The Letters of Ada Lovelace

The Poetry of Mathematics

Thinking Machines

Georgina Ferry presents part one of the correspondence of Ada Lovelace, dramatized by an all-star cast. Uninterested in Ada the feminist icon or crazy fantasist, she reveals the intense inner world of a young Victorian lady who anticipated our digital age, when steam power was still the new big thing.

Ada Lovelace was the abandoned daughter of the romantic poet Lord Byron. Concerned that Ada might inherit her father's feckless and 'dangerous' poetic tendencies, her single mother Lady Byron made sure she was tutored thoroughly in mathematics, and regularly prescribed 'more maths' to improve her mental health.

When she came out in London society, Ada met the man who would change her life, but not in the way most debutantes would have imagined. The distinguished mathematician, Charles Babbage became her life-long friend and mentor:

Ada was fascinated by his steam-powered calculating machines. Supported by her husband William, she defied society's expectations, studying mathematics with extraordinary passion and determination when she was married with three small children; and later suggesting boldly to Babbage that he might like to work with her on his innovative thinking machines.

Cast:

Ada Lovelace.........Sally Hawkins

Lady Byron.........Olivia Williams

Charles Babbage.........Anthony Head

Michael Faraday.........Sam Dale

William.........George Watkins

Produced by Anna Buckley

https://1drv.ms/f/s!ArrWZcg2lV80hS873_gzvDru7XqF

2 Files: each 25MB. 28 minutes long. Bitrate 128kbps

Some background on 19th Century British Mathematics, especially de Morgan.

Newton invented the Calculus in 1666, used it to move some planets around and then forgot about it.
That was the lone peak of British maths for another century.

Leibniz invented it independently ten years later and spent the rest of his life defending his claims against Newton's attack dogs. Basically, N invented derivatives and L invented Integration and the two are inverse operations of each other.
L's notation was much easier to use.

While they were squabbling, the French took Calculus and really made it sing.
Laplace, Lagrange, Legendre and a bunch of other L's applied it to the Universe and figured out planetary motion.
They got hung up on the question "Is the Universe stable?". It is, unless something bumps it.

The mathematical arena moved from France to Germany.
Gauss used the Calculus to locate the asteroid Ceres. He only had three shaky astronomical observations, then Ceres disappeared behind the Sun. Calculus alone wasn't enough, so he invented Least Squares Analysis and Error Analysis and a bunch of other math we now use every day, to make his prediction.
That March, astronomers pointed to his zenith/azimuth and there it was, more or less.

Gauss put Probability on a firm footing and invented Gaussian Elimination, Gaussian curves and many other Gaussian things. What we now call Bayesian Statistics was Gauss taking a paper and a few scribbles from an English country parson and then mathematizing it. By then it was agreed not to name everything after him, so Rev. Bayes got to keep the title.

Euler invented Number Theory, Graph Theory, much of Topology and wrote so many papers that scholars are still cataloging them to this day.

Calculus was extraordinarily effective, but nobody could really explain how it worked.
A bunch of German Herr Doktor Professors set about applying Mathematical Rigour to the Field.
Riemann, Weierstrauss, Dedekind, et. al. gave us the completely unnecessary "epsilon-delta" definition that weeds out otherwise promising undergraduates from the sciences.

By the early eighteen hundreds, the Brits came back into the game. Cayley, Sylvester, de Morgan invented Matrix Theory and extended it to the Calculus, Imaginary Numbers, Abstract Algebra and beyond. Maxwell systematized the slapdash set of rules of thumb into the Maxwell Equations we know today.

Many of those mixed fields of Algebraic Geometry, Functional Analysis, Mathematical Statistics and such came about as Mathematicians realized they were all just different parts of the same elephant they were grabbing.

de Morgan's Law is that the negation of this and that is not this or not that, and vice versa.
de Morgan, as we learned from the program, was the professor who gave Ada Lovelace a few years of correspondence training in higher maths. That description of her as a 'talented undergraduate' seems accurate. Like Gauss and Newton, if her progress was halted, she knew how to develop a new tool to get around it.

