The Most Powerful Computers You've Never Heard Of

Summary

The script explores the history and functionality of analog and digital computers. It highlights the Antikythera mechanism, an ancient Greek analog computer, and contrasts it with digital computers. It discusses the rise of digital computing with the advent of transistors and how it became dominant. However, with Moore's Law reaching its limits and the growing demands of machine learning, analog computers may be poised for a resurgence, as startups are now developing new analog computing technologies.

Takeaways

• 🗺️ The Antikythera mechanism, discovered in 1901, is an ancient Greek analog computer used to predict astronomical positions and eclipses.
• 🔄 Analog computers operate on continuous physical quantities, unlike digital computers which work with discrete symbols like 0s and 1s.
• 🕒 Before the advent of digital computers, analog computers like the Antikythera mechanism and slide rules were used for complex calculations.
• 🌊 Lord Kelvin's harmonic analyzers were early analog computers used to predict tides, which played a crucial role in WWII, including D-Day.
• 🛰️ During WWII, analog computers were used for various military applications, such as aiming anti-aircraft guns and calculating artillery firing tables.
• 💡 Claude Shannon's master's thesis laid the foundation for digital computing by demonstrating that Boolean algebra could perform any numerical operation.
• 📉 Digital computers eventually surpassed analog computers due to their precision, noise resistance, and versatility.
• 🔄 The limitations of analog computers include sensitivity to component inaccuracies and the challenge of scaling to complex problems.
• 🔗 The term 'digital computer' originated from the need for fast calculators that could keep up with the rapid calculations required for military applications.
• 🔄 The development of solid-state transistors marked a significant shift towards digital computing, leading to the dominance of digital technology.
• 🔄 Despite their historical decline, analog computers may be experiencing a resurgence due to advancements in machine learning and the limitations of Moore's Law.

Q & A

What is the Antikythera mechanism and what does it signify in the history of computing?

The Antikythera mechanism is an ancient Greek artifact discovered in a shipwreck, dating back to around 100 or 200 BC. It is considered a sophisticated early analog computer, capable of modeling the motions of the sun and moon, and predicting eclipses. It signifies that complex mechanical computing devices were developed at least a thousand years before the advent of modern digital computers.

How does an analog computer differ from a digital computer?

Analog computers have a continuous range of inputs and outputs, where quantities of interest are represented by physical means, such as the amount a wheel has turned. Digital computers, on the other hand, work with discrete values and operate on symbols like zeros and ones. Analog computers are more susceptible to noise and inaccuracies due to their physical nature, while digital computers offer exact answers and are more robust to noise.

What was the role of analog computers in predicting tides?

Analog computers, particularly those developed by William Thompson (Lord Kelvin), played a critical role in predicting tides. They automated the process of combining multiple sine wave components, each representing different astronomical frequencies that contribute to the tide curve. This allowed for the accurate prediction of tides, which was essential for navigation and military operations.

How did Lord Kelvin's tide predicting machine work?

Lord Kelvin's tide predicting machine used a combination of mechanical devices to automate the process of predicting tides. It included a scotch yoke pulley system to add sine waves together and a ball and disk integrator to decompose the tide curve into its component frequencies. By understanding the amplitudes and phases of these sine waves, the machine could predict future tides.

What was the significance of analog computers during World War II?

Analog computers played a significant role during World War II, particularly in planning the Allied invasion on D-Day. They were used to predict tidal patterns, which were crucial for determining the timing of the invasion to ensure that landing craft could depart without getting beached. Analog computers were also used in anti-aircraft gun targeting systems, which improved the accuracy and efficiency of bringing down enemy planes.

How did the Norden bombsight exemplify the limitations of analog computers?

The Norden bombsight was a highly complex mechanical analog computer designed for precision bombing. Despite its advanced algorithms and funding, it did not perform as expected due to the inherent inaccuracies in analog systems. The physical components were prone to errors, which translated into computational inaccuracies. This led to the U.S. abandoning precision bombing in favor of more area-based strategies.

What was the pivotal discovery by Claude Shannon that influenced the development of digital computers?

Claude Shannon's pivotal discovery in his 1936 master's thesis was that any numerical operation could be carried out using the basic building blocks of Boolean algebra: two values (true or false, one or zero) and three operations (and, or, and not). This made digital computers versatile and ideal for performing a wide range of computations.

Why are analog computers potentially making a comeback?

The script hints at a potential comeback for analog computers, possibly due to advancements in machine learning and the limitations of Moore's Law in digital computing. Startups are actively working on new analog computer designs, suggesting that there may be benefits or applications where analog computing offers advantages over digital computing.

What is Moore's Law and why is it reaching its limit?

Moore's Law is the observation that the number of transistors on a microchip doubles approximately every two years. It is reaching its limit because transistors are now being manufactured at sizes close to the size of atoms, making further reductions in size challenging and potentially impractical.

