Story-P2

    The military had set up a trailer containing our offices at the looking g
lass site. I saw Gary walking toward the trailer, and ran to catch up with him
. "It's a semasiographic writing system," I said when I reached him.
    "Excuse me?" said Gary.
    "Here, let me show you." I directed Gary into my office. Once we were ins
ide, I went to the chalkboard and drew a circle with a diagonal line bisecting
it. "What does this mean?"
    "'Not allowed'?"
    "Right." Next I printed the words NOT ALLOWED on the chalkboard. "And so
does this. But only one is a representation of speech."
    Gary nodded. "Okay."
    "Linguists describe writing like this--" I indicated the printed words "-
-as 'glottographic,' because it represents speech. Every human written languag
e is in this category. However, this symbol--" I indicated the circle and diag
onal line "--is 'semasiographic' writing, because it conveys meaning without r
eference to speech. There's no correspondence between its components and any p
articular sounds."
    "And you think all of heptapod writing is like this?"
    "From what I've seen so far, yes. It's not picture writing, it's far more
complex. It has its own system of rules for constructing sentences, like a vi
sual syntax that's unrelated to the syntax for their spoken language."
    "A visual syntax? Can you show me an example?"
    "Coming right up." I sat down at my desk and, using the computer, pulled
up a frame from the recording of yesterday's conversation with Raspberry. I tu
rned the monitor so he could see it. "In their spoken language, a noun has a c
ase marker indicating whether it's a subject or object. In their written langu
age, however, a noun is identified as subject or object based on the orientati
on of its logogram relative to that of the verb. Here, take a look." I pointed
at one of the figures. "For instance, when 'heptapod' is integrated with 'hea
rs' this way, with these strokes parallel, it means that the heptapod is doing
the hearing." I showed him a different one. "When they're combined this way,
with the strokes perpendicular, it means that the heptapod is being heard. Thi
s morphology applies to several verbs.
    "Another example is the inflection system." I called up another frame fro
m the recording. "In their written language, this logogram means roughly 'hear
easily' or 'hear clearly.' See the elements it has in common with the logogra
m for 'hear'? You can still combine it with 'heptapod' in the same ways as bef
ore, to indicate that the heptapod can hear something clearly or that the hept
apod is clearly heard. But what's really interesting is that the modulation of
'hear' into 'hear clearly' isn't a special case; you see the transformation t
hey applied?"
    Gary nodded, pointing. "It's like they express the idea of 'clearly' by c
hanging the curve of those strokes in the middle."
    "Right. That modulation is applicable to lots of verbs. The logogram for
'see' can be modulated in the same way to form 'see clearly,' and so can the l
ogogram for 'read' and others. And changing the curve of those strokes has no
parallel in their speech; with the spoken version of these verbs, they add a p
refix to the verb to express ease of manner, and the prefixes for 'see' and 'h
ear' are different.
    "There are other examples, but you get the idea. It's essentially a gramm
ar in two dimensions."
    He began pacing thoughtfully. "Is there anything like this in human writi
ng systems?"
    "Mathematical equations, notations for music and dance. But those are all
very specialized; we couldn't record this conversation using them. But I susp
ect, if we knew it well enough, we could record this conversation in the hepta
pod writing system. I think it's a full-fledged, general-purpose graphical lan
guage."
    Gary frowned. "So their writing constitutes a completely separate languag
e from their speech, right?"
    "Right. In fact, it'd be more accurate to refer to the writing system as
'Heptapod B,' and use 'Heptapod A' strictly for referring to the spoken langua
ge."
    "Hold on a second. Why use two languages when one would suffice? That see
ms unnecessarily hard to learn."
    "Like English spelling?" I said. "Ease-of-learning isn't the primary forc
e in language evolution. For the heptapods, writing and speech may play such d
ifferent cultural or cognitive roles that using separate languages makes more
sense than using different forms of the same one."
