Let's start by drawing a diagram of what
we might call the eternal triangle
really, There's Charles Babbage but then
there's this other well-known person
that we need to include in our story
Ada Lovelace. And in the end among
Charles Babbage's many proposed designs
there was one for what really is the
world's first, stored-program,
Turing-complete computer. It's the
Analytical Engine. The only problem is
it's totally mechanical. Let me link these
with double-headed arrows and we'll move
about this diagram - sort of keep it in
view most of the time. The sources of
material?  Really I became aware of these
when I went to an Ada Lovelace symposium,
last December. And, yes, it's taken me
almost a year to digest it all and to
prepare these talks. Let's begin at the
beginning and let's begin at the top left of
my diagram.
Some of you may recall that actually I did
mention Charles Babbage - in a video I did
on "Why Binary", trying to explain why the
binary system came to dominate in computers:
[video insert]  "Large scale automation of
manufacture wasn't quite there in
Babbage's time and he moaned like mad at
the invoices - the bills - he had to pay to ..."
We're talking about the 1820s,
roughly, where the story starts and
saying that he was a very celebrated
mathematician, but his big forte was that
he wanted to actually be able to
automate the production, initially, of log
tables. Now those of you at the older end
of the audience may well, at high school,
have been taught - before, y'know, hand
calculators even came in - that the way to
do multiplications was to turn them into
additions by using things called
'logarithms'. So tabulating log tables was
the most enormously important thing to
do. I've got here the log tables I used
at school and Stephen Wolfram in his blog
says that even he, who was rather younger
than me, did do multiplication by 
adding together
logarithms and then taking the so-called
'antilog' of themm when he was at High
School. Those are four-figure precision
log tables. Here - very ancient book I
bought second-hand ages ago -
these are seven-figure log tables.
So, therefore, yeah, you looked up logs, you
added the logs, you turned them backwards
with things called 'antilogs' and that  was
the only [faster] way, for years, of doing
complicated multiplications. So Charles
Babbage actually did supervise the
production of log tables - as it were 'by
hand' -  before he ever got interested in
mechanizing it. So, a lot of the early Victorian log
tables have got Charles Babbage's name on
them. But it drove him mad, because first
of all there was the problem of computing
these log tables. Worst of all, and he saw
very clearly, another big problem was
getting them printed. The mathematicians
who drew them up might well have got
them perfectly right but they handed
them over to the typesetters for
printing. And the typesetters, of course, tried
their darnedest,  couldn't read the
handwriting, and made typo mistakes all
through. And just checking them was a pain !
He came from a sort of gentlemanly
background - was not fabulously wealthy -
but well enough off to afford a good
lifestyle. During his career at Cambridge
he eventually became the Lucasian
Professor of Mathematics. Those of you
into the history of maths - keen followers
of 'Numberphile' - will know that perhaps
the most famous Lucasian Professor was
Isaac Newton himself. And more recently
- until very recently I think - when he's
given up, it's Stephen Hawking [who is] the
Lucasian Professor of Mathematics at Cambridge.
Charles Babbage was not in my view as 
illustrious as those two,
I mean Newton and Gauss and people [like that] 
were just at a level of genius way beyond
most mortals but you know he was a
perfectly creditable appointment. And like
his predecessor, Newton, oh boy! was he
thin-skinned! He couldn't take criticism
and what's more, if he was around
today, he would have been banned from
Email, Facebook and Twitter already! He
loved flaming people - people who were
stupid not to realize the value of what
he wanted to do and even more the stupid
grant givers. Because he did get grants
to build these engines they were so
penny-pinching and  stupid and lacking in
foresight. And when people said to him
"Look Babbage, you are your own worst enemy!
Why do you do this?",  he had a bright idea:
he would continue to flame but he would
write anonymously. Of course his writing
style and the fact that nobody else would rant on
immediately gave the game away. Yes it's
Babbage again! So this was the backdrop
then, but he did actually draw up designs
for a very general kind of
hand-cranked engine that could do more
than just log tables. From the mathematical
point of view it could be set up to do
any mathematical problem that could be
represented as a function of polynomials.
