Muse 2020-09

September 2020 Volume 24 Number 07 cricketmedia.com $6.95

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SEPTEMBER 2020 ®

Which numbers a peCrafencyt obuubbblolew?
are perfect?

Have you ever
seen a perfect
work of art?

WHAT IS
PERFECTION?

muse® 42

Ammonites

In math and metaphor

by Wailana Kalama

FEATURES 30 32 38

20 A Genius Builds a Dome Good Gaming Perfectly Imperfect

The Art of the Filippo Brunelleschi, Game designers work In nature, variation
Golden Ratio ingegno hard to avoid perfection. contributes to success.

Math meets design by Peg Lopata by Stuart Maine by Donna Bozzone

by Rachel Kehoe

EDPEAPRATRMTMENETNSTS SEPTEMBER 2020

2 Parallel U: Time Out Volume 24, Issue 07

by Caanan Grall DIRECTOR OF EDITORIAL James M. “No” O’Connor
EDITOR Johanna “One” Arnone
6 Muse News Kathryn “Is” Hulick
CONTRIBUTING EDITOR Tracy “Perfect” Vonder Brink
by Elizabeth Preston CONTRIBUTING EDITOR Emily “Ellipses” Cambias
Stacey “That’s” Lane Smith
14 Science@Work: ASSISTANT EDITOR Nicole “Why” Welch
ASSISTANT EDITOR Morgan “Pencils” Atkins
Dr. Sheila Josephs Caanan “Have” Grall
ART DIRECTOR
by Peg Lopata DESIGNER

17 Do the Math: What’s CARTOONIST

So Great about 8128? RIGHTS & PERMISSIONS David “Erasers” Stockdale
BOARD OF ADVISORS
by Alice Andre-Clark
ONTARIO INSTITUTE FOR STUDIES IN EDUCATION,
26 Science@Work: UNIVERSITY OF TORONTO
Carl Bereiter
Rodney Mullen
ORIENTAL INSTITUTE, UNIVERSITY OF CHICAGO
by Bethany Ericson John A. Brinkman

47 Your Tech NATIONAL CREATIVITY NETWORK
Dennis W. Cheek
by Kathryn Hulick
COOPERATIVE CHILDREN’S BOOK CENTER, A LIBRARY
48 Last Slice OF THE SCHOOL OF EDUCATION, UNIVERSITY OF
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YOUR TURN K. T. Horning

3 Muse Mail FREUDENTHAL INSTITUTE
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Leon Lederman
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UNIVERSITY OF CAMBRIDGE
House of Cards Sheilagh C. Ogilvie

by Jim Still-Pepper WILLIAMS COLLEGE
Jay M. Pasachoff
24 Art Space
UNIVERSITY OF CHICAGO
by Rachel Kehoe Paul Sereno

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2

Muse Mail

Old Cats, Old Friends LETTER International Muser
of the of Mystery

MONTH I am a Violet, a 12-year-
old girl who usually lives
My name is Izzy and I love horses, reading, writing, in Massachusetts and
and Muse. I especially loved the invention issue (February 2019) loves reading Muse when
it comes. But my dad’s
because it inspired me to invent. I have always wanted a coat of work means my family and
I have to live in Malaysia
fur, and the issue on survival in freezing climates (January 2019), (in southeast Asia) for
six months. It’s new and
explained why we humans don’t have fur. I think you should do an exciting and everything . . .
but I can’t get Muse here!!!!!
article about the growing demand for cats in nursing homes. My neighbor/friend was in
the area, so she visited and
—IZZY G. / Maryland brought with her the issues I
have missed since I’ve been
_________________ here. I cried when I read
them. I don’t understand
Ad Psychology how all these people writing
from other planets get Muse,
I wish I could say I am the queen (ruler, commander, etcetera) of while I’m still on Earth and
something, like nearly everyone else does. But all I can claim is that I am I can’t!!! Anyways, it would
10-year-old girl who really likes Muse. I am wondering if you could write an be amazing if you made it
issue about the psychology of advertising, and the different strategies employed. possible to get Muse in
I think that many Muse readers would like that, because many of us seem to like other countries too.
psychology, things to do with brains, nerves, etcetera. I am wondering about Goodbye for now.
nudges in particular, along with loss leaders. I am wondering why too many
nudges cause people to avoid the things you are trying to nudge them towards. —VIOLET
Do not drop this in the electronic FMP, please, or I will be extremely sad. Also,
how did the legend of the FMP get started? If you do not publish this letter, I will P.S. I will not do anything
send millions of tiny nanobots constructed out of cubic zirconium to your HQ, to Muse HQ if you don’t
and since it is kind of harder than diamond, they will conquer your HQ very fast! publish this, but one 12-year-
(Using pneumatic techniques, of course.) Cubic zirconium is cheap compared to old girl on the other side of
diamonds, so I will send my bots in the zillions to your HQ. the world will be heartbroken.
YOU HAVE BEEN WARNED. Very, very heartbroken.

—EMI T. / age 10 / British Columbia, Canada

I wonder if I could use ads to make Cate remember she has to pick up her side

of the room . . .

—AARTI

3

Muse Mail Does Whatever a
Spider-Goat Can
Cooking Something Up Oceanic Approval They’re
sister and I like cats. So . . . since I like
I’ve been reading Muse for I am writing this letter brother! cats, it’s kinda weird that I
three years now, and I love not as a queen, not as am writing about goats and
the interesting articles a werewolf, but as your spiders. But goats really can
about unusual subjects. average kid who LOVES your produce spider silk. Not all
Whenever I get a new issue, magazines. If this does not goats of course. Can you
I’m usually finished with get published, I am not afraid please do an issue about
every article in a day or two. to send my companion and them? It’s really cool! My
Being a Boy Scout, some of teddy bear, AJ, to send all of brother says that if these aren’t
my favorite issues are the you at Muse HQ into peril. He published, he will unleash his
ones such as the search and is VERY powerful! And cute. dragon named Eldest on Muse
rescue article in the May/June Anyway, my favorite issue HQ. Eldest will bring an army
2019 issue. I think you should was about the ocean. The sea of dragons too. And my cat
do an issue on the science drawings were incredible. army will attack as well. You
behind cooking and baking, The most I can draw are stick have been warned . . .
because I really want to know figures (which I’m proud of).
why when you put a bunch I am hoping for you to do an —ZAARA H., KITTY QUEEN / age
of ingredients together in the article (or a whole issue) about 10 / New Jersey
right proportions they can creativity. I am a writer and
make something delicious, like this topic is really important P.S. I also request that you
cake. If you do not publish this to me. Also, Whatsi, can you do an issue on cats later in the
letter, I will send an army of please invent pizza-flavored year. They are cooler and more
flying penguins to break into ice cream? I really want to interesting than people think
Muse HQ and erase all the r’s taste that! they are.
in your next issue. _________________
—KAITLIN / age 10 / New Jersey
—JACK A. / New York Royal Brother
Pizza-flavored ice cream? I
I love inventing new gotchu. Hope you don’t I am the brother Kitty Queen
recipes, especially mind pineapple on top. talked about. Studying
with veggies from our It’s my favorite. dinosaurs is my hobby, but
community garden. making and programming
But Whatsi’s the star —WHATSI technology is what I do most
of the time. Technology is
baker—he’s better at amazing. Could you pleeeease
chemistry than me. do an issue about futuristic
technology like flying cars,
—O holographic phones, and
solar-powered cars. Muse
is my favorite magazine
EVERRRR! The reason I want
you to do an issue about these
is because when someone
reads it, they might invent
something similar someday.

—AMAN H., KING OF DRAGON
RIDERS / age 7 / New Jersey

P.S. My sister was right. I
WILL send my dragon Eldest
and his army of dragons and
destroy Muse HQ by putting on
a laser disco show. If this does
not get published that is.

4

Authorial Intent Space to Wonder

I’m not a royal dragon from I love music, math, history, and especially science.
a far-off planet, I’m actually Muse is the best thing ever and I have been getting it for a
just a nerdy 11-year-old little over a year. I am curious about human emotions and
girl. I’ve been reading Muse memories and chemistry in general, but I especially LOVE
since the AI issue in Nov/Dec outer space. It is mysterious and there is so much to learn
2017, and I love it! I got the about it. I think Parallel U is cool but a little confusing at
subscription as a Christmas times. Anyway if you don’t publish this I will send:
gift, and I would take the
magazine with me to school. 1. My very vicious cat to meow at you all day (trust me it’s
One of my favorite articles was annoying)
the artificial intelligence one. 2. Genetically engineered geckos with dagger tails
Robots are sooo cool!!! As I 3. A black hole to suck everything up
was saying earlier, I am a huge
nerd and bookworm. Reading By the way I am Hera, Queen of the Greek gods or a fire-
is probably something I spend breathing dragon or a curious girl asking why all the time
the most time on. I would love but apparently people don’t like someone annoying them by
it if you could do an issue on wondering things.
authors and their process of
writing and publishing a book. —LILA C.M. / age almost 13
Also just because I don’t have
a huge army doesn’t mean Hey Lila. I think everyone gets Something to say?
you should throw my letter a little confused sometimes— Send letters to Muse Mail,
in the FMP. So please don’t about weird time travel tales 70 E. Lake St., Suite 800,
toss it carelessly into the FMP.
Thanks!!! and life in general. Chicago, IL 60601,
To me, it’s a sign or email them to
—ABBY / age 11 / Washington you’re paying [email protected].
attention.
P.S. I think the HPB are
sooooo cute and I would highly —CATE
appreciate it if Aarti and Cate
would send me one! 5

art by Peter Wartman

BY ELIZABETH PRESTON

Muse News

There it is!

text © 2020 by Elizabeth Preston One of
these stories is
FALSE. Can you
spot which one?
The answer is on

page 46.