    He considered it. "I see what you mean. Maybe they think our form of writ
ing is redundant, like we're wasting a second communications channel."
    "That's entirely possible. Finding out why they use a second language for
writing will tell us a lot about them."
    "So I take it this means we won't be able to use their writing to help us
learn their spoken language."
    I sighed. "Yeah, that's the most immediate implication. But I don't think
we should ignore either Heptapod A or B; we need a two-pronged approach." I p
ointed at the screen. "I'll bet you that learning their two-dimensional gramma
r will help you when it comes time to learn their mathematical notation."
    "You've got a point there. So are we ready to start asking about their ma
thematics?"
    "Not yet. We need a better grasp on this writing system before we begin a
nything else," I said, and then smiled when he mimed frustration. "Patience, g
ood sir. Patience is a virtue."
* * *
    You'll be six when your father has a conference to attend in Hawaii, and
we'll accompany him. You'll be so excited that you'll make preparations for we
eks beforehand. You'll ask me about coconuts and volcanoes and surfing, and pr
actice hula dancing in the mirror. You'll pack a suitcase with the clothes and
toys you want to bring, and you'll drag it around the house to see how long y
ou can carry it. You'll ask me if I can carry your Etch-a-Sketch in my bag, si
nce there won't be any more room for it in yours and you simply can't leave wi
thout it.
    "You won't need all of these," I'll say. "There'll be so many fun things
to do there, you won't have time to play with so many toys."
    You'll consider that; dimples will appear above your eyebrows when you th
ink hard. Eventually you'll agree to pack fewer toys, but your expectations wi
ll, if anything, increase.
    "I wanna be in Hawaii now," you'll whine.
    "Sometimes it's good to wait," I'll say. "The anticipation makes it more
fun when you get there."
    You'll just pout.
* * *
    In the next report I submitted, I suggested that the term "logogram" was
a misnomer because it implied that each graph represented a spoken word, when
in fact the graphs didn't correspond to our notion of spoken words at all. I d
idn't want to use the term "ideogram" either because of how it had been used i
n the past; I suggested the term "semagram" instead.
    It appeared that a semagram corresponded roughly to a written word in hum
an languages: it was meaningful on its own, and in combination with other sema
grams could form endless statements. We couldn't define it precisely, but then
no one had ever satisfactorily defined "word" for human languages either. Whe
n it came to sentences in Heptapod B, though, things became much more confusin
g. The language had no written punctuation: its syntax was indicated in the wa
y the semagrams were combined, and there was no need to indicate the cadence o
f speech. There was certainly no way to slice out subject-predicate pairings n
eatly to make sentences. A "sentence" seemed to be whatever number of semagram
s a heptapod wanted to join together; the only difference between a sentence a
nd a paragraph, or a page, was size.
    When a Heptapod B sentence grew fairly sizable, its visual impact was rem
arkable. If I wasn't trying to decipher it, the writing looked like fanciful p
reying mantids drawn in a cursive style, all clinging to each other to form an
Escheresque lattice, each slightly different in its stance. And the biggest s
entences had an effect similar to that of psychedelic posters: sometimes eye-w
atering, sometimes hypnotic.
* * *
    I remember a picture of you taken at your college graduation. In the phot
o you're striking a pose for the camera, mortarboard stylishly tilted on your
head, one hand touching your sunglasses, the other hand on your hip, holding o
pen your gown to reveal the tank top and shorts you're wearing underneath.
    I remember your graduation. There will be the distraction of having Nelso
n and your father and what's-her-name there all at the same time, but that wil
l be minor. That entire weekend, while you're introducing me to your classmate
s and hugging everyone incessantly, I'll be all but mute with amazement. I can
't believe that you, a grown woman taller than me and beautiful enough to make
my heart ache, will be the same girl I used to lift off the ground so you cou
ld reach the drinking fountain, the same girl who used to trundle out of my be
droom draped in a dress and hat and four scarves from my closet.