I worked on a Project Gutenberg book of Mathematical Quotations that was just about as interesting as you think it is.
However, the book came alive whenever a snappy quote from de Morgan came along.
Many selections come from "A Budget of Paradoxes," available on gutenberg.org.

The moving power of mathematical invention is not
reasoning but imagination.--DE MORGAN, A.
Geometrical reasoning, and arithmetical process, have each
its own office: to mix the two in elementary instruction, is
injurious to the proper acquisition of both.--DE MORGAN, A.
Remember this, the rule for giving an extempore lecture
is--let the mind rest from the subject entirely for an interval
preceding the lecture, after the notes are prepared; the thoughts
will ferment without your knowing it, and enter into new
combinations; but if you keep the mind active upon the subject up
to the moment, the subject will not ferment but stupefy.
It is easier to square the circle than to get round a
mathematician.--DE MORGAN, A.
De Morgan was explaining to an actuary what was the chance
that a certain proportion of some group of people would at the
end of a given time be alive; and quoted the actuarial formula,
involving π, which, in answer to a question, he explained
stood for the ratio of the circumference of a circle to its
diameter. His acquaintance, who had so far listened to the
explanation with interest, interrupted him and exclaimed, “My
dear friend, that must be a delusion, what can a circle have to
do with the number of people alive at a given time?”

--BALL, W. W. R.
A few days afterwards, I went to him [the same actuary
referred to in 945] and very gravely told him that I had discovered
the law of human mortality in the Carlisle Table, of which he
thought very highly. I told him that the law was involved in this
circumstance. Take the table of the expectation of life, choose
any age, take its expectation and make the nearest integer a new
age, do the same with that, and so on; begin at what age you like,
you are sure to end at the place where the age past is equal, or
most nearly equal, to the expectation to come. “You don’t mean
that this always happens?”--“Try it.” He did try, again and again;
and found it as I said. “This is, indeed, a curious thing; this
_is_ a discovery!” I might have sent him about trumpeting the law
of life: but I contented myself with informing him that the same
thing would happen with any table whatsoever in which the first
column goes up and the second goes down;....--DE MORGAN, A.

Replies

Couch Potato January 22, 2018 at 8:01am

Thank you!
Tim Szeliga January 19, 2018 at 2:18pm

a bit longwinded, but provides background to an excellent program.

Read "The Counterfeiters" by Hugh Kenner for info on Babbage.
- william warren > Tim Szeliga January 20, 2018 at 12:27pm
  
  Thanks Tim.
  
  I have just spent some time exploring Wikipedia attempting to get my head around the subjects raised in your posting.
  
  I will admit most of it is way above my head, but fascinating nonetheless.
  
  Where would we be if it wasn't for the likes of these mathematicians and their determination to explore numbers?
- Gayle Crane > william warren January 21, 2018 at 11:11am
  
  Excellent!! Thanks, William.
Tim Szeliga January 19, 2018 at 11:07am
Some background on 19th Century British Mathematics, especially de Morgan.

Newton invented the Calculus in 1666, used it to move some planets around and then forgot about it.
That was the lone peak of British maths for another century.

Leibniz invented it independently ten years later and spent the rest of his life defending his claims against Newton's attack dogs. Basically, N invented derivatives and L invented Integration and the two are inverse operations of each other.
L's notation was much easier to use.

While they were squabbling, the French took Calculus and really made it sing.
Laplace, Lagrange, Legendre and a bunch of other L's applied it to the Universe and figured out planetary motion.
They got hung up on the question "Is the Universe stable?". It is, unless something bumps it.

The mathematical arena moved from France to Germany.
Gauss used the Calculus to locate the asteroid Ceres. He only had three shaky astronomical observations, then Ceres disappeared behind the Sun. Calculus alone wasn't enough, so he invented Least Squares Analysis and Error Analysis and a bunch of other math we now use every day, to make his prediction.
That March, astronomers pointed to his zenith/azimuth and there it was, more or less.

