Let ε < 0.


What is 2 x 2?

Filed under: Diff'rent strokes — Travis @

Several professionals were asked the following question: What is 2 x 2 ? Here were the responses.

  • A trained mathematician:
  • A poorly trained mathematician:
    “I don’t what the answer is, but I can tell you, an answer exists.”
  • A physicist, after consulting technical references, and setting up the problem on his computer:
    “It lies between 3.98 and 4.02.”
  • An engineer, after consulting his slide rule:
  • A philosopher:
    “But what do you mean by 2 x 2 ?”
  • An accountant, after closing all the doors and windows, in a whisper:
    “What do you want the answer to be?”
  • A computer hacker, after 2 hours of breaking into the NSA super-computer:


Contemporary music and wave functions

Filed under: Academic humor, Diff'rent strokes, Puns — Travis @

The analysis of contemporary music using harmonious oscillator wave functions

H. J. Lipkin
Department of Musical Physics
Weizmann Institute of Science

The importance of Harmonious Oscillation in music was well known [1] even before the discovery of the Harmonious Oscillator by Stalminsky [2]. Evidence for shell structure was first pointed out by Haydn [3], who discovered the magic number four and proved that systems containing four musicleons possessed unsual stability [4]. The concept of the magic number was expressed by Mozart, who introduced the ‘Magic Flute’ [5], and a Magic Mountain was later introduced by Thomas mann [6]. A system of four magic flutes playing upon a magic mountain would be triply magic. Such a system is probably so stable that it does not interact with anything at all, and is therefore unobservable. This explains the fact that doubly and triply magic systems have never been observed.

A fundamental advance in the application of spectroscopic techniques to music is due to Rachmaninoff [7], who showed that all musical works can be expressed in terms of a small number of parameters, A, B, C, D, E, F, and G, along with the introduction of Sharps [8]. Work along lines similar to that of Rachmaninoff has been done by Wigner, Wagner, and Wigner [9] using the Niebelgruppentheorie. Relativistic effects have been calculated by Bach, Feshbach, and Offenbach, using the method of Einstein, Infeld, and Hoffman [10].

There has been no successful attempt thus far to apply the Harmonious Oscillator to modern music. The reason for this failure, namely that most modern music is not harmonious, was noted by Wigner, Wagner, and Wigner [11].

A more unharmonious approach is that of Brueckner [12], who uses plane waves instead of harmonious oscillator functions. Although this method shows great promise, it is applicable strictly speaking only to infinite systems. The works of the Brueckner School are thus suitable only for very large ensembles.

A few very recent works should also be mentioned. There is the Nobel-Prize-winning work of Bloch [13] and Purcell [14] on unclear resonance and conduction. The work of Primakofiev should be noted [15], and of course the very fine waltzes presented by Strauss [16] at the ‘Music for Peace’ Conference in Geneva.


[1] G. F. Handel, The Harmonious Blacksmith (london, 1757)

[2] Igar Stalminsky, Musical Spectroscopy with Harmonious Oscillator Wave Functions, Helv. Mus. Acta. 1 (1801) 1

[3] J. Haydn, The alpha-Particle of Music; the String Quartet Op 20 (1801) No 5

[4] A. B. Budapest, C. D. Paganini, and E. F. Hungarian, Magic Systems in Music

[5] W. A. Mozart, A Musical Joke, K234567767 (1799)

[6] T. Mann, Joseph Haydn and His Brothers (Interscience, 1944)

[7] G. Rachmaninoff, Sonority and Seniority in Music (Invited Lecture, International Congress on Musical Structure, rehovoth, 1957)

[8] W. T. Sharp, Tables of Coefficients (Chalk River, 1955)

[9] E. Wigner, R. Wagner, and E. P. Wigner, Der Ring Die Niebelgruppen. I Siegbahn Idyll (Bayrut, 1900)

[10] J. S. Bach, H. Feshbach, and J. Offenbach, Tales of Einstein, Infeld and Hoffman (Princeton, 1944)

[11] E. P. Wigner, R. Wagner, and E. Wigner, Gotterdammerung!! and other unpublished remarks made after hearing ‘Pierrot Lunaire’

[12] A. Brueckner, W. Walton, and Ludwig von Beethe, Effective Mass in C Major

[13] E. Bloch, Schelomo, an Unclear Rhapsody

[14] H. Purcell, Variations on a Theme of Britten (A Young Person’s Guide to the Nucleus)

[15] S. Primakofiev, Peter and the Wolfram-189

[16] J. Strauss, The Beautiful Blue Cerenkov Radiation; Scient’s Life; Wine, Women and Heavy Water; Tales from the Oak Ridge Woods

From the Proceedings of the Rehovoth Conference on Nuclear Structure, held at the Weizmann Institute of Science, Rehovoth, September 8-14, 1957.


