Laurel’s birthday: March 15. A few of her favorite things:

I

call

our

world

Flatland

not

because

we

call

it

so

but

to

make

its

nature

clearer

to

you

my

happy

readers

who

are

privileged

to

live

in

Space

Imagine

a

vast

sheet

of

paper

on

which

straight

Lines

Triangles

Squares

Pentagons

Hexagons

and

other

figures

instead

of

remaining

fixed

in

their

places

move

freely

about

on

or

in

the

surface

but

without

the

power

of

rising

above

or

sinking

below

it

very

much

like

shadows

only

hard

with

luminous

edges

and

you

will

then

have

a

pretty

correct

notion

of

my

country

and

countrymen

Alas

a

few

years

ago

I

should

have

said

my

universe

but

now

my

mind

has

been

opened

to

higher

views

of

things

In

such

a

country

you

will

perceive

at

once

that

it

is

impossible

that

there

should

be

anything

of

what

you

call

a

solid

kind

but

I

dare

say

you

will

suppose

that

we

could

at

least

distinguish

by

sight

the

Triangles

Squares

and

other

figures

moving

about

as

I

have

described

them

On

the

contrary

we

could

see

nothing

of

the

kind

not

at

least

so

as

to

distinguish

one

figure

from

another

Nothing

was

visible

nor

could

be

visible

to

us

except

Straight

Lines

and

the

necessity

of

this

I

will

speedily

demonstrate

Place

a

penny

on

the

middle

of

one

of

your

tables

in

Space

and

leaning

over

it

look

down

upon

it

It

will

appear

a

circle

But

now

drawing

back

to

the

edge

of

the

table

gradually

lower

your

eye

thus

bringing

yourself

more

and

more

into

the

condition

of

the

inhabitants

of

Flatland

and

you

will

find

the

penny

becoming

more

and

more

oval

to

your

view

and

at

last

when

you

have

placed

your

eye

exactly

on

the

edge

of

the

table

so

that

you

are

as

it

were

actually

a

Flatlander

the

penny

will

then

have

ceased

to

appear

oval

at

all

and

will

have

become

so

far

as

you

can

see

a

straight

line

The

same

thing

would

happen

if

you

were

to

treat

in

the

same

way

a

Triangle

or

a

Square

or

any

other

figure

cut

out

from

pasteboard

As

soon

as

you

look

at

it

with

your

eye

on

the

edge

of

the

table

you

will

find

that

it

ceases

to

appear

to

you

as

a

figure

that

it

becomes

in

appearance

a

straight

line

Take

for

example

an

equilateral

Triangle

who

represents

with

us

a

Tradesman

of

the

respectable

class

Figure

1

represents

the

Tradesman

as

you

would

see

him

while

you

were

bending

over

him

from

above

figures

2

and

3

represent

the

Tradesman

as

you

would

see

him

if

your

eye

were

close

to

the

level

or

all

but

on

the

level

of

the

table

and

if

your

eye

were

quite

on

the

level

of

the

table

and

that

is

how

we

see

him

in

Flatland

you

would

see

nothing

but

a

straight

line

When

I

was

in

Spaceland

I

heard

that

your

sailors

have

very

similar

experiences

while

they

traverse

your

seas

and

discern

some

distant

island

or

coast

lying

on

the

horizon

The

far

off

land

may

have

bays

forelands

angles

in

and

out

to

any

number

and

extent

yet

at

a

distance

you

see

none

of

these

unless

indeed

your

sun

shines

bright

upon

them

revealing

the

projections

and

retirements

by

means

of

light

and

shade

nothing

but

a

grey

unbroken

line

upon

the

water

Well

that

is

just

what

we

see

when

one

of

our

triangular

or

other

acquaintances

comes

towards

us

in

Flatland

As

there

is

neither

sun

with

us

nor

any

light

of

such

a

kind

as

to

make

shadows

we

have

none

of

the

helps

to

the

sight

that

you

have

in

Spaceland

If

our

friend

comes

closer

to

us

we

see

his

line

becomes

larger

if

he

leaves

us

it

becomes

smaller

but

still

he

looks

like

a

straight

line

be

he

a

Triangle

Square

Pentagon

Hexagon

Circle

what

you

will

a

straight

Line

he

looks

and

nothing

else

You

may

perhaps

ask

how

under

these

disadvantagous

circumstances

we

are

able

to

distinguish

our

friends

from

one

another

but

the

answer

to

this

very

natural

question

will

be

more

fitly

and

easily

given

when

I

come

to

describe

the

inhabitants

of

Flatland

For

the

present

let

me

defer

this

subject

and

say

a

