So now I'm going to look at
this other aspect of
property, quantity.
Though of course this is
not separate from quality.
In the modern world
we are constantly
transposing quality
and quantity.
We use digital devices
to measure qualities -
colors, temperatures,
speeds, weight,
and such things.
And we give these alphanumeric
names, which are
much of the time
almost impossible to speak.
These are some of the
ways we represent
quantity in text, where
some numbers are
too long to say
and some equations
too complicated.
And let me jump
to speech for
a moment. Only
a few numbers
are speakable in
spontaneous speech and
memorable for the
purposes of later
speaking, like the
36 apples we just
counted on the tray
or the year 2020.
If we need
anything more than
this, we have to read it
out which is not the
same as speaking in
the normal sense.
It is a multimodal
practice
reliant on text. 
Quantity
can also be represented
two-dimensionally
in image,
three-dimensionally in
space, in the physics
of objects, in
the sensations
of our bodies, how they feel
and as temperature, and in
sound in musical
notation, which
represents
fractions of time
and levels of pitch.
And here is
Gottfried Lieibniz,
the great 17th to
18th century philosopher
and mathematician.
Now Leibniz had
a fantasy that
if all meanings in
the world could
be expressed in
numbers, every truth in
the world would
be determined
mathematically.
Then, he said famously,
"where there are
disputes among persons,
we can simply say,
Let us calculate,
without further
ado, in order to
see who is right." 
Moving forward now into
the 19th century, we meet
another mathematical
genius Ada Lovelace.
She had inherited her love
of mathematics
from her mother,
Anna Isabella Noel Byron,
the 11th Baroness
of Wentworth.
Anna's husband and Ada's
father was the poet
Lord Byron. 
Ada's father
dismissively
called his wife
the "Princess of
Parallelograms."
Dismissiveness like
this has been the fate
of women thinkers
like these women for
a long time. At the
age of 18, Ada
Lovelace was introduced to
the inventor Charles
Babbage at one of
the high society soirees
he regularly held at
his home in London.
She was attending
with her mother.
On display in the
drawing room of
Babbage's house was
his "Difference Engine,"
an elaborate
mechanical calculator.
Ada was transfixed.
This began a long
professional association
between Babbage
and Lovelace.
Their work together
culminated in
1843 with the
publication by
Lovelace of
a 20 thousand word
journal article about
Babbage's design for
a new analytical
engine. Lovelace simply
sign the article
with her initials
A.A.L. In those days,
who would have
imagined that this
was written by
a woman? Over a 100
years later, one of
the main founders of
modern computing
Alan Turing
turned up Lovelace is
largely forgotten article
and was able to build on
some of her key
propositions.
Here are some of the words
Ada Lovelace used
in her article.
And I'm sure you
will agree for
someone writing in 1843,
these words are
remarkably prescient.
So she says
by mathematical
representation and
calculation it may
be possible to
"express the greatest facts
of the natural world,
and those unceasing
changes of
mutual relationships,
which visibly or
invisibly, consciously
or unconsciously,
to our immediate
physical perceptions
are interminally
going on in
the agencies of
the creations
we live amidst."
Lovelace continues.
She says "The analytical
engine weaves
algebraic patterns
just as the Jacquard-loom
weaves leaves
and flowers," she said. In
these ways, and I'm
continuing to quote her
now, "not only the
mental and the material,
but the theoretical
and the practical in
the mathematical
world are brought
into more intimate and
affective connection
with each other."
The model for such
mechanical possibility,
Lovelace went on, was,
quoting her again,
"the principle which Jaccard
devised for regulating
by means of
punch cards, the most
complicated patterns
in the fabrication
of brocaded stuffs."
Lovelace was truly
another modern genius,
imagining how the qualities
of the sensuous world
might be transposed into
the quantities for
the purposes of
their representation and
communication. Ada Lovelace
had imagine how in
the future in which
you and I now live, we
might be able to
build machines
which manage the
transpositions
of quality into quantity.
