Lauren Ipsum: A Story About Computer Science and Other Improbable Things (15 page)

In the real world, jargon doesn’t look like a mouse-dog, or even a dog-mouse; it looks
just like an ordinary word! Computer scientists (and really, all scientists) love inventing new
words. We call these specialized words
jargon
or
argot
.
Jargon can be good, because it saves time when you’re discussing things with your colleagues.
It can also be bad, because it excludes nonexperts from the conversation.

When you’re just starting out with programming, all the jargon, argot, and weird new
words can be intimidating, but don’t let that stop you from learning. Jargon can be silly, or
powerful, or dangerous, depending on how you use it. But no matter what words you use, if you always
obfuscate instead of explicate, no one will understand you!

The
Traveling Salesman problem
is a classic computer science question.
Given a group of cities, your goal is to find the shortest
Hamiltonian path
, a
route that lets you visit each city only once. If you have a large number of cities, it would take a
very long time to calculate that path, even for a computer. So the Wandering Salesman might be on
the road for quite a while!

Instead of calculating the exact answer, the salesman looks for a path through all the towns
that’s
close enough
to being the shortest. A very interesting aspect of
the Traveling Salesman problem is that humans are pretty good at solving small examples by hand.
There is much discussion about what algorithm people use in their heads while solving it. See also
Hugh Rustic
(
Chapter 8
;
Chapter 8: More Than One Way to Do It
).

In Userland, the Upper Bounds are a mountain range, as tall as anything can be. The Lower
Bounds are valleys as low and deep as anything can be. Nothing can be higher and nothing can be
lower than these two bounds.

In the real world, finding an upper and lower limit on a problem can simplify things a lot.
Say you have to guess a person’s age. It’s unlikely that anyone is over 150 years old,
and no one can be younger than 0 years old. So, 150 is the
upper limit
and 0 is
the
lower limit
. You can narrow down the bounds even more with simple
questions. Is the person still in school? If so, then he is probably younger than 30. Can the person
drive a car? If so, then he is probably older than 15.

You sometimes see signs that mark a point on a highway, like “Mile 14.” Now, if
there is a Mile 14, then there must be a Mile 13, and a Mile 12, and so on. Everything has to start
somewhere, and Zero is where it starts. Possibly the most famous Mile Zero is in Key West, Florida.
It’s at the beginning of US Route 1, which goes all the way to Canada. If you look carefully
and are very lucky, you might find a Mile Zero near where you live.

When you say “A or B,” you mean that you want one of those two things, or maybe
both! If you say “A xor B,” then you mean you want
one and only one
of those two things, not both. That’s why Xor keeps turning rainbow colors: Xor and the thing
he’s currently resting on can’t be blue at the same time. If he’s sitting on a
blue sign, then he must turn any color that
isn’t
blue! Not a great form
of camouflage, is it?

Steganography
is the art of hiding information inside other information,
and it’s used in both the digital and the physical world. For example, you might hide a secret
message by writing it with invisible ink on a piece of paper. With a computer program, you could
even hide words inside sounds and pictures. A Steganosaurus is, therefore, a dinosaur that can hide
itself anywhere.

Eponymous Bach is a composer, but she works with ideas instead of music.
Composing
is the act of combining small ideas into bigger ones to solve a
problem in steps. Almost every idea is composed of smaller ideas. For example, multiplying whole
numbers isn’t anything special. You can think of it as adding a number to itself and
repeating:

See also
Decomposing
(
Chapter 17
;
Chapter 17: Chasing Elegants
) and
Relating
(
Chapter 17
;
Relating
). Composing, decomposing, and relating are
problem-solving methods that lie at the root of all math, logic, and computer science.

Don’t let any new idea escape without putting a name on it. A name is like a handle that
makes the idea easier to use.

It’s better to put a name on Ideas than on Things, because Ideas last longer.

As an idea becomes more useful and famous, its name becomes shorter and lowercase. This law
eventually affected Eponymous’s friend, Andy Ampère, and his discovery about
electricity.

André-Marie Ampère discovered that when electricity flows through parallel wires,
the wires will either attract or repel each other, causing the wires to bend. By measuring how much
they bend, you can measure how much electricity is flowing. Ampère used this idea to lay the
foundation for nearly everything we know about electricity, and we measure electrical current in
amperes
(or
amps
) in his honor. (See
Bach’s Third Law of Eponymy
for Eponymous’s theory on why we
don’t call the unit an
Ampère
nearly as often.)

Programmers and mathematicians sometimes use a pair of ideas, called the
solution
space
and the
problem space
, to describe finding an answer to a
problem.

Say you need to move a heavy box so you can unpack it; anything related to moving the box is
in your problem space. Try to imagine every single thing you could possibly do to try to move that
box. You could walk forward, walk backward, stick out your tongue, sing a song, write an equation,
use a lever, call for help, look for a forklift, or do literally anything else you can think of.
Write down as many of these possibilities as you can fit on a piece of paper.

