Why A4 Paper Is a Mathematical Miracle
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Downloadthis is not just a sheet of paper it is
an invitation
to everything that exists for this paper
is metric which has a special property
other pages don't dividing into each
twain is half the whole
uh obviously i guess but each half is
also the same
shape as the whole the ratio of its
sides identical
this only works for metric though for
origami and letter paper their halves
are half as big but
different shapes which is far less
satisfying a full sheet of metric is
named
a4 and each half a5 and each half of
that
a6 all the same shape again and so it
goes in the opposite direction
double a4 to get same shaped a3 again to
a2
to a1 to zero which is one square meter
of paper exactly and
exactly the same shape as a4 with metric
paper
everything from posters to postage can
be designed on the a4
before you and scaled up or down
perfectly no fuzzing with the margins
and everything can fit on a roll of a
zero exactly for printing
it's so satisfying and practical and
mathematical
each sheet of a4 so hypnotizing
this a4 is a door to
the exponential spiral of everything
begin with one sheet of a4 metric paper
divide in half
then half the half again and again
always creating the same shape dividing
down to
the size of a b and then smaller to
the size of the organs of the bee and
the detailed limit of human vision
but no need to stop here at 24 divisions
are the cells of the bee
each just as alive as the animal they
form and each with their own
organs carrying out the business of
animating inert matter
defending themselves from viruses things
so small as to
hover on the edge of what can be alive
32 divisions down
and we enter the mechanical brain of
this animal cell
containing chromosomes of dna the
operating system of life
tightly coiled but it's here the lights
go out
just 39 divisions is already smaller
than visible light
and seeing in a meaningfully human way
with
limited human eyes is meaningless so
let us turn on atomic vision to explore
what's here
56 divisions down is the width of a
strand of dna where
hexagonal arrangements of atoms interact
mechanically to build living things
to build more dna 64 divisions down is
the size of a single hydrogen atom and
we fall through its electron orbital to
enter the interior and
discover the truth of matter it is made
of mostly nothing
everything you touch everything physical
you care about
is an electron cloud creating the
illusion of something
over nothing at the center of the atom
there is but the tiniest speck of matter
the hydrogen nucleus a single proton 1
100 the size of the atom that contains
it
before yet even a hundred half divisions
down from the a4 where we started
begins to stretch human
comprehensibility the proton isn't a
sphere but
a sea of quarks appearing and
disappearing
averaging out two three bound together
with the strongest force
here we hover above the edge of the
abyss of quantum deep before
plunging down into the nothing falling
for twice as many divisions down as we
have already traveled until we reach
quantum madness at the very floor of the
universe and
the limit of our current theories the
planck length
there is nothing here yet this is the
smallest size
the least distance that can be moved or
measured
a sort of reality pixel which is best
not to think about so
let us fly back up the quantum well
doubling and doubling to return to the
world of quarks and nuclei
and atoms and light and the illusory
cloud of the physical
back to life back to our sheet of a4
paper
which now unfolds itself to a sheet
twice the size
doubling to the size of a desk then a
room
then a home the building the home is in
the street the building is on continuing
this same shape spiral to double to the
size of the neighborhood around the
street
then the size of a town a small city
a thing which is not alive but a meta
organism which
lives through the actions of its human
cells just
36 doublings of a sheet of a4 is the
size of the largest cities and
it is at this scale the accomplishments
of the human species are most visible
and impressive
but just a few doublings later every
structure that humans hath wrought
fades to invisibility and only the light
we
create can be seen at twice the distance
the earth is wide are the farthest
satellites passing light around earth
for
instant terran communication sixty
doublings brings the moon's orbit
into view and at this scale the speed of
light
instance just a moment ago is now slow
enough to watch
move a beam from earth to the moon
taking
one second as far as we know this is the
speed limit
of the universe nothing can travel
faster
communication between earth and moon
will always have a delay
and as we resume doublings it will not
be long before the speed of light proves
heartbreakingly slow past 68 doublings
earth becomes too small to see
so we must draw her orbit instead and at
76 doublings we can see the orbits of
venus and mars
light now takes two minutes to reach
venus and
14 to reach mars 80 dumplings is the
distance to the sun
our home star and doublings beyond this
reveal the orbits of the outer planets
and eventually the whole of the solar
system which
light takes eight hours to cross beyond
the orbit of pluto is the voyager 1
space probe
the farthest any object produced by
human civilization has traveled
yet at the scale of all that exists our
species has explored
nothing there are yet still 20 doublings
to go before we've left our home
star after what would take a month
traveling at the speed of light we
entered the oort cloud i see
planetesimals occasionally knocked from
orbits to fall inward
becoming comets it would take another
year at light speed to leave the oort
cloud and
the realm of the sun's dominance 124
doublings is wide enough to reach our
closest neighboring stars but
at this scale they are only points of
light and
thus the truth of space it is made of
mostly nothing
stars with their own planets and
potentially their own life
Key Vocabulary (50)
toward
"Go to school."
belonging
"Cup of tea."
also
"You and me."
inside
"In the house."
specific
"That book."
A third-person singular pronoun used to refer to an object, animal, or situation that has already been mentioned or is clear from context. It is also frequently used as a dummy subject to talk about time, weather, or distance.
Used to show who is intended to have or use something, or to explain the purpose or reason for an action. It is also frequently used to indicate a specific duration of time.
A function word used to express negation or denial. It is primarily used to make a sentence or phrase negative, often following an auxiliary verb or the verb 'to be'.
A preposition used to indicate that something is in a position above and supported by a surface. It is also used to indicate a specific day or date, or to show that a device is functioning.
A preposition used to indicate that people or things are together, in the same place, or performing an action together. It can also describe the instrument used to perform an action or a characteristic that someone or something has.
A conjunction used to compare two things that are equal in some way. It is most commonly used in the pattern 'as + adjective/adverb + as' to show similarity.
A preposition used to indicate a specific point, location, or position in space. It is also used to specify a particular point in time or a certain state or activity.
Used to identify a specific person, thing, or idea that is physically close to the speaker or has just been mentioned. It can also refer to the present time or a situation that is currently happening.
A coordinating conjunction used to connect two statements that contrast with each other. It is used to introduce an added statement that is different from what has already been mentioned.
Used to indicate the starting point, source, or origin of something. It can describe a physical location, a point in time, or the person who sent or gave an item.
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- Thank you, Bonnie Bees, for making this video possible: https://www.patreon.com/cgpgrey ## Related Videos Powers of Ten: https://www.youtube.com/watch?v=0fKBhvDjuy0 The Secret City of...
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