How did the M9 Gun Director improve the efficiency of anti-aircraft guns during World War II?

The M9 Gun Director was an analog computer that used operational amplifiers to solve ballistics equations for anti-aircraft guns. It could rapidly calculate the correct trajectory and few settings based on radar and optical site data. This significantly improved the efficiency of anti-aircraft guns, reducing the average number of rounds needed to shoot down an enemy plane from 17,000 to just 90 in 1943.

What is the connection between the video script and Brilliant's educational platform?

The video script mentions Brilliant as a sponsor and suggests that viewers brush up on artificial intelligence and calculus, which are topics covered by Brilliant's interactive courses. Brilliant is an educational platform that helps users learn STEM concepts through interactive lessons and challenges, which is relevant to the themes of computing and technology discussed in the script.

Outlines

00:00

🔍 The Antikythera Mechanism: Early Analog Computing

The paragraph discusses the discovery of the Antikythera mechanism, an ancient Greek analog computer, in a shipwreck off the island of Antikythera in 1901. Dating back to 100-200 BC, the mechanism was found to contain 37 interlocking bronze gears that could model celestial motions and predict eclipses. It represents a sophisticated device that wouldn't be matched for a millennium. The mechanism is contrasted with digital computers, showing how analog computers work with continuous inputs and outputs, represented by physical movements like the turning of gears, while digital computers operate on discrete values like bits.

05:05

🌊 Tidal Predictions and the Birth of Analog Computing

This section delves into the historical challenge of predicting tides, which was crucial for sailors. Pierre-Simon Laplace derived a set of differential equations to describe tidal flow in the late 1700s, but these had no analytical solution and were initially unusable. William Thompson, later Lord Kelvin, took on the challenge in the 1860s, using tide gauges and the work of Joseph Fourier to decompose tidal curves into sine waves. Kelvin's innovation led to the creation of analog computers that could predict tides by combining multiple sine waves, which were critical in World War II and used until the 1960s.

10:06

🛠️ The Innovation of Mechanical Computing in War

The paragraph highlights the use of analog computers in World War II, particularly in planning the D-Day invasion. The allies used tide predictions to time their landings, which was crucial in avoiding German obstacles. It also discusses the development of the M9 Gun Director, an analog computer that improved the accuracy of anti-aircraft guns极大地, reducing the number of rounds needed to shoot down enemy planes. The Norden bombsight, another analog computer, was designed for precision bombing but ultimately failed to meet expectations due to manufacturing inaccuracies.

15:07

💡 The Shift from Analog to Digital Computing

This section contrasts the precision and repeatability of digital computers with the inaccuracies inherent in analog computers. It discusses the development of digital computers like the Colossus machines and ENIAC, which were more reliable and versatile. Claude Shannon's work is credited with opening the door to digital computing by showing that any numerical operation could be carried out using Boolean algebra. The advantages of digital computers, such as noise resilience and the ability to perform any computation with a few components, led to their dominance over analog computers.

20:07

🔄 The Resurgence of Analog Computing

The final paragraph suggests a resurgence of analog computing, with startups working on new analog computers. It raises questions about the benefits of analog computing in the modern digital age and hints at a sequel video that will explore this topic further. The paragraph also includes a sponsorship message for Brilliant, an educational platform that offers courses in STEM, including artificial intelligence and calculus, which are relevant to understanding the evolution of computing.

Keywords

💡Antikythera Mechanism

The Antikythera Mechanism is an ancient Greek artifact discovered in a shipwreck in 1901. It is a sophisticated analog computer from around 100-200 BC, composed of 37 interlocking bronze gears that modeled the motions of the sun and moon and predicted eclipses. The video uses this as an example of an early analog device to explain the difference between analog and digital computers.

💡Analog Computer

An analog computer is a computing device that represents data with physical quantities such as the rotation of gears or the movement of dials. The video highlights how analog computers, like the Antikythera Mechanism, compute using continuous inputs and outputs, contrasting this with digital computers that operate using discrete values like zeros and ones.

💡Digital Computer

A digital computer operates using binary (ones and zeros) to process data. These machines provide exact answers by manipulating discrete symbols rather than physical quantities. The video compares digital computers, which became dominant with the advent of transistors, to analog computers, emphasizing the precision and consistency of digital devices.

💡Fourier Analysis

Fourier analysis is a mathematical method used to decompose complex waveforms into simpler sine waves. In the video, it is introduced as the key tool used by Lord Kelvin to analyze tidal data by breaking down tidal patterns into their frequency components, enabling more accurate tidal predictions.

💡Tide Prediction

Tide prediction refers to the process of forecasting the rise and fall of sea levels based on astronomical and environmental factors. The video explains how Pierre-Simon Laplace's equations laid the foundation for understanding tides, and how Lord Kelvin created an analog computer to predict tides using sine wave components derived from tidal data.