word

or

two

about

the

climate

and

houses

in

our

country

SECTION

2

Of

the

Climate

and

Houses

in

Flatland

As

with

you

so

also

with

us

there

are

four

points

of

the

compass

North

South

East

and

West

There

being

no

sun

nor

other

heavenly

bodies

it

is

impossible

for

us

to

determine

the

North

in

the

usual

way

but

we

a

method

of

our

own

By

a

Law

of

Nature

with

us

there

is

a

constant

attraction

to

the

South

and

although

in

temperate

climates

this

is

very

slight

so

that

even

a

Woman

in

reasonable

health

can

journey

several

furlongs

northward

without

much

difficulty

yet

the

hampering

effort

of

the

southward

attraction

is

quite

sufficient

to

serve

as

a

compass

in

most

parts

of

our

earth

Moreover

the

rain

which

falls

at

stated

intervals

coming

always

from

the

North

is

an

additional

assistance

and

in

the

towns

we

have

the

guidance

of

the

houses

which

of

course

have

their

side

walls

running

for

the

most

part

North

and

South

so

that

the

roofs

may

keep

off

the

rain

from

the

North

In

the

country

where

there

are

no

houses

the

trunks

of

the

trees

serve

as

some

sort

of

guide

Altogether

we

have

not

so

much

difficulty

as

might

be

expected

in

determining

our

bearings

Yet

in

our

more

temperate

regions

in

which

the

southward

attraction

is

hardly

felt

walking

sometimes

in

a

perfectly

desolate

plain

where

there

have

been

no

houses

nor

trees

to

guide

me

I

have

been

occasionally

compelled

to

remain

stationary

for

hours

together

waiting

till

the

rain

came

before

continuing

my

journey

On

the

weak

and

aged

and

especially

on

delicate

Females

the

force

of

attraction

tells

much

more

heavily

than

on

the

robust

of

the

Male

Sex

so

that

it

is

a

point

of

breeding

if

you

meet

a

Lady

on

the

street

always

to

give

her

the

North

side

of

the

way

by

no

means

an

easy

thing

to

do

always

at

short

notice

when

you

are

in

rude

health

and

in

a

climate

where

it

is

difficult

to

tell

your

North

from

your

South

Windows

there

are

none

in

our

houses

for

the

light

comes

to

us

alike

in

our

homes

and

out

of

them

by

day

and

by

night

equally

at

all

times

and

in

all

places

whence

we

know

not

It

was

in

old

days

with

our

learned

men

an

interesting

and

oft

investigate

question

What

is

the

origin

of

light

and

the

solution

of

it

has

been

repeatedly

attempted

with

no

other

result

than

to

crowd

our

lunatic

asylums

with

the

would

be

solvers

Hence

after

fruitless

attempts

to

suppress

such

investigations

indirectly

by

making

them

liable

to

a

heavy

tax

the

Legislature

in

comparatively

recent

times

absolutely

prohibited

them

I

alas

I

alone

in

Flatland

know

now

only

too

well

the

true

solution

of

this

mysterious

problem

but

my

knowledge

cannot

be

made

intelligible

to

a

single

one

of

my

countrymen

and

I

am

mocked

at

I

the

sole

possessor

of

the

truths

of

Space

and

of

the

theory

of

the

introduction

of

Light

from

the

world

of

three

Dimensions

as

if

I

were

the

maddest

of

the

mad

But

a

truce

to

these

painful

digressions

let

me

return

to

our

homes

The

most

common

form

for

the

construction

of

a

house

is

five

sided

or

pentagonal

as

in

the

annexed

figure

The

two

Northern

sides

RO

OF

constitute

the

roof

and

for

the

most

part

have

no

doors

on

the

East

is

a

small

door

for

the

Women

on

the

West

a

much

larger

one

for

the

Men

the

South

side

or

floor

is

usually

doorless

Square

and

triangular

houses

are

not

allowed

and

for

this

reason

The

angles

of

a

Square

and

still

more

those

of

an

equilateral

Triangle

being

much

more

pointed

than

those

of

a

Pentagon

and

the

lines

of

inanimate

objects

such

as

houses

being

dimmer

than

the

lines

of

Men

and

Women

it

follows

that

there

is

no

little

danger

lest

the

points

of

a

square

or

triangular

house

residence

might

do

serious

injury

to

an

inconsiderate

or

perhaps

absentminded

traveller

suddenly

running

against

them

and

therefore

as

early

as

the

eleventh

century

of

our

era

triangular

houses

were

universally

forbidden

by

