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There have been some fairly incontinent attacks on Lovelace's

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reputation and my bottom line is much the same as Doran's.

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I wanna present some hard evidence that these incontinent attacks

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on a kind of universal plane, I want to present you some concrete,

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hard evidence that actually that these attacks are not warranted.

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There are people who I read when I first started getting into this, great,

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thank you.

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Who I read when I first started getting into this and

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I really have no right to be here.

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I think I was asked in, I can't remember when Ursula asked me.

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I think it's only because I was boasting

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that it was the 50th anniversary of me writing my first computer program.

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And Ursula, in the way that those of you have worked with her will know,

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bounced up and down and said, oh you're just the person to convey Ada's excitement

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in presenting the details of the analytical engine.

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So, maybe I was just the person or maybe I wasn't just the person.

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But I went on, what you might call, where's the, here,

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have you got a, Thank you.

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Does that change it?

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>> Yes, it's working.

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>> Which is the button?

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>> This is the microphone.

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>> Oh, this is microphone.

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Okay.

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[LAUGH] Thank you.

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Please.

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50 years a programmer, and I still can't press buttons.

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>> [LAUGH] >> Thank you.

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So, I went on what you might call a programmer's journey of discovery.

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So, how many people are programmers sitting here?

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Oh, damn there's enough of you.

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Right? [LAUGH] Okay so,

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you're going to understand.

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You may understand more of what I have to say than I might have been

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expecting you to.

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In which case, I apologize for any of the technical mistakes.

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Here, incidentally, is a piece of paper that I wanted to hand out to you.

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What you would see on the piece of paper, which is actually reproduced as a fold out

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in the inside of the stuff that you got in your goodie bag.

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And at some point I'm gonna be referring to it.

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This in the end is going to be the object of the study.

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This is the table for the computation of the Bernoulli numbers.

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So, we're gonna see if we can take the programmer's journey through Ada's paper,

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learning as I did, a huge amount about the analytical engine.

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I only knew it as reputation.

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I only knew what Ada had done in the same way that

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probably 90% of you sitting here knew it.

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She wrote the first programs, the DOD, name, day, programming language after her.

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She was the first computer programmer.

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Those of you who are more inclined to be sympathetic to general

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notions of heroics and visionaries, will also have digested

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what I didn't know until I started reading the general literature on her,

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which is that her reputation as a visionary, a pioneer,

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the person who essentially did it on her own.

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And as I think Torrence pointed out extremely well,

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she didn't exactly do it on her own.

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But here's some of the stuff that she did that impressed me as a geek, an aged geek,

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long term programmer, rooting through essentially the documentation.

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And I urge every single one of you, sorry, I urge you all [LAUGH].

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The logicians in the audience will understand the difference between

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those two statements.

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I urge you all to go read the paper.

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There's a huge amount in it.

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There is, whoever you are,

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there is a thread in this material that you will want to pick up on.

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If you are historically minded, one of the threads for

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the historically minded Is the way that you'll

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find yourself as a historically minded geek getting incredibly impatient with.

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While you're all programmers,

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I don't know whether the people who

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subscribe to the heroics school are gonna take this lying down or not.

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There's an overwrought to some of the language in the paper.

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One of the things that I found difficult as a geek in getting to grips with what I

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had to get to grips with was there's a procession of

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facts and then there's a long philosophical disquisition.

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Eventually, you get back to the facts.

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In other words, Ada writes more or less how I lecture.

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So I'm going to.

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>> [LAUGH] >> Okay.

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So, here's the warning up front which I have not completed.

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I'll complete it at the end, roughly speaking what she says is,

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you get very excited at the beginning.

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When you're considering a new subject, you overrate it like mad.

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And then by natural reaction, you undervalue the true state of the case when

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we discover there are Tanibal.

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Some of the incontinent attacks I think, count as underrating,

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and some of the stuff that I'm gonna say today,

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I hope will be a sort of partial defense anyway of Lovelace.

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Another part of the bottom line, in case I rub it on far too long,

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is that [INAUDIBLE] was a programmer.

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That this, despite the fact, and of course you can't see the little red marks,

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despite the fact that there are errors in the table, works.

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It is not a program for producing the Bernoulli numbers.

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It is a scheme for a sequence of programs,

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each of which will produce the next Bernoulli number, okay?

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The reason that it could not be a program is that the machine,

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which never existed anyway, it's abstract in more senses than one,

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never had a facility for addressing, for calculating, places in the store.

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Maurice Wilkes put it best.

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Many of you will know who he is, and those of you who don't, it doesn't matter.

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Maurice Wilkes put it best, he said The numbers of the columns, the V North,

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V1, V2, V3.

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Those numbers are just names, right?

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Not one, two, etc,, were not addresses that could be calculated.

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This is the fundamental limitation of the machine and

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it's the fundamental limitation of the program.

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We'll get to that in a second.

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Let's just so, what are you gonna get if you're a programmer,

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which I was, reading the paper over the last few months?

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I kind of blurred snapshot of developing idea of the analytical engine.

