Number Theory

What’s the funniest number? Yale physicist Emily Pottebaum proposed the Perceived Specificity Hypothesis, which states that “for nonnegative integers < 100, the funniness of a number increases with its apparent precision." She surveyed 68 acquaintances and found that:

  • Among integers divisible by 10, 0 is funniest.
  • Odd numbers are consistently funnier than even.
  • “Furthermore, the most oddly specific numbers — odd numbers with a degree of specificity of 2 — are the most funny, according to the data presented here.”

The degree of specificity characterizes the distance between an integer and the nearest multiple of 5:

https://arxiv.org/abs/2503.24175
Image: arxiv.org

So 3, 7, 13, 17, etc. were judged to be funniest.

“I acknowledge my Ph.D. advisor, who I shall not name out of respect for her academic integrity, for her exasperation upon learning about this study. I thank her for putting up with my antics and plead that she continue to do so until I graduate.”

(E.G. Pottebaum, “What Is the Funniest Number? An Investigation of Numerical Humor,” arXiv preprint, arXiv:2503.24175 [2025].)

| Science & Math

Late Word

https://commons.wikimedia.org/wiki/File:Jim_Croce_publicity_portrait_ABC_Records_(cropped).jpg

A week after songwriter Jim Croce died in a plane crash in 1973, his wife, Ingrid Jacobson, received this letter:

Dear Ing,

I know I haven’t been very nice to you for some time, but I thought it might be of some comfort, Sweet Thing, to understand that you haven’t been the only recipient of JC’s manipulations. But since you can’t hear me and can’t see me, I can’t bullshit, using my sneaky logic and facial movements. I have to write it all down instead, which is lots more permanent. So it can be re-read instead of re-membered, so, it’s really right on the line.

I know that you see me for who I am, or should I say, as who I are. ‘Cause I’ve been lots of people. If Medusa had personalities or attitudes instead of snakes for her features, her name would have been Jim Croce. But that’s unfair to you and it’s also unhealthy for me. And I now want to be the oldest man around, a man with a face full of wrinkles and lots of wisdom.

So this is a birth note, Baby. And when I get back everything will be different. We’re gonna have a life together, Ing, I promise. I’m gonna concentrate on my health. I’m gonna become a public hermit. I’m gonna get my Master’s Degree. I’m gonna write short stories and movie scripts. Who knows, I might even get a tan.
Give a kiss to my little man and tell him Daddy loves him.

Remember, it’s the first sixty years that count and I’ve got 30 to go.
I Love you,
Jim

(From Ingrid’s 2012 memoir, I Got a Name: The Jim Croce Story.)

| Death · Entertainment

Piecework

In the Spring 1957 issue of Pi Mu Epsilon Journal, C.W. Trigg points out that, by two continuous cuts, the surface of a cube can be divided into two pieces that can be unfolded and assembled into a hollow square:

https://commons.wikimedia.org/wiki/File:Cube-h.svg
Image: Wikimedia Commons

The cuts divide the cube’s surface into two congruent pieces, each composed of six connected isosceles right triangles. Joining these two pieces forms a hollow square with exterior side 2\sqrt{2}x and interior side \sqrt{2}x , where x is the length of the cube’s edge.

| Science & Math

“A Reading in Unlove”

This poem is widely purported to have been written by a 15-year-old boy two years before he ended his life:

Once on a yellow paper with green lines
he wrote a poem
and he called it “chops” because that
was the name of his dog
and that’s what it was all about
and his teacher gave him an “A” and
a gold star
and his mother hung it on the kitchen door
and read it to all his aunties
that was the year father tracy took
all the kids to the zoo and let them
sing on the bus
and that was the year his baby sister
was born with tiny toenails and no hair
and his mother and father kissed a lot
and the girl around the corner sent
him a valentine signed with a row of x’s
and his father always tucked him
in bed at night
and was always there to do it.

Once on a white paper with green lines
he wrote a poem
and he called it “autumn” because
that was the name of the season
and that’s what it was all about
and his teacher gave him an “A” and
told him to write more clearly
and his mother never hung it on
the kitchen door because it had just
been painted
and the other kids told him that
father tracy smoked cigars and left
the butts in the pews
and that was the year his sister got glasses
with thick lenses and black frames
and the girl around the corner laughed
at him when he went to see Santa Claus
at Macy’s
and the kids told him why his
mother and father kissed a lot
and his father never tucked him in
bed at night and he got mad when
he got mad and cried for him to do it.

