Good afternoon and welcome to our demonstration
of Babbage's Difference Engine.
My name's Tim, this is Chuck.
We're volunteers here and we're going to fire
this machine up for you.
Now, I'd like to begin
by asking how many people in the group here
remember things like this?
Books of mathematical tables.
If you're old enough to have gray hair, or
no hair, you probably remember this.
So any engineer or scientist would walk around
with a book of tables like this
and a slide rule, of course.
The slide rule for the quick calculations
and the book of tables when you wanted greater
precision.
Well, if you did use books like this,
did you ever stop to think how they were created?
I know I didn't.
Well, they were laboriously created by human
computers doing the calculations by hand.
With pencils and paper.
And then when they'd done the calculations,
printers had to set the movable type to go
and print the books.
Not surprisingly, the books contained errors.
And in the early part of the 19th century,
at the height of the Industrial Revolution
in Britain,
an English mathematician by the name of Charles
Babbage was appalled by the state of the tables.
Engineers building bigger and bigger structures,
navigators at sea doing complex calculations
and trigonometry to figure out where they
are,
and he said, well, if the books have errors,
lives and property are at stake.
And so he set about providing a machine which
would solve this problem, and produce flawless
tables.
Now to give you a sense of what that involved,
I'm going to ask Chuck here to turn this machine
on,
so you can see it briefly in operation,
and I'll tell you a little bit more, and show
you once more, in a moment.
I'll step aside here, so everyone can
see it.
So Chuck is our power source! No electricity,
of course.
Well, when Babbage proposed to build his machine,
it was about 1823.
And he said he was going to build a machine
which would require 25,000 precision mechanical
parts,
at a time when a complex machine, maybe a
steam engine, had maybe 100 parts,
all laboriously finished by hand.
This was before the time of mass production
and so on.
It was going to be an extremely expensive
undertaking.
So he appealed to the British government for
support.
Now, unlike today, back then, the governments
generally didn't support science;
science was a rich gentleman's pastime.
And although Babbage himself was a rich gentleman,
he wasn't nearly rich enough to undertake
this project on his own.
But because of the importance of these tables
to navigation,
and the fact that Britain was the preeminent
maritime nation at the time,
the government thought this was a worthy cause,
and said "Sure, we will support you."
And so he started a project to actually try
and build this machine.
He estimated it would take him three years.
Well, he ended up spending about £17,000
of the British government's money,
which doesn't sound a lot today, but back
then, somebody figured out,
it was enough to buy 29 brand new steam engines,
steam locomotives.
So it was a huge sum of money.
And ten years into the project, things went
wrong.
Not for technical but rather for political
and financial reasons, the project collapsed.
He was only halfway through making those 25,000
parts.
He put together a small demonstration piece,
today they call it the "Beautiful Fragment,"
and in our Revolution exhibit you can see
a half-scale model of it.
It worked perfectly, demonstrated that his
machine would have worked if it had been completed.
And it still works to this day.
But there it rested.
Now you might have thought, having put so
much into the project which collapsed,
he would have had enough of calculating engines
and would have moved on to other things.
But no, in fact he had already had the ideas
for how to make a much more sophisticated
machine,
which he ultimately called his "Analytical
Engine."
Now, he only designed it on pencil and paper,
but had he built it,
it would have been recognizable to us as a
general-purpose programmable digital computer.
Programmed on punch cards. Tremendously complex
machine.
Well, from that effort, he learned how to
simplify his mechanisms,
and in 1848 he said "I know know how to build
a Difference Engine
much better than the original one that I thought
I was going to build.
It only needs 1/3 the number of parts, has
greater calculating capacity."
He offered the idea to the British government,
and they said "thank you very much,
but we've spent enough money on your projects,
we don't want it."
And so there it lay.
After he died, he passed largely into obscurity,
the materials all passed through his family's
estate,
and eventually ended up in the archives of
the Science Museum in London.
Now if you'd read in the history books up
to about 1980, they would tell you that Babbage
failed,
because the Victorian engineering of his day
could not make parts to sufficient precision
for his machine to work.
We now know that's absolutely not the case.
But it took until the 1980s for anybody to
really go and seriously understand what Babbage
had done.
Now, before we get there, let's take a closer
look at what we actually see here.
So this is called his Difference Engine No.
2.
It's called a Difference Engine because of
the mathematical principle on which it is
based.
Something called the Method of Finite Differences.
