Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang

III. Methods and tools
mathmatis is ommonly undrstood
Knowing
th aility to rason through mathmatial
as
and symols. Is it possil to know
formula
in othr ways, not as languag or
mathmatis
ut as ativity or prforman—
rprsntation
as know-how? Exampls from
mathmatis
show that th mind is not
thnomathmatis
only hannl into th ralm of mathmatis,
our
that it an “known” through th whol
ut
as an modid prati, and vn through
ody
arrangmnt of othr ojts in th physial
th
If w an do and find mathmatis
world.
of th human mind, how far an w go
outsid
for mathmatis?
looking
slugs do maths, electrons do maths, minerals
Sea
maths. Rainbows do an incredible mathematical
do
Euler’s 18th-century formula, with its unique
Leonhard
properties, is enacted here by a bird.
mathematical
th link to rad th full artil: “How to
Follow
Mathmatis”.
Play
trms: Aon Thr’s
Sarh
maths in slugs
mor
can we say that sea slugs and corals know
But
geometry? I want to argue here that in
hyperbolic
sense they do. … The world is full of mundane,
some
unconscious things materially embodying
meek,
complex pieces of mathematics. How can
endishly
make sense of this? I’d like to propose that …
we
natural systems are engaged in what we
modest
call the performance of mathematics. Rather
might
thinking about maths, they are doing it. In the
than
of their beings and the ongoing continuity of
bres
growth and existence they enact mathematical
their
and become mathematicians-by-
relationships
… Rather than being a remote abstraction,
practice.
can be conceived of as something more
mathematics
music or dancing; an activity that takes place not
like
much in the writing down as in the playing out.
so
do ths raturs hallng what it mans
How
“know” mathmatis? Wrthim likns
to
to musi; th intrstion of th two
mathmatis
has a omprhnsiv disours in
disiplins
aross many diffrnt ultural traditions.
itslf,
ragas of Indian lassial musi, for xampl,
Th
passd down aurally from mastr
traditionally
studnt, ar rognizd as inhrntly
to
Th Sanskrit word prastara mans
mathmatial.
study of mathmatially arranging ragas and
th
What is th diffrn twn trating
1.
as a languag vrsus
mathmatis
(a) Do you hav to know how to writ
2.
to do mathmatis?
mathmatis
(b) To what xtnt is this th as in th
To what xtnt is playing musi without
3.
al to rad musi omparal to
ing
mathmatis without ing al to
doing
mathmatis?
rad
11
III.4 In what ways can mathematics
be known?
(Wertheim 2017)
… Next time you see a good rainbow,
performance
and take a look … classical geometric optics
stop
begin to capture its complexity. A stunning
doesn’t
of mathematical performance is enacted by a
piece
falcon as it hurtles towards its prey; with its
peregrine
held straight so it can x one eye steadily on the
head
at a constant angle of 40 degrees, it swoops
quarry
at 200 mph in a perfect logarithmic spiral.
down
rhythms into plasing ompositions.
(Wertheim 2017)
For discussion
Language, reading and writing
trating it as an ativity?
othr AOKs?
Figure 11.7 Sa slug
344