UP IN SPACE

Hello, and Goodbye, to a Mini-Moon

IN FEBRUARY, ASTRONOMERS MADE A SURPRISING ANNOUNCEMENT: EARTH HAD TWO MOONS, NOT ONE.
The first was the big moon we all know and love. The second moon was tiny in comparison, only about as big as a
car. It likely started as an asteroid flying through space, then got caught in Earth’s gravity and started circling our
planet instead. Astronomers named the mini-moon 2020 CD3. They calculated that it may already have been
orbiting Earth for a few years.
But the friendship between Earth and our new rocky pal didn’t last long. By mid-March, 2020 CD3 had spun away,
pulled by the sun’s stronger gravity. Now it’s orbiting the sun—just like we are.

6

HOT TAKE PALEONTOLOGY

Quick: What’s This Picture? This Ancient
Bird Was a
DO YOU SEE A ZOOMED-IN CORNCOB? A treasure chest of gold? Mishmash
Any other guesses?
If you said “the surface of the sun,” congratulations! This is one of the first IN A PIECE OF ROCK FROM
BELGIUM THAT’S ABOUT 67
images from a new telescope. Sitting high on a Hawaiian mountain, it’s the largest MILLION YEARS OLD,
telescope ever built for staring at the sun. PALEONTOLOGISTS
DISCOVERED A NEARLY
The shapes you can see in this picture come from the movement of plasma— COMPLETE SKULL. They say it’s
the super-hot gas the sun is made of. Like bubbles in a pot of boiling water, hot the oldest skull of a modern bird
plasma rises to the sun’s surface, then falls again as it cools. Each of the “bubbles” ever found. The bird lived before
in this picture is about the size of Texas. today’s land birds and water
birds split into different types.
PSYCHOLOGY So it looks a little bit like both:
the bones on the back of its head
Practice Makes Imperfect look like they come from a duck,
but the face and beak resemble a
WE’VE ALL HEARD THE SAYING “PRACTICE MAKES PERFECT.” But chicken or turkey.
new research shows that practicing something too much might actually
make you worse. 7

Researchers recruited three groups of kids and
teens: pianists, basketball players, and
spelling bee competitors. They gave each
group a skill to work on. The musicians
learned a piano piece; the athletes
worked on their free throws; and
the spellers studied a new word
list. Within each group, the
researchers told half the
participants to practice six hours
every day for a month. But they
told the other half to practice only
until they felt they had gotten pretty
good and then stop.

At the end of the month, everyone’s
new skills were tested. The people who
had practiced less performed a little better.
The scientists say that overpracticing
may cause physical and mental exhaustion. Good news: You can give
that violin solo a rest!

Muse News

I wonder BIOFLUORESCENCE
which one
has pee that Shining
Salamanders,
glows! Fancy Frogs

LIKE A SUPERHERO’S ALTER EGO, THAT
ORDINARY FROG YOU SAW HOPPING
INTO A POND MAY HAVE BEEN HIDING A
SPECIAL POWER. Scientists have discovered
that many kinds of amphibians can glow.

Frogs don’t light up in the same way
fireflies do. Those bugs use chemical reactions
to make their own light. Instead, scientists
checked frogs and other critters for
biofluorescence. This occurs when molecules
in an animal’s body absorb light and then
send it back out as a different color. But you
can’t see the glow with your eyes.

Researchers tested 32 amphibian species
for biofluorescence. They included
salamanders, frogs, and weird legless
creatures called caecilians. The scientists
shone blue or ultraviolet light onto the
animals and used a camera with a filter to
look for a green or yellow glow. Every single
animal lit up. Some had glowing skin; others
had fluorescent slime or even fluorescent pee.
The scientists don’t know why amphibians
have this power. It might help the animals
communicate or find each other.

Oops, I
meant to say

“Heyyy.”

TECH DESK

How to Make a Mummy Talk ››

NESYAMUN WAS AN EGYPTIAN SCRIBE AND PRIEST WHO LIVED ABOUT 3,000 YEARS

AGO. After he died, he was made into a mummy. Now scientists have

re-created Nesyamun’s voice—making him the first ancient human to

speak to us from the dead.

The researchers put the mummy in a scanner to make a detailed

3D map of his vocal tract. The vocal tract is all the spaces inside a That’s the news!
person’s nose, mouth, and throat down to their vocal cords. The Go to page 46 to
shape of your vocal tract determines what your voice sounds like. see if you spotted
The scientists used a 3D printer to print a replica of Nesyamun’s the false story.
vocal tract. Then they attached it to an artificial larynx, or voice

box, to make Nesyamun talk.

The researchers couldn’t make the mummy’s re-created voice say

full words. But they did produce one sound: “ehhhh.”

9

Hands-On

Rebecca E. Hirsch

POP!

Play around with perfect bubbles.

LET’S BLOW SOME BUBBLES! How long has it been since you spent an afternoon creating and watching these delicate
globes as they float and float and float and . . . pop! Bubbles are not just fun, they’re terrific for doing tricks and for scientific
experimentation. Bubbles are models of scientific principles, following precise laws of mathematics, physics, and chemistry.

What Is a Bubble?

A bubble is soap film wrapped around a pocket of air. The soap film is made of three layers, much like a sandwich. The
outside and inside layers (the slices of bread) are made of soap. The layer in between (the filling) is made of water.

Bubbles form because water molecules are attracted to one another. They cling together. This is called surface tension.
But if water molecules cling together too much, you won’t get good bubbles. The molecules have to be able to pull apart
from each other to form bubbles. So in addition to water, good bubbles require soap.

Soap lowers the surface tension of water. It helps the water molecules become stretchy, more like a piece of taffy. You
can see this elastic nature if you blow a bubble through a long wand. As you let air whoosh through the wand, the bubble
will stretch and bend.

The perfect bubble is one that looks good and lasts a while. Bubble solutions typically include one final ingredient to give
the bubbles staying power. When water spreads out over the surface of a bubble, it tends to evaporate quickly into the air.
Think of how you get chilly immediately after climbing out of a pool. That’s because the water is evaporating quickly from
your skin. As the water evaporates from a bubble, a hole forms in the soap film, and the bubble bursts. To make bubbles last
longer, you need something to hold onto the water. Substances that hold onto water are called hygroscopic. One common
hygroscopic ingredient in bubble solutions is glycerin. It chemically holds the water in place and slows evaporation.
Glycerin helps the bubble last.

10

Waves of Color The Formula: Perfect Bubble Solution

Bubbles show off the 1. Pour the dish soap into the water and stir until well-mixed.
swirling colors of the
rainbow because of the 2. Add the glycerin and stir.
way light waves fan out
across the bubble. Light 3. You can use it right away or cover and let it sit overnight.
diffracts, or spreads out, as
it passes through the front You’ll need
and back layers of the soap
film. This is similar to the Clean glass or other container
ripples created when you 1 cup water (distilled is best)
throw a pebble on a pond. If 1 Tbsp liquid dish soap like Dawn
you throw two pebbles, the or Joy
ripples interact. Some of the Spoon for stirring
waves get bigger and some 1/2 Tbsp glycerin (available at
get smaller. Light waves drug stores)
behave like the interacting
ripples in a pond, creating
patterns of color. At the
same time, bubbles also
reflect what’s around them,
which is why you might see
your own face peering at
the bubble amid the
iridescent patterns.

11

Hands-On

You’ll need

Perfect Bubble Solution
Bubble wand, straw, and/or
plastic pipette
Scissors
Flat, water-safe surface

1) Bubble Shapes and Chains

To blow a bubble, you can use a bubble wand, plastic straw, or plastic pipette. To convert a pipette into a bubble wand,
simply cut off part of the fat tip with a pair of scissors. You’ll dip the fat end into the bubble solution and blow into the
skinny end. You can even try other household items, like a funnel or a toilet paper tube.

1. Begin by practicing your bubble-blowing technique. Blow a bubble and let it go. It will form a sphere. Why? A bubble
shrinks into a shape with the lowest surface area for the amount of volume. In free air, that shape is a sphere.

2. Once you’ve mastered the basics, smear a water-safe table, pan, or other flat surface with bubble solution. See if you
can blow a bubble on the wet surface. It will take the shape of a perfect half-sphere. Wet your bubble wand with bubble
solution again and carefully insert it into the first bubble. Try to blow another bubble inside the bubble. This may take some
practice. How many bubbles can you fit inside?

3. Next, try blowing two half-spheres next to one another. The bubbles will try to minimize their surface area, so two
bubbles touching will join together with a shared wall. If you blow three bubbles together, they will meet at the center,
and the walls will form 120-degree angles. Try it and see. You might try making a chain of bubbles all in a row. What other
bubble designs can you create?

12

3) Bubble Tricks

1. Bend pieces of wire to make frames of different
shapes. (Ask an adult for help!) Try some of the shapes
shown below. A cube is a fun one. Twist the wire around
itself securely so it doesn’t come apart. You can use a
pair of needle-nose pliers to twist the wire tight.

You’ll need

Perfect Bubble Solution
Medium or large dipping
container
Pieces of bendable wire
Needle-nose pliers

2) Bouncing Bubbles

1. Try to catch a bubble. It’s likely to
instantly pop. Why? Your skin has oil
on it, which chemically reacts with the
soap film.

