Kind: captions
Language: en
in 1901 this ancient greek artifact was
discovered in a shipwreck off the island
of antikythera
3d x-ray scans have revealed it contains
37 interlocking bronze gears allowing it
to model the motions of the sun and moon
and predict eclipses decades in advance
constructed around 100 or 200 bc the
antikythera mechanism represents a
sophisticated early computer the likes
of which would not be seen again for at
least a thousand years
now of course this computer didn't work
like modern digital computers it works
by analogy
the gears were constructed in such a way
that the motions of certain dials are
analogous to the motion of the sun and
moon
it is an analog computer
here is a simple analog computer for
adding two numbers together if you turn
the black wheel some amount and then
turn this white wheel a different amount
the gray wheel shows the sum of the two
rotations
in contrast this is a digital mechanical
computer where you can add two single
bit numbers so 0 plus zero equals zero
zero plus one equals one
and one plus one equals two
these two devices illustrate the
differences between analog and digital
computers
analog computers have a continuous range
of inputs and outputs whereas digital
only works with discrete values
with analog computers the quantities of
interest are actually represented by
something physical like the amount a
wheel has turned whereas digital
computers work on symbols like zeros and
ones if the answer is say two there is
nothing in the computer that is twice as
much as a one in analog computers there
is
for thousands of years people used
analog devices like the antikythera
mechanism or slide rules alongside
digital devices like abacuses and up
until the 1960s the most powerful
computers on the planet were actually
analog
digital computers exploded onto the
scene with the advent of solid-state
transistors now almost everything is
digital most people have never even
heard of analog computers
but today that may all be changing
moore's law the idea that you can double
the number of transistors on a chip
every two years it's reaching its limit
because transistors are nearly the same
size as atoms simultaneously
advancements in machine learning are
straining the capabilities of digital
computers
the solution to these challenges may
well be a new generation of analog
computers
[Music]
one of the most important problems
humans have faced for millennia is
predicting the tides
napoleon and his men nearly died
crossing the red sea due to a
miscalculation of the rising tide
and sailors routinely needed to know the
tides to bring their ships into port
without running aground
most coastal locations on earth
experience too high and too low tides
per day
but their exact timing varies as does
their magnitude and this is partly
caused by local factors like the depth
of the seabed and the shape of the
shoreline
in the late 1700s to describe the tidal
flow of the oceans pierre simon laplace
derived a set of complicated
differential equations
they had no analytical solution so at
the time they were basically useless
but in the process of deriving his
equations laplace made a key finding
tides are driven at only a few specific
astronomical frequencies including the
moon
the sun
and the eccentricity of the lunar orbit
each one of these factors contributes a
sine wave of a particular amplitude and
phase to the total tide curve
if someone could figure out how to
correctly combine these frequency
components well the tides could finally
be predicted
it took nearly a century but in the
1860s william thompson later lord kelvin
took up the challenge having completed
several voyages to lay the first
transatlantic telegraph cable he
developed a fascination with the sea and
subsequently he threw his full
scientific effort into measuring and
predicting the tides
tide gauges at the time used a buoy to
record the height of the sea onto a
paper roll
kelvin set out to determine how sine
waves with the frequencies identified by
laplace could add together to produce
the observed tidal curve
the key was to apply the work of french
mathematician joseph fourier who had
shown how to decompose any function into
a sum of sine waves
most english scientists were skeptical
of the work but thompson was enthralled
by it his first paper published at 17
was a defense of fourier
while it was straightforward to apply
fourier's analysis to title curves the
computation required was enormous
first divide the tide curve up into
short time intervals and for each
interval multiply the tide level by a
sine wave with the frequency of interest
add up the area of all these rectangles
and divide by the total time
and this gives you a single coefficient
the amplitude of the sine wave with this
frequency
then you have to repeat the process for
a cosine function with the same
frequency kelvin found that to make
accurate predictions he actually needed
10 different frequency components so
that is a lot of multiplication and
addition to characterize the tides at
just one location
for each additional location you have to
perform this analysis all over again
and this is only half the problem
once you have the amplitudes and phases
of the sine functions you have to add
them up to predict future tides
lord calvin spent years analyzing and
predicting tides by hand
then he had a stroke of inspiration
could you design a machine to carry out
these calculations automatically in
kelvin's words to substitute brass for
brains
the resulting analog computers were in
use for nearly a century they even
played a critical role in the outcome of
world war ii
kelvin started with the problem of
prediction adding the sine waves
together given you know their amplitudes
and phases
he knew he could create sinusoidal
motion with a device called a scotch
yoke it extracts one dimension from
uniform circular motion
but to make a tide prediction he needed
a way to combine 10 sine waves together
he needed a mechanical analog for
addition
stuck on this problem in 1872 calvin
boarded a train for a meeting with the
main sponsor of his title research the
british association
on the train calvin bumped into a friend
inventor beauchamp tower to whom he
explained his dilemma
tower suggested he used wheatstone's
plan of a chain passing round a number
of pulleys
and this was exactly the addition
mechanism calvin was looking for
by attaching a pulley to each scotch
yolk and running a weighted cord around
them he could mechanically add all of
their contributions at once
