Let ε < 0.


The electron in gold

Filed under: Harmonic analysis, Science humor — Travis @

–Arthur H. Snell

There was an electron in gold
Who said, “Shall I do as I’m told?
Shall I snuggle down tight
With a brief flash of light
Or be Auger outside in the cold?”

Said the K-shell electron in gold,
“I’m thinking of leaving the fold
To be hit like a hammer
By an outgoing gamma.
In freedom I’ll live till I’m old.”

Said the K-shell electron in gold,
“I wonder if I might be bold
And make a slight shift
From this circular drift
And change this damned atom to platinum.”

If your physics needs a little help, the three stanzas refer to fluorescent yield, internal conversion, and electron capture, respectively.



Filed under: CS silliness, Harmonic analysis — Travis @

Mathematicians’ cheer

e to the x dx,
e to the y dy,
Sine x, cosine x,
Natural log of y,
Derivative on the left
Derivative on the right
Integrate, integrate,
Fight! Fight! Fight!

e to the x dx dy
Radical transcendental pi
Secant cosine tangent sine
Come on folks let’s integrate!

e to the i dx dy
e to one over y dy
Cosine secant log of pi
Disintegrate ‘em RPI !!!

Square root, tangent
Hyperbolic sine,
e to the x dy dx
Sliderule, slipstick,

Programmers’ cheer

Shift to the left, shift to the right!
Pop up, push down, byte, byte, byte!



Filed under: Harmonic analysis — Travis @

–Courtney Gibbons


Courtney Gibbons was a student of mine when I taught at Colorado College. You might know her better as the genius behind Brown Sharpie.


The axes not analyzed

Filed under: Harmonic analysis — Travis @

–Jonnie Pober
Haverford College

(Modeled on “The Road Not Taken,” by Robert Frost)

Two masses oscillated on a spring of wood,
And sorry that I could not separate both
And be in Descartes’ plane, long I stood
And looked down Hilbert space as far as I could
To where initial positions were plotted on axes’ spokes;
Then looked again, new axes just as fair,
And having perhaps the better claim,
Because normal mode eigenvectors were plotted there;
And as for that the analysis where
Normal modes superpose shall be the game,
Though both axes equally lay
In space no intro-physics work had penciled black.
Oh, I kept the first axes for another day!
Yet knowing inner products of eigenvectors and position lead the way,
I doubted I should need to come back.
I will multiply these coefficients with eigenvectors P and B
And let them oscillate in time for ages and ages hence.
Two masses oscillated on a spring, and me -–
I superposed their normal modes with glee
And that has made all the difference.

According to Jonnie, this poem is about a pair of pendula, coupled together by a spring. Analyzing this problem by considering the motion the two pendula is very difficult. However, if instead we use a rotated set of axes in Hilbert space, axes corresponding to the motion of the two normal modes (the pendulum mode with eigenvector P, and the breathing mode with eigenvector B), the problem becomes much easier.


4:45 AM

Filed under: Harmonic analysis — Travis @

One of my former students, a swell guy named Brian Grimsely, turned the following poem with one of his Advanced Calculus homework assignments. (I was the TA for that class.) His comments:

“Travis, I thought you might get a kick out of this. I stumbled upon it, not really remembering having written it, back in the first quarter, at the start of Rudin’s Chapter 3. Hope you don’t dock points for it. –Brian.

I keep writing things down
and then losing the pieces of paper
because individually the work isn’t any good
but collectively it’s enough to scare Clive Barker.

Now I study sequences and series
and spend much of my time
showing where things tend as
they approach infinity.

Infinity is strange.
There is no concept of
next to within its grasp
and yet it can be countable.

I keep studying math
because to me I have always
found myself immensely satisfied
when I come up with the right answer.

Now it seems the further I go
I find myself with less answers
and more questions and I only
hope that math will know.

I like the quiet of night
when the sleeping world
reaches its serendipitous pinnacle
and I can listen to no one talk.

In that delicate moment of the
restless yearning for rest I can
see answers on the insides of
my eyelids written in bright
flashes of neon light.

The few times that I
switch on the lamp to write
them down, they are no longer
there to be seen.

–Brian Grimsley
4:45 A.M.
November 3, 1999

P.S. I didn’t dock any points.


Tell a joke!

Filed under: Meta — Travis @

Hey! Do you have a joke you’d like to add? Tell it to the comments, and if it fits the theme of the site, it’ll get posted on the front page!

About the site

Filed under: Meta — Travis @

Welcome to “Let ε < 0," a site dedicated to mathematical funny business, flimflam, fallacies, and feghoots. I've done my best to collect and disseminate those bits of mathematical, scientific, and academic humor that I've come across. If you've got one you'd like to include, feel free to share!

In the spirit of academic honesty, I should point out that almost nothing here is original, and much of it has been circulated across the world wide web. However, when I can find a citation, I do my best to include it.

The blog’s name, by the way, comes from a classic joke from real analysis:

Q: What’s the shortest mathematical joke?
A: “Let ε < 0."

With that said, enjoy the silliness.

16 reasons why God would never get tenure

Filed under: Academic humor — Travis @
  1. He had only one major publication.
  2. And it was in Hebrew.
  3. And it had no references.
  4. And it was not published in a refereed journal.
  5. And some even doubted that He wrote it Himself.
  6. It may be true that He created the world, but what has He done since then?
  7. His cooperative efforts have been quite limited.
  8. The scientific community has had a very rough time trying to replicate His results.
  9. He never applied to the Ethics Board for permission to use human subjects.
  10. When one experiment went awry, He tried to cover it up by drowning the subjects.
  11. When subjects did not behave as predicted, He often punished them, or just deleted them from the sample.
  12. He rarely came to class: He just told students to read the book.
  13. He has his son teach the class.
  14. He expelled His first two students for learning too much.
  15. Although there were only ten requirements, most students failed His tests.
  16. His office hours were infrequent, and usually held on a mountain top.