Different strokes

Filed under: Diff'rent strokes — Travis @

A mathematician is a person who says that, when 3 people are supposed to be in a room but 5 came out, 2 have to go in so the room gets empty.

A statistician is a person who, if his head was in an oven and his feet were ice, would say that on the average he feels fine.1

An economist is a person who is good with numbers but lacks the personality to be an accountant.

An engineer thinks that his equations are an approximation to reality.
A physicist thinks reality is an approximation to his equations.
A mathematician doesn’t care.

A mathematician belives nothing until it is proven.
A physicist believes everything until it is proven wrong.
A chemist doesn’t care, and a biologist doesn’t understand the question.

Biologists think they are biochemists,
Biochemists think they are Physical Chemists,
Physical Chemists think they are Physicists,
Physicists think they are Gods,
And God thinks he is a Mathematician.2

Chemistry is physics without thought.
Mathematics is physics without purpose.

Philosophy is a game with objectives and no rules.
Mathematics is a game with rules and no objectives.

Physicists defer only to mathematicians, but mathematicians defer only to God.

Relations between pure and applied mathematicians are based on trust and understanding. Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.

The graduate with a Mathematics degree asks, “Why does it work?”
The graduate with a Science degree asks, “How does it work?”
The graduate with an Engineering degree asks, “How does one build it?”
The graduate with an Accounting degree asks, “How much will it cost?”
The graduate with a Liberal Arts degree asks, “Do you want fries with that?”

To mathematicians, solutions mean finding the answers.
To chemists, solutions are things that are still all mixed up.


1. Anyone who has taken a statistics class has probably heard this gag at least once, but few have ever bothered to look at very unusual physical conditions assumed by the joke. If the said statistician burns only paper in the oven (so the temperature of the oven is 451 degreed F, as a famous science fiction story reminds us), and if he is comfortable at 98 degrees F (the normal body temperature), then calling the ice temperature X and doing the simplest method of averaging, we find:

(451 + X)/2 = 98
451 + X = 196
X = -255

This is some unusually cold ice!

2. The last line is based on Plato, who said “God geometrizes.”


Evolution of mathematical teaching

Filed under: Diff'rent strokes, Lower-division jokes — Travis @

Version 1: the potato problem


A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?


A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?

1970s (new math):

A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the set of profits?


A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word “potatoes” and discuss with your classmates.


A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue versus costs. Run the POTATO program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

Adapted from The American Mathematical Monthly, Vol. 101, No. 5, May 1994.

Version 2: the logging problem


A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount. What is his profit?


A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount, i.e. $80. What is his profit?

1970s (new math):

A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100. The set C of production costs contains 20 fewer points. What is the cardinality of Set P of profits?


A logger cuts and sells a truckload of lumber for $100. Her cost is $80 and her profit is $20. Find and circle the number 20.


An unenlightened logger cuts down a beautiful stand of 100 trees in order to make a $20 profit. Write an essay explaining how you feel about this as a way to make money. Topic for discussion: How did the forest birds and squirrels feel?

Adapted from Reader’s Digest, February 1996.



Filed under: Diff'rent strokes, Upper-division jokes — Travis @

An engineer, a physicist, and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations, the engineer realizes the situation and starts laughing. A few minutes later the physicist understands, too, and chuckles to himself happily as he now has enough experimental evidence to publish a paper.

This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.


Train story

Filed under: Diff'rent strokes — Travis @

A math convention and an engineering convention were being held in the same city. Consequently, a bunch of mathematicians and a bunch of engineers were on the same train headed for the city. Each of the engineers had his/her train ticket. The group of mathematicians had only ONE ticket for all of them. The engineers started laughing and snickering.

Then, one of the mathematicians said “here comes the conductor” and then all of the math majors went into the bathroom. The engineers were puzzled. The conductor came aboard and said “tickets please” and got tickets from all the engineers. He then went to the bathroom and knocked on the door and said “ticket please” and the mathematicians stuck the ticket under the door. The conductor took it and then the mathematicians came out of the bathroom a few minutes later. The engineers were dumbfounded.