2. Now slip on a thin cloth glove. Can you
catch your bubble with the gloved hand,
or bat it around?

3. Next, wet your bare hand with bubble
solution. What happens when you try to
catch a bubble? Does it stick?

You’ll need 2. Try to predict what shape the bubble solution will text © 2020 by Rebecca E. Hirsch
take on your wire frame. Then dip your wire wand into
Perfect Bubble Solution bubble solution and look at it before you blow. Did your
Bubble wand prediction come true?
Cloth glove
3. Now blow a bubble. What shape did it form this time?

Rebecca E. Hirsch is a biologist and writer in central Pennsylvnia.
She believes you are never too old to play with bubbles.

13

Science@Work

by Peg Lopata

DR. SHEILA JOSEPHS

PSYCHOLOGIST

Do you ever feel really afraid of failing? Do you think you have
to be perfect all the time? If you do, someone like Sheila Josephs,
a psychologist, may be able to help. She’s an expert at helping
perfectionists, especially kids, not be so hard on themselves.
Josephs initially became interested in helping people overcome
their anxieties while she was a camp counselor. “I helped a girl
who had completely stopped speaking overcome her fears.
Seeing her ultimately give a speech to the whole camp was
amazing. Through that experience I learned that I could make a
big difference in kids’ lives through providing caring, empathy,
and support,” says Josephs.

14

If you repeatedly For example, if you imagine other people are judging you very
crumple up harshly for very small mistakes you are making, you are likely
pages with small a perfectionist. Perfectionists set really unrealistic goals for
mistakes, you may themselves, such as, I will make honor roll every year or never miss
be a perfectionist. a step in that dance sequence. When they don’t meet these goals,
they feel it’s a catastrophe. This kind of thinking means you view
WHAT IS UNHEALTHY situations as all good or all bad—nothing in between.
PERFECTIONISM? ________________

Perfectionism in any shape or LIKE DURING EVERY SOCCER MATCH I PLAY, I BELIEVE
form is unhealthy! It is a way of THAT I HAVE TO GET A GOAL EVERY TIME I SHOOT.
thinking that says that I have AND IF I MISS, I THINK THAT THE WHOLE GAME WAS
to act perfectly at all times—no AWFUL AND I’M THE WORST SOCCER PLAYER EVER
mistakes allowed. Ultimately, AND I FORGET ABOUT THAT GREAT GOAL I MADE IN
perfectionism limits you THE FIRST HALF.
from learning positive things
from your less-than-perfect Exactly. This type of thinking drives perfectionism and anxiety
experiences. because it makes you judge your performance with a too-strict rule
________________ of whether it’s perfect or not. Let’s say you’re writing a story and
think: “This is completely bad!” That type of thinking causes anxiety
HOW DO YOU KNOW because it makes you feel like you are doing worse than you really
IF YOU ARE A are. If you instead look at your writing and think, “Well, my story
PERFECTIONIST? begins with a lot of exciting details, but my conclusion needs some
revising,” then you are looking at the situation more realistically,
If you get very upset over small which decreases both perfectionism and anxiety.
mistakes that you think you ________________
made and then imagine that
makes the whole thing you are IT MUST BE HARD TO CHANGE THE WAY
working on wrong, then you PEOPLE THINK.
are probably a perfectionist.
For example, if you repeatedly Absolutely, but it is definitely possible to learn how to think
crumple up pictures that differently! Perfectionists are afraid to change their behavior because
you draw because you think they think things will get a lot worse for themselves if they do. So the
they have small mistakes first step is to teach them, using examples from their own lives, that
in them, you might be a perfectionism makes their anxiety worse and their performance—
perfectionist. and, overall, their lives—actually worse, not better.
________________ ________________

ARE THERE OTHER SO HOW DO YOU HELP PEOPLE CHANGE THE WAY
WAYS OF KNOWING THEY THINK?
IF YOU ARE
PERFECTIONIST? I have my clients learn different ways of thinking and behaving.
The first step is to help them identify their thoughts about a situation
Perfectionists think that if that’s distressing. I suggest they ask themselves, “What is going
they don’t act perfectly, they through my mind right now?” Then, if their next thought is along the
are really bad or worthless. lines of all-good or all-bad thinking such as “I made a mistake and
Perfectionists usually think now my project is ruined,” I suggest they ask themselves something
other people are also using about that thought. They could ask, “If there a way to see my
the same unreasonably high situation as not all good or bad, but as something in between?”
standards to judge them.
________________

HOW ELSE CAN YOU HELP A PERFECTIONIST?

Family members can help by asking such questions like I just
described. A parent could ask, for example, “In what way is it less
bad than you think?” With this powerful method of questioning,
perfectionists can also be encouraged to set more realistic standards
for defining their success and to still feel worthwhile even when they
make mistakes.

15

Science@Work Dr. Josephs helps
clients notice their
own thoughts. Then
they might start
asking questions
like, “Is there a way
to see my situation
as not all good or bad,
but as something
in between?”

SETTING REALISTIC GOALS SOUNDS LIKE A CRUCIAL problems they have or the text © 2020 by Peg Lopata
PART OF TRYING TO AVOID PERFECTIONISM, WHILE way they deal with them. So
STILL BEING MOTIVATED TO DO WELL. specific techniques have to be
slightly adapted towards
Yes, contrary to what most people think, you can still become very each person.
successful without being a perfectionist! I help people become ________________
what I call “positive strivers.” This is someone who has healthy
motivations for success. A positive striver sets realistic goals, enjoys SOUNDS LIKE
challenging themselves, and appreciates success without linking it REWARDING
so rigidly to their self-worth. They can fail at a task and more easily WORK. HOW DOES
bounce back from that failure. SOMEONE BECOME A
________________ PSYCHOLOGIST?

SUCH AS: EVEN THOUGH I MISSED THE GOAL, A psychologist can be
IT WAS A FUN GAME AND I AM GETTING BETTER transformative! You can
AT IT! INSTEAD OF THINKING: MAYBE I SHOULD contribute to a significant
QUIT SOCCER. change in a person’s
well-being. To become a
Absolutely, perfectionists sometimes avoid challenges for fear of psychologist, you have to learn
failing. A girl once told me, “I don’t want to try out for the musical the science of psychology in
because people might find out that my singing isn’t perfect.” college. If you like figuring
Perfectionism triggers anxiety, and while moderate anxiety can things out, you’ll enjoy
be motivating in some circumstances, too much anxiety can be psychology because there’s an
disabling. When perfectionism is reduced, people are more willing endless amount of puzzling
to take a risk and try something new, even though it may be very situations to deduce.
challenging.
________________ Peg Lopata, a freelance writer
in Somerville, Massachusetts, is
HOW DID IT FEEL TO HELP THAT GIRL? never perfect, especially on the
tennis court. But she keeps
It felt wonderful. Being a psychologist who teaches people how trying anyway.
to conquer their fears is very satisfying. It’s fascinating, ever-
changing work because no two people are exactly alike in the

16

BY ALICE ANDRE-CLARK

Do the Math Perfect numbers aren’t the
only colorful mathematical
Investigating perfect numbers One is a factor of every number. Other characters. Factors of abundant text © 2020 by Alice Andre-Clark
factors of 28 are 2, 4, 7, and 14, because numbers add up to more than
Picture, if you will, the perfect number. 2 x 14 and 4 x 7 = 28. Add up all factors the number, while factors of
Do you think of the date of your aside from 28 itself: 1 + 2 + 4 + 7 + 14 = deficient numbers add up to
birthday? Maybe a neatly rounded 28. So 28 is perfect. less than the number. A pair
number like 8 or even 100, the perfect of numbers is amicable if the
test score? What probably didn’t leap So far, mathematicians have factors of each one add up to
to mind are 6, 28, 496, and 8128, the discovered 51 perfect numbers, all the other. (For instance, 220 and
first four entries on mathematicians’ even, and all ending in 6 or 8. The 284 are amicable—try adding up
list of perfect numbers. biggest has over 49 million digits. their factors!) An almost perfect
It’s hard to multiply millions of number has factors that add up
How to Spot Perfection digits on paper, so all but the first to one less than that number.
12 perfect numbers were discovered
In math, a number x is perfect if all on computers after 1950. The What’s Perfect about
its factors—the numbers that divide search became a little easier when Perfect Numbers?
evenly into x—also add up to x. Take mathematicians found another group
the number 28. First, find its factors. of numbers, Mersenne primes, that can But what, you may be wondering,
help point the way to perfect numbers. are perfect numbers good for?
For the ancient Greeks, perfect
numbers were part of their
belief in numerology, the idea
that numbers have special and
mysterious significance in our
lives. Greek mathematician
Nicomachus compared abundant
numbers to animals “with
ten mouths, or nine lips” and
deficient numbers to animals
with one eye or no tongue. A later
philosopher noticed that the
phases of the moon are a perfect
28 days.

Modern mathematicians
haven’t found many uses for
perfect numbers but still find
them fascinating. Many people
are drawn to math because they
are looking for beauty and order
in numbers—and they can find
both in a number whose factors
add up to itself. If you agree, you
can help. Anyone can volunteer
a computer to run the Great
Internet Mersenne Prime
Search program to look for the
numbers that help identify new
perfect numbers.

Alice Andre-Clark is a writer who is
quite sure she has the perfect
number of kids. (Mathematicians
would say three is a deficient
number, but what do mathemati-
cians know?)

