges, which say, this piece belongs to this assembly.

475
00:26:15,375 --> 00:26:16,875
And there are cause arrows,

476
00:26:16,875 --> 00:26:20,825
which involve an action point to action point arrangement.

477
00:26:20,825 --> 00:26:24,765
So the graph is not as you might imagine,

478
00:26:24,765 --> 00:26:28,980
that the nodes in the graph or the parts and the edges in the interaction.

479
00:26:28,980 --> 00:26:29,625
[INAUDIBLE] And their label.

480
00:26:29,625 --> 00:26:30,815
Not at all.

481
00:26:30,815 --> 00:26:35,415
There are nodes for the interactions which have lines between them.

482
00:26:35,415 --> 00:26:36,785
This is hard, actually.

483
00:26:36,785 --> 00:26:38,205
It's really quite hard to think about.

484
00:26:38,205 --> 00:26:41,425
Here are some examples that are derived from

485
00:26:41,425 --> 00:26:43,445
a paper written by Henry Prevost Babbage.

486
00:26:43,445 --> 00:26:45,075
So I'm doing a bit of an aider here.

487
00:26:45,075 --> 00:26:46,045
I haven't invented my own stuff.

488
00:26:46,045 --> 00:26:49,425
I've nicked it from another paper.

489
00:26:49,425 --> 00:26:52,355
These are the examples here.

490
00:26:52,355 --> 00:26:56,335
So, we've got a bevelled gear here which is rotating, one at the top there, and

491
00:26:56,335 --> 00:26:59,325
driving the bottom bevel gear.

492
00:26:59,325 --> 00:27:02,255
Now, if 3p, 3b, and 3d are all rigidly connected to each other,

493
00:27:02,255 --> 00:27:08,205
that's what the 3 means, the letters tell you that those are individual pieces.

494
00:27:08,205 --> 00:27:11,785
And this strange formula up here, which can be compressed to here,

495
00:27:11,785 --> 00:27:17,925
tells you that there is motion, or force, being injected via 3B.

496
00:27:17,925 --> 00:27:22,969
Which is turning 3B and as outputs have 3D and 3B up there.

497
00:27:22,969 --> 00:27:24,223
Here's a related example.

498
00:27:24,223 --> 00:27:26,145
It's essentially the same structure.

499
00:27:26,145 --> 00:27:29,835
There's a sleeve rotating on an axle.

500
00:27:29,835 --> 00:27:35,495
In this case the axle is called 3P and everything is called 2D 2B,

501
00:27:35,495 --> 00:27:39,765
because they're now independently non-fixed elements.

502
00:27:39,765 --> 00:27:43,605
And again if I drive it, then 2B Is driving and

503
00:27:43,605 --> 00:27:48,805
the parentheses mean it's rotating around that axle.

504
00:27:48,805 --> 00:27:51,325
You begin to see why the machinations of the day might

505
00:27:51,325 --> 00:27:52,915
not have enjoyed this very much.

506
00:27:52,915 --> 00:27:55,335
It's actually quite hard to use.

507
00:27:55,335 --> 00:27:58,025
This is why I borrowed examples from Henry Provost.

508
00:27:58,025 --> 00:28:00,345
I'm now being told to shut up.

509
00:28:00,345 --> 00:28:02,325
That's fine.

510
00:28:02,325 --> 00:28:10,126
One last slide, we're building software simulations,

511
00:28:10,126 --> 00:28:13,433
as you might expect, of this stuff, and we're building 3D printed systems and