pretend you're me and you're in math
class actually never mind i'm sick so
i'm staying home today so please pretend
you're stannislav ulam instead what i'm
about to tell you is a true story so
you're stan ulam and you're at a meeting
but there's this really boring
presentation so of course you're
doodling and because you're ulim and not
me you really like numbers i mean super
like them so much that what you're
doodling is numbers just counting
starting with one and spiraling them
around i'm not too fluent in
mathematical notation so i find things
like numbers to be distracting but
you're a number theorist and if you love
numbers who am i to judge thing is
because you know numbers so intimately
you can see beyond the confusing
squiggly lines you're drawing right into
the heart of the numbers and because
you're a number theorist and everyone
knows number theorists are enamored of
prime numbers which is probably why they
named them prime numbers the primes
you've doodled suddenly jump out at you
like the exotic indivisible beasts they
are so you start drawing a heart around
each prime i mean it was actually boxes
but in my version of the story it's
hearts because you're not afraid to
express your true feelings about prime
numbers you can probably do this
instantly but it's going to take me a
little longer i'm all like does 27 have
factors besides 1 and itself oh yeah
it's 3 times 9 not prime what about 29
pretty sure it's prime but as a number
theorist you'll be shocked to know it
takes me a moment to figure these things
out but even though you've got your
primes memorized up to at least a
thousand that doesn't change that primes
in general are difficult to find i mean
if i asked you to find me the highest
even number you'd be like that's silly
give me the even number you think is the
highest and i'll just add 2 to it bam
but guess what the highest prime number
we know is
2 to the power of 43 million 112
609 minus 1.
just to give you an idea of what a big
deal prime numbers are the guy who found
this one won a hundred thousand dollar
prize for it
i mean we sent our largest known prime
number into space because scientists
think aliens will recognize it as
something important not just some
arbitrary number so they'll be able to
figure out our alien space message so if
you ever think you don't care about
prime numbers because they're not useful
remember that we use prime numbers to
talk to aliens i'm not even making this
up it makes sense because mathematics is
probably one of the only things all life
has in common
anyway the point is that you started
doodling this because you were bored but
ended up discovering some neat patterns
see how the primes tend to line up on
the diagonals why do they do that
also this sort of skeletal structure
reminds me of bones so let's call these
diagonal runs of primes prime ribs but
how do you predict when a prime rib will
end i mean maybe this next number is
prime but my head is too fuzzy for this
right now so you tell me anyway
congratulations you've discovered the
ulum spiral so that's a bit of
mathematical doodling history for you
you can stop being ulum now or you could
continue maybe you like being a limb
that's fine but you could also be blaze
pascal
here's another number game you can do
using pascal's triangle i don't know why
i'm so into numbers today but i have a
cold so if you'll just indulge my sick
pet elections maybe i'll manage to
infect you with my enthusiasm pascal's
triangle is the one where you get the
next row in the triangle by adding up
two adjacent numbers constructing
pascal's triangle is in itself a sort of
number game because it's not just about
practicing adding but trying to find
patterns and relationships in the
numbers so that you don't have to do all
the adding i don't know if this was
discovered through doodling but it was
discovered independently in france italy
persia china and probably other places
too so it's possible someone did right
so i don't actually care about the
individual numbers right now you're
still um right so like you would do you
pick a property and highlight it for
example whether it's even or odd if you
circle all the odd numbers you'll get a
form which might be starting to look
familiar to you and it makes sense that
you'd get zerpinski's triangle because
an odd number plus an even number equals
an odd number odd plus odd is even and
even plus even is even so it's just like
the crash and burn binary tree game best
part about it is that knowing these
properties you can forget about the
details of the numbers
you don't have to know that this number
will be 9 to know that it's going to be
odd
but instead of two colors let's try
three we'll color them depending on what
the remainder is when you divide the
number by three instead of two here's a
chart so all the multiples of three i'm
a color red remainder one will be black
and two will be green the structure is a
little different from sierpinski's
triangle already but i'm tired of
figuring out remainders based on
individual numbers so let's figure out
the rules if you add up two multiples of
three you always get another multiple of
three which is the sort of fact you use
every day in math class but here it
means red plus red is red and when you
add a multiple of three to something
else it doesn't change the remainder of
that something else so red plus green is
green and red plus black is black
remainder one plus remainder one equals
remainder two two plus two is four and
the remainder of four divided by three
is one and one plus two is three
remainder zero the bottom line is that
you're making up some rules as to what
colored dots combine to get what other
colored dots and then you're following
those rules to their mathematical and
artistic conclusion the numbers
themselves were never necessary to get
this picture anyway those are just a
couple examples of number games that are
out there but you should also try making
up your own for example i have no idea
what you get if you highlight the prime
numbers in pascal's triangle maybe
nothing interesting who knows or what
happens if instead of adding to get the
next row you start with a 2 and a c of
invisible ones and multiply to get the
next row no idea what happens there
either or if it's already a thing people
do or what oh wait powers of two
i know another way to write this okay
that makes sense and then there's also a
thing called floyd's triangle where you
put the numbers like this so maybe you
can do something with that too man it
seems like everyone has a triangle these
days i'm gonna take a nap