Let ε < 0.

05.6.09

Murphy’s Law

Filed under: Science humor, Upper-division jokes, Urban legends — Travis @

–D. L. Klipstein

Murphy’s Law, in its simplest form, states that “If anything can go wrong, it will.” Or to state it in more exact mathematical form:

where ↵ is the mathematical symbol for “hardly ever.”

To show the all-pervasive nature of Murphy’s work, the author offers a few applications of the law to the electronic engineering industry.

Mathematics

1. Any error that can creep in, will. It will be in the direction that will do the most damage to calculations.

2. All constants are variables.

3. In a complicated calculation, one factor from the numerator will always move into the denominator, or conversely.

General engineering

4. A patent application will be preceeded by one week by a similar application made by an independent worker.

5. The more innocuous a design chage appears, the further its influence will extend.

6. All warranty and guarantee clauses become void on payment of invoice.

7. An important Instruction Manual or Operating Manual will have been discarded by the Receiving Department.

Prototyping and production

8. Any wire cut to length will be too short.

9. Tolerances will accumulate unidirectionally towards maximum difficulty of assembly.

10. Identical units tested under identical conditions will not be identical in the field.

11. If a project requires n components, there will be (n – 1) units in stock.

12. A dropped tool will land where it can do most damage; the most delicate component will be the one to drop. (Also known as the principle of selective gravity.)

13. A device selected at random from a group having 99 percent reliability will be a member of the 1 percent group.

14. A transistor protected by a fast-acting fuse will protect the fuse by blowing first.

15. A purchased component or instrument will meet its specifications long enough, and only long enough, to pass Incoming Inspection.

16. After an access cover has been secured by 16 hold-down screws, it will be discovered that the gasket has been omitted.

Condensed from “The Contribution of Edsel Murphy to the Understanding of Behaviour in Inanimate Objects,” in EEE: The Magazine of Circuit Design, August 1967.

05.4.09

Good reasons for not doing your math homework

Filed under: Lower-division jokes, Puns, Upper-division jokes — Travis @

I accidentally divided by zero and my paper burst into flames.

I have the proof, but there isn’t room to write it in this margin.

I could only get arbitrarily close to my textbook. I couldn’t actually reach it.

I was watching the World Series and got tied up trying to prove that it converged.

I couldn’t figure out whether i am the square of negative one or i is the square root of negative one.

I locked the paper in my trunk but a four-dimensional dog got in and ate it.

I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to dunk.

I could have sworn I put the homework inside a Klein bottle, but this morning I couldn’t find it.

I’ve included a reference to the solutions manual, reducing this assignment to one previously solved.

I had too much π and got sick.

03.3.09

The mathematical theory of big game hunting III

Filed under: Academic humor, Lion hunting, Upper-division jokes — Travis @

Following the seminal paper by H. Petard in 1938 introducing to the mathematical theory of big game hunting, a good many others were prompted to add to this literature. The following is one of these articles.

On a theorem of H. Petard

– Christian Roselius
Tulane University

In a classical paper [4], H. Petard proved that it is possible to capture a lion in the Sahara desert. He further showed [4, no. 8, footnote] that it is in fact possible to capture every lion with at most one exception. Using completely new techniques, unavailable to Petard at the time, we are able to sharpen this result, and to show that every lion may be captured.

Let L denote the category whose objects are lions, with “ancestor” as the only nontrivial morphism. Let C be the category of caged lions. The subcategory C is clearly complete, is nonempty (by inspection), and has both a generator and cogenerator [3, vii, 15-16]. Let F : C ® L be the forgetful functor, which forgets the cage. By the Adjoint Functor Theorem [1, 80-91] the functor F has a coadjoint G : L ® C, which reflects each lion into a cage.

We remark that this method is obviously superior to the Good method [2], which only guarantees the capture of one lion, and which requires an application of the Weierkafig Preparation Theorem.