17

Hands-On

Jim Still-Pepper Greta Songe

HOUSE OF CARDS

TRY THE PERFECT EXPERIMENT—AND THEN REFLECT ON HOW IT WENT.

EVER THOUGHT YOUR LIFE MIGHT BE PERFECT IF ONLY . . . ?
Ever wondered how close to perfect one person is able to be?
You may never fully answer all those questions, but you can take a closer look at them with this Perfect Experiment. It is going

to ask you to be perfect, but really, the goal is to have fun.
You can try this on your own, or you can get a couple of people together and lead them through this experiment. The results

are especially interesting with other people! Whether you are attempting this life experiment solo or with others, but sure to think
through or talk about the reflection questions on the facing page.

Perfect Experiment: 1. Using 5 playing cards, build a You’ll need
Level One house of cards.
5 playing cards
If you’re in a group, take 2. Using 5 dominos, build a tower. 5 dominos
turns trying level one. While 3. Recite the alphabet backwards.
standing on one leg, you must
do the following things in When you are done, talk about
order, perfectly. this question.

Once you lift a leg, try not What made it hard to be
to put it back down. And do not perfect during level one?
hold onto anything to balance
yourself. (Please make your own If you are up for a challenge, try
adjustments for safety.) level two now.

18

text © 2020 by Jim Still-Pepper art © 2020 by Greta Songe

Perfect Experiment: Level Two Perfect Experiment: Reflection

While hopping on one foot, you must do the following things in Now pick a couple of these questions and spend some time
order, and perfectly. discussing them. If you did the experiment on your own, you
might journal your answers.
Once you lift a leg, try not to put it back down. And do not
hold onto anything to balance yourself. (Again, please make What made it hard to be perfect during level three?
your own adjustments for safety.) Which level was the hardest for you?
How is this experiment related to being perfect in life?
1. Place one playing card to start your card tower, which you can Was it possible to be perfect with these activities?
hold in place, then . . . Is it possible to be perfect in life?
How close to perfect are you?
2. Place one domino to start the domino tower, then . . . Do you expect others to be perfect?
3. Starting with the letter P and going backwards, say one letter What is the difference between being perfect and doing
your best?
of the alphabet. How important is it to be perfect?
4. Repeat till you are completely done with building the house Does anyone expect you to be perfect?

of cards and the tower. Jim Still-Pepper is not prfect. Sometmes he misssplls words. But he
is learning that it is OK. He spends his days working with youth at a
When you are done, talk about this question. counseling center.
What made it hard to be perfect on level two?

Perfect Experiment: Level Three

Try level one or level two again—but do it with your eyes closed.
(Please continue to make your own adjustments for safety!)

A Different Focus • Try to make someone smile.
• Try to make someone laugh.
Here is a cool thing to know about perfection. You and I can • Put a big squiggle on a piece of paper. Now try to draw a
worry about it, but no one can ever achieve it. Remember, picture with the squiggle in it.
people can look like they are perfect, or like they have a • Help someone today.
perfect life, but those impressions are not accurate. • Thank someone for a specific reason.
• Look in the mirror and say to yourself, “I’m good.” (Feel free
Wanting to be perfect can ruin fun times. If you spend all
your time worrying, you will have no time to spend living. to say more positive things too.)
Are you a perfectionist? Your life will change when you start Can you pick one or two of these and try to experiment with
to focus less on whether you’re perfect and more on the them in your own life?
following feel-good ideas:
19

by Rachel Kehoe

RatioGoldenThe Art of the
Where math meets design

hat do Leonardo 21 13
da Vinci’s Mona Lisa b
and the Disney logo 21 34
13 a
Whave in common?
Both excite fans = 1.618
of the golden ratio. The golden
ratio, or 1:1.618, is a mathematical 34 a
proportion that some believe to be 21
the secret to perfection in design. = 1.618
In geometry, architecture, and
art, this unique number produces a+b
a balanced and visually pleasing
composition. Once you start to rectangle will have the same proportions as the first one.
notice the golden ratio, you’ll Continue to subdivide the shape, and you will see that the
see it everywhere. golden rectangle reproduces itself indefinitely.

What Is the Golden Ratio? Phi has a special connection to the Fibonacci sequence,
a series of numbers that Western mathematicians learned
The first recorded mention of the golden ratio in history about in 1202 AD. Each number in the Fibonacci sequence
dates back to 300 BCE. The Greek mathematician Euclid is the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13,
called it the “extreme and mean ratio.” Its actual value is 21, 34, 55, 89, 144, and so on. If you divide each number by
1.61803398874989484820 . . . . The dots mean it goes on the previous one, a familiar pattern emerges. The higher the
forever without repeating. But it is usually rounded up numbers get, the closer that ratio comes to equaling 1.618!
to three decimal places, or 1.618. At the beginning of the
twentieth century, American mathematician Mark Barr Superimposing a golden rectangle on a famous painting
gave it the name phi (φ), pronounced fee or fie, after the (such as the Mona Lisa) is one way to explore the connec-
Greek sculptor Phidias. tion between math and art.

The golden ratio exists when a line is divided into two 8 13
parts and the longer section (a) divided by the smaller 52
section (b) is equal to the entire length of the line (a+b)
3
a+b

a b
a + b is to a as a is to b
21

divided by the longer section (a). Or, a/b = a+b/a = 1.618. If
you use this ratio to draw a rectangle, you will get a golden
rectangle. The long side is 1.618 times the length of the
short side.

If you draw a line inside this rectangle to form a perfect
square, something interesting happens. The remaining

21

What patterns do you see in Salvador Dali’s
Sacrament of the Last Supper?

What happens if you draw a series of squares with Drawing an arc in each square inside a golden rectangle
dimensions that follow the Fibonacci sequence? It looks produces a “golden spiral.”
just like the image of the reproducing golden rectangle.
compose your pictures.” The very dimensions of the picture
If you draw quarter-circle arcs in each square, a golden form a golden rectangle. In the foreground, a table divides
spiral will start to appear. People are drawn to patterns. the height of the composition into two golden rectangles.
Some see the golden spiral as a fundamental shape in Similarly, the left and right halves of the painting each contain
nature. They have found it in the spiral of a seashell and golden spirals. A dodecahedron (a 3D shape consisting of 12
in galaxies in space. These claims likely go too far—shells pentagon-shaped faces), hovers over the table. Pentagons
and galaxies may come close to the golden spiral in shape exhibit golden ratios in their dimensions.
but rarely match it exactly. However, artists can choose to
reproduce it. Leonardo da Vinci, Salvador Dali, and others Some critics say our enthusiasm for patterns makes us too
have used the golden ratio to achieve beauty, balance, and quick to see the golden ratio in nature and art. But for many
harmony in their work. people, the golden ratio is a simple way to create aesthetically
pleasing designs.
Woven into the World of Art
Silver’s Golden Design
Leonardo da Vinci is often associated with the golden ratio.
He illustrated a book, The Divine Proportion, that recognized Stephen Silver is a character designer who has worked for big
phi as an expression of perfect beauty. His most famous studios such as Disney, Nickelodeon, Warner Brothers, and
painting, the Mona Lisa (1503–1506), seems to contain
several examples of this geometric proportion. Did da Vinci
deliberately divide his painting this way? It appears likely,
but we will never know for sure.

On the other hand, there no doubt that Salvador Dali used
the golden ratio to create his painting Sacrament of the Last
Supper (1955). In his book, Fifty Secrets of Magic Craftsmanship,
Dali celebrates the golden ratio and urges artists to “make
use of the geometric science of guiding lines of symmetry to

22

Designer Stephen Silver Sony Pictures text © 2020 by Rachel Kehoe
has been sketching Animation. In
characters his whole these roles, he has
life. He considered designed characters
the golden ratio when for popular animated
creating the animated television shows such as Kim
superhero Danny Possible and Danny Phantom. He is
Phantom and others. the author of several books and owner
of the Silver Drawing Academy, an online
art school. As a guest speaker at colleges and
animation studios around the world, Silver
shares the secret of how to create flawless
designs using the golden ratio.
Silver has been sketching characters all his life. But when
he heard about the golden ratio, he started to see “a kind of
magic going on.” This magic has a simple explanation; the
golden ratio prevents him from designing characters that
are too evenly spaced. Silver invented the term “avoiding
the ladder” to describe the habit of creating equal spaces
in design. “Characters with an even design tend to lack
movement,” says Silver. “They feel ordinary and quickly
lose appeal.” Instead, he applies the golden ratio to break
up proportions to create “more contrast and variation in
shape,” he says. “It makes your characters come alive.”
Silver’s character Danny Phantom illustrates the
golden ratio. For example, consider the proportions of
the characters’ hair in relation to his face. Also, golden
proportions appear in the length of Danny’s arm compared
to the section with his glove. These dimensions “add
harmony and versatility,” says Silver. An observer who
doesn’t know about phi would only see an eye-catching
character design. But understanding phi helps make the
connection between math and art.
Silver isn’t the only graphic artist who thinks the
golden ratio is special. Golden geometry can be found in
the Pepsi, Twitter, and Disney logos. Disney’s logo seems
to purposefully incorporates the golden ratio by
using the uppercase symbol for phi
(ĭ) to dot the ‘i,’ and the lowercase
symbol (ij) for the ‘y.’ “The golden ratio
is a wonderful tool to have on your
side,” says Silver. Next time you draw
a picture or design a logo, you can try
it out!

Rachel Kehoe is a freelance science writer
whose sketches are far from perfect. Learning
about the golden ratio helped her appreciate
art in a completely new way.