And it's No. 2 because this is his second
design.
Now, this particular one is also No. 2 because
there are two of these in existence in the
world,
and this is the second one.
The way those human computers, or one of the
ways those human computers produced these
tables
was using this method of differences.
And it's a nice trick that reduces the problem
to just a long string of additions and subtractions,
nothing more complex than that once you get
started.
So you can think this machine really is just
an elaborate adding machine.
But what's important about it was that it
was automatic.
Once set, Chuck over there is providing power,
but nothing else.
At least in principle, he doesn't need to
understand the mathematics,
and he doesn't need to understand the mechanism.
He's just a power source.
Now, in practice, it's not quite that simple.
It's a very fussy machine, so it's a skilled
job operating it.
What you can see, if you look closely, are
columns of wheels with numbers engraved on
them.
Each of these columns can store a single decimal
number of up to 31 digits.
There are 8 columns, and in the method of
differences we're going to take each column,
and add it to the column on its left, all
the way down the line.
And after seven additions, we have a new result
on the column over here.
Now, Babbage knew it was no use having a human
reading the numbers off this column.
We'll do that, in fact.
We're doing a calculation today of a mathematical
expression that mathematicians call a polynomial.
This is it. Remember a little bit of algebra?
The sum of terms of some variable x raised
to a power multiplied by a number and all
these terms added up and so on.
This is the way mathematicians would approximate
the table,
and then we're going to make a table of values
of this with different values of x.
Well, this is what we're doing, and right
now x has the value of 350.
If I asked you to work this out for x = 350,
it would take a while with a pencil and paper,
right?
I'd like somebody to help here.
Would you care to check these numbers for
me?
I want you to hold this, and you see the line
that says 350?
I'm going to read what the machine says, and
I want you to compare it with that and see
if it's right.
So, the answer we have on here right now says...
5 1 2 9 7 8 4 0 2 4 5 1 2 4 8 3 9 4 1.
That what it says?
Yeah.
We've got a modern computer to tell us what
to expect.
Well, it does get the answer right, it does.
Well, Babbage knew that it was no good having
me read that number off and hand it to the
printer to go print the table,
because one or the other of us would make
a mistake.
So instead this machine has what would have
been the world's first automatic typesetter
attached to the end of it here.
As the results are produced, they get sent
through here, through gears and ratchets and
so on,
down to this other print reel, and you can
see the paper here.
Now, if you look closely you'll see that there's
nothing on the paper.
That's because this is Victorian printing
technology, it uses water-based inks.
If we put ink in it, then we have to strip
the whole thing down, clean it and dry it,
it takes many hours, and we're volunteers.
So it'll go through the motions, but it won't
actually...
But the more important output was actually
not that.
That's really just for checking, so we can
see we've set it right, and we're getting
the answers that we expect.
The more important output would have been
produced in the trays below.
These would have been filled with a soft material
like plaster of Paris,
and as each result is produced, punchers come
down and make an impression in that, regarding
the numbers.
And the tray moves, so we can fill a whole
page of results.
Once it's done, and the plaster is set,
we can pour hot lead on it and make a printing
plate to go in our printing press, so with
no human interaction.
And you can see an example in our display
cabinet over there, it's a completed tray.
Okay, so, we're going to fire it up again,
and what I want you to watch is, on this end,
this is the control mechanism.
This is where all the [inaudible] stuff is.
A set of cams that, as they rotate, move levers
back and forth, driving past through here,
and orchestrate a series of lifting and turning
motions which accomplish the arithmetic.
And then, towards the end of each calculation,
you'll see the printer become active as it
records that result.
Give us a few more cycles here.
You'll see the lifting of columns and the
turning of the wheels.
And it'll take it about 8 seconds to produce
each result.
4 turns of that crank.
And we get the next result.
Now what I'd like everybody to do is to move
around the back of this machine.
Because on the front we can see the numbers,
but around the back is some rather interesting
stuff.
You know if you do arithmetic with pencil
and paper, when you add two numbers together,
if the answer comes out to be bigger than
9, you're going to have to carry 1 to the
next column, right?
I ask you to add 1 to 999, you're going to
say "9 + 1, that's 0, carry the 1,
ooh, now I've got 1 + 9, that's another 0,
carry the 1," so we have to make a lot of
[inaudible].
Well, this machine is doing the same arithmetic.
It has to do the same thing.