References

[1] P. Freyd, Abelian categories, New Yor, 1964.

[2] I. J. Good, A new method of catching a lion, Amer. Math. Monthly, 72 (1965) 436.

[3] Moses, The Book of Genesis.

[4] H. Petard. A contribution to the mathematical theory of big game hunting, Amer. Math. Monthly 45 (1938) p446-447.

Amer. Math. Monthly 74 (1967), p. 838-839.

03.1.09

The mathematical theory of big game hunting I

The following is the famous, seminal paper by H. Petard*, which appeared in the American Mathematical Monthly in 1938 and introduced to the academic community at large the mathematical theory of big game hunting. As is evident from the other articles in this section, Petard’s work prompted a good many others to add to this literature. This, together the subsequent articles we shall reproduce this week, do not form a complete compendium, but they do provide the interested reader a solid introduction into this exciting branch of mathematics.

A contribution to the mathematical theory of big game hunting

– H. Petard
Princeton, New Jersey

This little known mathematical discipline has not, of recent years, received in the literature the attention which, in our opinion, it deserves. In the present paper we present some algorithms which, it is hoped, may be of interest to other workers in the field. Neglecting the more obviously trivial methods, we shall confine our attention to those which involve significant applications of ideas familiar to mathematicians and physicists.

The present time is particularly fitting for the preparation of an account of the subject, since recent advanaces both in pure mathematics and theorectical physics have made available powerful tools whose very existence was unsuspected by earlier investigators. At the same time, some of the more elegant classical methods acquire new significance in the light of modern discoveries. Like many other branches of knowledge to which mathematical techniques have been applied in recent years, the Mathematical Theory of Big Game Hunting has a singularly unifying effect on the most diverse branches of the exact sciences.

For the sake of simplicity of statement, we shall confine our attention to Lions (Felis leo) whose habitat is the Sahara Desert. The methods which we shall enumerate will easily be seen to be applicable, with obvious formal modifications, to other carnivores and to other portions of the globe. The paper is divided into three parts, which draw their material respectively from mathematics, theoretical physics, and experimental physics.

The author desires to acknowledge his indebtedness to the Trivial Club of St. John’s College, Cambridge, England; to the MIT chapter of the Society for Useless Research; to the F o P, of Princeton University; and to numerous individual contributors, known and unknown, conscious and unconscious.

1. Mathematical methods

1. The Hilbert, or axiomatic, method. We place a locked cage onto a given point in the desert. After that we introduce the following logical system:

  • Axiom I. The set of lions in the Sahara is not empty.
  • Axiom II. If there exists a lion in the Sahara, then there exists a lion in the cage.
  • Rule of procedure. If P is a theorem, and if the following is holds: “P implies Q”, then Q is a theorem.
  • Theorem 1. There exists a lion in the cage.

2. The method of inversive geometry. We place a spherical cage in the desert, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the lion is inside the cage, and we are outside.

3. The method of projective geometry. Without loss of generality, we can view the desert as a plane. We project the surface onto a line, and then project the line onto an interior point of the cage. Thereby the lion is projected onto that same point.

4. The Bolzano-Weierstrass method. Divide the desert by a line running from N-S. The lion is then either in the E portion or in the W portion; let us assume him to be in the W portion. Bisect this portion by a line running from E-W. The lion is either in the N portion or in the S portion; let us assume him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion ultimately surrounded by a fence of arbitrarily small perimeter.

5. The “Mengentheoretisch” method. We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.

6. The Peano method. Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked [1]that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion to move a distance equal to its own length.

7. A topological method. We observe that a lion has at least the connectivity of a torus. We transport the desert into four-space. Then it is possible [2] to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then completely helpless.

8. The Cauchy, for function theoretical, method. We examine a lion-valued function f(z). Let ζ be the cage. Consider the integral

where C represents the boundary of the desert. Its value is f(ζ), i.e. there is a lion in the cage [3].