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You can tell when you're reading that she's not writing about quite the same

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machine that Manabrias paper describes and there's some tension there.

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We expect to read things that are in some sense coherent and

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consistent 100, however, many 180 years after the fact, I can't do the arithmetic.

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Somebody do the arithmetic, 180 years after the fact nearly 200 years

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after the fact, that's good enough, isn't it.

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We're now used to seeing things very focused and

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when someone writes a paper or presents a paper, you're expecting to

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see consistency between the beginning of the paper and the end.

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And you're very uncomfortable, especially as a programmer geek like me, when you see

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something at the beginning that's not quite the same assuming at the end.

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And you have to learn to live with this and I haven't quite which is one of

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the reasons for my over excitement at the moment.

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You'll see several related notations for programming calculations in the engine.

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Calculations for the engine.

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And if you'll forgive me I'm gonna continue to call them calculations,

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because until we get to the punchline you'll see that that's

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what they actually are, I mean, straight line calculations rather than algorithms.

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There are suggestions of algorithms, but what's in the tables

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are straight line calculations, something you could do on a programmer with

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Hewlett Packard calculator which didn't have loops or branching.

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so and you're gonna see,

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as I say, you'll see if you read it, the derivation of an algorithm and

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it's near implementation as a program for the engine.

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Okay, so here's the context, I think it's important to understand context,

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particularly when you do this kind of time travel.

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If you talk to people who don't know algorithms and

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who don't know algorithmics, they'll tell you Ada wrote the first algorithms.

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You know that she didn't.

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The first algorithms, probably written by the Greeks or

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the Babylonians expressed by the Greeks or the Babylonians.

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There were certainly some non trivial algorithms and they'd been studied for

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a long time by the time of the Greeks.

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But between the time of the Greeks and at this time mathematicians

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really never developed a proper notation for describing dynamic processes.

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Roughly, the best you could get was

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sort of recurrence relations, and that was fine, but control was always expressed.

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In a very informal way when you were describing,

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when you were describing our rhythms.

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Here's another part of the context, this is a context which I hit first when I

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came to study the paper or to read the paper anyway.

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So, Allen Bromley was a very distinguished

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engineer who studied Babbage's drawings extensively.

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Morris Wilkes, arguably designed the first computer that ever produced,

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that ever delivered a proper computing service to non-computer experts.

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I mean he called it computers, his reputation rests on that.

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There are other aspects to his reputation that we can talk about privately.

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But his scientific reputation rests on him having developed EDSAC and so on.

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Anyway, so this is Allen Bromley, writing to Maurice Wilkes,

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when Allen Bromley was already kind of sick.

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Although he had done extensive work on Babbage's drawings.

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He says, I just worked again through Babbage's notebooks concerning his work on

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the engine.

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I've been greatly disappointed by what I found.

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Through most of the period, the operation cards provided for

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only four operations addition, subtraction, multiplication, and division.

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Well we know that's enough to do the kind of calculations that we want to do.

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What is the only there refers to the fact that

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there are no realized mechanisms in the machine for allowing I

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use a level program to write conditionals or loops.

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That's where his disappointment rested, and it's a curious disappointment.

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And it's a curious fact that Babbage, although he could write perfectly well

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write what we would now write what we would call microcode which had loops and

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so on, indeed, you saw the loops, the barrels going round and round.

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That was not offered I think this is fair isn't it,

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it's not offered, that is to say Babbage never

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developed the machinery to enable this to be offered at the programmers level.

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This is Bromlie's disappointment, okay?

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There's another physical fact about the machinery that need to [INAUDIBLE] us now,

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because it's gonna detain us a little later.

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Okay, so Manabrius says, very early on in the translation,

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that the machine's not a thinking being.

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It's simply an automaton.

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Babbage had to work really hard on devising machinery to do

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things like division, okay?

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What Manabrius is saying is, but you don't have to know how he did it.

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If you read a little lower in here, it says, under the impossibility of

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my here explaining the process through which this end is attained that is to say,

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the full arithmetic.

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Done by now, what we would now call microcode.

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We must limit ourselves to admitting that the first four operations of arithmetic,

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dah, dah, dah, dah,

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dah, can be performed in a direct manner through the intervention of the machine.

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That's it, here we have the detachment, in Manabrius' paper,

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translated appropriately by Lovelace, from the machinery.

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This is what makes our discussion a discussion, now,

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of an abstract machine, Lovelace says.

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Says something similar indeed, she's contrasting Manabrius'

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presentation of the abstractions of the machine to an exposition

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given by Dionysius Lardner, another scientific writer,

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who had written, essentially, an anatomy of the machine.

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He described the machine at the physical level in much the same way that

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Doran described Babbage's Presentation

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of the machine essentially discussing the clinking and clanking of the machinery.

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What Lovelace says, is you don't need to understand, you don't need to hear

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the clink and clank of the machinery to understand the machine,

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to understand what it does, to understand it's function, okay?

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[INAUDIBLE] on the contrary exclusively develops, her spelling not mine.

