In engineering,

uncertainty is usually as welcome as sand in a salad. The development

of digital technologies, from the alphabet to the DVD, has been

driven in large part by the desire to eliminate random fluctuations,

or noise, inherent in analog systems like speech or VHS tapes. But

randomness also has a special ability to make some systems work

better. Here are five cases where a little chaos is a critical part

of the plan:

**Stochastic
Resonance**

Scientists who make

sensitive detectors often go to extreme lengths to eliminate noise.

If they are trying to spot neutrinos, for example, they’ll build their detector at the bottom of a mine

to stop the results from being swamped

by regular cosmic radiation. But there

are times when adding noise is the only way

to pick up a weak periodic signal.

This

phenomenon is called stochastic resonance, and it works something

like this: Imagine you’re trying to count the number of waves at

the seashore, and your detector is a wall built across the middle of

a beach. The height of the wall represents the threshold of

detection: Only if water washes over the top of the wall will it be

registered. But our imaginary wall is high enough that the swell of

the water never quite rises to the top of the wall. Adding noise is

like adding some rapidly changing wind—it whips up waves in a

random pattern. With the right amount and right variation of wind,

when the wave comes in the water will splash over the top of the wall

and be detected. If there’s too little wind, the calmer waves will

never make it over the top; too much wind and the water level may

stay over the wall for long stretches, drowning out the signal of the

waves.

There are times when adding noise is the only way to pick up a weak periodic signal.

And stochastic

resonance doesn’t just apply to scientific instruments: There’s

evidence that our own nervous systems use it to detect signals between cells,

and that it also plays a role in our perception

of sight, touch, and hearing. For example, the balance of elderly

people can be improved by fitting their shoes with insoles that produce “noisy” vibrations

below the threshold of sensation. This improves the seniors’ sense

of touch in their feet, which leads to better balance. Researchers

believe this works because the sub-threshold stimulation primes

sensory neurons to fire when a foot contacts the floor. The

stimulation has to be somewhat random because otherwise the sensory

neurons would adapt to, and ultimately ignore, the additional

stimulation.

**Cryptography**

Codes

and ciphers are a case where being predictable can literally get you

killed. The goal of cryptography is to turn a message—the

“plaintext”—into a meaningless jumble—the “ciphertext.”

Ideally, the ciphertext should be indistinguishable from a random

string of letters or numbers: If code-breakers discern any pattern in

the ciphertext, they can use it to help reveal the plaintext.

For example, during

World War II, Germany relied on a code machine called Enigma. An

operator would push a button on its keyboard, and a letter on a panel

would light up, as determined by a system of rotating wheels inside.

Crucially for the Allies, the setup was such that a letter couldn’t

be encrypted as itself; that is, a “b” could be encoded as any

letter except “b.” This might sound like a good thing—shouldn’t

all the ciphertext be completely different from the plaintext? But in

fact, it was a critical weakness, reducing the number of

possibilities code-breakers had to consider.

Modern cryptography

encrypts messages by combining plaintext with randomly generated

digital keys using various algorithms. The security of the system

depends on the algorithm chosen, the length of the keys, and the keys

being truly random. The algorithms and keys used today are so good

that it should take longer than the current age of the universe

to break a properly encrypted message. Nonetheless, some

security-conscious individuals and organizations are worried that new

code-breaking techniques may be found. Consequently, researchers have created and deployed some quantum encryption systems,

which rely on fundamentally random subatomic processes and, in

theory, can *never*

be broken.

**Genetic
Engineering**

Evolution created a

noise-resistant digital code to store the blueprints of life: DNA,

with its four-letter alphabet. DNA allows organisms to replicate a

single cell over and over to make an entire human body composed of

trillions of cells, each with an identical genome. Our cells even

have elaborate systems to repair and correct damaged DNA.

Consequently, although these systems can break down, as in cancer,

for any given cell the chances of a DNA mutation are low. Also as in

cancer, most mutations are likely to have a negative, or at best

neutral, impact on the cell’s functioning. This is a problem for

genetic engineers who want to produce lots of mutated cells quickly

so they can find the rare variation that’s useful, like a corn cob

with bigger kernels.

So they rely on

mutagens. Mutagens are factors that jumble DNA, and there are a huge

variety to choose from, depending on the organism and the degree of jumbling

that is desired. Exposure to gamma rays—the same thing that turned

mild-mannered scientist Bruce Banner into

the Hulk—is

one popular mutagen, and even caffeine can do the trick, especially

when working with bacteria or fungi. Fortunately for the enormous

number of people for whom caffeine is one of the major food groups,

its mutating powers are confined to cells in petri dishes.

**Gambling**

Gaming operators

must walk a fine line. To keep

players interested—and law enforcement agencies *un*interested—their

games must be fair. But they must also be guaranteed to

generate a profit in the long run. Casinos need to know just how

likely a 21 in blackjack or a red 32 in roulette is, so they can set

appropriate payouts (or, when it comes to virtual games like

electronic slot machines, what the odds of three cherries turning up

*should* be).

This requires being

able to calculate odds with precision. So it probably shouldn’t be

a surprise that our modern mathematical understanding of probability

came about largely because of gaming. Antoine Gombauld was a

17th-century gambler who had a friend in one of the greatest geniuses

of all time, Blaise Pascal. (Among many other contributions, Pascal

invented the first mechanical calculator when he was 19 years old.)

Gombauld was trying to figure out the correct odds of throwing two

sixes with a pair of dice, and asked Pascal for help.

To keep players interested—and law enforcement agencies uninterested—their games must be fair.