💡Scotch Yoke

A scotch yoke is a mechanical device that converts rotational motion into linear motion, used to generate sinusoidal motion. The video explains that Lord Kelvin used scotch yokes in his analog computer to simulate sine waves for tidal predictions by mechanically adding multiple waveforms together.

💡Harmonic Analyzer

The harmonic analyzer is a device created by Lord Kelvin to decompose tidal curves into their frequency components, using a mechanical system of ball and disk integrators. This invention allowed for the automation of tidal analysis, making it a pivotal tool for predicting tides and even aiding military operations during World War II.

💡Moore’s Law

Moore's Law is the observation that the number of transistors on a microchip doubles approximately every two years, leading to the exponential growth of computing power. The video discusses how Moore's Law is approaching its limits as transistors reach atomic sizes, which could lead to a resurgence of interest in analog computing as an alternative.

💡Claude Shannon

Claude Shannon was a mathematician and electrical engineer who is considered the father of information theory. In his 1936 thesis, he demonstrated how Boolean algebra could be used to perform any numerical operation with binary values (ones and zeros), which laid the foundation for the modern digital computer. The video credits Shannon's work for accelerating the digital revolution.

💡Operational Amplifier (Op-Amp)

An operational amplifier, or op-amp, is an analog electrical device that can perform mathematical operations like addition and multiplication with voltages. The video mentions that op-amps were used in the development of analog computers during World War II, particularly for calculating the trajectories of anti-aircraft guns, exemplifying the real-world applications of analog computing.

Highlights

The Antikythera mechanism, discovered in 1901, is an ancient Greek artifact that modeled celestial motions and predicted eclipses.

The mechanism contains 37 interlocking bronze gears, showcasing early analog computing technology.

Analog computers represent quantities physically, unlike digital computers that use symbols like zeros and ones.

Digital computers became dominant with the advent of solid-state transistors in the 1960s.

Moore's Law is reaching its limit due to the atomic size of transistors, suggesting a potential resurgence of analog computing.

Advancements in machine learning are straining the capabilities of digital computers, indicating a possible role for analog computers.

Tides, a significant problem for millennia, were initially modeled using complex differential equations by Pierre-Simon Laplace.

William Thompson, later Lord Kelvin, developed a fascination with the sea and aimed to predict tides.

Kelvin applied Fourier's work to decompose tidal curves into sine waves to predict tides.

Kelvin's harmonic analyzers automated the process of predicting tides using analog computers.

The tide predicting machines were critical for planning the allied invasion on D-Day.

Analog computers were used in World War II for various applications, including anti-aircraft gun aiming.

The Norden bombsight, a complex mechanical analog computer, was a significant but flawed military investment.

Digital computers like ENIAC demonstrated the power and versatility of digital computing post-World War II.

Claude Shannon's master's thesis laid the foundation for digital computing with Boolean algebra.

Startups are currently working on analog computers, suggesting a potential comeback for this technology.

Transcripts

- In 1901, this ancient Greek artifact

was discovered in a shipwreck of 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 zero 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.

And 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.

(soft upbeat 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 two high and two 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 sea bed

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 that 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 that 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 tidal 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 the future tides.

- Lord Kelvin 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, Kelvin boarded a train

for a meeting with the main sponsor of his tidal research,

the British Association.

On the train, Kelvin bumped into a friend,

inventor Beauchamp Tower, to whom he explained his dilemma.

Towers suggested he used Wheatstone's plan

of a chain passing around a number of pulleys.

And this was exactly the addition mechanism

Kelvin was looking for.

By attaching a pulley to each scotch yoke

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,

Kelvin 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 tidal 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, Kelvin needed a machine

capable of multiplying the tide curve times the sine wave,

and then taking its integral.

What would such a device even look like?

With his older brother, James Thompson,

Kelvin came up with a mechanical integrator.

It consists of a ball on a rotating disk.

Due to the rotation of the disk,

the further the ball is from the center,

the faster it spins.

If the ball is at the very center of the disk,

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 disk

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 wanna integrate the function.

We first wanna 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 disk,

but also on how the disc is turning at an instant.

You trace the tide curve with the stylus,

which moves the ball back and forth on the oscillating disk,

and the roller sums up the integral of the tide curve

times the sine wave.

Simply divide by the total time to get the coefficient.

Several of these ball and disk 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 the future tides

using his scotch yoke pulley machine.

- [Derek] Kelvin's harmonic analyzers

were the basis for a landmark analog computer

called the differential analyzer,

and his tide 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 change tack.

Instead, they plan 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 Kelvin'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 Stibitz

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 and 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.

(radio tatters)

(mystical music) (gun firing)

"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 sites 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 few 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 I, 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 bombsight.

Unfortunately, they didn't get their money's worth.

- Designed by the eccentric Dutch engineer,

Carl Norden, the Norden bombsight 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.

(bomb exploding)

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 Norden 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 bombsite

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 Kelvin'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 master's 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 these 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.

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