Professor Carr finished his inspection of the first of the five sheets.
"Yes," he said, "these are undoubtedly equations in symbolic logic."
Norman had been pretty sure they were, but he was glad to hear a
mathematician say so. The hurried reference he had made to _Principia
Mathematica_ had not altogether satisfied him.
"The capitals stand for classes of entities, the lower case letter for
relationships," he said helpfully.
"Ah ... yes--" Professor Carr's voice became a trifle diffident, and he
rubbed his chin beneath the white Vandyke. "But what do they ... refer
to ... if I may ask?"
"You could perform operations on the equations, couldn't you, without
knowing the references of the individual symbols?" Norman countered,
"Most certainly. And the results would be valid--always providing that
the original references had been made correctly."
"Then here's my problem," Norman went on hastily. "There are seventeen
equations on that first sheet. As they stand, they are not consistent
with each other. Now I'm wondering if one simple, underlying equation
doesn't appear in each of the seventeen, jumbled up with a lot of
nonessential terms and meaningless procedures. Each of the other sheets
presents a similar problem."
"Hm-m-m--" Professor Carr began to finger a pencil, and his eyes
started to go back to the intriguing sheet, but he checked the
movement. "I must confess I'm rather curious about those references,"
he said, and added innocently, "I wasn't aware that there had been
attempts to apply symbolic logic to sociology."
Norman was prepared for this. "I'll be frank with you, Linthicum," he
said. "I have a pretty wild, off-trail theory, and I've promised myself
I won't discuss it until I have a better idea of whether or not there's
anything to it."
Carr's face broke into a reminiscent smile. "I think I understand your
sentiments," he said. "I can still recall the disastrous consequences
of my announcement that I had trisected the angle.
"Of course, I was only in high school at the time," he added hastily.
"Though I'm still convinced that I gave my teacher a bad half-hour," he
finished with a touch of pride.
When he next spoke, there was a sly twinkle in his eyes. "Nevertheless,
I'm very much piqued by those symbols. As it stands, they might
refer ... hm-m-m ... to anything."
"I'm sorry," said Norman. "I know I'm asking a lot of you."
"Not at all. Not at all." Twiddling the pencil Carr glanced again at
the sheet. Something seemed to catch his eyes. "Hm-m-m ... this is
very interesting," he said. "I hadn't noticed this before." And his
pencil began to fly about the sheet, deftly striking out terms, neatly
inscribing new equations. The single vertical furrow between his gray
eyebrows deepened. In a moment he was wholly absorbed.
With an unbreathed sigh of relief, Norman leaned back. He felt
dog-tired, and his eyes hurt. Those five sheets represented twenty
hours of uninterrupted work. Tuesday night, Wednesday morning, part
of Wednesday afternoon. Even at that he couldn't have done it without
Tansy to take notes from his dictation. He trusted the accuracy of her
mindless neurons more than those of a conscious person.
The agile old fingers had half filled a fresh sheet of paper with
derived equations. Their swift, orderly movements did not disturb but
rather intensified the quiet almost monastic, mathematical atmosphere
of the small office.
If Mrs. Gunnison had not shown herself to be so resourceful, he was
thinking, he might have managed without using symbolic logic and Carr.
But she was no Evelyn Sawtelle, to strike out viciously and then
collapse. No, her competence and coolness under fire were of quite
a different sort. She had become very elusive, and he had even been
balked in the simple job of secretly planting a certain object in her
home. And even if he had managed, he was doubtful whether he would have
succeeded with the rest of the plan. Something of a decidedly stronger
sort was necessary. Something new. Something basic.
Carr shoved a paper toward him, and immediately started working on the
next sheet.
"You've found the underlying equation?"
Carr seemed almost annoyed at the interruption. "Surely ... of course."
His pencil was once more darting about.
"Sorry to be making all this work for you," said Norman, wondering just
what was the meaning of the brief ultimate equation. He could not tell
without his code.
Carr spared him a glance. "Not at all. I'm enjoying it. I always did
have a knack for these things, though it's not exactly my field." And
then he was busy again.
* * * * *
The afternoon shadows deepened. Norman switched on the overhead light,
and Carr thanked him with a quick, preoccupied nod. The pencil flew.
Three more sheets had been shoved across to Norman, and Carr was
finishing the last one, when the door opened.
"Linthicum!" came the sweet voice, with hardly a trace of
reproachfulness. "Whatever's keeping you? I've waited downstairs
fifteen minutes."
"I'm sorry, dear," said the old man, looking at his watch and his wife.
"But I had become so absorbed--"
She saw Norman. "Oh, I didn't know you had a visitor," she said.
"_Whatever_ will Professor Saylor _think_! I'm afraid that
I've given him the impression that I tyrannize over you."
And she accompanied the words with such a quaint smile that Norman
found himself echoing Carr's "Not at all."
"Professor Saylor looks _dead_ tired," she said, peering at Norman
anxiously. "I hope you haven't been wearing him out, Linthicum."
"Oh, no, my dear, I've been doing all the work," her husband told her.
She walked around the desk and looked over his shoulder. "What is it?"
she asked, pleasantly.
"I don't know," he said. He straightened up and, winking at Norman,
went on, "I believe that, behind these symbols, Professor Saylor is
revolutionizing the science of sociology. But it's a great secret. And
in any case I haven't the slightest idea of what the symbols refer to.
I'm just being a comptometer."
With a polite, by-your-leave nod toward Norman, Mrs. Carr picked up one
of the sheets and studied it through her thick glasses. But when she
saw the massed rows of symbols, she put it down.
"Mathematics is not my forte," she explained. "I was _such_ a poor
scholar."
"Nonsense, Flora," said Carr. "Whenever we go to the market, you're
much quicker at totaling the bill than I am. And I try to beat you,
too."
"But that's such a _little_ thing," cooed Mrs. Carr delightedly.
"I'll only be a moment more," said her husband, returning to his
calculations.
Mrs. Carr spoke across to Norman in a half-whisper. "Oh, Professor
Saylor, _would_ you be so kind as to convey a message to Tansy?
I want to invite her for bridge tomorrow night--that's Thursday--with
Hulda Gunnison and Evelyn Sawtelle. Linthicum has a _meeting_."
"I'll be glad to," said Norman quickly. "But I'm afraid she might not
be up to it." And he explained about the food poisoning.
"How too, too _terrible_!" observed Mrs. Carr. "Couldn't I come
over and help her?"
"Thank you," Norman lied, "but we have someone staying with her."
"How _wise_," said Mrs. Carr, and it sounded as if she really
meant it.