Law

the

only

exceptions

being

fortifications

powder

magazines

barracks

and

other

state

buildings

which

is

not

desirable

that

the

general

public

should

approach

without

circumspection

At

this

period

square

houses

were

still

everywhere

permitted

though

discouraged

by

a

special

tax

But

about

three

centuries

afterwards

the

Law

decided

that

in

all

towns

containing

a

population

above

ten

thousand

the

angle

of

a

Pentagon

was

the

smallest

house

angle

that

could

be

allowed

consistently

with

the

public

safety

The

good

sense

of

the

community

has

seconded

the

efforts

of

the

Legislature

and

now

even

in

the

country

the

pentagonal

construction

has

superseded

every

It

is

only

now

and

then

in

some

very

remote

backward

agricultural

district

that

an

antiquarian

may

still

discover

a

square

house

SECTION

3

Concerning

the

Inhabitants

of

Flatland

The

greatest

length

or

breadth

of

a

full

grown

inhabitant

of

Flatland

may

be

estimated

at

about

eleven

of

your

inches

Twelve

inches

may

be

regarded

as

a

maximum

Our

Women

are

Straight

Lines

Our

Soldiers

and

Lowest

Class

of

Workmen

are

Triangles

with

two

equal

sides

each

about

eleven

inches

long

and

a

base

or

third

side

so

short

often

not

exceeding

half

an

inch

that

they

form

at

their

vertices

a

very

sharp

and

formidable

angle

Indeed

when

their

bases

are

of

the

most

degraded

type

not

more

than

the

eighth

part

of

an

inch

in

size

they

can

hardly

be

distinguished

from

Straight

lines

or

Women

so

extremely

pointed

are

their

vertices

With

us

as

with

you

these

Triangles

are

distinguished

from

others

by

being

called

Isosceles

by

this

name

I

shall

refer

to

them

in

the

following

pages

Our

Middle

Class

consists

of

Equilateral

or

Equal

Sided

Triangles

Our

Professional

Men

and

Gentlemen

are

Squares

to

which

class

I

myself

belong

and

Five

Sided

Figures

or

Pentagons

Next

above

these

come

the

Nobility

of

whom

there

are

several

degrees

beginning

at

Six

Sided

Figures

or

Hexagons

and

from

thence

rising

in

the

number

of

their

sides

till

they

receive

the

honourable

title

of

Polygonal

or

many

Sided

Finally

when

the

number

of

the

sides

becomes

so

numerous

and

the

sides

themselves

so

small

that

the

figure

cannot

be

distinguished

from

a

circle

he

is

included

in

the

Circular

or

Priestly

order

and

this

is

the

highest

class

of

all

It

is

a

Law

of

Nature

with

us

that

a

male

child

shall

have

one

more

side

than

his

father

so

that

each

generation

shall

rise

as

a

rule

one

step

in

the

scale

of

development

and

nobility

Thus

the

son

of

a

Square

is

a

Pentagon

the

son

of

a

Pentagon

a

Hexagon

and

so

on

But

this

rule

applies

not

always

to

the

Tradesman

and

still

less

often

to

the

Soldiers

and

to

the

Workmen

who

indeed

can

hardly

be

said

to

deserve

the

name

of

human

Figures

since

they

have

not

all

their

sides

equal

With

them

therefore

the

Law

of

Nature

does

not

hold

and

the

son

of

an

Isosceles

i

e

a

Triangle

with

two

sides

equal

remains

Isosceles

still

Nevertheless

all

hope

is

not

such

out

even

from

the

Isosceles

that

his

posterity

may

ultimately

rise

above

his

degraded

condition

For

after

a

long

series

of

military

successes

or

diligent

and

skillful

labours

it

generally

found

that

the

more

intelligent

among

the

Artisan

and

Soldier

classes

manifest

a

slight

increase

of

their

third

side

or

base

and

a

shrinkage

of

the

two

other

sides

Intermarriages

arranged

by

the

Priests

between

sons

and

daughters

of

these

more

intellectual

members

of

the

lower

classes

generally

result

in

an

offspring

approximating

still

more

to

the

type

of

the

Equal

Sided

Triangle

Rarely

in

proportion

to

the

vast

numbers

of

Isosceles

births

is

a

genuine

and

certifiable

Equal

Sided

Triangle

produced

from

Isosceles

parents

footnote

1

Such

a

birth

requires

as

its

antecedents

not

only

a

series

of

carefully

arranged

intermarriages

but

also

a

long

continued

exercise

frugality

and

self

control

on

the

part

of

the

would

be

ancestors

of

the

coming

Equilateral

and

a