    And after graduation, you'll be heading for a job as a financial analyst.
I won't understand what you do there, I won't even understand your fascinatio
n with money, the preeminence you gave to salary when negotiating job offers.
I would prefer it if you'd pursue something without regard for its monetary re
wards, but I'll have no complaints. My own mother could never understand why I
couldn't just be a high school English teacher. You'll do what makes you happ
y, and that'll be all I ask for.
* * *
    As time went on, the teams at each looking glass began working in earnest
on learning heptapod terminology for elementary mathematics and physics. We w
orked together on presentations, with the linguists focusing on procedure and
the physicists focusing on subject matter. The physicists showed us previously
devised systems for communicating with aliens, based on mathematics, but thos
e were intended for use over a radio telescope. We reworked them for face-to-f
ace communication.
    Our teams were successful with basic arithmetic, but we hit a road block
with geometry and algebra. We tried using a spherical coordinate system instea
d of a rectangular one, thinking it might be more natural to the heptapods giv
en their anatomy, but that approach wasn't any more fruitful. The heptapods di
dn't seem to understand what we were getting at.
    Likewise, the physics discussions went poorly. Only with the most concret
e terms, like the names of the elements, did we have any success; after severa
l attempts at representing the periodic table, the heptapods got the idea. For
anything remotely abstract, we might as well have been gibbering. We tried to
demonstrate basic physical attributes like mass and acceleration so we could
elicit their terms for them, but the heptapods simply responded with requests
for clarification. To avoid perceptual problems that might be associated with
any particular medium, we tried physical demonstrations as well as line drawin
gs, photos, and animations; none were effective. Days with no progress became
weeks, and the physicists were becoming disillusioned.
    By contrast, the linguists were having much more success. We made steady
progress decoding the grammar of the spoken language, Heptapod A. It didn't fo
llow the pattern of human languages, as expected, but it was comprehensible so
far: free word order, even to the extent that there was no preferred order fo
r the clauses in a conditional statement, in defiance of a human language "uni
versal." It also appeared that the heptapods had no objection to many levels o
f center-embedding of clauses, something that quickly defeated humans. Peculia
r, but not impenetrable.
    Much more interesting were the newly discovered morphological and grammat
ical processes in Heptapod B that were uniquely two-dimensional. Depending on
a semagram's declension, inflections could be indicated by varying a certain s
troke's curvature, or its thickness, or its manner of undulation; or by varyin
g the relative sizes of two radicals, or their relative distance to another ra
dical, or their orientations; or various other means. These were non-segmental
graphemes; they couldn't be isolated from the rest of a semagram. And despite
how such traits behaved in human writing, these had nothing to do calligraphi
c style; their meanings were defined according to a consistent and unambiguous
grammar.
    We regularly asked the heptapods why they had come. Each time, they answe
red "to see," or "to observe." Indeed, sometimes they preferred to watch us si
lently rather than answer our questions. Perhaps they were scientists, perhaps
they were tourists. The State Department instructed us to reveal as little as
possible about humanity, in case that information could be used as a bargaini
ng chip in subsequent negotiations. We obliged, though it didn't require much
effort: the heptapods never asked questions about anything. Whether scientists
or tourists, they were an awfully incurious bunch.
* * *
    I remember once when we'll be driving to the mall to buy some new clothes
for you. You'll be thirteen. One moment you'll be sprawled in your seat, comp
letely unself-conscious, all child; the next, you'll toss your hair with a pra
cticed casualness, like a fashion model in training.
    You'll give me some instructions as I'm parking the car. "Okay, Mom, give
me one of the credit cards, and we can meet back at the entrance here in two
hours."
    I'll laugh. "Not a chance. All the credit cards stay with me."
    "You're kidding." You'll become the embodiment of exasperation. We'll get
out of the car and I will start walking to the mall entrance. After seeing th
at I won't budge on the matter, you'll quickly reformulate your plans.