23

ART SPACE BY RACHEL KEHOE

DOODLE SPACE

USING THE GOLDEN RATIO
IN CHARACTER DESIGN

1 Close your eyes and 5 2
imagine what you want 7
to draw. Create a story Try drawing
behind it to help give the eye inside
personality to your the spiral
character. to attract
attention.
2 Think of a shape that
ZLOO ğW WKH FKDUDFWHU
you’ve envisioned (i.e.,
circle, rectangle, oval,
triangle). Use the golden
spiral as a guide and
lightly sketch the outline
of the head and body.

3 Draw the details of
the face, including the
eyes, ears, and nose.

4 Add a gesture. Lightly
sketch the arms and
hands in a way that
suggests movement,
such as eating.

5 Draw your character’s
legs and feet. They might
be straight or bent to
show motion. Break
up your proportions,
or avoid the ladder, by
drawing the feet near
the end of the spiral.

6 Include any additional
features. In this case, the
character gets a tail!

7 Finally, add depth to
your character with color,
shading, and texture.

$ ĠXII\ WDLO
echoes the
VKDSH RI D VSLUDO

24

YOUR TURN text and art © 2020 by Rachel Kehoe

When Stephen Silver designs popular animated characters, he thinks about the golden ratio of 1:1.618.
Its pleasing geometry helps him avoid “the ladder”—his description of dull, even spacing. Now it’s your
turn to plan and draw a character using the power of the golden ratio! Here’s how.

25

Science@Work

by Bethany Ericson

RODNEY MULLEN

SKATEBOARDING LEGEND, ENTREPRENEUR, SPEAKER

Meet Rodney Mullen, unstoppable freestyle skateboarding champion. He is known as the “godfather of
modern street skating” for inventing most of today’s tricks. Mullen brought us the flat ground ollie, the kickflip,
heelflip, and 360-flip, as well as dozens of more advanced tricks from his freestyle days, including kickflip-
underflips and dark-slides. His hours of practice reimagining what he could do with a skateboard resulted in
not just technical perfection, but mesmerizing grace. He left studies in chemical engineering to co-found a
successful skateboarding company.

26

And no one knows better they were in a “tube.” They were so rooted in that culture that they
that to solidly master a trick, frowned upon anyone that strayed from it.
a skateboarder must fall and
then get up again. Over and I vividly remember one day I was skating a snake-run, a banked-
over. Your mindset during path that snaked its way downhill. At the bottom, I found myself
these experiences can rob standing with this older surfer-looking dude. As another kid just
you of your love for the behind me was trying a cool new trick, all the surfer did was sneer
sport—or provide a lifetime at how this kid had “no style.” He was blind to how good the trick
of joy. was—maybe just afraid—so all he did was disparage what didn’t fit
his generation’s mold. I was all of 11 yet knew that all I wanted to do
Mullen’s creative genius was turn this upside down. That still hasn’t left me.
in exploring the mind-body ________________
connection has attracted
tech luminaries. Whether SO, HOW COULD YOU REBEL AGAINST REBELLION?
speaking in Silicon Valley,
or as a Fellow at the MIT By the time I was 13, Stacy Peralta put me on his elite team, the Bones
Media Lab, he loves sharing Brigade. Within about a year, I’d meet Tony Hawk. Both of us felt like
his experience with groups outsiders, so our mutual bond meant that much more. The essence
studying all kinds of flow of skate culture is rebellion, yet this becomes slippery when you find
states, concentration, yourself rebelling against “rebels” who dress the part with all the cool-
creativity, and resilience. guy lingo. All we wanted was to push skating to new levels. We’d win
the next decade of contests—me in freestyle, Tony on vert ramp.
________________ ________________

HOW DID YOU YOU WON YOUR FIRST CHAMPIONSHIP AT 14, THEN
FIRST GET INTO WON YOUR NEXT 35 OUT OF 36 FREESTYLE CONTESTS.
SKATEBOARDING? LET’S TALK ABOUT PERFECTION.

When I started, Back in the day, there was no video; sponsors picked riders up
skateboarding was an generally by showing up at contests and picking the standouts. You
offshoot of surfing. Surfers did a two-minute run and there was a strict interpretation of how
would have little ramps perfectly you did it.
at the end of streets, and
they’d be painted like waves. Contest records and their ripple effects are a big thing for me—
Guys would skate barefoot, because a fixation on perfection can turn your ambition into an
“hanging ten” and pretending anchor.
________________

HOW DID THESE CONTESTS END UP BEING
A PROBLEM?

One of the most insidious ways to define perfection is by other
people’s standards, because you’ll end up on a treadmill, defined by
what others think of you. And contests became that for me.

Once you win a couple, you realize anything less than that
is losing. Your identity gets bound up in holding onto this title:
sponsors, media, friends—even family—will only ask if you won or
not. So your mindset drifts into doing whatever it takes not to lose.
By then, there’s no more winning—just a sigh of relief with a trophy.

Arbitrarily, I aimed for a decade of this. Finally, I got it. After the
contest, I found myself walking around San Francisco’s City Hall in
the cold air with the blowing trash, soaking in the hollowness of
it all. Victory isn’t found in holding onto titles that mean more to
others than to yourself. I had ended up working on consistency for a
two-minute perfect little run, and I became a slave to it—sidelining
the joy of learning anew.

27

Science@Work After the contest,
I found myself
HOW DID YOU MOVE ON? walking in the
cold air with
Street skating was just starting to get a foothold after that contest the blowing
in San Francisco, and the new sport gave me a fresh start. It took trash, soaking
three or four years for my freestyle ideas of “perfection” to loosen in the
their grip, as I became liberated to delve into the unknown and be a hollowness
beginner again in a new environment.
— Rodney Mullen
28
WHAT WAS IT LIKE
TO GO BACK TO
SQUARE ONE?

As we learn, we stack and
nestle deeper skill sets. It’s
almost impossible to undo
such deep integration. That’s
one of the reasons it was
so hard for me to go from
freestyle to street: though I
had good board control, I
was worse than a beginner
because I never learned basic
things, such as looking up
to gauge timing, which left
me plowing into benches. I
mean, something as subtle as
the way you hold your eyes
and train your focus has to be
uprooted and relearned. It’s
insane how deep that goes.
________________

HOW DO YOU
“UNLEARN” AND
CHANGE WHEN YOU’RE
WRAPPED UP IN SELF
PERFECTION?

Just throw yourself into stuff.
Think, “I can’t do that, SO
LET ME TRY.” Had I not been
willing to be a beginner again
and look like a complete
fool, I would have never been

After 10 years of winning THE FAIL! INITIATIVE text © 2020 by Bethany Ericson
contests, Rodney Mullen AT MIT
found a new way to
define victory. High-achieving Massachusetts
Institute for Technology (MIT)
able to do what I’ve done. students are under pressure to
Perhaps the most important perform their best. Some of the
state of mind is simply one university’s community came
of humility; by embracing together to create gatherings
that, you’re free to truly let where people can share stories
go. Beyond that, look inward, about failure. Why? Because
rather than looking toward being afraid of failure can
others for approval. cause people to avoid taking
________________ worthwhile risks and limit their
ability to lead meaningful lives.
AND IS FUN Rodney Mullen recently spoke at
IMPORTANT TOO? a FAIL! Conference.

In order to do anything at Francesco Benedetti and Richard
a high level for a sustained Zhang are two of the MIT students
amount of time, you have to behind the FAIL! events. They suggest
love it. Otherwise, it will—at using your mistakes to learn, and
best—leave you hollow in the learning to talk about how you feel.
end. Loving what you do is Honestly share all the moments along
key and maintaining a sense the way, they urge—not just the “right”
of playfulness is what keeps or beautiful ones. Otherwise we’ll all feel
it fresh. like we are the only one experiencing
problems. But, really,
Bethany Ericson is a writer and everybody fails sometimes.
artist from Cambridge, Massa-
chusetts. She grew up riding
down hills on a bright yellow
plastic JAWS skateboard and
somehow made it to adulthood.
She was grateful to chat with
Rodney Mullen while sheltering
in place from COVID-19.