9. The Wiener-Tauberian method. We obtain a tame lion, L0, from the class L(-¥, ¥), whose Fourier transform vanishes nowhere, and release it in the desert. L0 then converges toward our cage. By Wiener’s General Tauberian Theorem [4], any other lion, L (say), will converge to the same cage. Alternatively we can approximate arbitrarily closely to L by translating L0 through the desert [5].)

10. The Eratosthenian method. Enumerate all the objects in the desert. Examine them one by one, and discard all those that are not lions. A refinement will capture only prime lions.

2. Methods from theoretical physics

11. The Dirac method. We observe that wild lions are, ipso facto, not be observable in the Sahara desert. Consequently, if there are any lions at all in the Sahara, they are tame. We leave catching a tame lion as an exercise to the reader.

12. The Schroedinger method. At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.

13. The nuclear physics method. Place a tame lion into the cage, and apply a Majorana exchange operator [6] on it and a wild lion.

As a variant, let us suppose, to fix ideas, that we require a male lion. We place a tame lioness into the cage, and apply the Heisenberg exchange operator [7] which exchanges spins.

14. A relativistic method. We distribute about the deser lion bait containing large portions of the Companion of Sirius. When enough bait has been taken, we project a beam of light across the desert. This will bend right around the lion, who will hen become so dizzy that he can be approahced with impunity.

3. Experimental physics methods

15. The thermodynamics method. We construct a semi-permeable membrane, permeable to everything except lions, and sweep it across the desert.

16. The atom-splitting method. We irradiate the desert with slow neutrons. The lion becomes radioactive, and a process of disintegration set in. When the decay has proceeded sufficiently far, he will become incapable of showing fight.

17. The magneto-optical method. We plant a large lenticular bed of catnip (Nepeta cataria), whose axis lies along the direction of the horizontal component of the earth’s magnetic field, and place a cage at one of its foci. We distribute over the desert large quantities of magnetized spinach (Spinacia oleracea), which, as is well known, has a high ferric content. The spinach is eaten by herbivorous denizens of the desert, which in turn are eaten by lions. The lions are then oriented parallel to the earth’s magnetic field, and the resulting beam of lions is focus by the catnip upon the cage.

References

[1] After Hilbert, cf. E. W. Hobson, “The Theory of Functions of a Real Variable and the Theory of Fourier’s Series” (1927), vol. 1, pp 456-457

[2] H. Seifert and W. Threlfall, “Lehrbuch der Topologie” (1934), pp 2-3

[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion except for at most one.

[4] N. Wiener, “The Fourier Integral and Certain of its Applications” (1933), pp 73-74

[5] N. Wiener, ibid, p 89

[6] cf e.g. H. A. Bethe and R. F. Bacher, “Reviews of Modern Physics”, 8 (1936), pp 82-229, esp. pp 106-107

[7] ibid

This first apperared in Amer. Math. Monthly 45 (1938) p446-447. In fact, the Method 10 included here did not actually appear in the original Monthly version, but in a slightly expanded version of that appeared in Eureka.

* It is perhaps generally not known that Petard’s** full initials are H. W. O., standing for “Hoist With Own.”

** Actually, H. Petard is the pen-name for the mathematician E. S. Pondiczery***, who preferred to publish the paper pseudonymously.

*** In fact, Pondiczery himself was a fictious mathematician invented by Ralph P. Boas and Frank Smithies.****

**** This was published in The American Mathematical Monthly, 1938, with one editorial alternation: a “footnote to a footnote was ruthlessly removed.” Consider this last footnote to a footnote to a footnote of a footnote as our nod to the masters.

02.28.09

Trivia Mathematica

Filed under: Academic humor, Puns, Upper-division jokes — Travis @

In 1940 over lunch, Norbert Weiner and Aurel Winter amused themselves by inventing titles for articles in a journal to be called Trivia Mathematica. Wiener was enormously amused by the results, and insisted on showing them to Tibor Rado, who was well known to have no sense of humor, and was not amused. This is that list.