Give us another cycle from this side.
What does that remind you of?
DNA, yes, it's the machine's DNA.
Well, this helical structure you see here
is not just made so that it looks pretty.
There was a very good reason for this.
The mechanism on the backside of the machine
here is where the machine stores the information
that says,
a wheel has gone past 9, we need to carry
1.
And after we're done with adding all the wheels
together on the front, we're going to have
to process all those carries.
And they have to be done in sequence, from
the low digit to the high digit.
So as that column rotates, these steel arms
you see sticking out here,
all those registers, one digit at a time,
from the bottom to the top, everything happens
in the right sequence.
All over in the blink of an eye, it's very
hard to actually see it in operation, but
that's what's going on back here.
Okay. Now, the last part of the mechanism
-- this machine has 8,000 parts in it.
4,000 of them are in that calculating section,
you can see lots of repetition.
The other 4,000 are in the printing apparatus
here, where there's hardly any repetition
at all.
There's a lot of complexity here, but it's
not very obvious.
What Babbage was concerned about was laying
out the page with the results.
So he gave us the provision on the end here,
it's a control that we go down a row and then
down a--
sorry, down a column and then down the next
column, or do we go along a row, and then
along the next row?
We can control how many rows and columns on
a page, what the spacing between rows and
columns are,
we can put extra space every 5th row to guide
the eye and make it a little easier to read,
and so on.
He even has two different font sizes!
It's all controlled mechanically by the apparatus
on the end here.
Now, remember, this was designed with pencil
and paper, and he never actually built this
machine.
But he thought through every little detail.
So, for example, with the method of differences,
it turns out every answer depends on the previous
answer.
That's why it's called the method of differences,
because what we do to get the next answer
is add the difference from the previous answer...
So if every answer depends on the previous
one, it's very important when we get to the
end of a page, that we stop!
Because we need to put the fresh plaster in
there to catch the next result.
And if we overshoot, we're going to lose an
answer and we're going to have to go back
and set the machine again.
So he thought of that too.
When you get the last answer on the last row,
it drops a weight over here,
pulls a cord that runs across the front of
the machine and disconnects the handle,
so that Chuck down there can't produce any
more results until we put a new tray in.
Every little detail worked through.
Okay, so, watch this end of the machine here.
We have two weights, these are providing the
power, they move the tray in two directions,
you can see as they pass the paper through
you should see the tray moving.
There it goes onto the next row.
So, ready for the [inaudible]?
And it's all entirely automatic, get to the
end of a row, [inaudible] the weights rewind,
just... magic.
Okay, so come back around the front.
...
You wouldn't do the entire book, because the
method of using a polynomial is an approximation.
And you have to figure out over what range
it's valid and you can switch the difference
approximation.
There's a lot of technicalities with that
sort of thing.
[inaudible]
Well, we've calculated, for instance... the
other thing you can see in our display case
over there
is an example book of tables that's a seven-figure
logarithm table.
Babbage's own.
We estimate to produce that book on this machine
would take Chuck here practically eight hours
a day for a month.
So, it would be a big undertaking.
You can see that this thing has got a gear
reduction system on it.
It was originally designed with the crank
right on the main shaft.
So it was a 1:1 turn.
And when we first built the machine, we quickly
discovered that that's about 140 pounds of
force.
Well, the Victorians were obviously a lot
stronger than we are, so.
So they put this 4:1 reduction here so the
little [inaudible] of us could [inaudible].
You've got to keep it steady.
So I get about 25 [inaudible].
So this machine has a certain speed it likes
to go at, if you go too fast or too slow it
has a tendency to jam.
So it's actually quite a skilled job, turning
that crank, because you've got to keep it
steady, keep the load very similar.
Well, so I mentioned that Babbage's work fell
in London, and there it lay until about 1980
when scholars really went into that archive
and started to study what was there, and were
astounded by what they found.
The level of detail.
There were something like 5,000 pages of handwritten
notebooks,
thousands of pages of drawings, notations;
he invented a system of mechanical notation
that allowed him to reason in symbols
about how parts in a machine would work.
And what they discovered was that there were
a set of 20 drawings that described Difference
Engine No. 2,
and they looked fairly complete and consistent.
So the new curator of computing then, Doron
Swade, got to wondering,
well, if the old story said that Babbage couldn't
build this because Victorian engineering wasn't
good enough,
why hasn't somebody come back later and actually
built it?