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The apolitical view taking it for

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granted that the mechanism is able to perform certain processes but

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without attempting to explain how every computer scientist teaching your first

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programing class That's the kind of thing you want to say to the students, isn't it?

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You don't have to understand how the bits and

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bytes are arranged, or what the bus does.

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You just have to take for granted that this is what it does and we operate

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at the level of the abstract machine, we might sometimes say the virtual machine.

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Loveless, clearly understood,

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so many at door and sadness presentation made me think that she might be

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thinking of herself and of garbage when she wrote this.

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It is obvious, with the invention of a calculating engine,

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these two branches of the subject, I mean mechanism and function

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what it is versus what it achieves in the abstract.

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Mechanism and function, are equally essential fields of investigation and

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beyond their mutual adjustment one to the other must depend all success.

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They are indissolubly connected, though so

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different in their intrinsic nature that perhaps the same mind

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might not be likely to prove equally profound or successful in both.

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Now if you want to have a little, metaphysical fantasy here you can think,

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she's some, she's thinking of loveless in her.

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She does function, he does structure, clicking and clanking.

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Okay, so he's getting on to the business now.

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This is Menabrea and what he's describing

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here is the interesting thing here is if you only read the paper, as I have.

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I've never seen any drawings of the analytical engine or anything in fact, yet

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the first time I saw the connection between the machinery that was going

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to clink and clank and these columns called V1, V2,

237
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V3 etc was when Dorin sent me his slides on Saturday afternoon.

238
00:17:17,315 --> 00:17:24,458
[LAUGH] I thought, of course, but that's what you think, isn't it?

239
00:17:24,458 --> 00:17:28,471
Okay, in general, we have a series of columns consisting of discs which columns

240
00:17:28,471 --> 00:17:31,362
we will designate as [SOUND] we may require, for instance,

241
00:17:31,362 --> 00:17:35,079
to divide the number written on the column V1 by the one on the column V4 and

242
00:17:35,079 --> 00:17:36,930
to obtain the results in column V7.

243
00:17:36,930 --> 00:17:40,488
Well, everybody else that has ever read this paper or read anything about and

244
00:17:40,488 --> 00:17:42,842
read anything by anybody who's read the paper, or

245
00:17:42,842 --> 00:17:46,720
anything by anybody who's read anything by anybody's who's read the paper.

246
00:17:46,720 --> 00:17:51,270
This is the way that knowledge about the paper is transmitted, incidentally.

247
00:17:51,270 --> 00:17:53,990
Few people appear to go back to the paper.

248
00:17:53,990 --> 00:18:00,400
I went back to the paper so you don't have to, but actually I recommend that you do.

249
00:18:00,400 --> 00:18:06,489
You find out, this is interesting.

250
00:18:06,489 --> 00:18:11,168
We're dividing the number written on the column, B one by that in the column obtain

251
00:18:11,168 --> 00:18:15,930
the result in column B seven, it's a three address machine, well sort of, okay.

252
00:18:15,930 --> 00:18:20,500
To effect this operation we must impart on the machine two distinct arrangements.

253
00:18:20,500 --> 00:18:24,230
Through the first it's prepared for executing a division and

254
00:18:24,230 --> 00:18:28,690
through the second of the columns it is to, sorry.

255
00:18:28,690 --> 00:18:32,920
And through the second, the columns it is to operate on are indicated to and

256
00:18:32,920 --> 00:18:36,020
also the column on which the results is to be represented.

257
00:18:36,020 --> 00:18:38,670
That's true to three address machine.

258
00:18:38,670 --> 00:18:41,610
Canoothy even describes it as a three address machine somewhere other in

259
00:18:41,610 --> 00:18:46,010
his description of early algorithmic notation.

260
00:18:46,010 --> 00:18:49,890
One specifies the operation, the other specifies the upper end result columns.

261
00:18:49,890 --> 00:18:54,220
We need not detain us here in understanding how it is, I think, and

262
00:18:54,220 --> 00:19:00,287
you can tell me whether I'm right or wrong, how it is the arrival of the result

263
00:19:00,287 --> 00:19:04,030
address that triggers the mill to do its business.

264
00:19:04,030 --> 00:19:05,950
Maybe that's wrong, Tim?

265
00:19:05,950 --> 00:19:07,890
>> Yeah.

266
00:19:07,890 --> 00:19:08,467
>> Is it right?

267
00:19:08,467 --> 00:19:09,889
>> Depends on which version you look at.

268
00:19:09,889 --> 00:19:14,870
>> Okay. >> [LAUGH]

269
00:19:14,870 --> 00:19:15,610
>> Yeah, we should of

270
00:19:15,610 --> 00:19:16,835
acknowledged Microsoft,

271
00:19:16,835 --> 00:19:22,939
[LAUGH] earlier on they would of said the same thing about his PowerPoint, right?

272
00:19:22,939 --> 00:19:25,130
>> [LAUGH] >> Okay,

273
00:19:25,130 --> 00:19:27,450
the two mechanisms must be distinct.