29

A Geniub

Builds a Dome

̞FILIPPO

BRUNELLESCHI,
INGEGNO

here is a dome in Italy, an architect- leads educational tours of the great
ural perfection built before there sites of Italy, including Florence
were backhoes, modern cranes, or Cathedral. He says, “What makes
electricity. Standing for almost six the dome architecturally perfect is
centuries, it seems to defy gravity! Is it magic? that Brunelleschi was able to find
solutions to very complex engineering
Masonry Marvel been intentional on his part so that problems, while still making the
for all of time no brick dome could overall structure beautiful.”
Filippo Brunelleschi’s masonry surpass his? Who was this person?
dome atop Florence Cathedral is the Construction Secrets
largest one in the world. (Masonry is A Famous Fool
the art of building from stone, clay, Many dome shapes need extra
brick, or concrete.) It’s wider than Though not an experienced builder, support during construction.
the width of a soccer field. With its Brunelleschi was a thinker and an Otherwise they would fall apart. To
stone, mortar, and some four million innovator. He made his living as a build without central support or
bricks, it weighs about 37,000 tons. goldsmith and sculptor but was also scaffolding, and to keep the dome
That’s heavier than the Statue of a bit of a trickster and magician. strong forever after, Brunelleschi
Liberty. When he came up with an idea for designed a brickwork pattern that
how to build the dome, some called is one of its most famous features,
Unfortunately, the man who him a babbling fool. However, he had though it is mostly hidden. Bricks are
designed the dome, Filippo taught himself much by studying laid both vertically and horizontally.
Brunelleschi (broon-l-ES-kee), was ancient Roman monuments and The vertically laid bricks work like
extremely secretive. He left behind won a competition to be in charge bookends, holding the horizonal
no models or drawings. Could it have of building a dome to top the late bricks in place. In other places,
medieval cathedral in the city of bricks form a zigzag, or herringbone,
WdtohhmaeLteetgdwoeopansdyoofisnuasanptyhisreiengmdkgy?.by Florence. Eventually, the project pattern. Ancient Romans used this
would make him famous through- pattern in paving their roads because
out the world. it makes for an extremely durable
and stable surface. Though not a new
Work began on the dome in method for walls at the time, this
August 1420. Sixteen years later— was the first time this technique was
despite many obstacles, includ- used in so large a structure and with
ing a short stint in prison such a high degree of precision.
for Brunelleschi—the dome was
finished. It is a wonder of const- The herringbone pattern was not
ruction geometry and creativity. all it took to keep the dome from
Today he is often called the founding collapsing as it was constructed.
father of Renaissance architecture, According to Ross King, author of
his iconic dome considered an Brunelleschi’s Dome, “Filippo’s real
international treasure. stroke of genius was in creating a
kind of circular skeleton over which
Unconventional Beauty the external octagonal structure of text © 2020 by Peg Lopata
the dome took shape.” The dome is,
Some say one illustration of its in fact, two domes, one nested inside
perfection is that its designer the other.
was not an architect, but a
creative genius who didn’t follow Capri says, “Human ingenuity
conventional thinking. “The dome and creative thinking have no limits.
is an example of thinking beyond [Brunelleschi’s dome] is a perfect
the boundaries of what was once example of how confidence, belief
thought to be possible,” says Steve in yourself, our minds, and human
Capri, a consulting engineer in Glen passion can create incredible things.”
Cove, New York. Brick by brick, Brunelleschi built a
structure that still inspires people,
Rocky Ruggiero is a Renaissance over a half a millennium later.
art historian who offers lectures and
Writer Peg Lopata lives in Somerville,
Massachusetts, in a house built about 500
years after Brunelleschi’s dome.

31

32

gawaWvmoohriedkyspsd?oeorhdfaeercsdtigtnoers am a game developer. When my co-
workers and I talk about “perfection” in
by Stuart Maine games—whether video or board games,

Iwar games or roleplaying games—we
don’t mean it in the way you might expect.
That’s because no game is the “best,” and
experts can’t agree on what that would look
like anyway. Take even the most beloved game
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)RU H[DPSOH \RX PLJKW ğQG D JDPH WRR HDV\
ZKLOH , ğQG LW WRR GLIğFXOW 2U \RX PLJKW SUHIHU
multiplayer battles, but I want my games to be
single player and story focused.

Instead, when game developers These players are said to have
use the word perfect, they’re talking “perfected” Tic-Tac-Toe. That means
about games being “perfected.” they’ve found the perfect (also called
And for the people making these optimum) strategy to play that game
games, it’s usually a bad thing if that and so don’t have to strategize which
happens. But to explore what we move is best. They can simply play on
mean by games being perfected and autopilot.
why it’s bad, we need to look at how
games have “width” and “depth.” Game designer Sid Meier once
said that a good game is a “series of
Games = Decisions interesting choices.” He should know
because he designed classic games
Consider Tic-Tac-Toe as an like Civilization, a strategy game in
example. This simple game of taking which you build a world empire. What
turns to write Xs and Os on a 3x3 he means is that for any game to be
grid can be fun for young kids, but fun, it has to challenge you, either
you don’t often see older kids, teens by asking you to make decisions or
or adults choosing to play it. The testing your physical skills. If you
game isn’t very wide or very deep, can truly say you’ve mastered the
which means it doesn’t take long for decisions and skills needed to play
players to learn the best possible that game, then you have perfected it
way to play it. If you’re the first
player, then as long as you start by 33
placing your X in the center square,
or a corner you can always win or
tie (also called a draw) unless you

make a mistake. If the second
player also knows to start in the
center or a corner, and then to
block your moves every time,
then every game will end in
a draw—unless someone
makes a mistake.

and are likely to get bored and move on
to the next game.

Maybe you’re thinking “What
decisions do I make in a game?” You
might be surprised. Some decisions are
conscious ones—the grand, strategic
choices you make. In Fortnite, an example
would be where to craft your base. Other
decisions are instinctive, such as those
made under time pressure. Things like
where to land your parachute: you might
choose to drop by a certain building. But
then you see another player there and
have to make the split-second decision
whether to go ahead or swerve off (and
which way to swerve is a decision, too).

A good game is a “series
of interesting choices.”

In fact, the vast majority of decisions right choice. Your body is capable WLoiodkthinagnCdloDseeprtaht
you make in a video game are made of pulling off the right move exactly
instantaneously and without thoughtful when it needs to. And as I mentioned The wider a game is, the more things
consideration, such as whether to block earlier, perfecting a game is bad because there are for you to do in it. In video
or attack, or whether to jump now or a it turns out that players often quit games we call these ‘mechanics’, and
split-second later. games that no longer challenge them. they’re all the possible actions you
can take in that game. For example,
tThhee PHreoabrlteomf All this (finally) leads us back to in Minecraft you can move, dig, fight,
talking about a game’s width and combine resources to make new ones,
So if you’ve perfected a game, it has no its depth, because these are the two ride, jump, swim, use Redstone to
more questions to ask you, or at least no methods game developers use to create logic, and so on and on.
interesting ones. You always know the ensure it’s difficult for players to
perfect their games. Wide games are difficult to perfect
because they offer so much to do that
it takes a very long time to master
every part of the game. Even if each
part of the game is quite shallow
and easy to master there’s always

something new to try. Which Is Better? RECOMMENDED
Compare Nintendo’s READING
Super Smash Bros. It’s important to note that a
to Capcom’s Street wide game isn’t better than If you’d like to dig a little deeper
Fighter. Both are a deep game. And the other into the secrets behind designing
fighting games, way around. They’re just two games, I recommend:
and I’d argue that ways of achieving the goal of
Street Fighter is keeping players challenged A Theory of Fun for Game Design
a more complex and enjoying themselves. by Raph Koster
game. But the huge However, game designers This book takes a look at why
roster of characters, must make choices humans play games and the topics of
stages, and pickups in Smash Bros. carefully. Wide games tend perfection and challenge. Essential
make it endlessly fun to try new to be expensive to make, as there are a lot for anyone who makes activities for
combinations. of mechanics to create and polish, while other people to do and wants them to
deep games can feel scary to new players be as fun as possible.
On the other hand, deep games and might drive them away.
keep players interested by making Also, there’s still an audience for GameTek: The Math and Science of
their mechanics extremely difficult shallow and narrow games—some Gaming by Geoff Engelstein
to master. They might do this people like to play games that they’ve This book digs quite deeply into
through making their rules hard perfected. Solitaire, for example, how numbers and player psychology
to understand, so you have fun requires almost no skill and offers affect games, but because it’s made
figuring them out, or by including nothing new to discover, but it can be up of short, easy-to-read pieces
randomness, so you have to react to a relaxing way to pass the time. Not it’s not too intimidating. Great for
sudden suprises. Multiplayer games everyone is looking to push their brain anyone looking to design board
use the other players for the same or body with a challenge. As another games.
effect—you never know what another example, you might play a game you’ve
player is going to do, so have to keep perfected simply to hang out with your
reacting and changing your plans. friends—the video game Destiny was
purposefully designed to be a fun, social
Golf is a great example of a deep way to blast monsters with buddies.
game, because it’s so difficult to play
well. If you think about it, golf’s rules Making It Personal
make no sense. You have to stand a
long way from the hole and use a stick Next time you become hooked on a
with a tiny head to hit an even smaller game, or find one boring, try to think
ball. And even worse, someone has about how wide and deep that game
dug pits all over the place and filled is. Are you enjoying the game because
them with sand or water! But all it has so much “stuff” there’s always
these elements combine to give golf something new to do, or because it’s
incredible depth, both in the decisions giving you a real challenge to try and
players need to make and the physical master? Alternatively, are you bored
skills needed to get the ball where because it’s too simple or because you
they want. Just look at how often feel that you’ve seen everything it has
professional players mess up shots to to offer? Looking at games this way can
see how basically impossible golf is to help when choosing what to play based
master. on your mood, or when picking a new
game to try. So while no game can ever
be exactly right for everyone, at least
you can find the games that are perfect
for you.

Stuart Maine has worked as a video game
designer for 22 years across console, mobile,
and PC, and he’s still on the eternal quest
to become the perfect designer. He’s pretty
sure it helps to play as many games as
possible, but hopes it also has something
to do with cake.

HOW DEEP, HOW WIDE?

This graph shows some examples of
wide or deep games. Which have you
tried and enjoyed—or not liked? Is
there a pattern that suggests you
prefer easy-to-grasp, accessible games,
or games that push you to learn and
struggle to master them?