Upgrade to graduate students

Filed under: Academic humor — Travis @


The upgrade path to the most powerful and satisfying computer:

  • Pocket calculator
  • Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
    (Choose any of these)
  • IBM PC
  • Apple Macintosh
  • Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
  • Minicomputer (HP, DEC, IBM, SGI: your choice)
  • Mainframe (IBM, Cray, DEC: your choice)

And then you reach the pinnacle of modern computing facilities…

Graduate students!

Yes, you just sit back and do all of your computing through lowly graduate students. Imagine the advantages:

Multi-processing, with as many processes as you have students. You can easily add more power by promising more desperate undergrads that they can indeed escape college through your guidance. Special student units can even handle several tasks on their own!

Full voice recognition interface. Never touch a keyboard or mouse again. Just mumble commands and they will be understood (or else!).

No hardware upgrades and no installation required. Every student comes complete with all hardware necessary. Never again fry a chip or $10,000 board by improper installation! Just sit that sniveling student at a desk, give it writing utensils (making sure to point out which is the dangerous end) and off it goes.

Low maintenance. Remember when that hard disk crashed in your Beta 9900, causing all of your work to go the great bit bucket in the sky? This won’t happen with grad. students. All that is required is that you give them a good *whack!* upside the head when they are acting up, and they will run good as new.

Abuse module. Imagine yelling expletives at your computer. Doesn’t work too well, because your machine just sits there and ignores you. Through the grad student abuse module you can put the fear of god in them, and get results to boot!

Built-in lifetime. Remember that awful feeling two years after you bought your GigaPlutz mainframe when the new faculty member on the block sneered at you because his FeelyWup workstation could compute rings around your dinosaur? This doesn’t happen with grad. students. When they start wearing and losing productivity, simply give them the PhD and boot them out onto the street to fend for themselves. Out of sight, out of mind!

Cheap fuel: students run on Coca Cola (or the high-octane equivalent — Jolt Cola) and typically consume hot spicy chinese dishes, cheap taco substitutes, or completely synthetic macaroni replacements. It is entirely unnecessary to plug the student into the wall socket (although this does get them going a little faster from time to time).

Expansion options. If your grad. students don’t seem to be performing too well, consider adding a handy system manager or software engineer upgrade. These guys are guaranteed to require even less than a student, and typically establish permanent residence in the computer room. You’ll never know they are around! (Which you certainly can’t say for an AXZ3000-69 150gigahertz space-heater sitting on your desk with its ten noisy fans….) [Note however that the engineering department still hasn't worked out some of the idiosyncratic bugs in these expansion options, such as incessant muttering at nobody in particular, occasionally screaming at your grad. students, and posting ridiculous messages on world-wide bulletin boards.]

So forget your Babbage Engines and abacuses (abaci?) and PortaBooks and DEK 666-3D’s and all that other silicon garbage. The wave of the future is in wetware, so invest in graduate students today! You’ll never go back!


Ultimate test

Filed under: Academic humor — Travis @

In honor of the end of the semester, I present the following in-class exam. I’ve been told you can find this in William Nivak’s “The Big Book of New American Humor.”

Read each of the following fifteen problems carefully. Answer all parts to each problem.
Time limit: 4 hours. Begin immediately.

Describe the history of the papacy from its origin to the present day, concentrating especially, but not exclusively, on it social, political, economic, religious, and philosophical impact on Europe, Asia, America and Africa.
Be brief, concise and specific.

You have been provided with a razor blade, a piece of gauze, and a bottle of Scotch. Remove your appendix.
Do not suture until your work has been inspected. You have 15 minutes.

2500 riot-crazed aborigines are storming the classroom. Calm them. You may use any ancient language except Latin or Greek.

Create life. Estimate the differences in subsequent human culture if this form of life had developed 50 million years earlier, with special attention to its probable effect on the English parliamentary system. Prove your thesis.

Write a piano concerto. Orchestrate it and perform it with flute and drum. You will find a piano under your desk.

Based on your knowledge of their works, evaluate the emotional stability, degree of adjustment, and repressed frustrations of each of the following: Alexander of Aphrodites, Ramses II, Gregory of Nicea, and Hammurabi.
Support your evaluation with quotations from each man’s work, making appropriate references. It is not necessary to translate.

Estimate the sociological problems which might accompany the end of the world. Construct and experiment to test your theory.

The disassembled parts of a high-powered rifle have been placed on your desk. You will also find and instruction manual, printed in Swahili. In ten minutes a hungry Bengal tiger will be admitted to the room. Take whatever action you feel appropriate. Be prepared to justify your decision.

Develop a realistic plan for refinancing the national debt. Trace the possible effects of your plan in the following areas: Cubism, the Donatist controversy, and the wave theory of light. Outline a method for preventing these effects. Criticize this method from all possible points of view. Point out the deficiencies in your point of view, as demonstrated in your answer to the last question.

There is a red telephone on the desk beside you. Start World War III. Report at length on its social-political effects, if any.

Take a position for or against truth. Prove the validity of your position.

Create a small rapidly rotating black hole. Investigate and report on its effects on the opto-electric properties of Seaborgium (element #106). Clean up your experiment after you’ve finished.

Sketch the development of human thought and estimate its significance.
Compare with the development of any other kind of thought.

Define the universe. Give three examples.

Describe in detail. Be objective and specific.

Older Posts »

Powered by WordPress