274
00:19:27,450 --> 00:19:33,380
So here, as someone who's really into the abstract machine, you're

275
00:19:33,380 --> 00:19:37,820
being presented with a concrete detail of the machine, which is a bit disturbing.

276
00:19:37,820 --> 00:19:40,010
What does it mean the two mechanisms must be distinct?

277
00:19:40,010 --> 00:19:45,622
Meaning the mechanism for imparting the operation, setting up the mill,

278
00:19:45,622 --> 00:19:51,144
the mechanism for sending the operand addresses that we would call them or

279
00:19:51,144 --> 00:19:55,972
actually the operand names as Wilks would call them and result.

280
00:19:55,972 --> 00:19:59,846
If this division is to be followed for example by the addition of two numbers

281
00:19:59,846 --> 00:20:03,845
taken on other columns, the two original arrangements of the machine must be

282
00:20:03,845 --> 00:20:07,720
simultaneously altered that is to say the op code and the operand.

283
00:20:07,720 --> 00:20:11,630
If on the contrary, a series of operations of the same nature is to be gone through,

284
00:20:11,630 --> 00:20:14,470
then the first of the original arrangements will remain and

285
00:20:14,470 --> 00:20:16,562
the second alone must be altered.

286
00:20:16,562 --> 00:20:18,259
Okay, so

287
00:20:18,259 --> 00:20:23,440
you've got a series of multiplications, you set up a multiplication,

288
00:20:23,440 --> 00:20:27,110
and then you start screaming the, operands and the results to it.

289
00:20:27,110 --> 00:20:33,280
Or maybe even you maybe only stream the results if the operands are the same and

290
00:20:33,280 --> 00:20:39,090
sending the result to the same place, to different places maybe that [INAUDIBLE].

291
00:20:39,090 --> 00:20:41,970
As a program you don't want to know this detail, you really don't.

292
00:20:41,970 --> 00:20:45,880
And actually the great achievement of Loveless If you follow through

293
00:20:45,880 --> 00:20:47,290
the paper or maybe it was [INAUDIBLE] but

294
00:20:47,290 --> 00:20:51,710
anyway, between them they manage to convince you that it doesn't matter, okay?

295
00:20:51,710 --> 00:20:56,020
So here we go from a paper of

296
00:20:56,020 --> 00:21:02,430
very concrete detail of the clinking and clanking.

297
00:21:02,430 --> 00:21:04,100
So let's see about ten minutes, right?

298
00:21:04,100 --> 00:21:08,251
Okay, I know I need the algorithm myself.

299
00:21:08,251 --> 00:21:14,676
Oh well, okay, so.

300
00:21:14,676 --> 00:21:20,920
Okay, let's just look here, the details almost don't matter.

301
00:21:20,920 --> 00:21:24,061
Doran showed you some of this anyway.

302
00:21:24,061 --> 00:21:30,650
You see the he's calculating [INAUDIBLE] table is calculating.

303
00:21:30,650 --> 00:21:36,620
In this case, he's calculating the X

304
00:21:36,620 --> 00:21:42,210
as part of the XY solution of this two linear equations, okay?

305
00:21:42,210 --> 00:21:49,136
What you need to look at here, I'll point at it.

306
00:21:49,136 --> 00:21:52,244
Is you see there there's four multiplications.

307
00:21:52,244 --> 00:21:56,993
Different operands, different operands, and

308
00:21:56,993 --> 00:22:01,747
two subtractions, and then a division, okay?

309
00:22:01,747 --> 00:22:06,375
Now look, this takes three operations cards it's so designed, so

310
00:22:06,375 --> 00:22:11,571
here in Manobrium's paper is something that turns out to be distracting and

311
00:22:11,571 --> 00:22:16,270
a bit of a red herring through some of the rest of the presentation.

312
00:22:16,270 --> 00:22:19,000
I don't want you to be distracted by that when you eventually get to

313
00:22:19,000 --> 00:22:22,680
read the paper as you all will.

314
00:22:22,680 --> 00:22:25,870
Okay, okay.

315
00:22:25,870 --> 00:22:30,560
Lovelace and giving her account of the general purpose nature of the engine.

316
00:22:30,560 --> 00:22:35,170
I at first thought, because I have to say I paid more attention to

317
00:22:35,170 --> 00:22:38,830
the incontinent attacks than I had to the paper for a while, and

318
00:22:38,830 --> 00:22:45,270
I base myself in front of the fandom for

319
00:22:45,270 --> 00:22:49,180
having done that, but I hope I'm gonna redeem myself.

320
00:22:49,180 --> 00:22:52,920
I thought was found a major distraction.

321
00:22:52,920 --> 00:22:55,090
Anyways, here she's doing something very positive,

322
00:22:55,090 --> 00:22:59,970
explaining the general purpose nature of the machine.

323
00:22:59,970 --> 00:23:07,580
Here's what happens if you have written in the the bottom of the column.