GOLF

CHESS

TETRIS SAYONARA
WILD HEARTS
NARROW

less to do

SUBWAY SURFERS

GO FISH SOLITAIRE

TIC-TAC-TOE CANDYLAND

36

DEEP DUNGEONS
& DRAGONS
harder to master

DOTA 2

MAGIC: THE GATHERING FORTNITE
SOCCER

WARHAMMER 40,000 WIDE

MINECRAFT more to do

SMASH BROS ANIMAL CROSSING

text © 2020 by Stuart Maine

SHALLOW 37

easier to master

by Donna Bozzone

I auttssthueaoannmlltyeitooopnlnoaheoytokoawm.chottorshweey

Perfectly

WHEN VARIATION IS THE KEY TO SUCCESS

Swimmer Michael
Phelps holds the
record for most
Olympic medals—
in any sport.

T he artist Leonardo da is as long as what you would expect the animal kingdom. Imagine a
Vinci, perhaps best to see in a man who is 6 feet 8 inches population of brown rabbits and
known for painting the tall. His legs are the length typical of white rabbits in a snowy field. Under
Mona Lisa, produced a man who is 5 feet 10 inches. Phelps these conditions, predators are less
a drawing called the has long arms too. Like the Vitruvian likely to see and catch the white
Vitruvian Man. In it, da Vinci Man, most people have a wingspan rabbits. In a summertime field—all
depicted his idea of the perfectly roughly the same as their height. brown soil and green and golden
sized and proportioned male Phelps’ wingspan is 6 feet 7 inches, plants—white rabbits are more
body. But is this really what a three inches longer than his height. visible and easier to catch. Neither
perfect body looks like? And white nor brown fur is perfect for
if it’s perfect, does that make His ankles are (reportedly) double rabbit survival. Rabbits need different
HYHU\ RWKHU W\SH RI ERG\ ĠDZHG" jointed, and thus extremely flexible.
Or maybe those are the wrong And his feet are big—he wears size 14 Do sytoaundthoinukt?
questions and the idea of a shoes. So Phelps’ legs act like flippers we
“perfect” body is actually when he swims.
ZKDWłV ĠDZHG
No one could argue that Phelps
has a perfect body in da Vinci’s
sense. But is it correct to say
it is imperfect? What does
“perfection” mean when we are
talking about human biology?
Does it even exist?

An Imperfect Man What Is Physical text © 2020 by Donna Bozzone
Perfection?
Consider Michael Phelps. The
winningest swimmer of all time, Maybe perfection has more
Phelps earned 28 Olympic medals. His to do with how a body works
body does not look like the Vitruvian than how it looks. How we
Man. In fact, Phelps’ body is quite function actually depends
unusual. The best swimmers tend upon how well we fit into our
to have long torsos and short legs. environment.
Phelps is 6 feet 4 inches, but his torso
Here’s an example from

39

bodies for different seasons. And prevent people from Simone Biles has
in fact, in some types of rabbits, fur reproducing, though. earned more world
color changes with the seasons. Like Amazingly, most of championship med-
rabbits, all organisms, including us function extremely als than any other
people, adapt to their environments. well despite these gymnast in history.
The process of evolution selects for flaws. Some of us
the survival of organisms that thrive function spectacularly. our survival. Human variation has
in their specific environments. But allowed us to live in wildly different
evolution isn’t engineering. Often, Variation as environments—the tropics, deserts,
imperfections that don’t affect an Element and the Arctic—and to develop
survival too badly get passed on of Success many different physical, intellectual,
through the generations. and emotional talents. Not only is
Michael Phelps’ there no ideal human body, but our
Odd Parts and Compromises body is not perfectly species also thrives because we are
symmetrical or different from one another, each of us
People have plenty. Here are just a few balanced. His physical particularly suited for our own way
imperfections in the human body. Our variations, however, of living.
knees are less flexible than some of may have given him
our other joints, which makes injury the raw materials to How might Michael Phelps,
common. Unlike most other animals, be a close-to-perfect Usain Bolt, and Simone Biles define
we cannot make vitamin C and need swimmer. Phelps’ case is not unique; perfection? Perhaps they might say
to make sure we get it in our diets. elite athletes highlight dramatic that perfection, or close to it, occurs
And our jaws are too small to easily variability that provides them the in peak athletic performance. Their
fit all our teeth, which is why wisdom physical characteristics to approach physical traits certainly helped them
teeth usually need to be removed. perfection in action. Usain Bolt, an excel at their sports. However, it was
Olympic sprinter, has an abundance hard work, dedication, and training
All our odd parts and functional of fast-twitch muscle fibers that make that allowed them to soar.
compromises exist because evolution him speedy and legs so long that it
builds on what came before. Our takes him four to five fewer steps to How do you define perfection?
ancestors walked on four legs, not complete a 100-meter race than his Maybe something about you
two. Our knees are a compromise that competitors. seems different. Can you combine
allow us to be bipedal. More recent your unique physical, mental, and
ancestors of humans lost the ability Simone Biles, another Olympic gold emotional skills and your attitude in
to make vitamin C, but we figured medalist, is both strong and small. a way that works toward your version
out a way to solve this problem with The combination is ideal for her sport of perfection?
a change in diet. Humans’ primate of gymnastics. She may also have a
ancestors grew bigger jaws than we better-than-average ability to sense Donna Bozzone is a 5-foot-2 biology
do, because they ate tougher foods. where her body is in space, perhaps professor and author of books about science.
Now our teeth are crowded. None of making jumps, spins, and somersaults 7KDQNV WR KHU KHLJKW VKH FDQ ğW FRPIRUWDEO\
these flaws are so serious that they a tad easier than for an average person. LQ VPDOO SODFHV VXFK DV WKH VHDWV LQ DQ
No athlete is born with the skills airplane and rarely hits her head on
Sprinter Usain Bolt to win gold medals, though. Those low-hanging things. Because she is left-
holds world records achievements require years of effort. handed, she would have advantages boxing,
in three different EDVHEDOO FULFNHW DQG WHQQLV FRPSDUHG WR
distances. Using Variation to right-handed people, if she played any of
Your Advantage these sports.
40
Da Vinci’s drawing of the Vitruvian Man
combined mathematics and art. To
da Vinci, the Vitruvian Man depicted
ideal proportions. It was his image of
the perfectly formed man. Da Vinci is a
time-honored artist, but is there really
such thing as a perfect body?

No.
In biology, there is no such thing
as one ideal body. In fact, variation in
all living things, including us, is the
rule. This variation is essential for

BY EMILY CAMBIAS

Q&A

Why is a group itself as a manual on “how to callback to that association.
of crows called be a lord” with sections about As fun as they are, nowadays
hunting, hawking, fishing, and
a “murder?” heraldry. The hunting section people that work with animals,
—Laura M., Alabama includes a number of these particularly scientists and
terms of venery for animals, like researchers, don’t use terms of
Poor crows. They can’t venery unless they’re playing
. . . a sleuth of bears a trivia game. A group of birds
A: help it that they’re . . . a parliament of owls is almost always called a flock,
such a Halloween-y . . . a murmuration a group of herbivores a herd.
looking bird, and on of starlings. But these terms are part of
top of that we saddled “Murder of crows” doesn’t an interesting slice of history.
them with a word like “murder.” actually appear in Book of St. Maybe it’s time we come up
But they’re actually not the only Albans, but it comes from terms with our own! Perhaps “a hush
animal with an unusual group of venery as well. Meat is very of librarians?” Or “a learning of
name. These words for groups important to a crow’s diet, and students?” Or maybe it’s time
of animals are called terms of they will often scavenge meat we give those friendly crows
venery. “Venery” is an old word from dead animals or people. their due with “an invitation
for “hunting.” During the Medieval Crows are friendly, intelligent of crows?”
period in England, the rich and birds, and they’ll share the
powerful developed their own location of fresh meat with —Emily
kind of hunting language— their friends and family. But
hundreds of specialized words for like many scavengers (like Have any questions?
animals, equipment, and people. the much-maligned vulture), Send them to Muse Q&A,
Coming up with clever or poetic crows’ love of meat meant that 70 E. Lake St., Suite 800,
terms of venery was a way of humans associated them with
showing off how educated and death. Making “murder” the Chicago, IL 60601,
intelligent you were. You might term of venery for a group of or email them to
have heard some famous terms of crows was probably a clever [email protected].
venery that came from this, like “a
pride of lions”, “a pod of whales,”
or “a pack of dogs.”
One source for many old terms
of venery is The Book of St. Albans,
published in 1486, which bills

41

AGESAmmoni THE SPIRA
FO
LLOWING
THEL THROUGH
in Math & Met

42

itesbyWailanaKalam o better known fossil
perhaps exists than the
ammonite,” wrote Sir
Theodore A. Cook in his

“N  1914bookonperfect
geometry in nature. Famed for its
beautiful spiral shape, the ammonite
has captured the imaginations
of artists, mathematicians, and
storytellers for centuries. As a
symbol of perfection, this fossil
remains a source of awe and
superstition even today.

WHAT IS AN AMMONITE?

Ammonites were marine mollusks that flourished at
the same time as the dinosaurs. Closely related to the
octopus and cuttlefish, they look much like the modern-
day nautilus. During their successful 335-million-year
existence, they inhabited practically every corner of the
ocean. Though they died out around 66 million years ago,
as a result of the same asteroid collision that doomed the
dinosaurs, ammonite fossils are still found all across the
world. These remains come in all shapes and sizes, from
spears to hooks to snail-like coils. But their most famous
shape is the planispiral, a flat, tubular spiral rippled with
rib-like chambers. A favorite of collectors, ammonite
shells are admired for their beauty and symmetry.

Ammonite shells
are the attractive
remains of now-
extinct marine
mollusks.

taphor text © 2020 by Wailana Kalama

43

A shape that widens
as it curves is a loga-
rithmic spiral. Think
of a spiral galaxy or
a hurricane—or an
ammonite fossil.