And so they set about a project to do just
that, and to answer two questions:
Could it have been done with the methods and
materials available to Babbage?
And if it had been built, would it have worked?
And, as I hope you've just seen, the answer
to both of those questions is a resounding
yes.
And the goal was to complete it by 1991, that
would have been the bicentennial of Babbage's
birth.
He was born in 1791, and the Science Museum
in London was mounting an exhibit to celebrate
Babbage's 200th birthday.
With the centerpiece being the Difference
Engine.
Well, it turned out they only managed to complete
the calculating part.
They had many of the same problems that Babbage
himself did; raising the money, for one.
One of their prime contractors went out of
business partway through the project, so all
sorts of difficulties.
So by 1991 they did indeed finish the calculating
part, and they fired it up and it worked.
Just like Babbage said it would.
There were a few little rough edges, a few
things that had to be modified and corrected,
but remember, this was an engineering project
that had been sitting around for 150 years
just waiting to be completed.
If any of you are engineers, you know, there's
always this phase in this kind of project,
we call it debugging.
I couldn't find [inaudible]. There were a
few things, but nothing of principle.
Now, they also knew that it was essential
in Babbage's concept to build the printing
apparatus.
Because the whole point of this machine was
to produce the plates,
from which you could print mass-produced books,
with no errors.
But they couldn't build a printing apparatus
because they simply didn't have the money.
And so the project was sacked.
And then several years later, I think it was
1995, an event was held at the Science Museum.
A young man you've probably heard of, Bill
Gates, had just written a book called "The
Road Ahead,"
where it was predicting the future, and he
decided to have the European launch of that
book
in the Science Museum, standing in front of
the Difference Engine.
Well, Doron Swade, the curator, joined up
a few dots and said, Bill Gates -> Microsoft
-> money.
Maybe they will fund us to build the printer.
Well, it turned out that Microsoft politely
declined, said "Sorry, we don't get into that
kind of thing.
But we do have an executive who's interested
in this kind of stuff, and we suggest you
talk to him."
His name is Nathan Myhrvold, he used to be
the chief technical officer at Microsoft for
a while.
And eventually he agreed and said yes, I will
fund the museum to build the printing apparatus.
But I'm going to put a condition on it:
When you've done it, I want you to build a
complete second copy of the machine for my
private collection.
And that is the machine you see before you.
He has generously loaned it to us so that
we can demonstrate it to you.
So what you see here was actually completed
as the second one, it was completed in 2008.
They packaged it in a great big crate, stuck
it on a 747, and flew it all the way here.
And we are now very happy to be able to demonstrate
it to you.
It's pretty much identical to the first copy
which is still in the Science Museum in London,
but whereas we fire this up and show you it
every day,
the one in London is only demonstrated very
rarely these days.
So this is a unique opportunity to actually
see this thing.
You said that part of the point was to prove
that it could be made in Babbage's time?
in particular that Beautiful Fragment which
was assembled in 1832,
and they made measurements, they did metallurgy
to find out what materials were used,
and bought the materials that were equivalent.
And then they made parts where they required
no closer tolerance
than we know from measurements that they were
able to achieve.
And in fact this particular machine you see
took six years to assemble from the parts,
because they were all hand-fitted in just
the way they would have been in Babbage's
day.
So they were fitted together just like they
would have been hand-fitted back then.
But the actual parts were modern?
Oh, the parts were unashamedly made on modern
numerically controlled equipment.
Otherwise we'd still be waiting on gears,
you know.
They had this crazy idea when they started
the project back in 1985 that they might use
the authentic methods
of manufacturing [inaudible].
So they quickly decided that was probably
a bad move.
So yes, so the parts were made to no greater
precision than we know Babbage was able to
achieve,
it was just the fact that back then, it was
so huge, labor-intensive, phenomenally expensive,
Because these tables, after all, already existed.
People had calculated them by hand.
Let me ask you if you've got any questions
here, on things that I may or may not have
talked about here.
What maintenance does this machine need?
Oh, we maintain it roughly once a month, which
is mostly just lubrication.
Occasionally we have things go wrong and we
have to deal with them.
Like any piece of Victorian machinery like
that, it does require a lot of maintenance.
Of course, we only give it, you know, 20 cycles
a day or something when we demonstrate it.
If it had been in real use, of course, they
would have been cranking it day in and day
out.
So it would have probably been quite a good
deal more.