Those of you who have done this stuff will know
Taylor series, Maclaurin series - all this kind of
stuff. Yes, a big class of problems
including producing sine tables or cosine
tables, and lots of others. So you could
say that this these so-called Difference
Engines of Babbage's were, if you like,
Special Purpose computers. People at the
time thought they were totally
wonderful - but do remember they are special
purpose; they can do calculations but
only things that can be expressed
as sums of polynomials. Think if you like
- for those of you who have watched the Bletchley 
Park series - a bit like programming the Bombe
for whatever is the settings on Enigma
today. That electro- mechanical
calculator, the Bombe, is a special purpose
computer. It can do wonderful things but
they have to be related to the settings
for Enigma machines. The Difference
Engines could do wonderful things but
only to things that could, in the end, be
reduced to the Method of Differences. So
don't think these are general-purpose
computers they're not. There you were in
the 1820s - which was before precision
machinery became available - driven by
electricity. That couldn't happen until the
end of the 19th century. And yet you needed
not a few dozen cogwheels, that you
might need for a clock - you know
a typical clock, maybe a dozen [or] two dozen
cogwheels, highly carefully done by
precision engineers and all this
kind of stuff. You needed hundreds and
thousands of these wretched things! And
so the bills from the gear cutting
technicians, to Babbage, sent him into a
rage. He then passed these on to the
government who were funding him
And despite all of this only little bits
of Difference Engines I and II 
were built which he kept to give people
demos and the yells came from the
funders: "When are we ever going to see this
with these machines realized?  You want
more money? Babbage you are joking we have 
now given
you at the end of Difference Engine II,
first stage - we've given you 17,000
pounds! Babbage, that is enough to build
two battleships. Two of Lord Nelson's
'Victory's could be built for 17,000
pounds". Babbage had not delivered, but
like every bad software supplier you've
ever known Babbage had the perfect answer
to these critics. Whenever they
said: "But you haven't delivered!" it was
always: "Tell you what, let's forget about
the Mark I. It was not good anyway. I've had
a far better idea. Here's my set of plans for 
Mark II. And of 
course they bought it between Difference
Engine I and Difference Engine II. Maybe a
little bit more money would cause it to
happen? But when he started getting a
whole load of flak about not being able
to deliver Difference Engine II, he had an
even better idea: "Let's forget Difference
Engine II. I've had a far better idea for
a machine that will far transcend only
what can be done by Sums of Polynomials
or the Method of Differences. This will be
able to do, basically, an infinitely wide
range of computations - not just different
variants on the same thing.
It's wonderful and I'm going to call it the
Analytical Engine. Of course, it will need
at least ten, or a hundred, times the
number of cogs than the ones I haven't
built, that never mind! It would be silly
to waste more money on Difference Engine
II when I've had this great vision for
the Analytical Engine". Did Difference
Engine II ever get built?
Yes it did, in the early 1990s
His drawings and his technology
were absolutely spot-on and the curator -
one of the heroes of our story here - is a
guy called Doron Swade.
He got the Difference Engine built at
the [UK] Science Museum.  Once you've built one
of them for the Science Museum, which you
can see ...  After a request from Bill Gates
and Nathan Myhrvold, respectively of
course, CEO and Chief Technical Officer
of Microsoft at the time, they built
another Difference Engine, shipped out to
Microsoft headquarters in Seattle. Then I
think sent out to the Museum of
Computing History in Mountain View. But the
last I heard is it's migrated back to
Seattle. Whether back to Microsoft, or
somewhere else, I don't know. Maybe to some
other museum. So, anyway, it did get built.
And what Doron Swade proved was that the
tolerances that Babbage set on those
gearwheels - how far apart the teeth
were apart and all that - were perfectly 
do-able. And I think it was built in the
precision workshops down in the basement of 
the Science Museum but basically here's the
wonderful thing, you know: "What did you
need to do this properly?"  Answer:
"A computer-controlled gear-cutting machine 
in orderto get this early technology working".
Which really wasn't the technology of
choice for doing this kind of thing.
>> Sean: I've just been wondering if it's 
possible, maybe, to do that with 3D printing now?"
>> DFB: "You probably could you know! I've never
thought of that" 
>> Sean: "But if people could 3D print ..."
>> DFB: I wonder if you could 3D print ...? So anyway
>> Sean: There's a challenge to the viewers!
>> DFB: Yeah! So here we are then here is somebody 
who could
never finish things. The next release
would always solve it. The next release
would always cost ten times more to
develop than the present one - which was
already way over budget.
He did have the vision and his massive
number of drawings, diagrams and so on
were vital. And they did work. However,
reverting back to the guru, Doron Swade,
again let's just finish with the
following observations:  Charles Babbage
adorned his drawings with all sorts of
his own short-hand. It was called the Mechanical
Notation. He never wrote a user manual
for it. So you had to, more or less, work
out from the circumstances what these
little squiggles meant. And as Doron
explained to me it didn't matter too much
when he was building Difference Engine II
because that was so close to other
calculators - which go all the way back to
Blaise Pascal in 1642 - you didn't need to
understand every single squiggle. You
just could get the idea straight away of
what to do.
Not so with the Analytical Engine, which
is far more complicated.
Is there going to be an attempt to
rebuild the Analytical Engine?
Yes, and it's under way and Doron Swade is in charge 
of the BCS [British Computer Society] specialist
little group looking at this. And if it ever
gets built it'll be built at Bletchley
Park - I think is the current idea. So I
asked Doron and I said: "Well, if I understand
rightly the Analytical Engine has got
so many cogs you can't hand-crank it -
it's out of the question?"  Babbage was going to
drive it by steam. "I do hope, if you ever
built a replica ..." And his face went ...
and he said: "You can forget
any idea, if we ever get this thing built
 - and we're talking decades not
single years, right - we're not going to
drive it by steam! And also we really
cannot make progress until we understand
Babbage's notation". So, that's the
state-of-the-art at the moment. They're trying
to understand some of the really obscure
things in the Analytic [Engine] design which just
have to be understood before they can
make real progress.