Gauss put Probability on a firm footing and invented Gaussian Elimination, Gaussian curves and many other Gaussian things. What we now call Bayesian Statistics was Gauss taking a paper and a few scribbles from an English country parson and then mathematizing it. By then it was agreed not to name everything after him, so Rev. Bayes got to keep the title.

Euler invented Number Theory, Graph Theory, much of Topology and wrote so many papers that scholars are still cataloging them to this day.

Calculus was extraordinarily effective, but nobody could really explain how it worked.
A bunch of German Herr Doktor Professors set about applying Mathematical Rigour to the Field.
Riemann, Weierstrauss, Dedekind, et. al. gave us the completely unnecessary "epsilon-delta" definition that weeds out otherwise promising undergraduates from the sciences.

By the early eighteen hundreds, the Brits came back into the game. Cayley, Sylvester, de Morgan invented Matrix Theory and extended it to the Calculus, Imaginary Numbers, Abstract Algebra and beyond. Maxwell systematized the slapdash set of rules of thumb into the Maxwell Equations we know today.

Many of those mixed fields of Algebraic Geometry, Functional Analysis, Mathematical Statistics and such came about as Mathematicians realized they were all just different parts of the same elephant they were grabbing.

de Morgan's Law is that the negation of this and that is not this or not that, and vice versa.
de Morgan, as we learned from the program, was the professor who gave Ada Lovelace a few years of correspondence training in higher maths. That description of her as a 'talented undergraduate' seems accurate. Like Gauss and Newton, if her progress was halted, she knew how to develop a new tool to get around it.

I worked on a Project Gutenberg book of Mathematical Quotations that was just about as interesting as you think it is.
However, the book came alive whenever a snappy quote from de Morgan came along.
Many selections come from "A Budget of Paradoxes," available on gutenberg.org.
- The moving power of mathematical invention is not
  reasoning but imagination.--DE MORGAN, A.
- Geometrical reasoning, and arithmetical process, have each
  its own office: to mix the two in elementary instruction, is
  injurious to the proper acquisition of both.--DE MORGAN, A.
- Remember this, the rule for giving an extempore lecture
  is--let the mind rest from the subject entirely for an interval
  preceding the lecture, after the notes are prepared; the thoughts
  will ferment without your knowing it, and enter into new
  combinations; but if you keep the mind active upon the subject up
  to the moment, the subject will not ferment but stupefy.
- It is easier to square the circle than to get round a
  mathematician.--DE MORGAN, A.
- De Morgan was explaining to an actuary what was the chance
  that a certain proportion of some group of people would at the
  end of a given time be alive; and quoted the actuarial formula,
  involving π, which, in answer to a question, he explained
  stood for the ratio of the circumference of a circle to its
  diameter. His acquaintance, who had so far listened to the
  explanation with interest, interrupted him and exclaimed, “My
  dear friend, that must be a delusion, what can a circle have to
  do with the number of people alive at a given time?”
  
  --BALL, W. W. R.
- A few days afterwards, I went to him [the same actuary
  referred to in 945] and very gravely told him that I had discovered
  the law of human mortality in the Carlisle Table, of which he
  thought very highly. I told him that the law was involved in this
  circumstance. Take the table of the expectation of life, choose
  any age, take its expectation and make the nearest integer a new
  age, do the same with that, and so on; begin at what age you like,
  you are sure to end at the place where the age past is equal, or
  most nearly equal, to the expectation to come. “You don’t mean
  that this always happens?”--“Try it.” He did try, again and again;
  and found it as I said. “This is, indeed, a curious thing; this
  _is_ a discovery!” I might have sent him about trumpeting the law
  of life: but I contented myself with informing him that the same
  thing would happen with any table whatsoever in which the first
  column goes up and the second goes down;....--DE MORGAN, A.
abby January 18, 2018 at 7:43am

Thanks!
Tim Szeliga January 17, 2018 at 11:04am

Oooh, this looks good!

Thanks

This reply was deleted.

Classic & Contemporary Drama

Replies