he scribbled down the entire plan for
this predictor machine by the end of the
train ride he pitched it to the british
association and secured funding to build
it all before he returned home
if you knew the relative contributions
of different frequency components calvin
now had a machine to automate the
tedious task of predicting future tides
this was a great leap forward
four hours of cranking the handle
yielded a full year of title predictions
but for many years the harder half of
the problem was still done by hand
breaking apart an existing tide curve
into its component frequencies
to automate this step calvin needed a
machine capable of multiplying the tide
curve times a sine wave and then taking
its integral
what would such a device even look like
with his older brother james thompson
calvin came up with a mechanical
integrator it consists of a ball on a
rotating disc
due to the rotation of the disc the
further the ball is from the center the
faster it spins
if the ball is at the very center of the
disc it doesn't turn at all
and if it's on the left side it turns in
the opposite direction
now the motion of the ball is converted
into an output via a roller which moves
a pen up or down on the output graph
paper
so the way it works is you trace the
function you want to integrate with a
stylus and the stylus controls the
position of the ball on the disc and
hence its speed of rotation
this is transferred through the roller
to the output which plots the integral
of the original function
now to decompose a tide curve we don't
just want to integrate the function we
first want to multiply it by a sine wave
of a particular frequency
and the way to do this is to make the
disk rotate back and forth at that
specific frequency
now the rotation of the ball depends not
only on where it is on the disc but also
on how the disc is turning at that
instant
you trace the tide curve with the stylus
which moves the ball back and forth on
the oscillating disc and the roller sums
up the integral of the tied curve times
the sine wave
simply divide by the total time to get
the coefficient
several of these ball and disc
integrators can be connected in parallel
with each disk oscillating at a
different frequency to calculate the
coefficients for multiple frequency
components at the same time
kelvin's analog computers revolutionized
our ability to predict tides
tidal curves from anywhere in the world
could be turned into a set of sinusoidal
coefficients using the ball and disk
harmonic analyzer
and the resulting sinusoids could be
added together to predict future tides
using his scotch yoke pulley machine
kelvin's harmonic analyzers were the
basis for a landmark analog computer
called the differential analyzer and his
tied predicting machines were used well
into the 1960s in fact they were later
overhauled to include 26 frequency
components and used to plan the allied
invasion on d-day
the germans expected any invasion to
come at high tide to minimize the time
allied soldiers would be exposed on the
beaches so they installed millions of
obstacles that would be underwater by
mid-tide many with explosive mines
attached but the allies spotted the
obstacles and changed tack instead they
planned to begin the invasion at low
tide this would allow demolition teams
to first clear channels through the
obstacles then the main forces could
come through those gaps as the water
rose
this would also give landing craft
enough time to depart without getting
beached the low water times were
different at the five landing beaches by
over an hour so the invasion times were
staggered according to the tide
predictions
this wasn't the only use of analog
computers in world war ii
dive bomber aircraft would plummet out
of the sky directly toward their targets
at up to an 80 degree angle and their
rapid descents made them very difficult
to shoot down
so the u.s began searching for devices
to automatically aim guns at dive
bombers
most of the proposed solutions fell into
one of two categories
some were analog machines like lord
calvin's others were essentially fast
calculators mechanical calculating
machines like the abacus had been around
for millennia but they were far too slow
to respond to dive bombers these new
calculating machines sped things up by
using electrical pulses the committee
considered naming these devices after
the pulses they used but member george
stibits proposed a more general name
digital because these machines operated
on numbers themselves or digits
and this is the origin of the term
digital computer
but digital would have to wait of all
the proposals an innovative analog
machine from david parkinson won out
at bell labs in new york parkinson had
been working on a device to chart
telephone data called an automatic level
recorder it used a variable resistor
called a potentiometer to control the
motion of a pen
one night after hearing reports of the
harrowing allied evacuation of dunkirk
parkinson had a dream that he was on the
front lines
[Music]
i found myself in a gun pit with an
anti-aircraft gun crew
a gun there was firing occasionally and
the impressive thing was that every shot
brought down an airplane
after three or four shots one of the men
in the crew smiled at me and beckoned me
to come closer to the gun
when i drew near he pointed to the
exposed end of the left trunnion
mounted there was the control
potentiometer of my level recorder
when he woke up parkinson realized the
device he was building to control a pen
could be scaled up to control an
anti-aircraft gun
he shared this idea with his supervisor
and after receiving approval from the
military they set out to make
parkinson's dream a reality
researchers at bell labs had recently
invented an analog electrical device
called an operational amplifier or
op-amp it could perform mathematical
operations with voltages like addition
and multiplication
they used these op-amps to create an
analog computer that could solve the
ballistics equations for anti-aircraft
guns
using radar and optical sights to obtain
the speed altitude and direction of
enemy planes the m9 gun director as the
computer was called could rapidly
calculate the correct trajectory and
fuse setting
potentiometers were used to ascertain
the direction the gun was pointing
this was not the first electric analog
computer but it was an important one
in world war one it took an average of
17 000 rounds to take down a single
airplane in 1943 after the invention of
the m9 it took an average of only 90.