Announcement of the Revival
of a Distinguished Journal
TRIVIA MATEHMATICA
founded by Norbert Wiener and Aurel Winter
in 1939.

“Everything is trivial once you know the proof.” — D. V. Widder

The first issue of Trivia Mathematica (Old Series) was never published. Trivia Mathematica (New Series) will be issed continuously in unbounded parts. Contributions may be written in Basic English, English BASIC, Poldavian, Peanese and/or Ish, and should be directed to the Editors at the Department of Metamathematics, University of the Bad Lands. Contributions will be neither acknowledged, returned, nor published.

The first issue will be dedicated to N. Bourbaki, John Rainwater, Adam Riese, O. P. Lossers, A. C. Zitronenbaum, Anon, and to the memory of T. Rado, who was not amused. It is expected to include the following papers.

  • On the well-ordering of finite sets.
  • A Jordan curve passing through no point on any plane.
  • Fermat’s Last Theorem I: The case of even primes.
  • Fermat’s Last Theorem II: A proof assuming no responsibility.
  • On the topology im Kleinen of the null circle.
  • On prime round numbers.
  • The asymptotic behavior of the coefficients of a polynomial.
  • The product of large consecutive integers is never a prime.
  • Certain invariant characterizations of the empty set.
  • The random walk on one-sided streets.
  • The statistical independence of the zeros of the exponential.
  • Fixed points in theorem space.
  • On the tritangent planes of the ternary antiseptic.
  • On the asymptotic distribution of gaps in the proofs of theorems in harmonic analysis.
  • Proof that every inequation has an unroot.
  • Sur un continu d’hypotheses qui equivalent a l’hypothese du continu.
  • On unprintable propositions.
  • A momentous problem for monotonous functions.
  • On the kernels of mathematical nuts.
  • The impossibility of the proof of the impossibility of a proof.
  • A sweeping-out process for inexhaustible mathematicians.
  • On transformations without sense.
  • The normal distribution of abnormal mathematicians.
  • The method of steepest descents on weakly bounding bicycles.
  • Elephantine analysis and Giraffical representation.
  • The twice-Born approximation.
  • Pseudoproblems for pseudodifferential operations.

The Editors are pleased to announce that because of a timely subvention from the National Silence Foundation, the first issue will not appear.

02.17.09

A note of piffles

Filed under: Academic humor, Upper-division jokes — Travis @

by A. B. Smith

A. C. Jones in his paper “A Note on the Theory of Boffles,” Proceedings of the National Society, 13, first defined a Biffle to be a non-definite Boffle and asked if every Biffle was reducible.

C. D. Brown in “On a paper by A. C. Jones,” Biffle, 24, answered in part this question by defining a Wuffle to be a reducible Biffle and he was then able to show that all Wuffles were reducible.

H. Green, P. Smith, and D. Jones in their review of Brown’s paper, Wuffle Review, 48, suggested the name Woffle for any Wuffle other than the non-trivial Wuffle and conjectured that the total number of Woffles would be at least as great as the number so far known to exist. They asked if this conjecture was the strongest possible.

T. Brown, “A collection of 250 papers on Woffle Theory dedicated to R. S. Green on his 23rd Birthday” defined a Piffle to be an infinite multi-variable sub-polynormal Woffle which does not satisfy the lower regular Q-property. He stated, but was unable to prove, that there were at least a finite number of Piffles.

T. Smith, L. Jones, R. Brown, and A. Green in their collected works “A short introduction to the classical theory of the Piffle,” Piffle Press, 6 gns., showed that all bi-universal Piffles were strictly descending and conjectured that to prove a stronger result would be harder.

It is this conjecture which motivated the present paper.

This was actually written by A. K. Austin as “Modern Research in Mathematics,” Math. Gaz. 51 (May 1967) 150.

