The Case of the Murdered Mathematician, page 13
“Moreover,” Quiribus elaborated, seeing he’d been asked for a “professional” opinion, “this particular exam is distinctly in the field of ‘applied trigonometry,’ and not ‘theoretical trig.’ For this man here—” he shook his head deploringly—“had odd and advanced teaching theories. And just as the exam itself brings out in Question 6—the conventional old-school answer to which, by the way, Mr. Clarvoe, would be r cos beta—how he hated the Greek letters—he also divided trig into two sciences, Theoretical and Applied, and—but that’s all you want to know, I believe, Mr. Clarvoe—and not what you yourself would guess, much less know, from knowing Professor Munstergale—namely, that this paper was to be used only in the local University classes and not in the correspondence course they had; and that Professor Munstergale was a very human man, even though known as a—a—a ‘tough nut!’”
Clarvoe nodded.
“You get the fact of its local use from his local references to Chicago, of course—which wouldn’t be known to outside students—and the fact of his being a human man through his—”
“We-ell,” laughed Quiribus, “it sure is the first time I ever encountered ‘pretty girls’ in a problem, or Crackerjack boxes or drunkards!”
“I see,” nodded Clarvoe, who plainly had never in his life encountered any examination papers other than perhaps, one for a city detective. “Well, okay then.” He pulled out a notebook with encased pencil. Made a note or two. “Exam paper in Applied Trigynommytry. Okay.” He replaced the book in his hip pocket with one hand, taking the paper back with his other, and in a second was restoring the latter to its proper position, with uncapped fountain-pen atop it.
Now he gazed speculatively, thoughtfully, about this mathematician’s study once more, as a man wondering whether there was anything further to ask a mathematician—while one was on the premises, and at arm’s length. He even opened his mouth once, as though to speak, as his eyes rested momentarily upon the thin sets of intersecting strings held in the strange-looking holders, as one, in fact, about to ask what on earth and heaven those “musical” harps might be; then, as one realizing he was in a world ’way over his head, he shut his mouth and withdrew his gaze. And Quiribus, watching the performance, was glad the other had not asked about those objects. For to explain how an actual 3-dimensional curve could come into existence through nothing else than the intersection of two impossible and 100 per cent non-existing bodies was quite beyond the giant. As much indeed as it would have been for him to explain precisely how, through axis rotation in the field of vector analysis, Einstein’s famous non-existent square root of minus 1 came into being!
And now Clarvoe, with a sigh, was stepping to the wide cabinet of horizontal drawers at the end of the room. Though not, as was to eventuate, to withdraw one of the fatter drawers in the card-filing set, much less a card, or even, so far as that went, to pull down one of the dozen or so gold-stamped identically blue-bound books standing atop it between upended bricks. And all of which books, through squinting his eyes, Quiribus could now see bore the word DIARY stamped down their backbones, with, in every case, in the blank space above the letters, a pair of hand-inked dates, obviously inclusive dates with respect to each volume’s contents, and revealing the volumes to be quite elastic as to time-extents, each one’s notes commencing plainly where the last one’s had ended—and running up to where the next one’s—took up again! Clarvoe had stepped here to lift, ever so gently and adroitly, from behind the cabinet—and over—was already doing so, in fact!—a small portable panel blackboard, crimson of frame, and about 4 feet long by 3 feet wide, which plainly had been set by him a while earlier safely behind that case, and resting no doubt on the base ledge and back against the wall, so that its vital inscriptions, involved in no less than murder, could not accidentally be scuffed off by anyone in slightest degree; was lifting it gently out and over the top of the cabinet, turning it as he did so endwise, and bringing it forth still edgewise, so completely so, in fact, as far as Quiribus was concerned, that watching its production from where he stood he could see nothing but the red strip made by the blackboard’s enamelled frame.
And still holding it edgewise towards the giant, as one subconsciously hating to the last moment to reveal to an outsider a vital, precious something that belonged at this second only to his own department, Clarvoe swung the light board dexterously over and above the work-ledge, lowering it till it stood, still partly edgewise to the giant, atop the very ledge. And now, almost reluctantly, almost with a groan in his voice, the Homicide Department head spoke.