patient

systematic

and

continuous

development

of

the

Isosceles

intellect

through

many

generations

The

birth

of

a

True

Equilateral

Triangle

from

Isosceles

parents

is

the

subject

of

rejoicing

in

our

country

for

many

furlongs

round

After

a

strict

examination

conducted

by

the

Sanitary

and

Social

Board

the

infant

if

certified

as

Regular

is

with

solemn

ceremonial

admitted

into

the

class

of

Equilaterals

He

is

then

immediately

taken

from

his

proud

yet

sorrowing

parents

and

adopted

by

some

childless

Equilateral

who

is

bound

by

oath

never

to

permit

the

child

henceforth

to

enter

his

former

home

or

so

much

as

to

look

upon

his

relations

again

for

fear

lest

the

freshly

developed

organism

may

by

force

of

unconscious

imitation

fall

back

again

into

his

hereditary

level

The

occasional

emergence

of

an

Equilateral

from

the

ranks

of

his

serf

born

ancestors

is

welcomed

not

only

by

the

poor

serfs

themselves

as

a

gleam

of

light

and

hope

shed

upon

the

monotonous

squalor

of

their

existence

but

also

by

the

Aristocracy

at

large

for

all

the

higher

classes

are

well

aware

that

these

rare

phenomena

while

they

do

little

or

nothing

to

vulgarize

their

own

privileges

serve

as

almost

useful

barrier

against

revolution

from

below

Had

the

acute

angled

rabble

been

all

without

exception

absolutely

destitute

of

hope

and

of

ambition

they

might

have

found

leaders

in

some

of

their

many

seditious

outbreaks

so

able

as

to

render

their

superior

numbers

and

strength

too

much

even

for

the

wisdom

of

the

Circles

But

a

wise

ordinance

of

Nature

has

decreed

that

in

proportion

as

the

working

classes

increase

in

intelligence

knowledge

and

all

virtue

in

that

same

proportion

their

acute

angle

which

makes

them

physically

terrible

shall

increase

also

and

approximate

to

their

comparatively

harmless

angle

of

the

Equilateral

Triangle

Thus

in

the

most

brutal

and

formidable

off

the

soldier

class

creatures

almost

on

a

level

with

women

in

their

lack

of

intelligence

it

is

found

that

as

they

wax

in

the

mental

ability

necessary

to

employ

their

tremendous

penetrating

power

to

advantage

so

do

they

wane

in

the

power

of

penetration

itself

How

admirable

is

the

Law

of

Compensation

And

how

perfect

a

proof

of

the

natural

fitness

and

I

may

almost

say

the

divine

origin

of

the

aristocratic

constitution

of

the

States

of

Flatland

By

a

judicious

use

of

this

Law

of

Nature

the

Polygons

and

Circles

are

almost

always

able

to

stifle

sedition

in

its

very

cradle

taking

advantage

of

the

irrepressible

and

boundless

hopefulness

of

the

human

mind

Art

also

comes

to

the

aid

of

Law

and

Order

It

is

generally

found

possible

by

a

little

artificial

compression

or

expansion

on

the

part

of

the

State

physicians

to

make

some

of

the

more

intelligent

leaders

of

a

rebellion

perfectly

Regular

and

to

admit

them

at

once

into

the

privileged

classes

a

much

larger

number

who

are

still

below

the

standard

allured

by

the

prospect

of

being

ultimately

ennobled

are

induced

to

enter

the

State

Hospitals

where

they

are

kept

in

honourable

confinement

for

life

one

or

two

alone

of

the

most

obstinate

foolish

and

hopelessly

irregular

are

led

to

execution

Then

the

wretched

rabble

of

the

Isosceles

planless

and

leaderless

are

either

transfixed

without

resistance

by

the

small

body

of

their

brethren

whom

the

Chief

Circle

keeps

in

pay

for

emergencies

of

this

kind

or

else

more

often

by

means

of

jealousies

and

suspicious

skillfully

fomented

among

them

by

the

Circular

party

they

are

stirred

to

mutual

warfare

and

perish

by

one

another

s

angles

No

less

than

one

hundred

and

twenty

rebellions

are

recorded

in

our

annals

besides

minor

outbreaks

numbered

at

two

hundred

and

thirty

five

and

they

have

all

ended

thus

Footnote

1

What

need

of

a

certificate

a

Spaceland

critic

may

ask

Is

not

the

procreation

of

a

Square

Son

a

certificate

from

Nature

herself

proving

the

Equal

sidedness

of

the

Father

I

reply

that

no

Lady

of

any

position

will

mary

an

uncertified

Triangle