324
00:23:07,580 --> 00:23:15,175
At first I thought, she thought, in the column that's the memorandum,

325
00:23:15,175 --> 00:23:19,396
that's what the computer scientists the abstraction relation.

326
00:23:19,396 --> 00:23:20,229
Being written there.

327
00:23:20,229 --> 00:23:21,660
So she writes a, n, and x.

328
00:23:21,660 --> 00:23:25,910
So the variables on those columns are a, n, and x.

329
00:23:25,910 --> 00:23:30,140
She's beginning to describe the programming notation that she's going

330
00:23:30,140 --> 00:23:31,920
to use a bit later.

331
00:23:31,920 --> 00:23:32,950
Okay.

332
00:23:32,950 --> 00:23:34,720
Da da da da da.

333
00:23:34,720 --> 00:23:36,400
Whatever the variables are,

334
00:23:36,400 --> 00:23:40,000
you can compute a variety of different functions of a, n, and x.

335
00:23:40,000 --> 00:23:43,870
And she gives us several, but here are two.

336
00:23:43,870 --> 00:23:48,760
To calculate ax to the n with these variables on its columns, it requires six

337
00:23:48,760 --> 00:23:54,570
multiplications to get x to the n, and one multiplication to get a times x to the n.

338
00:23:54,570 --> 00:23:57,430
And now just a curious use of notation here.

339
00:23:57,430 --> 00:24:00,300
And at first, I thought, what is.

340
00:24:00,300 --> 00:24:01,180
You struggle with this.

341
00:24:01,180 --> 00:24:03,861
You say, what is she doing?

342
00:24:03,861 --> 00:24:09,140
And you see there, that yeah, there are six multiplications, okay.

343
00:24:09,140 --> 00:24:13,130
But they're not six multiplications that arise necessarily from the structure of

344
00:24:13,130 --> 00:24:14,570
what's been written.

345
00:24:14,570 --> 00:24:18,580
So writing it down seven times is a bit strange.

346
00:24:18,580 --> 00:24:21,850
Okay. And you see this from time to time where,

347
00:24:21,850 --> 00:24:26,650
there is a counting of operations and because you don't know

348
00:24:26,650 --> 00:24:32,010
what the variables are going to be, you don't know really what the program is.

349
00:24:32,010 --> 00:24:38,830
This may be where the slogan, science of operations started to emerge.

350
00:24:38,830 --> 00:24:40,290
Fortunately it goes away again.

351
00:24:40,290 --> 00:24:43,970
As you read further you find that this distraction doesn't matter.

352
00:24:43,970 --> 00:24:47,990
For X times A to the N the operations would be,

353
00:24:47,990 --> 00:24:50,550
would be 34 multiplications here.

354
00:24:50,550 --> 00:24:51,150
Okay.

355
00:24:51,150 --> 00:24:57,220
But she's saying it's hard to detach itself

356
00:24:57,220 --> 00:25:02,082
from the idea that really what she's saying is 34 times

357
00:25:02,082 --> 00:25:06,830
is what you need to do, not 34 multiplications, is what happens.

358
00:25:06,830 --> 00:25:08,810
Eventually, you get away from it.

359
00:25:08,810 --> 00:25:10,630
There's Manabrea's complete table.

360
00:25:10,630 --> 00:25:17,930
Here's a simplification of it, where I have brought out something

361
00:25:17,930 --> 00:25:25,100
that sits there in the notation, but it sits there very quietly in the notation.

362
00:25:25,100 --> 00:25:30,820
Which is that when a variable appears as an operand,

363
00:25:30,820 --> 00:25:32,610
there's two ways of referring to it.

364
00:25:32,610 --> 00:25:37,460
And one way just means the variable in the variable column stays

365
00:25:37,460 --> 00:25:40,980
the same once it's been sent to the mill.

366
00:25:40,980 --> 00:25:45,680
And there's another form, which I've underlined in blue in this calculation,

367
00:25:45,680 --> 00:25:51,360
the precise role doesn't matter there, where those blue

368
00:25:51,360 --> 00:25:57,620
mentions denote a reading and then zeroing of the column.

369
00:25:57,620 --> 00:26:04,160
This is gonna prove decisive in one of the mistakes in the table.

370
00:26:04,160 --> 00:26:07,784
Reiner, I've corresponded with you but I don't know where you are.

371
00:26:07,784 --> 00:26:09,293
Can you put up your hand so I can see?

372
00:26:09,293 --> 00:26:11,173
Reiner?

373
00:26:11,173 --> 00:26:12,961
You're Reiner?

374
00:26:12,961 --> 00:26:15,950
Hello I'm Bernard.

375
00:26:15,950 --> 00:26:18,210
So I'm about to describe some work that Reiner and

376
00:26:18,210 --> 00:26:23,590
I essentially did along parallel tracks and then Dorin introduced us.

377
00:26:23,590 --> 00:26:26,460
And we discovered we'd been coming to the same conclusions,

378
00:26:26,460 --> 00:26:29,587
namely that there were mistakes in the.