02.15.09

Methods of proof: a guide for lecturers

Filed under: Academic humor, Upper-division jokes — Travis @

Proof by vigorous handwaving.
Works well in a classroom or seminar setting.

Proof by forward reference.
Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.

Proof by funding.
How could three different government agencies be wrong?

Proof by example.
The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.

Proof by omission.
Examples include: “The reader may easily supply the details,” or “The other 253 cases are analogous,” etc.

Proof by deferral.
“We’ll prove this later in the course.”

Proof by picture.
A more convincing form of proof by example. Combines well with proof by omission.

Proof by intimidation.
“Trivial.”

Proof by cumbersome notation.
Best done with access to at least four alphabets and special symbols.

Proof by exhaustion.
An issue or two of a journal devoted to your proof is useful.

Proof by obfuscation.
A long plotless sequence of true and/or meaningless syntactically related statements.

Proof by wishful citation.
The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.

Proof by eminent authority.
“I saw Karp in the elevator and he said it was probably NP-complete.”

Proof by personal communication.
“Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].”

Proof by reduction to the wrong problem.
“To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.”

Proof by reference to inaccessible literature.
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.

Proof by importance.
A large body of useful consequences all follow from the proposition in question.

Proof by accumulated evidence.
Long and diligent search has not revealed a counterexample.

Proof by cosmology.
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.

Proof by mutual reference.
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.

Proof by metaproof.
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

Proof by vehement assertion.
It is useful to have some kind of authority relation to the audience.

Proof by ghost reference.
Nothing even remotely resembling the cited theorem appears in the reference given.

Proof by semantic shift.
Some of the standard but inconvenient definitions are changed for the statement of the result.

Proof by appeal to intuition.
Cloud-shaped drawings frequently help here.

02.13.09

Perjorative calculus

Filed under: Academic humor, Bad proofs, Puns, Upper-division jokes — Travis @

On the nature of mathematical proofs

by Joel Cohen

Bertrand Russell has defined mathematics as the science in which we never what we are talking about or whether what we are saying is true. Mathematics has been shown to apply widely in many other scientific fields. Hence, most other scientists do not know what they are talking about or whether what they are saying is true. Thus, providing a rigorous basis for philosophical insights is one of the main functions of mathematical proofs.

To illustrate the various methods of proof we give an example of a logical system.

The perjorative calculus

Lemma 1: All horses are the same colour.

Proof by induction. It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour. Q.E.D.

Theorem 1: Every horse has an infinite number of legs.

Proof by intimidation. Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another colour, and by the lemma that does not exist. Q.E.D.

Corollary 1: Everything is the same colour.

Proof. The proof of Lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional “For all x, if x is a horse, then x is the same colour,” namely “is a horse” may be generalized to “is anything” without affecting the validity of the proof; hence, “for all x, if x is anything, x is the same colour.” Q.E.D.

Corollary 2: Everything is white.

Proof. If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular then: “for all x, if x is an elephant, then x is the same colour” is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain’s The Stolen White Elephant). Therefore all elephants are white. By corollary 1 everything is white. Q.E.D.

Theorem 2: Alexander the Great did not exist and he had an infinite number of limbs.

Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, “If Alexander the Great existed, then he rode a black horse Bucephalus.” But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist.

We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and “forewarned is four-armed.” This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs. Q.E.D.

It is not to be thought that there are not other types of proofs, which in print shops are recorded on the proof sheets. There is the bullet proof and the proof of the pudding. Finally, there is 200 proof, a most potent spirit among mathematicians and people alike.

Condensed from Opus, May 1961.

02.11.09

Tautologies I was not taught

Filed under: Discontinuous humor, Puns, Upper-division jokes — Travis @

Alcohol and calculus don’t mix. Never drink and derive!

A math professor is one who talks in someone else’s sleep.

Analysts use epsilons and deltas in mathematics because they tend to make errors.

Asked how his pet parrot died, the mathematician answered “Polynomial. Polygon.”