“Well, Big Boy, this is where your professional verdict completely, and conclusively, and finally, settles an idiotic argument between two detectives who don’t know enough about mathematics to decide their own fool arguments. And use care, now—gr-r-r-reat care!—for whichever way you decide that argument means, so far as I’m concerned, that one of two men in Chicago is going to be locked up, and charged with mur—” He stopped, as one who realized that his words, given in advance of “proof,” might come before him some day in a murder trial as “prejudice.” Attempted to alter his statement, only to make it more mystifying. “I mean that if—if you give me the wrong lowdown, I’ll be out pounding pavements in Hegewisch, as sure as my name is—” Again he stopped, downright ruefully.
“You ready?” he asked meaningfully.
CHAPTER XIV
Two Sides of a Blackboard
Quiribus, waiting patiently for the great mathematical show, or whatever it was, frowned. Deeply puzzled yet as to how two verdicts around here by non-mathematicians could already be giving rise to the possibility of the arrest of anybody. Even puzzled, in fact, as to how a “wrong” verdict on his part could put this man here in limbo, as “Hegewisch” must be!
Quiribus spoke.
“I’m ready to give you the mathematical lowdown,” he said, a bit coldly. “But whatever it is, it will be correct, rest assured of that.”
“Good!” Clarvoe shrugged his shoulders. “Well now, this, what I show you, Big Boy, is what the Professor drew on this board—a bit clumsily, maybe, with his fingers and thumb bound tightly about that stick of chalk—yet carefully, painstakingly, too, we’re all convinced—this is what he drew when I asked that first question of him. And which, if you recall all I’ve told you, was, ‘Can you set down anything at all, Professor—that will give us the name of the man who shot you—something known to you, maybe—but not to us; anything—’ And which, don’t forget, he confirmed later as being his answer to that question, by nodding definitely to my second question after he’d completed his piece of—of writing, my second question which ran—”
“‘This, what you have just set down, Professor Munster-gale,’” repeated Quiribus dryly, “‘conveys the name of the man who shot you?’”
“Your memory’s a good one, Big Boy!” commented Clarvoe appreciatively. “And so now—with all that out of the way, this—this is the thing he drew!”
And with no further delays or explanation, he swung the little board 90 degrees about, letting it rest lightly against the wall. And stood off, arms folded.
And there, depicted on the board’s jet-black surface in bright white chalk, its size about equal to the sweep of a forearm and part of an upper arm, some of its stretches a bit wavering as though from supreme overpowering weakness in their making, yet carrying about itself an air of unerring volition, of firm certitude, and the whole illumined by the bright light reflecting from the big wall blackboard in back of its new contemplator, one Quiribus Brown, mathematician, was the simple diagram:
If George Clarvoe had expected an immediate naming by the giant of precisely what this diagram was, meant, or stood for, he was destined to be disappointed, for Quiribus’s verdict was one that was, in many senses, even more important than would have been his naming this thing. For he said, very calmly:
“We-ell—before I even speak, I can be assured, at least, that I’ll be talking of something that doesn’t represent a chance wavering motion of a dying man trying to write.”
“You can? How?” The other man was all attention, eager, apparently glad to hear this.
“Because the diagram,” replied Quiribus, “which pictures one of the many known mathematical ‘curves’—”
“Good!” eagerly nodded Clarvoe. “That is what,” he explained sheepishly, “O’Cardigan and Keith both said that was—yeah, a ‘curve’—whatever else ’twas!”