379
00:26:29,587 --> 00:26:35,079
Oh, I'm going backwards and I should be going forwards, okay.

380
00:26:35,079 --> 00:26:41,024
Okay, so by the end of the first phase, before we hit note g,

381
00:26:41,024 --> 00:26:48,486
you've begun to get the flavor of the way in which g is describing as a table,

382
00:26:48,486 --> 00:26:56,040
the machine codes of the program, the instructions of the program.

383
00:26:56,040 --> 00:26:57,780
I've essentialized this.

384
00:26:57,780 --> 00:27:03,660
I've discarded quite a lot of this, the same height above that.

385
00:27:03,660 --> 00:27:09,340
Of stuff showing columns with zeros on them, and so on and so forth.

386
00:27:09,340 --> 00:27:12,320
So another kind of distraction you wanna watch for.

387
00:27:12,320 --> 00:27:14,180
So anyway, so just let's try and

388
00:27:14,180 --> 00:27:17,990
understand the Bernoullian under table in [INAUDIBLE] five, ha!

389
00:27:17,990 --> 00:27:22,750
All right, Richard Bornat was right.

390
00:27:22,750 --> 00:27:23,452
Too much material.

391
00:27:23,452 --> 00:27:25,116
Okay.

392
00:27:25,116 --> 00:27:31,060
However, I listened to him I put a conclusion first.

393
00:27:31,060 --> 00:27:39,160
Okay, so what the table actually demonstrates is the computation of B7,

394
00:27:39,160 --> 00:27:44,590
given that B1, B3 and B5 have already been computed, okay.

395
00:27:44,590 --> 00:27:50,030
So, actually I sort of disagree with Dorum,

396
00:27:50,030 --> 00:27:55,786
because as you read down the side of these tables, there is an implicit sequencing.

397
00:27:55,786 --> 00:27:57,676
There.

398
00:27:57,676 --> 00:28:02,400
Okay, and all straight line calculations we've seen so

399
00:28:02,400 --> 00:28:05,090
far, everything that didn't have a looping.

400
00:28:05,090 --> 00:28:07,090
That implicit sequence is enough and

401
00:28:07,090 --> 00:28:11,360
if you put each of those things on cards that would have been enough too.

402
00:28:11,360 --> 00:28:14,760
Right, but here's where she begins to show

403
00:28:14,760 --> 00:28:19,600
that she differs from Babbage in her view of what the machine can do.

404
00:28:19,600 --> 00:28:24,120
Okay, I mean can do mathematically even.

405
00:28:24,120 --> 00:28:27,348
Independent of what interpretations you give to it.

406
00:28:27,348 --> 00:28:30,726
Okay, so why would you do that?

407
00:28:30,726 --> 00:28:34,660
Why would you not try and describe a general program, right?

408
00:28:34,660 --> 00:28:39,245
You know, why didn't you write the preconditions, the loop in there in

409
00:28:39,245 --> 00:28:44,934
the [LAUGH] Okay, this style of explanation goes

410
00:28:44,934 --> 00:28:50,680
right back to Babylonian times if you look at how Babylonians explore the algorithm.

411
00:28:50,680 --> 00:28:55,980
They give you very concrete description of a particular calculation and then

412
00:28:55,980 --> 00:29:01,760
by the side, you'll see the generalized explanation of what is going on.

413
00:29:01,760 --> 00:29:06,010
This is mixed in the object of [INAUDIBLE] as you'll see

414
00:29:06,010 --> 00:29:11,870
open the inside of your goodie and you'll see

415
00:29:11,870 --> 00:29:16,460
there is both a concrete description of what she's the particular calculation she,

416
00:29:16,460 --> 00:29:19,810
she's talking about and

417
00:29:19,810 --> 00:29:23,875
some disconcerting here it's it looks like this touch panel has lost connection.

418
00:29:23,875 --> 00:29:29,290
[LAUGH] All right.

419
00:29:29,290 --> 00:29:30,810
But what her intention is and

420
00:29:30,810 --> 00:29:34,620
her explanation is, her discourse about the table.

421
00:29:34,620 --> 00:29:35,870
It's okay.

422
00:29:35,870 --> 00:29:40,265
It was just, I was telling the truth but it was sort of a pleasantry.

423
00:29:40,265 --> 00:29:44,160
[LAUGH] Right.

424
00:29:44,160 --> 00:29:48,070
So, Lovelace's intention is to show that the table can be interpreted

425
00:29:48,070 --> 00:29:50,530
more generally.

426
00:29:50,530 --> 00:29:56,200
And certainly, Reiner and I independently and then together,

427
00:29:56,200 --> 00:30:00,010
despite noticing bugs in the table, we've shown to our own satisfaction.

428
00:30:00,010 --> 00:30:03,200
And I think it would be to your satisfaction.

429
00:30:03,200 --> 00:30:07,150
If we have the time to explain it, that this is the case.

430
00:30:07,150 --> 00:30:10,460
Certainly I now believe that if the engine had existed,

431
00:30:10,460 --> 00:30:12,310
Lovelace would have noticed the bugs very quickly.