A professor’s enthusiasm for teaching precalculus varies inversely with the likelihood of his having to do it.

A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.

Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas.

Every proof is a one-line proof, provided you start sufficiently far to the left.

For a good prime call, 555.793.7319.

God is real, unless proclaimed an integer.

Graphing rational functions is a pain in the asymptote.

He thinks he’s really smooth, but he’s only C1.

How many problems will you have on the final? I think you will have lots of problems on the final.

If Einstein and Pythagoras were both right, then E = m(a2+b2)

I’ll do algebra, I’ll do trig, and I’ll even do statistics, but graphing is where I draw the line!

In the topologic hell the beer is packed in Klein’s bottles.

Klein bottle for rent. Apply within.

Life is complex. It has real and imaginary parts.
…..And the irrational parts infinitely outweigh the rational ones.

Math: putting the “fun” in “functions” since t=0.

Math is like love; a simple idea, but it can get complicated.

Math problems? Call 1-800-[4-x(2 pi)2]-sin(b)/xy.

Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.

Mobius strip no-wear belt drive! (Please see other side for warranty details.)

Moebius strippers only show you their back side.

My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.

Parallel lines never meet, unless you bend one or both of them.

Pie are squared?
No. Pie are not squared. Pie are round. Cornbread are squared.

Recursion [ri-kur'zhun] n. See recursion.

Sex is like math. Add the bed, subtract the clothes, divide the legs, and pray to God you don’t multiply.

Statistics are like a bikini: what they show you is tempting, but it’s what they hide that’s important.

The highest moments in the life of a mathematician are the first few moments after one has proved the result, but before one finds the mistake.

The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again.

The problems for the exam will be similar to the discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159…

The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people.

These days, even the most pure and abstract mathematics is in danger to be applied.

The world is everywhere dense with idiots.

To a mathematician, real life is a special case.

1 + 1 = 3, for large values of 1.

5 out of 4 people have problems with fractions.

97.3% of all statistics are made up.

02.6.09

Imperturbability of elevator operators

Filed under: Academic humor, Upper-division jokes — Travis @

On the imperturbability of elevator operators: LVII

S. Candlestickmaker
Institute for Studied Advances
Old Cardigan, Wales

(Communicated by John Sykes; received October 19, 1910)

Abstract

In this paper the theory of elevator operators is completed to the extent that is needed in the elementary theory of Field’s. It is shown that the matrix of an elevator operator cannot be inverted, no matter how rapid the elevation. An explicit solution is obtained for the case when the occupation number is zero.

1. Introduction

In an earlier paper (Candlestickmaker 1954q; this paper will be referred to hereafter as ‘XXXVIII’) the simultaneous effect of a magnetic field, an electric field, a Marshall field, rotation, revolution, translation, and retranslation on the equanimity of an elevator operator has been considered. However, the discussion in that paper was limited to the case when incivility sets in as a stationary pattern of dejection; the alternative possibility of overcivility was not considered. The latter possibility is known to occur when a Marshall field alone is present; and its occurance has been experimentally demonstrated by Shopwalker and Salesperson (1955) in complete disagreement with the theoretical predictions (Nostradamus 1555). The possibility of overcivility when no Marshall field is present has also been investigated (Candlestickmaker 1954t); and it has been shown that with substances such as U and I it cannot occur. It is therefore a matter of some importance that the manner of the onset of incivility be determined. This paper is devoted to this problem.

2. The reduction to a twelfth-order characteristic value problem in case operators A, B, and C are looking in the same direction

The notation is more or less the same as in XXXVIII:

Definitions:

γ = first occupant,
Bη = second occupant,
gg = third occupant,
O = operator,
M(O) = matrix of the operator,
a = acceleration of the elevation of the conglomeration,
Ω2l = critical Etage number for the onset of incivility,
Ω2l2 = Ω2l / π11/7.