    "Okay Mom, okay. You can come with me, just walk a little ways behind me,
so it doesn't look like we're together. If I see any friends of mine, I'm gon
na stop and talk to them, but you just keep walking, okay? I'll come find you
later."
    I'll stop in my tracks. "Excuse me? I am not the hired help, nor am I som
e mutant relative for you to be ashamed of."
    "But Mom, I can't let anyone see you with me."
    "What are you talking about? I've already met your friends; they've been
to the house."
    "That was different," you'll say, incredulous that you have to explain it
. "This is shopping."
    "Too bad."
    Then the explosion: "You won't do the least thing to make me happy! You d
on't care about me at all!"
    It won't have been that long since you enjoyed going shopping with me; it
will forever astonish me how quickly you grow out of one phase and enter anot
her. Living with you will be like aiming for a moving target; you'll always be
further along than I expect.
* * *
    I looked at the sentence in Heptapod B that I had just written, using sim
ple pen and paper. Like all the sentences I generated myself, this one looked
misshapen, like a heptapod-written sentence that had been smashed with a hamme
r and then inexpertly taped back together. I had sheets of such inelegant sema
grams covering my desk, fluttering occasionally when the oscillating fan swung
past.
    It was strange trying to learn a language that had no spoken form. Instea
d of practicing my pronunciation, I had taken to squeezing my eyes shut and tr
ying to paint semagrams on the insides of my eyelids.
    There was a knock at the door and before I could answer Gary came in look
ing jubilant. "Illinois got a repetition in physics."
    "Really? That's great; when did it happen?"
    "It happened a few hours ago; we just had the videoconference. Let me sho
w you what it is." He started erasing my blackboard.
    "Don't worry, I didn't need any of that."
    "Good." He picked up a nub of chalk and drew a diagram:
    "Okay, here's the path a ray of light takes when crossing from air to wat
er. The light ray travels in a straight line until it hits the water; the wate
r has a different index of refraction, so the light changes direction. You've
heard of this before, right?"
    I nodded. "Sure."
    "Now here's an interesting property about the path the light takes. The p
ath is the fastest possible route between these two points."
    "Come again?"
    "Imagine, just for grins, that the ray of light traveled along this path.
" He added a dotted line to his diagram:
    "This hypothetical path is shorter than the path the light actually takes
. But light travels more slowly in water than it does in air, and a greater pe
rcentage of this path is underwater. So it would take longer for light to trav
el along this path than it does along the real path."
    "Okay, I get it."
    "Now imagine if light were to travel along this other path." He drew a se
cond dotted path:
    "This path reduces the percentage that's underwater, but the total
length is larger. It would also take longer for light to travel along this pat
h than along the actual one."
    Gary put down the chalk and gestured at the diagram on the chalkboard wit
h white-tipped fingers. "Any hypothetical path would require more time to trav
erse than the one actually taken. In other words, the route that the light ray
takes is always the fastest possible one. That's Fermat's Principle of Least
Time."
    "Hmm, interesting. And this is what the heptapods responded to?"
    "Exactly. Moorehead gave an animated presentation of Fermat's Principle a
t the Illinois looking glass, and the heptapods repeated it back. Now he's try
ing to get a symbolic description." He grinned. "Now is that highly neat, or w
hat?"
    "It's neat all right, but how come I haven't heard of Fermat's Principle
before?" I picked up a binder and waved it at him; it was a primer on the phys
ics topics suggested for use in communication with the heptapods. "This thing
goes on forever about Planck masses and the spin-flip of atomic hydrogen, and
not a word about the refraction of light."
    "We guessed wrong about what'd be most useful for you to know," Gary said
without embarrassment. "In fact, it's curious that Fermat's Principle was the
first breakthrough;even though it's easy to explain, you need calculus to des
cribe it mathematically. And not ordinary calculus; you need the calculus of v
ariations. We thought that some simple theorem of geometry or algebra would be
the breakthrough."