432
00:30:12,310 --> 00:30:14,690
So you're nearly all programmers.

433
00:30:14,690 --> 00:30:19,505
Hands up, those of you whose first program,

434
00:30:19,505 --> 00:30:27,090
[LAUGH] You know the end of this I'm pleased.

435
00:30:27,090 --> 00:30:29,960
Okay.

436
00:30:29,960 --> 00:30:31,730
I do remember my first program.

437
00:30:31,730 --> 00:30:34,210
Actually I tell you there are endless stories I can tell.

438
00:30:34,210 --> 00:30:39,865
I'm just anecdotal is a word that could have been coined for me.

439
00:30:39,865 --> 00:30:42,800
[LAUGH] >> Okay.

440
00:30:42,800 --> 00:30:50,548
Had the engine existed Lovelace would have noticed the bugs very quickly.

441
00:30:50,548 --> 00:30:56,902
The really curious thing here and the thing that is irritating, I think to Dora,

442
00:30:56,902 --> 00:31:02,323
to me, to Reiner certainly, is that since this [INAUDIBLE] started,

443
00:31:02,323 --> 00:31:07,462
in this book, Audrey's book but this table denoted a program and

444
00:31:07,462 --> 00:31:11,407
that the program computed the delineate on this.

445
00:31:11,407 --> 00:31:17,216
Nobody's gone back to the table and try to verify or at least exam.

446
00:31:17,216 --> 00:31:20,046
Whether it computed anything remotely like the Bernoulli numbers.

447
00:31:20,046 --> 00:31:21,850
They've taken, right?

448
00:31:21,850 --> 00:31:23,427
I mean, here at Hartree,

449
00:31:23,427 --> 00:31:30,151
professor of what these days might be called computation at Cambridge says.

450
00:31:30,151 --> 00:31:32,675
The evaluation of the Bernoulli numbers from this recurrence

451
00:31:32,675 --> 00:31:34,820
relation is programmed for the analytical engine.

452
00:31:34,820 --> 00:31:38,050
This is the end of his stuff on Babbage's analytical engine, right.

453
00:31:38,050 --> 00:31:42,060
So he credits Ada with producing this producing the table,

454
00:31:42,060 --> 00:31:43,930
just says bang, it does it.

455
00:31:43,930 --> 00:31:49,700
Everybody else who's written about this,

456
00:31:49,700 --> 00:31:55,845
including the editor of the important volume Faster Than Thought,

457
00:31:55,845 --> 00:31:59,160
that's E.V. Boden, isn't it?

458
00:31:59,160 --> 00:32:03,730
Seems to have gone back to that and simply taken at face value that claim.

459
00:32:03,730 --> 00:32:08,220
Now, it's true and it's not true in the way that your program works and

460
00:32:08,220 --> 00:32:10,980
it doesn't work, right.

461
00:32:10,980 --> 00:32:16,000
What I mean is, not talking about Schrodinger's

462
00:32:16,000 --> 00:32:20,310
program, here.

463
00:32:20,310 --> 00:32:26,650
We do give an explanation, I'm not going to trouble you by taking you to the end.

464
00:32:26,650 --> 00:32:30,250
We simply believe that she would have noticed the bugs very quickly but

465
00:32:30,250 --> 00:32:34,310
we are mystified at the fact that there has been no acknowledgement

466
00:32:34,310 --> 00:32:37,620
of the bugs which are significant.

467
00:32:37,620 --> 00:32:40,210
I even looked into the literature, I read a lot in the literature.

468
00:32:40,210 --> 00:32:41,810
I read a Russian paper.

469
00:32:41,810 --> 00:32:44,045
Sorry, I read a translation of a Russian paper.

470
00:32:44,045 --> 00:32:46,920
>> [LAUGH] >> I can't

471
00:32:46,920 --> 00:32:49,040
lie in front of my coauthors, right?

472
00:32:49,040 --> 00:32:54,070
I read a translation of a Russian paper which claims

473
00:32:54,070 --> 00:32:57,080
we translated this program and it runs.

474
00:32:57,080 --> 00:33:03,040
Okay, but that's not what they did, that's not what they did, okay.

475
00:33:03,040 --> 00:33:07,025
If they had translated the table back literally as a simulation,

476
00:33:07,025 --> 00:33:10,728
which is what I did at first its where began to have my doubts.

477
00:33:10,728 --> 00:33:13,540
I'm trying desperately to understand what is going on here.

478
00:33:13,540 --> 00:33:16,675
I wrote a desperate letter to Doren saying, hey Doren,

479
00:33:16,675 --> 00:33:19,800
has anybody actually run this right?

480
00:33:19,800 --> 00:33:24,165
I sent a courtesy copy to our organizer who said haven't you guys got

481
00:33:24,165 --> 00:33:27,543
something better to do than to find errors >> [LAUGH]

482
00:33:27,543 --> 00:33:28,937
>> Right?

483
00:33:28,937 --> 00:33:29,890
>> Bless her.