The basic equations of the problem on hand are (cf. XXXVIII, eqs. [429] and [587])

(1) α / β = γ ω + n Ñ2 j

(2) (5 + π)Bη = a + b + c

(3) x = x

(4) gg = m v2 / 2 = 1

Using also the relation (Pythagoras 520)

(5) 32 + 42 = 52

we find, after some lengthy calculations,

(6) |M| = 0,

which shows that the matrix of the operator cannot be inverted. The required characteristic values Ω2l are the solutions of the equation (6). From the magnitude of the numerical work which was already needed for obtaining the solution for the purely rational case (cf. Candlestickmaker and Canna Helpit 1955) we may conclude that a direct solution of the characteristic value problem presented by equation (6) would be downright miraculous. Fortunately, as in XXXVIII, the problem can be solved explicity in the case when the occupation number is zero. This is admittedly a case which has never occured within living memory. However, from past experience with problems of this kind one may feel that any solution is better than none.

3. The equations determining the margin at state in the case when the occupying number is zero

For the reasons just given (i.e, because we cannot solve any other problem) we shall restrict ourselves in this paper to a consideration of the cases when the occupation number is zero. In this case Ω2l satisfies

(7) log Ω2l = 1,

the solution of which has been obtained numerically; it is approximately

(8) Ω2l » 2.7,

This result shows that the transition to overcivility occurs between the values 2 and 3 given by Giftcourt (1956), respectively, Bookshelf (1956), a result which should be capable of direct experimental confirmation. The author hopes to deal with this problem next Saturday afternoon.

In conclusion, I wish to record my indebtedness to Miss Canna Helpit, who carried out the laborious numerical work involved in deriving equation (8).

The research reported in the paper has in part been suppressed by the Office of Naval Research under Contract A1-tum-OU812 with the Institute for Studied Advances.

References

Bookshelf, M. F. 1956, J. Gen, Psychol., 237, 476.
Candlestickmaker, S. 1954a, Zool. Jahrb., 237, 476.
_____. 1954b, Parasitology, 237, 476.
_____. 1954c, Zentralbl. Bakt., 237, 476.
_____. 1954d, Trans. N.-E. Cst Inst. Engrs. Shipb., 237, 476.
_____. 1954e, R. C. Circ. mat. Palermo, 237, 476.
_____. 1954f, Adv. Sci., 237, 476.
_____. 1954g, Math. Japonicae, 237, 476.
_____. 1954h, Niol. Bull. Woods Hole, 237, 476.
_____. 1954i, Bull. Earthq. Res. Inst. Tokyo, 237, 476.
_____. 1954j, J. Dairy Sci., 237, 476.
_____. 1954k, Ann. Trop. Med. Parasitol, 237, 476.
_____. 1954l, Trab. Lab. Invest. biol. Univ. Madrid, 237, 476.
_____. 1954m, Cellule, 237, 476.
_____. 1954n, Bot. Gaz., 237, 476.
_____. 1954o, Derm. Zs., 237, 476.
_____. 1954p, J. Pomol., 237, 476.
_____. 1954r, Sci. Progr. twent. cent., 237, 476.
_____. 1954s, Portugaliae Math., 237, 476.
_____. 1954t, Abh. senckenb. naturf. Gesellsch., 237, 476.
Candlestickmaker, S., and Helpit, Canna E. 1955, Compositio Math., 237, 476.
Giftcourt. M. F. 1956, J. Symbolic Logic, 237, 476.
Nostradamus, M. 1955, Centuries (Lyons).
Pythagoras — 520, in: Euclid — 300, Elements, Book I, Prop. 47 (Athens).
Shopwalker, M., and Salesperson, F. 1955, Heredity, 237, 476.

Professor John Sykes’ famous spoof of Professor S. Chandrasekhar so delighted the ‘victim’ that he arranged to have it printed in the format of The Astrophysical Journal. Some librarians bound it in series without noticing.

Older Posts »

Powered by WordPress