So, on the way back from the convention, the group of engineers had one ticket for the group. They started snickering at the mathematicians, for the whole group had no tickets amongst them. Then, the mathematicians’ lookout said “Conductor coming!”. All the mathematicians went to the bathroom. All the engineers went to another bathroom. Then, before the conductor came on board, one of the mathematicians left the bathroom, knocked on the other bathroom, and said “ticket please.”


Nigh fidelity

Filed under: Diff'rent strokes — Travis @

A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress.

“For sure a mistress is better,” says the lawyer. “If you have a wife and want a divorce, it causes all sorts of legal problems.”

“No, no, it’s better to have a wife,” says the doctor, “because the sense of security lowers your stress and is good for your health.

“No, no, you’re both wrong,” replies the mathmatician. “It’s best to have both so that when the wife thinks you’re with the mistress and the mistress thinks you’re with your wife, you can slip away and do some mathematics.”


Deer hunting

Filed under: Animal farm, Diff'rent strokes — Travis @

Part I: Original Version

A mathematician, an engineer, and a physicist are out hunting together. They spy a deer in the woods.

The physicist calculates the velocity of the deer and the effect of gravity on the bullet, aims his rifle and fires. Alas, he misses; the bullet passes three feet behind the deer. The deer bolts some yards, but comes to a halt, still within sight of the trio.

“Shame you missed,” comments the engineer, “but of course with an ordinary gun, one would expect that.” He then levels his special deer-hunting gun, which he rigged together from an ordinary rifle, a sextant, a compass, a barometer, and a bunch of flashing lights which don’t do anything but impress onlookers, and fires. Alas, his bullet passes three feet in front of the deer, who by this time wises up and vanishes for good.

“Well,” says the physicist, “your contraption didn’t get it either.”

“What do you mean?” pipes up the mathematician. “Between the two of you, that was a perfect shot!”

Part II: How they knew it was a deer

The physicist observed that it behaved in a deer-like manner, so it must be a deer.

The mathematician asked the physicist what it was, thereby reducing it to a previously solved problem.

The engineer was in the woods to hunt deer, therefore it was a deer.

Statistician’s version of the joke

Three statisticians went deer hunting. They spied a deer in the woods. The first statistician shot, and missed the deer by being a foot too far to the left. The second statistician shot, and missed the deer by being a foot too far to the right. The third cried, “We hit it!”



Filed under: Diff'rent strokes, Lower-division jokes — Travis @

A team of engineers were required to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to keep the tape along the pole. They’d get it a bit up the pole, but then the tape would buckle and it would fal down.

A mathematician comes along and listens to their problem. After inspecting both the tape measure and the flag pole, he proceeds to remove the pole from its base in the ground. He lays it down flat, measures it easily with the tape measure, and then resets the pole in the ground.

When he leaves, one engineer says to the other and sighs. “Just like a mathematician! We need to know the height, and he gives us the length!”


Outside the box

Filed under: Diff'rent strokes, Upper-division jokes — Travis @

Version 1

A physicist, an engineer and a mathematician were all challenged to build the shortest possible fence around a small herd of resting cattle.

The physicist went first. He took out a piece of graph paper and plotted the position of each cow, giving each cow a pair of x-y coordinates. Then he determined the lines connecting all the points. Finally he constructed a fence based on his diagram. When he finished he turned to the others and said “I’m done. And since the interior region bounded by line segments connecting the cattle-points is convex, it follows that the boundary is minimal. Q.E.D.”

Then it was the engineer’s turn. First he secured a strong fence-pole near the cattle. Next he attached one end of a six-foot-high roll of wire fence to the pole and walked around the cows slowly letting out the roll of wire fence until he came back to the post. Then he gave the roll to the physicist and told him to start pulling. As he the physicist pulled, the engineer ran around the outside of the fence kicking the cows, flailing his arms, and screaming at them to make them get up and move into the middle; meanwhile while he was yelling “Pull the fence tighter! Pull the fence tighter!” Finally the cows were shoved so close together that they couldn’t move and the fence was wrapped around them so tightly that it was leaving marks on their hides. The engineer nailed the other end of the fence to the post, cut away the roll and said “There, that is the shortest fence.”

Finally it was the mathematician’s turn. He walked over to the roll of wire fence, cut off a small piece, wrapped it around himself and declared: “I’m on the outside.”

Version 2

One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence of the largest possible area with the least amount of fence.

The engineer made the fence in a circle and proclaimed that he had the most efficient design.

The physicist pointed out that fencing off half of the Earth was certainly a more efficient way to do it.

The mathematician just laughed at them. He built a tiny fence around himself and said “I declare myself to be on the outside.”

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