“Well, that’s right enough, all right,” admitted the giant, but a little puzzledly. “Though I take it that there’s something involved here that they didn’t agree on—instead of did agree on, and—but anyway, to get back to what I was starting to say back there, the reason I know this isn’t a chance wavering motion of a dying man trying to write is that it covers at least 720 degrees of arc, and starts and ends on a horizontal level, or what we mathematicians call the x-axis. And for which, believe me, I’m glad! For I was sort of hating to try and name the wandering motion of a dying man’s hand trying maybe just to write out—but here!—before I speak out, on this diagram, Mr. Clarvoe, may I see just what single thing he drew when you asked him where he’d crossed the path of the man whose identity he’d—he’d just depicted? That is, you understand, Mr. Clarvoe, I’m speaking generally now. For I know that you said to him, in actuality—said to him this: ‘Professor—write out—in your own language—as you did on the other side—where you met this person? Where—get that? Where?’ And—”
“Jumping Christopher!” ejaculated Clarvoe, shaking his head, “but you sure have a memory—even to pauses between words! Yes, that’s exactly what I said—and what’s encased right now in Keith’s pot-hooks on the conversation. For use—I hope!—in a forthcoming murder trial. And—but here you are.” He sighed volubly. “Here’s what Professor Munstergale set down on the board as the place—whereabouts—location—or what-have-you—where he first encountered the person who shot him.”
And stepping over in front of the board, he turned it about, though under cover of his own body, and then stepped nimbly out of the way again, revealing what lay chalked on the board’s reverse side. And which, strangely, proved to be not just one simple diagram, as Quiribus was anticipating it might be—but three!—or, as it could be put, the same diagram—twice repeated. And which stood:
A profound silence followed the revealment of the second installment of the dying man’s strange message. A silence in which Quiribus focused his attention on the thing on the board deeply, and, it must be confessed, puzzledly, bewilderedly, even helplessly. And suddenly the silence was broken by Clarvoe, almost harshly, impatiently.
“A-a-all right, Professor Brown!—snap out of it!—and let’s have it! For the Munstergale wasn’t talking to cops when he put all this down—nowsah!—he was talking to the mathematician the cops would sooner or later have to bring in. And you’re—him. So what—what now—in your field—are the correct names of these two diagrams—this one, and the one on the other side. Speak up, Big Boy—and commence earning that ten bucks.”
CHAPTER XV
The Human Mule!
Quiribus winced visibly at the suggestion that $10, and $10 only, had brought him here today—on his first, and probably only, case where his mathematics might ever be brought to apply. He opened his lips to expostulate fiercely—then closed them again. What was the use? What was—
“We-ell,” he said unsmilingly, and slowly, “to take these two blackboard sides in reverse order—commencing, that is, with the one now facing me—I will have to say, right off the bat, that that is no mathematical symbol, sign, emblem, or what-have-you. For—”
“You—you mean that, Big Boy?” The detective head was plainly elated. Radiant.
“Mean it?” echoed Quiribus, a bit puzzled at the other’s manifest jubilance. “Of course I mean it. For I say it, affirm it, as one who knows mathematics and hog-raising, even if he doesn’t know anything el—but anyway, I’ve got also to say that it sure is no chance wandering of a—a dying hand across a blackboard! For twice he’s repeated that reasonably perfect square he drew to the left. And—”
“Then,” put in the detective head, now actually rubbing his hands together, “since the chalk-pic is no mathematical symbol, if I asked you—say, on the witness stand—whether it could stand for 3 Squares—what would your answer be?”
“Why that it could, of course, of course,” replied Quiribus. “Since it is 3 squares! And nothing else. Unless, that is, a person wanted to be just a little—ah—hifalutin!—and termed the three squares—we-ell—triple quadrangles! Or something like that. Only, Mr. Clarvoe, this man was a mathematician, don’t forget; his language isn’t the same as—”
“This man,” corrected the detective head harshly, “was doing all he could for 3 coppers to put his killer in the electric chair. During a moment when he was suffering what the best brain specialist in Chi will eventually be testifying on a witness stand was ‘“traumatic amnesia” for words and letters’. And if three chalked squares would convey that mess—”
“I can presume then,” said Quiribus slowly, “that there is a street, or something, in Chicago, called 3 Squares?”
