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Herbert felt a begrudging admiration for Stensness; whatever his secret was, he was not giving it up easily.
Codes and ciphers had been part of Five training, at least to a level somewhere between elementary and intermediate. Although Herbert had taken the course several years before, and was therefore bound to have forgotten much, his crossword habit had surely kept his brain in some kind of requisite shape.
Hannah came back into the living room with a pot of coffee and two cups. She crooked the top joint of her finger over their rims so she knew when to stop pouring.
Herbert told her that this would take some time; several hours, perhaps.
She said that was fine, she was happy reading.
He watched her run her hands along the spines of the books on her shelves, up and down, up and down, feeling for their titles.
She found the one she was looking for, took it from the shelf, sat down, opened it, and began to read, eyes fluttering as her fingers danced across the pages.
Herbert found it hard to reconcile the knowledge that she was reading with the visual evidence that she did not once look at the book in front of her; but in the context of everything that had happened these past few days, it was just about the most reassuringly normal thing he could remember.
He smiled at Hannah, took a few quick breaths to make himself alert, and turned back to the microdot.
Peering through the viewer hour after hour would give him the mother of all headaches, so the first thing he had to do was transcribe the text onto a piece of paper. As he wrote, he could also keep a tally of the frequency
with which each letter appeared, without which he would have no hope of solving Stensness’ code.
He was already making several assumptions, but he figured that they were sensible and therefore likely to be true.
The text was clearly laid out as it had been originally written; word lengths, spaces, and punctuations were all unchanged. This suggested that Stensness had used a monoalphabetic cipher; substituting each letter with another, all the way from A to Z, according to a system Herbert had yet to work out.
Usual practice in such ciphers was that each letter had a unique proxy; that was, the cipher did not use any given letter to replace more than one letter in the original.
It sounded simple, and in essence it was, but the permutations were horrific. Herbert had forgotten what the actual figures were, concerning the number of ways in which twenty-six letters could be rearranged, but he remembered there being something in the region of twenty or thirty zeros tacked onto the end.
However, codes tended to use systems, and mono-alphabetic ciphers were usually based on a starting key: a word or phrase which filled the first few places of the cipher alphabet (minus duplicate letters and spaces, naturally), followed by the continuation of the original alphabet from the last letter in the key through to Z, and then by whichever letters had not yet been used, still in original alphabetical order.
This way, the decoder needed only to know the key to decipher the message.
Herbert, of course, had no key, so he had to try it another way: frequency analysis.
In normal English, some letters appeared much
more often than others. Herbert knew what these were; every cruciverbalist did.
By finding out which letters appeared most frequently in the coded text, he could match them to their originals.
So he drew a grid down one side of the paper, with a little box for each letter from A to Z, and as he transcribed Stensness’ code, letter by letter, he put a stroke next to each relevant box in the grid: four vertical strokes and one diagonal for the fifth, just as they had been taught in schoolboy mathematics.
It was not especially difficult work, but it was slow and painstaking.
He was especially concerned not to make mistakes at this stage, as an error now could skew his results and send him chasing up blind alleys all day.
Thus it took him almost an hour, including two full check-throughs at the end, before he had finished.
Only three letters had appeared more than fifty times:
M
and
X
, both with sixty-seven, and
H
, on fifty-one. Herbert decided to focus his attention here first.
It was fairly safe to assume that the three commonest letters in the cipher text probably represented the three commonest letters in the language proper—
e, t
, and
a
respectively—but in such a small sample, perhaps not in the same order.
In other words; he was sure that
M, X
, and
H
between them signified
e, t
, and
a
, but he could not be certain which was which.
He had more counting to do.
E
and
a
were vowels, and as such tended to be found next to pretty much most other letters, both before and after them.
But
t
was a consonant, and was therefore pickier about the company it kept. For instance, one rarely saw
t
next to
b, d, g, j, k, m, q
, or
v.
And so it proved here.
In the cipher text,
H
and
X
were sociable to a fault, spreading themselves throughout sentences with the ease of an ambassador at a cocktail party.
M
, on the other hand, was something of a recluse, lurking around only a few letters and avoiding many others outright.
Herbert had his first breakthrough.
M
represented the letter
t.
He wrote as such next to its box with the sixty-seven strokes.
H
and
X
therefore stood for
e
and
a
, but which one for which one? Did
H = a
and
X
=
e
, or vice versa?
He looked back through the text again.
Only two English words consisted of a single letter:
a
and
I.
There were four single-letter words in the text, all of them a simple
H.
Whereas texts without the first person singular were common, those without the indefinite article were rather rare.
So Herbert surmised that
H
stood for
a
, and therefore
X
for
e.
Since the word
MGX
appeared seventeen times, and Herbert knew the identity of the first and third letters, he figured that this combination must stand for the word “the,” which therefore meant that he could swap an
h
for the
G
.
With these four in mind, he amended the text to reflect what he knew.
He placed in lower case the four letters he had
already deciphered, while the ones he had yet to work out remained in capitals; for obviously, though he knew that
X, M
, and
H
stood for
e, t
, and
a
, he did not yet know what
E, T
, and
A
stood for.