during the war the u.s invested big in
analog computers if you break down their
total military budget the third largest
single expense was the development and
production of an incredibly complex
mechanical analog computer called the
norden bomb site
unfortunately they didn't get their
money's worth
designed by the eccentric dutch engineer
carl norton the norton bomb site was
built to enable high precision airborne
bombing it implemented 64 different
simultaneous algorithms including one
that compensated for the rotation of the
earth as the bomb fell
the norden was one of the most closely
guarded secrets of the war
to prevent the technology from falling
into enemy hands american bombardiers
carried handguns specifically to destroy
it in the event of a crash
but despite its hype and funding the
norton didn't work as advertised with
over 2 000 fine parts it required
extreme precision to manufacture
the problem with analog computers is
that the physical device is a model for
the real world
so any inaccuracy in the components
translates into inaccuracy of the
computation
and since there will always be some slop
in the connections between parts if you
run the same calculation twice you won't
get the exact same answer
in the american campaign against japan
bomber crews using the bomb site were
unable to destroy critical japanese war
infrastructure and ultimately the u.s
abandoned its precision bombing approach
and instead blanketed whole japanese
cities in napalm
as the war progressed digital computers
gained traction the digital and
electronic colossus machines of
bletchley park in the uk were critical
to breaking german codes
in the united states the military
invested in an enormously complex and
expensive digital machine known as eniac
it was designed to speed up the
calculation of land artillery firing
tables at the time these were computed
using differential analyzers the analog
mechanical computers based on calvin's
harmonic analyzer
although not finished until after the
war eniac demonstrated the power of
digital computers
it's considered by many to be the first
modern computer
what really opened the door to this
digital revolution was the discovery
made by claude shannon in his 1936
masters thesis
he showed that any numerical operation
can be carried out using the basic
building blocks of boolean algebra
two values true or false also notated as
one or zero and three operations and or
and not
this makes digital computers the ideal
versatile computing machines in contrast
each analog computer is an analog for
only one type of problem
furthermore since digital computers
operate on ones and zeros they are more
resilient in the face of noise it would
take a large error to mistake a one for
a zero or vice versa whereas even small
errors in analog computers can grow and
ultimately swamp the signal
so these days everything is digital our
phones computers and internet data
centers even tv and radio is now being
broadcast as digital the advantages are
obvious since digital devices operate on
symbols usually zeros and ones they
provide exact answers and repeat the
calculation and you get the same result
they are robust to noise plus since only
a few components are required to perform
virtually any computation those
components have been miniaturized and
optimized making digital computers the
ideal universal computing machines
so you would think analog computers
would be long gone a relic of the
distant past
but
analog may now be making a comeback
there are startups actively working on
analog computers
why is this happening what could be the
benefit of analog
i wanted to put all of this into one
video
but the story is too good to bury 20
minutes in so that is coming up in part
two be sure you're subscribed to the
channel to be notified when that comes
out
i'll give you a hint about the sequel in
this section of the video which is
sponsored by brilliant brilliant is a
website an app that uses interactivity
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sequel to this video it would be a good
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intelligence which you can do with
brilliance courses on neural networks
here you can analyze how a neural
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