“You can—yes,” nodded George Clarvoe. “Because if I attempted to tell you I didn’t know, you’d only find out after you left here, by asking somebody. Yes, on our great West Side there’s a new civic park and public lounging place—at least, it’s only a few years old—created by tearing down 3 complete blocks of old buildings; it has no name, so far as anybody knows, but the street of fine old residences facing it on its north side was re-named Three Squares Place.”
Quiribus turned and faced the 3 chalked squares far more interestedly now. Commenced, in fact, to wonder why he had been brought into this case, if everything in it was so apparent to the Powers that Were, as was this pictograph now facing him, and which—
He turned back curiously.
“Maybe,” he ventured, “you’ll let me ask one now!—since I’m doing so much answering?” And without even waiting to be told to go ahead, he fired his question. “Can I ask why you were so—so doggoned cheered up when I told you that chalk picture was no known mathematical symbol? For after all, you know, it’s not necessarily just a picture representing three Squares, but also, as I said, triple quadrangles, and—”
“You may, yes,” acknowledged the other. “Because I want your negativation of a certain hypothesis. Y’see, I came down on the streetcar this morning—my car was out of order—in back of two snot-nose high-school kids who talked of nothing, so help me God, but ge’metrial processions! No fooling. And when I contemplated that picture this afternoon, in the light of two beautiful interpr—it is, after all, you’ll admit,” he interpolated with great dignity, “a procession of rectangles—certainly if they were elephants, it’d be a procession of elephants—if it were geese it’d be a procession of geese—but—but being rectangles—well rectangles cert’nly are ge’metrical—so after all, why couldn’t you call that picture a ‘geometrical procession’ and—”
He stopped. For Quiribus was grinning from ear to ear. Despite the dead thing sitting there—and which to him was nothing but a collation of molecules travelling in perfect parallelism through Minkowski’s 4th dimension instead of weaving there through in “vital” processes. His grin even continued to grow from its first and initial stage. And there is nothing wider than a giant’s grin.
“That’s a good one, Mr. Clarvoe,” was all he could say. Gazed at the chalked picture. Grinned again. “What you heard those kids talking about were ‘geometrical progressions’—there’s no such thing in mathematics as a geometrical procession—and a geometrical progression is nothing but a series of numbers, each of which is the previous one multiplied by the same factor, such as, for instance, the series 3, 9, 27, 81, 243—where each number, you’ll note, is 3 times the one in back of it.”
“You can’t make me mad, Big Boy,” said Clarvoe elatedly. “By showing me that I can’t even listen to mathematical English right. For I was afraid as hell that that ‘ge’metrical procession’ I thought I heard was symbolized by that parade of three squares, in which case they could—just could, you know!—have signified our recent Process Fair. You know? Where all and everything in the way of processed foods were exhibited—plus the methods for doing same? And which was held on Navy Pier, and which thousands of people attended? And if the prof had met this guy, who later killed him, at that Fair—whooey!—well, that hypothesis is O—U—T—‘Out,’ isn’t it? So suppose we forget it?”
“Gladly,” assented Quiribus, “Since what’s on the board there isn’t even a geometrical progression—in picture form, in view of the fact that the squares themselves are all practically the same size. However, Mr. Clarvoe, as I was starting out to say back there, this man was a mathematician, and to—”
“Don’t dilate, please,” said the other man irritably and hurriedly. “Just answer my questions. Which is all I want. And–”
“Lead on,” said Quiribus, biting his lips.
Which Clarvoe did, by stepping forward and reversing the position of the board against the wall, and stepping once more off to one side so that the first-shown figure—the peculiar convolution—was exposed again.
“Now what I specifically want to know, Big Boy—and be careful as hell now when you reply—there must be no chance of error, whatever you do—remember, now, no error or chance of it!—well, what I want to know specifically is: what’s the technical mathematical name for that particular figure? Or curve—if I go to be super-technical here! For, according entirely to whether Keith, or O’Cardigan, is right, a certain man may have to—in fact, will have to, by heaven—be arrested, locked up without bail, questioned night and day, investigated—charged, even, with the murder of—” He stopped, said no more.