484
00:33:29,890 --> 00:33:32,164
There is something better to do,

485
00:33:32,164 --> 00:33:37,039
which is to say if the spirit of the programmer had been followed here and

486
00:33:37,039 --> 00:33:41,930
if she had been allowed to find the mistakes would the program have run?

487
00:33:41,930 --> 00:33:46,180
And the answer to that is unquestionably in my mind yes.

488
00:33:46,180 --> 00:33:49,030
And actually I'll go further than that.

489
00:33:49,030 --> 00:33:51,750
There are, she struggles.

490
00:33:51,750 --> 00:33:53,266
She argues at the end.

491
00:33:53,266 --> 00:33:58,196
That although she's given you a very specific description of

492
00:33:58,196 --> 00:34:06,745
the state of the machine having computed V5 and about to compute V7.

493
00:34:06,745 --> 00:34:13,748
Really the part of the table, oh, there's some Bernoulli numbers by way.

494
00:34:13,748 --> 00:34:17,720
>> [LAUGH] >> Right, right.

495
00:34:17,720 --> 00:34:20,490
The reason I show you these is that some of them

496
00:34:20,490 --> 00:34:23,660
are slightly under 50 digits long, right?

497
00:34:23,660 --> 00:34:26,130
And some of them are unquestionably not.

498
00:34:26,130 --> 00:34:30,378
So there's a whole other thread here for the numerical analysts in the audience.

499
00:34:30,378 --> 00:34:33,197
Hands up.

500
00:34:33,197 --> 00:34:38,507
>> [LAUGH] >> Which is, actually, just

501
00:34:38,507 --> 00:34:43,595
how far could the computation have gotten and calculated accurately these values.

502
00:34:43,595 --> 00:34:45,998
I've shown them as rational representation.

503
00:34:45,998 --> 00:34:53,358
[INAUDIBLE] I thought that was the safest way to do it.

504
00:34:53,358 --> 00:34:59,850
What she says is, by using this recurrence relation, we do

505
00:34:59,850 --> 00:35:04,120
a first series of computations that essentially computes B1, second series of

506
00:35:04,120 --> 00:35:09,700
computations that computes B3, a third series of computation that computes B5 and

507
00:35:09,700 --> 00:35:15,030
then that third series of computations which is what I describe as the body of

508
00:35:15,030 --> 00:35:23,230
the loop will compute any Bernoulli number from all of its predecessors.

509
00:35:23,230 --> 00:35:28,147
She argues very strongly that that is the case and she makes her case.

510
00:35:28,147 --> 00:35:30,787
When you read the paper or at least when you read my paper or

511
00:35:30,787 --> 00:35:33,162
Reiner's paper you will see that that is the case.

512
00:35:33,162 --> 00:35:38,485
And I think that we should applaud her for that and also her observation at the very,

513
00:35:38,485 --> 00:35:43,064
very end of all of this, which is [INAUDIBLE] God you were right Richard.

514
00:35:43,064 --> 00:35:45,850
>> [LAUGH] >> Right?

515
00:35:45,850 --> 00:35:47,680
Here's what she says.

516
00:35:47,680 --> 00:35:49,947
It's interesting to observe that so

517
00:35:49,947 --> 00:35:54,774
complicated a case as is calculation as the Bernoullian numbers nevertheless

518
00:35:54,774 --> 00:35:58,077
presents a remarkable simplicity in one respect is.

519
00:35:58,077 --> 00:36:03,065
It is that during the processes for the computation of millions of these numbers,

520
00:36:03,065 --> 00:36:08,054
no other arbitrary modification would be requisite in the arrangements except in

521
00:36:08,054 --> 00:36:10,603
the above simple and uniform provision.

522
00:36:10,603 --> 00:36:16,610
She's inventing loop body abstraction, uniform provision for

523
00:36:16,610 --> 00:36:23,730
causing one of the data periodically to receive the finite increment unity.

524
00:36:23,730 --> 00:36:29,210
Very last word, I programmed the simulator which equipped the machine

525
00:36:29,210 --> 00:36:31,610
with this ability to sequence through tables,

526
00:36:31,610 --> 00:36:35,790
in other words turning numbers of columns into addresses of columns.

527
00:36:35,790 --> 00:36:39,100
I literally took her literal but slightly corrected program.

528
00:36:39,100 --> 00:36:41,210
I mean couple of places where its wrong.

529
00:36:41,210 --> 00:36:43,990
But not drastically wrong.

530
00:36:43,990 --> 00:36:48,622
Run it and well okay so we actually went up by showing

531
00:36:48,622 --> 00:36:53,815
Bernoullian numbers we went up to about B 991, okay.

532
00:36:53,815 --> 00:36:57,239
And then my patience was exhausted, and your's is now.

533
00:36:57,239 --> 00:36:59,302
>> [LAUGH] >> Thank you for listening.

534
00:36:59,302 --> 00:37:02,953
>> [APPLAUSE]

535
00:37:02,953 --> 00:37:03,247
>> Sorry, [INAUDIBLE]