The text now read:
the Q-KhaDel DatteJZ TK ITAAJaLtTBZaWWR LhaJaLteJTKtTL BA a heWTLaW KtJNLtNJe. the ITaYBZI KtJNLtNJe KeJOeK tPB ANZLtTBZK. ATJKt, Tt TZITLateK that the DatteJZ JeDeatK aEBOe aZI EeWBP the LeZtJaW Q-KhaDe, KTCZaWTZC the LBZtTZNatTBZ BA the heWTQ. KeLBZI, Tt aJTKeK AJBY a JeCNWaJ KeJTeK, aWBZC the YBWeLNWaJ aQTK, BA the KNCaJ DhBKDhate CJBNDK that ABJY the YBWeLNWe’K EaLVEBZe. the KRYYetJTLaW DatteJZK BA the hBJTSBZtaW KYeaJK BZ the aJYK aZIWeCK BA the “Q” IeYBZKtJate that the heWTQ YaVeK a tPTKt at JeCNWaJ TZteJOaWK. the ABNJth WaReJ-WTZe BZ eaLh WTYE TK YTKKTZC; thTK YaR hTZt at a IBNEWe heWTQ, PTth the YTKKTZCWaReJ-WTZe JeDJeKeZtTZC the DBTZt at PhTLh the tPB KtJaZIK LJBKK eaLh BtheJ.
Herbert looked through the text again, and his eye fell on the word
YBWeLNWe’K.
An apostrophe tended to precede only two letters—
t
, as in “wouldn’t,” and
s
, as in “someone’s.”
But he already had
t
accounted for. He knew, too, that
s
appeared at the end of many words, mainly third person verbs and plural nouns.
When he searched the text for the letter
K
, he
found it on the end of nineteen words, which was proof enough for him.
This in turn gave him several instances of the words
Tt
and
Ts
, which would be either “it” and “is” or “at” and “as;” but he already had his
a
, so
T
became
i.
By now he had a word
aJises
, so
J
became
r
—there was no other alternative. This in turn left him with a
Bther
, and
B
became
o
.
He remembered something from the cryptographic exercises Five had set them; that there came a time when deductive progress stopped being linear and began to become exponential, a point where the decipherer felt solid ground beneath his feet, as it were, when one clue led so rapidly to another and another and another that they appeared faster than they could be followed up.
It was like the initiation of a chain reaction in atomic physics; once the critical threshold was passed, the reaction propagated itself.
Herbert had been at it for more than two hours now, and by rights he should have been exhausted, for, without human or mechanical assistance, it was a mentally wearing process; but the sight of the finish line infused him with a zeal that felt for a moment superhuman.
He knew already that he wanted to be worthy of Hannah. In a strange way, he realized, he wanted to be worthy of Stensness, too.
He looked again at the paper.
the Q-shaDel DatterZ is IiAAraLtioZaWWR LharaLteristiL oA a heWiLaW strNLtNre. the IiaYoZI strNLtNre serOes tPo ANZLtioZs. Airst, it IZIiLates that the DatterZ reDeats aEoOe aZI
EeWoP the LeZtraW Q-shaDe, siCZaWIZC the LoZtiZNatioZ oA the heWiQ. SeLoZI, it arises AroY a reCNWar series, aWoZC the YoWeLNWar aQis, oA the sNCar DhosDhate CroNDs that AorY the YoWeLNWe’s EaLVEoZe. the sRYYetriLaW DatterZs oA the horiSoZtaW sYears oZ the arYs aZIWeCs oA the “Q” IeYoZstrate that the heWiQ YaVes a tPist at reCNWar iZterOaWs. the AoNrth WaRer-WiZe oZ eaLh WiYE is YissiZC; this YaR hiZt at a IoNEWe heWiQ, Pith the YissiZCWaRer-WiZe reDreseZtiZC the DoiZt at PhiLh the tPo straZIs Lross eaLh other.
Pieces were coming thick and fast now, clambering on top of one another in their haste to be discovered, and Herbert no longer cared about progressing in the most efficient way, for there were so many paths he could take.
Lross
gave him his
c. SecoZI
and
aZI
coughed up
n
and
d.
From
centraW
came
l
;
diaYond
was clear even to a moron, as were, in rapid succession,
Dattern, strNctNre, siCnallinC, douEle, interOals, aQis, Aourth, sRmmetrical, Phich, bacVbone
, and finally, joyfully,
horiSontal.
He wrote the whole text out again, with capitals in the right places, and sighed in a mixture of satisfaction, amusement and resignation; because, though it plainly made sense, it would be meaningful only to someone far more scientifically versed than Herbert was.
The X-shaped pattern is diffractionally characteristic of a helical structure. The diamond structure serves two functions. First, it indicates
that the pattern repeats above and below the central X-shape, signaling the continuation of the helix. Second, it arises from a regular series, along the molecular axis, of the sugar phosphate groups that form the molecule’s backbone. The symmetrical patterns of the horizontal smears on the arms and legs of the “X” demonstrate that the helix makes a twist at regular intervals. The fourth layer-line on each limb is missing; this may hint at a double helix, with the missing layer-line representing the point at which the two strands cross each other.
He went through it several times, unable to shake the sensation that, the more he read it, the less he understood.
Then he took the viewer and looked at the first microdot again.
It was clear that the text referred to the image. Stensness had mentioned an X-shaped pattern, a diamond structure and horizontal smears, all of which were visible even to a duffer layman like Herbert.
He looked at his two sets of alphabets; the cipher one in order from A to Z, and their clear text counterparts, necessarily jumbled.
He took a new piece of paper and reversed the process, writing the original alphabet out in order, and then matching it to its cipher. This way, he could see the code Stensness had used.
It came out like this:
So H E L I X A C G T was the key.
H E L I X was “helix,” the proposed structure of whatever the X-shaped object represented, that was obvious enough.
As for A C G T, Herbert thought, with some aptness, that he hadn’t the foggiest.
He had been so engrossed in the decryption that he had been oblivious to everything else, even Hannah’s presence.
He looked over at her with a quick flush of anxiety, wondering if she would think him impossibly rude.