THE LOGARITHMIC SPIRAL flower, in honeybee colonies, even in the human body.
Though not all logarithmic spirals possess this unique
Geometric spirals have long fascinated ratio, many come close to it. And an ammonite that only
mathematicians. The Greek mathematician and loosely sticks to golden ratio dimensions still has an
scientist Archimedes wrote a whole book on the shape aesthetically pleasing shape.
around 225 BCE and even had one named after him—
the Archimedean spiral. This is what you might imagine The seventeenth-century mathematician Jacob
when you hear the word, “spiral,”—a coil where the Bernoulli was enraptured by this spiral’s beauty. He called
distance between its coils stays constant as they wind it the spira mirabilis, the “wonderful spiral,” a symbol
around a central point. of change and resurrection. He even commissioned a
headstone engraved with the spiral and the motto Eadem
But the ammonoid spiral is slightly different. As mutata resurgo. It translates to “Although changed, I shall
this unique spiral coils around itself, it widens and arise the same.” Unfortunately, the stonemasons made
curves outward—in a shape known as a logarithmic a mistake and carved an Archimedean spiral onto his
spiral. Think of a spiral galaxy. As the spiral unwinds gravestone instead!
itself from a central point, the width between each
arm and the central point grows larger. You can see THE AMMONITE IN FOLKLORE
this even clearer on an ammonite fossil by observing
its chambers. Each of its chambers is larger than the Myths of ammonites differ from region to region, but
one that came before, but the ratio of its dimensions they have often been used as good luck charms or
stays the same. This is known as self-similarity. As the as medicines for divine healing. The earliest known
ammonite grows, the chamber replicates itself in a reference to these “serpent-like stones” was in seventh-
slightly larger version. Other logarithmic spirals are century BCE Assyrian medical texts. They were used as a
found in nautilus shells, hurricanes, and even the charm against an affliction known as a “hand of a ghost.”
Milky Way. Early Indian texts describe snake-shaped stones as good
luck charms for a healthy and happy life.
What is it about this shape that’s so unusual? You
may have heard of the golden ratio, a special number To the Greeks, the ammonite looked like a goat horn,
that most mathematicians and artists agree creates and horns were a symbol of the god Zeus-Ammon.
attractive shapes and compositions. Also called the So they named it after him: cornu Ammonis, the horn
“divine proportion,” the golden ratio seems to be of Zeus-Ammon. This god was a Greek version of the
widespread in nature. The proportion sometimes Egyptian god Ammon, who, as you may have guessed,
appears in the way sunflower seeds grow in their gave his name to the word ammonite.

44 In early Europe, ammonites were used as medicine
to try to treat cramps, snakebites, and blindness. In
Germany, they were called dragon stones. Cowherds
placed them in empty pails as a charm thought to
encourage cows to produce milk. The Blackfoot peoples
of North America call them buffalo stones, after their
resemblance to sleeping buffalo.

An ancient tomb in southwest England fea-
tures an ammonite shape in the door.

On England’s Jurassic Coast, craftsmen carved snake religious charms as far back as the
heads into ammonite fossils. second century BCE.

In early Christianity, ammonites took on a Thanks in part to the Jurassic
more menacing meaning. Christians in the British Coast, the ammonite also appears
Isles claimed that ammonites were once snakes, in Great Britain’s architecture. One
cursed by the saints. One well-known legend tells ancient example is the ammonite-
the story of St. Hilda of Whitby, a powerful, semi-mythical shaped impression in the door at
saint from the seventh century. In the story, St. Hilda the entrance of Stoney Littleton
enchanted evil snakes and turned them into stone. The Long Barrow in southwest
town of Whitby is located on the Jurassic Coast, a shoreline England. This chambered tomb is believed to date back
in England known for countless ammonites and other to 3500 BCE. The limestone used in the door may have
prehistoric fossils, which may have given rise to the legend. been transported from as far as 5 miles (8 km) away.
The Whitby legend became so popular that local craftsmen It was likely considered valuable to be carried such a
began to carve snake heads, eyes, and mouths into the distance by these ancient builders.
fossils and sell them to tourists. By the early eighteenth century, fossil collecting
was in fashion. Ammonites became popular among
THE AMMONOID MOTIF IN ART museums, scientific collectors, and especially architects.
& ARCHITECTURE London architect George Dance decorated his
Shakespeare Gallery with ammonite motifs in 1788. He
The beautiful shape of the ammonite has been a favorite invented the ammonite order, fluted columns topped
among artists and architects for ages. To this day, Whitby’s with ammonite-shaped curls. Many builders used his
coat of arms still depicts three coiled serpents in memory of innovative pattern.
their local legend. Another famous architect who loved the shape of the
ammonite was Amon Wilds, who—perhaps because of
Ammonites are a frequent design element in Indian his name—carved ammonites on the top of columns
art, in part because they resemble an outside of Castle Place in the small town of Lewes,
important element of Hindu belief: England. To this day, you can still
circular points of energy on the body visit the castle and see its columns
called chakras. The Hindu god Vishnu is topped with curly logarithmic spirals.
said to have a spinning, disk-like chakra If you find yourself wandering among
with 108 serrated edges—similar to the cottages in southeast London, you
ribbed chambers of the ammonite— might just glimpse a few lesser-
and statues often depict him gripping known examples, though who carved
one. In North India and Nepal, pebbles these, nobody knows.
of black limestone that contain This ancient creature’s shape
ammonites, called saligrams, have been combines magic and math, art and
considered sacred. People have placed science. What stories and structures
them in temples and households as might the ammonite inspire next?

Eighteenth-century architect George Dance Wailana Kalama is a writer with a
designed columns topped with ammonite-
shaped curls. pretty collection of polished ammonites.

She’s found they make a handy cure for

writer’s block.

CONTEST

NEW CONTEST

—ANNA J. / age 9 / New York

Bubble Head ANNOUNCING —OLIVIA G. / age 14 / Georgia
—EMILY P. / Colorado
We gave you the perfect recipe, now CONTEST WINNERS!
show us the perfect bubble! Is it In March 2020, we asked for a
colorful or clear? Round or shaped picture of how you fit into your
like a cat? Singular or in a bunch? own personal place in the
Send in a picture of your superb world. We saw backyards and
soapy spheres and we’ll put them bedrooms, imaginary lands
together in a frothy display. and creatures. Here are some
niches to celebrate.
CONTEST RULES
1. Your contest entry must be your RUNNERS-UP
very own original work. Ideas and
words should not be copied. Honorable Mention
This month’s runner-up is
2. Be sure to include your name, age, Ursa G., age 10, California.
and full address on your entry.

3. Only one entry per person, please.

4. If you want your work returned,
enclose a self-addressed,
stamped envelope.

5. All entries must be signed by a
parent or legal guardian, saying
that this is your own work and
no help was given and granting
permission to publish. For detailed
information about our compliance
with the Children’s Online Privacy
Protection Act, visit the policy page
at cricketmedia.com/privacy.

6. Your entry must be received by
September 30, 2020. We will publish
winning entries in the January 2021
issue of Muse.

7. Send entries to Muse Contest,
70 East Lake Street, Suite 800,
Chicago, IL 60601 or via email to
[email protected].
If entering a digital photo or scan,
please send at 300 dpi.

ANSWERS

PAGES 6–9 MUSE NEWS
Muse News False Story “Practice Makes Imperfect”

46

Your Tech BY KATHRYN HULICK These unfair comparisons
may lead to feelings of
IS YOUR TIKTOK FEED jealousy or failure. In
TOO PERFECT? the worst cases they can
contribute to anxiety,
EVERYONE’S LIFE LOOKS PERFECT ON SOCIAL MEDIA. depression, or other serious
On TikTok, Instagram, SnapChat, YouTube, and similar mental health issues. Today’s
apps, people tend to share their happiest, most picturesque young people are experiencing
moments. They carefully compose any text to get the these types of issues in greater
message just right. They use filters and enhancements to numbers than in the past.
glam up images and videos. The app sorts the posts with A recent study found that
the most likes and comments to the top. The end result? All perfectionism is rampant
you see of others’ lives is the best of the best. among young people and may
help explain the increase.
Your own life may not seem to measure up. Things
happen every day that you’d never dare share. You Is social media part of the
also see all of your posts that don’t get many likes. problem? Many people think
You may unfairly compare the worst of your life to so. In 2015, the Australian
the very best of others’ lives. “I do feel I need to be Instagram star Essena O’Neill
perfect and compare myself to others all the time,” quit posting. She said, “I just
15-year-old Maddie McGowan of Southampton, want younger girls to know
UK, told the Guardian. this isn’t candid life, or cool
or inspiration. It’s contrived
perfection made to get
attention.”

But social media isn’t all
bad. In one survey, around
75 percent of 13- to 17-year-
olds said social media
doesn’t affect their mental
health, while the remaining
25 percent said it has a
positive effect. The ability to
instantly reach out to a huge
community of friends and
peers can provide emotional
support as well as an outlet
for creativity, self-expression,
and even grassroots social
movements.

Yes, social media can
make teens feel flawed or
inadequate. But it also brings
them together in ways that
other technology can’t. What
do you think? Is perfectionism
on social media a problem?
What can kids do about it?

Kathryn Hulick likes looking at

plants on Reddit and Instagram

and sometimes gets garden

jealousy! She is the author of many

books for kids and teens, including
Strange But True: The Future, which

comes out in 2021.

47