    "Curious indeed. You think the heptapods' idea of what's simple doesn't m
atch ours?"
    "Exactly, which is why I'm dying to see what their mathematical descripti
on of Fermat's Principle looks like." He paced as he talked. "If their version
of the calculus of variations is simpler to them than their equivalent of alg
ebra, that might explain why we've had so much trouble talking about physics;
their entire system of mathematics may be topsy-turvy compared to ours." He po
inted to the physics primer. "You can be sure that we're going to revise that.
"
    "So can you build from Fermat's Principle to other areas of physics?"
    "Probably. There are lots of physical principles just like Fermat's."
    "What, like Louise's principle of least closet space? When did physics be
come so minimalist?"
    "Well, the word 'least' is misleading. You see, Fermat's Principle of Lea
st Time is incomplete; in certain situations light follows a path that takes m
ore time than any of the    other possibilities. It's more accurate to say th
at light always follows an extreme path, either one that minimizes the time ta
ken or one that maximizes it. A minimum and a maximum share certain mathematic
al properties, so both situations can be described with one equation. So to be
precise, Fermat's Principle isn't a minimal principle; instead it's what's kn
own as a 'variational' principle."
    "And there are more of these variational principles?"
    He nodded. "In all branches of physics. Almost every physical law can be
restated as a variational principle. The only difference between these princip
les is in which attribute is    minimized or maximized." He gestured as if th
e different branches of physics were arrayed before him on a table. "In optics
, where Fermat's Principle applies, time is the attribute that has to be an ex
treme. In mechanics, it's a different attribute. In electromagnetism, it's som
ething else again. But all these principles are similar mathematically."
    "So once you get their mathematical description of Fermat's Principle, yo
u should be able to decode the other ones."
    "God, I hope so. I think this is the wedge that we've been looking for, t
he one that cracks open their formulation of physics. This calls for a celebra
tion." He stopped his pacing and turned to me. "Hey Louise, want to go out for
dinner? My treat."
    I was mildly surprised. "Sure," I said.
* * *
    It'll be when you first learn to walk that I get daily demonstrations of
the asymmetry in our relationship. You'll be incessantly running off somewhere
, and each time you walk into a door frame or scrape your knee, the pain feels
like it's my own. It'll be like growing an errant limb, an extension of mysel
f whose sensory nerves report pain just fine, but whose motor nerves don't con
vey my commands at all. It's so unfair: I'm going to give birth to an animated
voodoo doll of myself. I didn't see this in the contract when I signed up. Wa
s this part of the deal?
    And then there will be the times when I see you laughing. Like the time y
ou'll be playing with the neighbor's puppy, poking your hands through the chai
n-link fence separating our back yards, and you'll be laughing so hard you'll
start hiccuping. The puppy will run inside the neighbor's house, and your laug
hter will gradually subside, letting you catch your breath. Then the puppy wil
l come back to the fence to lick your fingers again, and you'll shriek and sta
rt laughing again. It will be the most wonderful sound I could ever imagine, a
sound that makes me feel like a fountain, or a wellspring.
    Now if only I can remember that sound the next time your blithe disregard
for self preservation gives me a heart attack.
* * *
    After the breakthrough with Fermat's Principle, discussions of scientific
concepts became more fruitful. It wasn't as if all of heptapod physics was su
ddenly rendered transparent, but progress was steady. According to Gary, the h
eptapods' formulation of physics was indeed topsy-turvy relative to ours. Phys
ical attributes that humans defined using integral calculus were seen as funda
mental by the heptapods. As an example, Gary described an attribute that, in p
hysics jargon, bore the deceptively simple name "action,"which represented "th
e difference between kinetic and potential energy, integrated over time," what
ever that meant. Calculus for us; elementary to them.