Out of that huge space of possibilities, imagine only the ones that have a good chance of
moving the box. Circle those with a red pen. The circled ones are in the solution space. They
make sense
because they would accomplish your goal, and the rest don’t
make sense. Now, look again at all of the circled possibilities and think about which one is best
(fastest, cheapest, easiest, most reliable, and so on). Underline that one in green. That’s
the most
sensible
answer out of all the ones that make sense.

The point of this exercise is to avoid a very human, very common error: we tend to grasp at
the first solution we think of and forget to consider other possibilities. This is what Eponymous
means when she tells Laurie that the Wandering Salesman’s solution isn’t sensible. See
also
Hugh Rustic
(
Chapter 8
;
Chapter 8: More Than One Way to Do It
) and
Five Whys
(
Chapter 14
;
Chapter 14: In the Abstract
).

The Robins aren’t really evil—they’re just hungry. They cooperate in
everything they do, taking turns and making sure the work is balanced among them. Sharing work is a
great way to get things done faster, and computers can share work, too!

You can find the Round Robin method almost anywhere. Imagine a bus route that takes an hour to
complete. If you put two buses on that route, a bus will arrive at each stop every 30 minutes. With
three buses, you’d see a bus every 20 minutes, and four means you’d see one every 15
minutes. With five buses, you’d see one every 12 minutes, and so on. Just divide 60 (the
number of minutes in an hour) by the number of buses to see how often a bus should come.

But you have to be careful to make sure the buses arrive at each stop at evenly spaced times.
Five buses reaching one stop all at once wouldn’t be balanced. Also, if one bus breaks down
and gets delayed, this could cause all the other buses to back up!

Recursion
is a way to repeat the same process over and over until you
find the answer you’re looking for. When you use recursion, you run though the process, and if
the answer is the one you want, you stop. If it’s not, you take the answer you found, plug it
into the same process, and run it again.

Let’s look at an example of recursion in action right here in Userland. Recall from
Chapter 10
that Jane Hecate has a single, gigantic book of names. The
name
Lauren
starts with
L
, so Jane should find it in the
L
section of her book, but that could take a while with so many pages. If Jane
wants a faster way to look for
Lauren
, she can divide the book into two equal
halves and see if
L
is in the first half or the second half.

Since
L
is in the first half, Jane can then divide the first half of the
book in half, giving her two quarters of the book to search.

Lauren
should be in the second quarter, so Jane can divide that quarter
in half, giving her two eighths of the alphabet:

Jane can continue dividing the letter groups containing
L
in half until
eventually she ends up with just the
L
section. (How many more times would Jane
have to divide a set of letters in half to find
L
?) This way of searching for a
particular piece of information is called a
binary search
.

See also
The Garden of Forking Paths
(
Chapter 19
;
Chapter 19: Branching Out
) and
Chasing Your Tail
(
Achilles and the Tortoise
).

These two characters were used by a philosopher named Zeno of Elea almost 2,500 years ago to
talk about infinity. From Aristotle to Lewis Carroll to Marvin Minsky to Douglas Hofstadter,
mathematics is full of stories about their adventures. It’s Tortoises all the way down.

Chasing your own tail is not always a waste of time! In computer science, there’s a type
of recursion that sounds a bit like running around in circles, and it’s quite useful. In
tail recursion
, you perform a process, then perform the process again on the
result, and repeat until you reach the final answer. For example, Jane Hecate’s binary search
for the
L
section of her book might look something like this:

See also
Recursion
(
Chapter 4: What the Tortoise Said to Laurie
).

When people say there’s an
infinite
amount of something, they mean
there’s no limit to how much of that thing exists. When Tortoise demonstrates how an infinite
string can be less than two inches long, he shows that you can split that string into an infinite
number of smaller pieces.

Infinity is
big
, bigger than you can imagine. But you can hold infinity
in your mind simply by saying a few words. There are infinite odd numbers: 1, 3, 5, 7, and so on, up
to forever. There are infinite even numbers, too: 0, 2, 4, 6, 8, and so on. No matter how hard you
look, you will never find an odd number in the list of even numbers or an even number among the odd
ones. That means there are at least two kinds of infinity: the even numbers and the odd
numbers.

There are also
infinite kinds of infinity
. Think about all the numbers
divisible by 3 and all the numbers
not
divisible by 3 (or 4, or 5). Now imagine
all the numbers that no one else has thought of before. That’s another kind of
infinity!

If you think about how you think, you might then start thinking about how you think about how
you think, and then about how you think about how you think about how you think, and so on. This is
a form of argument called
infinite regress
, and it can have no end. The first
time you fall into this mental trap, it can be confusing or even scary. The trick is not to take it
too seriously.

If you think this sounds related to recursion, you’re correct! It would be quite
troubling to get stuck in a recursive process forever. In real computers, infinite recursion never
actually happens because no computer can hold an infinite amount of information. When the computer
runs out of room while working on something recursive, you never know what might happen. Laurie and
Xor experienced this firsthand at Recursion Junction. See also
Chasing Your
Tail
(
Achilles and the Tortoise
).