Square

offspring

has

sometimes

resulted

from

a

slightly

Irregular

Triangle

but

in

almost

every

such

case

the

Irregularity

of

the

first

generation

is

visited

on

the

third

which

either

fails

to

attain

the

Pentagonal

rank

or

relapses

to

the

Triangular

SECTION

4

Concerning

the

Women

If

our

highly

pointed

Triangles

of

the

Soldier

class

are

formidable

it

may

be

readily

inferred

that

far

more

formidable

are

our

Women

For

if

a

Soldier

is

a

wedge

a

Woman

is

a

needle

being

so

to

speak

ALL

point

at

least

at

the

two

extremities

Add

to

this

the

power

of

making

herself

practically

invisible

at

will

and

you

will

perceive

that

a

Female

in

Flatland

is

a

creature

by

no

means

to

be

trifled

with

But

here

perhaps

some

of

my

younger

Readers

may

ask

HOW

a

woman

in

Flatland

can

make

herself

invisible

This

ought

I

think

to

be

apparent

without

any

explanation

However

a

few

words

will

make

it

clear

to

the

most

unreflecting

Place

a

needle

on

the

table

Then

with

your

eye

on

the

level

of

the

table

look

at

it

side

ways

and

you

see

the

whole

length

of

it

but

look

at

it

end

ways

and

you

see

nothing

but

a

point

it

has

become

practically

invisible

Just

so

is

it

with

one

of

our

Women

When

her

side

is

turned

towards

us

we

see

her

as

a

straight

line

when

the

end

containing

her

eye

or

mouth

for

with

us

these

two

organs

are

identical

is

the

part

that

meets

our

eye

then

we

see

nothing

but

a

highly

lustrous

point

but

when

the

back

is

presented

to

our

view

then

being

only

sub

lustrous

and

indeed

almost

as

dim

as

an

inanimate

object

her

hinder

extremity

serves

her

as

a

kind

of

Invisible

Cap

The

dangers

to

which

we

are

exposed

from

our

Women

must

now

be

manifest

to

the

meanest

capacity

of

Spaceland

If

even

the

angle

of

respectable

Triangle

in

the

middle

class

is

not

without

its

dangers

if

run

against

a

Working

Man

involves

a

gash

if

collision

with

an

Officer

of

the

military

class

necessitates

a

serious

wound

if

a

mere

touch

from

the

vertex

of

a

Private

Soldier

brings

with

it

danger

of

death

what

can

it

be

to

run

against

a

woman

except

absolute

and

immediate

destruction

And

when

a

Woman

is

invisible

or

visible

only

as

a

dim

sub

lustrous

point

how

difficult

must

it

be

even

for

the

most

cautious

always

to

avoid

collision

Many

are

the

enactments

made

at

different

times

in

the

different

States

of

Flatland

in

order

to

minimize

this

peril

and

in

the

Southern

and

less

temperate

climates

where

the

force

of

gravitation

is

greater

and

human

beings

more

liable

to

casual

and

involuntary

motions

the

Laws

concerning

Women

are

naturally

much

more

stringent

But

a

general

view

of

Code

may

be

obtained

from

the

following

summary

1

Every

house

shall

have

one

entrance

on

the

Eastern

side

for

the

use

of

Females

only

by

which

all

females

shall

enter

in

a

becoming

and

respectful

manner

footnote

1

and

not

by

the

Men

s

or

Western

door

2

No

Female

shall

walk

in

any

public

place

without

continually

keeping

up

her

Peace

cry

under

penalty

of

death

3

Any

Female

duly

certified

to

be

suffering

from

St

Vitus

s

Dance

fits

chronic

cold

accompanied

by

violent

sneezing

or

any

disease

necessitating

involuntary

motions

shall

be

instantly

destroyed

In

some

of

the

States

there

is

an

additional

Law

forbidding

Females

under

penalty

of

death

from

walking

or

standing

in

any

public

place

without

moving

their

backs

constantly

from

right

to

left

so

as

to

indicate

their

presence

to

those

behind

them

others

oblige

a

Woman

when

travelling

to

be

followed

by

one

of

her

sons

or

servants

or

by

her

husband

others

confine

Women

altogether

in

their

houses

except

during

the

religious

festivals

But

it

has

been

found

by

the

wisest

of

our

Circles

or

Statesmen

that

the

multiplication

of

restrictions

on

Females

tends

not

only

to

the

debilitation

and

diminution

of

the

race

but

also

to

the

increase

of

domestic

murders

to

such

an

extent

that

a

State

loses

more

than

it

gains

by

a

too