Corresponding with

Pierre de Fermat (best known for his Last Theorem),

Pascal worked out ways to calculate probabilities without having to

tally up every possible outcome of a game one by one, something that

quickly becomes cumbersome when the games get complicated. This work

was the foundation of what’s now called probability theory,

and is used to understand all kinds of complex phenomena, from the

stock market to quantum physics.

Pascal’s analysis

highlights that one reason gambling is so lucrative is that our

intuitive understanding of the likelihood of a random event is often

quite wrong. Imagine tossing a fair coin 10 times and, by chance,

getting 10 tails in a row. Now, how much would you bet that you’re

going to get another tails on your next toss? Some people think that

because getting 10 tails in a row was already unlikely, an 11th

tails must be extraordinarily unlikely—that heads is “due.”

Other people would believe tails is on an unstoppable lucky streak,

so the chances of an 11th straight tails are great. But

Pascal showed us that that the odds in this case are, in fact,

exactly 50/50. The coin doesn’t “remember” what’s gone

before. But *players* remember, and they tend to believe that

their luck or instincts can outsmart randomness, so they under- or

overestimate their chances. The result is that a casino can be

completely upfront about the odds in their games, which are a lot

poorer than 50/50, and still have a steady stream of players willing

to put money down: The gaming industry raked in $430 billion in 2012,

according to the analyst firm Global Betting Gaming Consultants

(GBGC).

**Computer
Simulations**

Systems like

hurricanes or stock markets are hard to predict because they are so

complex. An analyst creates a computer model of the system she’s

trying to understand, feeds in a description of current conditions,

and lets the simulation evolve. Unfortunately, a lot of

approximations must be made: Only so many wind-speed measurements can

be taken, and no one can read the mind—or stock-trading program—of

every trader.

So

the analyst is left with a big question mark about how far she can

trust the simulation: If she’d happened to choose slightly

different starting approximations, would she have gotten radically

different predictions? The way to reduce this uncertainty is the Monte Carlo method,

named after the casino of the same name. The analyst runs the

simulation hundreds or thousands of times, with the initial

conditions randomly adjusted each time. Then she looks at the

collection of predictions. If 90 percent of weather forecast

simulations show a storm tracking straight up the East Coast, it’s

probably time to batten down the hatches.

**Generating
Randomness**

Creating true

randomness is a lot harder than thinking of a number between one and

10. Humans can’t be trusted to do it reliably. We mistake the

inevitable coincidences that arise in truly random sequences—such

as the same digit appearing three times in a row—as evidence of a

pattern. But by avoiding these coincidences we make sequences more

predictable.

But don’t feel

bad—computers are terrible at producing random numbers, too. This

is because they are digital systems ruled by logic—every number the

computer generates is in some way based on other numbers in its

memory. On its own, a computer can’t generate a truly random

number.

So when it’s

critical that a computer use truly random numbers, an external source

of noise must be used. These sources can include having the user

jiggle their mouse around, or even odd approaches like pointing a digital camera at a lava lamp.

This is often impractical, so computer scientists invented algorithms that produce pseudo-random numbers,

which are close enough to truly random for most purposes. The

algorithms start with a so-called seed and then generate a sequence

from that. Seeds are usually relatively small numbers, so programs

can either ask users to pick one, or can choose them by looking at something like the computer’s internal clock.

It’s important to

statistically test these algorithms: Some poor random number

generators don’t produce numbers that are evenly distributed over

the possible range of numbers, which can, for example, bias the

outcome of Monte Carlo simulations that rely on having a fair sample

of inputs. Other poor generators have been known to produce numbers

that are easily predictable: In 2003, geological statistician Mohan

Srivastava worked out how to identify winning scratch tickets from

the Ontario Lottery thanks to a pattern in the visible numbers

printed on the ticket.

**The Color of
Noise**

Engineers and

scientists refer to all sorts of randomness in a system as “noise,”

because that’s literally what it was—the audible pops, hisses,

and buzzes that interfered with messages sent via the early

electronic systems of telegraphs, radios, and telephones. Hence

telecommunications companies quickly developed a keen interest in

understanding noise and finding ways to reduce it, most famously at

AT&T’s Bell Labs in New Jersey. There, in 1948, Claude Shannon

published “A Mathematical Theory of Communication,”

founding the entire field of information theory by thinking about the

limits of transmitting information in the presence of noise.

Everybody is

familiar with white noise, the hissing sound associated with static.

White noise is random, in that any given sound frequency is as likely

to appear as any other. This is why it’s called white noise: Like

white light, it contains many frequencies evenly mixed together. But

it’s not the only kind of random noise possible; there’s actually

a whole spectrum of noises labeled with different colors, the most

important of which are pink and brown.

Pink noise

is also known as 1/f noise, which means that a frequency’s

likelihood of appearing is inversely proportional to that frequency.

That is, low-frequency sounds dominate over high frequency sounds.

Like white noise, the name comes by analogy to colors—the

low-frequency end of the visible spectrum is red, so the noise is

“tinted” pink. The pattern of pink noise actually turns up

naturally all over the place, most notably in music: If you plot the

distribution of frequencies in many compositions, it follows a 1/f

pattern.

Brown noise

is similar to pink noise, except that a frequency’s likelihood of

appearing is inversely proportional to the *square*

of the frequency (1/f^{2}).

This means low-frequency sounds dominate even more than with pink

noise. (This time the name doesn’t relate to visible light, but

comes from “Brownian motion”—the random movements of particles

suspended in a liquid or gas as they are knocked around by

molecules.) Like pink noise, it turns up naturally in a lot of

places—including the wiring of our neurons, although the exact role

it plays is not fully understood.

Stephen Cass

is a freelance science and technology journalist based in Boston, who

frequently covers physics, aerospace, and computing.