Now that we've seen that a number of 
models of computation are equivalent

to each other and we've expressed the 
Church-Turing Thesis that they jointly

represent what we can reasonably call
computable. Let's return to the question

of what things can do this. So, what 
complex systems ranging from chaotic

dynamical systems to mechanical devices,
can actually carry out the steps of a

computation. In fact long before Church 
and Turing and Rosa Peter and the other

theorists of computable theory came along,
Charles Babbage, in the 1800's, wanted to

build various mechanical computers. One of
them was called the Difference Engine. It

was really only capable of carrying out
certain types of calculus. Babbage's goal

was to have a machine which could print
out good nautical tables of sines and

cosines and logarithms and that sort of
thing. Hopefully steam powered so that

people wouldn't have to do it by hand. 
But Babbage also dreamed of a more

complicated machine called the Analytical
Engine which is really in modern terms,

would have been, had it been built, a 
universal computer. And Ada Lovelace

studied his designs and came up with
some very nice observations about them.

First of all, she wrote the first complex 
program with two nested 'for' loops that

would have computed a type of a number
called the Bernoulli numbers but she also

predicted something very interesting. She 
noticed that if you could represent

numbers in such a machine, then you could 
represent many other things as well.

For instance music and she imagined 
machines which could aid in the

composition of new musical pieces. 
And so the world we live in today where

the bits and bytes and integers that are 
stored inside computers can also

represent audio, video, images, movies, 
music, all the things we are used to,

that's really the world that Lovelace 
envisioned where we can represent

many different types of data with numbers,
digits, or bits inside of a computer.