    Conversely, to define attributes that humans thought of as fundamental, l
ike velocity, the heptapods employed mathematics that were, Gary assured me, "
highly weird." The    physicists were ultimately able to prove the equivalenc
e of heptapod mathematics and human mathematics; even though their approaches
were almost the reverse of one another, both were systems of describing the sa
me physical universe.
    I tried following some of the equations that the physicists were coming u
p with, but it was no use. I couldn't really grasp the significance of physica
l attributes like "action"; I couldn't, with any confidence, ponder the signif
icance of treating such an attribute as fundamental. Still, I tried to ponder
questions formulated in terms more familiar to me: what kind of world-view did
the heptapods have, that they would consider Fermat's Principle the simplest
explanation of light refraction? What kind of perception made a minimum or max
imum readily apparent to them?
* * *
    Your eyes will be blue like your dad's, not mud brown like mine. Boys wil
l stare into those eyes the way I did, and do, into your dad's, surprised and
enchanted, as I was and am, to find them in combination with black hair. You w
ill have many suitors.
    I remember when you are fifteen, coming home after a weekend at your dad'
s, incredulous over the interrogation he'll have put you through regarding the
boy you're currently dating. You'll sprawl on the sofa, recounting your dad's
latest breach of common sense: "You know what he said? He said, 'I know what
teenage boys are like.'" Roll of the eyes."Like I don't?"
    "Don't hold it against him," I'll say. "He's a father; he can't help it."
Having seen you interact with your friends, I won't worry much about a boy ta
king advantage of you; if anything, the opposite will be more likely. I'll wor
ry about that.
    "He wishes I were still a kid. He hasn't known how to act toward me since
I grew breasts."
    "Well, that development was a shock for him. Give him time to recover."

    "It's been years, Mom. How long is it gonna take?"
    "I'll let know when my father has come to terms with mine."
* * *
    During one of the videoconferences for the linguists, Cisneros from the M
assachusetts looking glass had raised an interesting question: was there a par
ticular order in which    semagrams were written in a Heptapod B sentence? It
was clear that word order meant next to nothing when speaking in Heptapod A;
when asked to repeat what it had just said, a heptapod would likely as not use
a different word order unless we specifically asked them not to. Was word ord
er similarly unimportant when writing in Heptapod B?
    Previously, we had only focused our attention on how a sentence in Heptap
od B looked once it was complete. As far as anyone could tell, there was no pr
eferred order when reading the semagrams in a sentence; you could start almost
anywhere in the nest, then follow the branching clauses until you'd read the
whole thing. But that was reading; was the same true about writing?
    During my most recent session with Flapper and Raspberry I had asked them
if, instead of displaying a semagram only after it was completed, they could
show it to us while it was being written. They had agreed. I inserted the vide
otape of the session into the VCR, and on my computer I consulted the session
transcript.
    I picked one of the longer utterances from the conversation. What Flapper
had said was that the heptapods' planet had two moons, one significantly larg
er than the other; the three primary constituents of the planet's atmosphere w
ere nitrogen, argon, and oxygen; and 15/28ths of the planet's surface was cove
red by water. The first words of the spoken utterance translated literally as
"inequality-of-size rocky-orbiter rocky-orbiters related-as-primary-to-seconda
ry."
    Then I rewound the videotape until the time signature matched the one in
the transcription. I started playing the tape, and watched the web of semagram
s being spun out of inky spider's silk. I rewound it and played it several tim
es. Finally I froze the video right after the first stroke was completed and b
efore the second one was begun; all that was visible onscreen was a single sin
uous line.
    Comparing that initial stroke with the completed sentence, I realized tha
t the stroke participated in several different clauses of the message. It bega
n in the semagram for    'oxygen,' as the determinant that distinguished it f
rom certain other elements; then it slid down to become the morpheme of compar
ison in the description of the two moons' sizes; and lastly it flared out as t
he arched backbone of the semagram for 'ocean.' Yet this stroke was a single c
ontinuous line, and it was the first one that Flapper wrote. That meant the he
ptapod had to know how the entire sentence would be laid out before it could w
rite the very first stroke.
    The other strokes in the sentence also traversed several clauses, making
them so interconnected that none could be removed without redesigning the enti
re sentence. The    heptapods didn't write a sentence one semagram at a time;
they built it out of strokes irrespective of individual semagrams. I had seen
a similarly high degree of integration before in calligraphic designs, particu
larly those employing the Arabic alphabet. But those designs had required care
ful planning by expert calligraphers. No one could lay out such an intricate d
esign at the speed needed for holding a conversation. At least, no human could
.
* * *
    There's a joke that I once heard a comedienne tell. It goes like this: "I
'm not sure if I'm ready to have children. I asked a friend of mine who has ch
ildren, 'Suppose I do have kids. What if when they grow up, they blame me for
everything that's wrong with their lives?' She laughed and said, 'What do you
mean, if?'"
    That's my favorite joke.
* * *
    Gary and I were at a little Chinese restaurant, one of the local places w
e had taken to patronizing to get away from the encampment. We sat eating the
appetizers: potstickers,    redolent of pork and sesame oil. My favorite.
    I dipped one in soy sauce and vinegar. "So how are you doing with your He
ptapod B practice?" I asked.
    Gary looked obliquely at the ceiling. I tried to meet his gaze, but he ke
pt shifting it.
    "You've given up, haven't you?" I said. "You're not even trying any more.
"
    He did a wonderful hangdog expression. "I'm just no good at languages," h
e confessed. "I thought learning Heptapod B might be more like learning mathem
atics than trying to speak another language, but it's not. It's too foreign fo
r me."
    "It would help you discuss physics with them."
    "Probably, but since we had our breakthrough, I can get by with just a fe
w phrases."
    I sighed. "I suppose that's fair; I have to admit, I've given up on tryin
g to learn the mathematics."
    "So we're even?"
    "We're even." I sipped my tea. "Though I did want to ask you about Fermat
's Principle. Something about it feels odd to me, but I can't put my finger on
it. It just doesn't sound like a law of physics."
    A twinkle appeared in Gary's eyes. "I'll bet I know what you're talking a
bout." He snipped a potsticker in half with his chopsticks. "You're used to th
inking of refraction in terms of cause and effect: reaching the water's surfac
e is the cause, and the change in direction is the effect. But Fermat's Princi
ple sounds weird because it describes light's behavior in goal- oriented terms
. It sounds like a commandment to a light beam: 'Thou shalt minimize or maximi
ze the time taken to reach thy destination.'"
    I considered it. "Go on."
    "It's an old question in the philosophy of physics. People have been talk
ing about it since Fermat first formulated it in the 1600's; Planck wrote volu
mes about it. The thing is,while the common formulation of physical laws is ca
usal, a variational principle like Fermat's is purposive, almost teleological.
"
    "Hmm, that's an interesting way to put it. Let me think about that for a
minute." I pulled out a felt-tip pen and, on my paper napkin, drew a copy of t
he diagram that Gary had drawn on my blackboard. "Okay," I said, thinking alou
d, "so let's say the goal of a ray of light is to take the fastest path. How d
oes the light go about doing that?"
    "Well, if I can speak anthropomorphic-projectionally, the light has to ex
amine the possible paths and compute how long each one would take." He plucked
the last potsticker from the serving dish.
    "And to do that," I continued, "the ray of light has to know just where i
ts destination is. If the destination were somewhere else, the fastest path wo
uld be different."
    Gary nodded again. "That's right; the notion of a 'fastest path' is meani
ngless unless there's a destination specified. And computing how long a given
path takes also requires information about what lies along that path, like whe
re the water's surface is."
    I kept staring at the diagram on the napkin. "And the light ray has to kn
ow all that ahead of time, before it starts moving, right?"
    "So to speak," said Gary. "The light can't start traveling in any old dir
ection and make course corrections later on, because the path resulting from s
uch behavior wouldn't be the    fastest possible one. The light has to do all
its computations at the very beginning."
    I thought to myself, the ray of light has to know where it will ultimatel
y end up before it can choose the direction to begin moving in. I knew what th
at reminded me of. I looked up at Gary. "That's what was bugging me."
* * *
    I remember when you're fourteen. You'll come out of your bedroom, a graff
iti-covered notebook computer in hand, working on a report for school.
    "Mom, what do you call it when both sides can win?"
    I'll look up from my computer and the paper I'll be writing. "What, you m
ean a win-win situation?"
    "There's some technical name for it, some math word. Remember that time D
ad was here, and he was talking about the stock market? He used it then."
    "Hmm, that sounds familiar, but I can't remember what he called it."
    "I need to know. I want to use that phrase in my social studies report. I
can't even search for information on it unless I know what it's called."
    "I'm sorry, I don't know it either. Why don't you call your dad?"
    Judging from your expression, that will be more effort than you want to m
ake. At this point, you and your father won't be getting along well. "Can you
call Dad and ask him? But don't tell him it's for me."
    "I think you can call him yourself."
    You'll fume, "Jesus, Mom, I can never get help with my homework since you
and Dad split up."
    It's amazing the diverse situations in which you can bring up the divorce
. "I've helped you with your homework."
    "Like a million years ago, Mom."
    I'll let that pass. "I'd help you with this if I could, but I don't remem
ber what it's called."
    You'll head back to your bedroom in a huff.
* * *
    I practiced Heptapod B at every opportunity, both with the other linguist
s and by myself. The novelty of reading a semasiographic language made it comp
elling in a way that Heptapod A wasn't, and my improvement in writing it excit
ed me. Over time, the sentences I wrote grew shapelier, more cohesive. I had r
eached the point where it worked better when I didn't think about it too much.
Instead of carefully trying to design a sentence before writing, I could simp
ly begin putting down strokes immediately; my initial strokes almost always tu
rned out to be compatible with an elegant rendition of what I was trying to sa
y. I was developing a faculty like that of the heptapods.
    More interesting was the fact that Heptapod B was changing the way I thou
ght. For me, thinking typically meant speaking in an internal voice; as we say
in the trade, my thoughts were phonologically coded. My internal voice normal
ly spoke in English, but that wasn't a requirement. The summer after my senior
year in high school, I attended a total immersion program for learning Russia
n; by the end of the summer, I was thinking and even dreaming in Russian. But
it was always spoken Russian. Different language, same mode: a voice speaking
silently aloud.
    The idea of thinking in a linguistic yet non-phonological mode always int
rigued me. I had a friend born of Deaf parents; he grew up using American Sign
Language, and he told me that he often thought in ASL instead of English. I u
sed to wonder what it was like to have one's thoughts be manually coded, to re
ason using an inner pair of hands instead of an inner voice.
    With Heptapod B, I was experiencing something just as foreign: my thought
s were becoming graphically coded. There were trance-like moments during the d
ay when my    thoughts weren't expressed with my internal voice; instead, I s
aw semagrams with my mind's eye, sprouting like frost on a windowpane.
    As I grew more fluent, semagraphic designs would appear fully-formed, art
iculating even complex ideas all at once. My thought processes weren't moving
any faster as a result,    though. Instead of racing forward, my mind hung ba
lanced on the symmetry underlying the semagrams. The semagrams seemed to be so
mething more than language; they were almost like mandalas. I found myself in
a meditative state, contemplating the way in which premises and conclusions we
re interchangeable. There was no direction inherent in the way propositions we
re connected, no "train of thought" moving along a particular route; all the c
omponents in an act of reasoning were equally powerful, all having identical p
recedence.
* * *