Once on a paper torn from his notebook
he wrote a poem
and he called it “question marked
innocense” because that was the name
of his girl
and his professor gave him an “A” and
a strange and steady look
and his mother never hung it on
the kitchen door because he never
showed it to her
that was the year father tracy died
and he forgot how the end of the
“apostles creed” went
and he caught his sister necking on
the back porch
and his mother and father never
kissed anymore or even talked
and the girl around the corner
wore too much makeup and made
him cough when he kissed her, but he
kissed her anyway
and at 3 a.m. he tucked himself in bed,
his father snoring soundly.

That’s why on the back of a pack of
matches he wrote another poem
and he called it “absolutely nothing”
because that’s what it was about
and he gave himself an “A”
and a slash on each damp wrist
and he hung it on the bathroom door
because he couldn’t reach the kitchen.

The earliest publication I can find attributes it to a Cathy Curtis, a 12-year-old student at the Abbot Academy, a girls’ boarding school in Andover, Mass., whose literary magazine published the poem in June 1971. The school closed the following year. I haven’t been able to learn anything more about Curtis.

| Poems

Five-Sided Story

pentagon

In a regular pentagon, all diagonals are drawn, as shown. Label each vertex of the pentagon and each intersection of the diagonals with the number 1. Now: In one step you can change the signs of all the numbers on a side or on a diagonal. Is it possible, by a sequence of such steps, to convert all the labels in the diagram to -1?

Click for Answer
| Puzzles

Double or Nothing

Carrying two brown satchels, one filled with $777,000 in $100 bills and the other empty, an unidentified man, dressed in jeans and cowboy boots, walked into Binion’s Horseshoe Casino in Las Vegas last week. He exchanged his money for $500 chips, strode to the craps table and put all of the chips on the back line, which meant that he was betting against the woman who happened to be rolling the dice. She first threw a six, then a nine and finally a seven. Said the dealer: ‘Pay the back line.’ The man scooped up his chips, traded them at the casino cage for $1,554,000 in cash and shook hands with Jack Binion, the stunned president of the casino. Said Binion: ‘It was the biggest bet in a gambling house that I have ever heard of.’ As the man walked out of the casino with his two brown satchels, both now stuffed with $100 bills, and climbed into his car, he told Binion: ‘You know, this damned inflation was just eroding this money. I figured I might as well double it or lose it.’ With that, he drove off into the night, still unidentified.

— Time, Oct. 6, 1980

(A few more details here.)

| Oddities

A Grim Friday

Two affecting episodes from the Johnstown Flood of 1889, in which a dam failure sent almost 15 million cubic meters of water down the Little Conemaugh river of western Pennsylvania:

Six-year-old Gertrude Quinn Slattery was riding a wet, muddy mattress through the floodwaters when a man leapt from a passing roof and struggled across to her. “I put both arms around his neck and held on to him like grim death.” They approached a white building from which two men were extending poles from an upper window to rescue victims floating by.

I was too far out for the poles, so the men called:

‘Throw that baby over here to us.’

My hero said: ‘Do you think you can catch her?’

They said: ‘We can try.’

So Maxwell McAchren threw me across the water (some say twenty feet, others fifteen. I could never find out, so I leave it to your imagination. It was considered a great feat in the town, I know.)

Anna Fenn Maxwell’s husband was washed away from a neighbor’s house moments before the flood struck the Fenn home.

I had the baby in my arms and the other children climbed on the lounge and table. The water rose and floated us until our heads nearly touched the ceiling. I held the baby as long as I could and then had to let her drop into the water. George had grasped the curtain pole and was holding on. Something crashed against the house, broke a hole in the wall land a lot of bricks struck my boy on the head. The blood gushed from his face, he loosed his hold and sank out of sight. Oh it was too terrible!

My brave Bismark went next. Anna, her father’s pet, was near enough to kiss me before she slipped under the water. It was dark and the house was tossing every way. The air was stifling, and I could not tell just the moment the rest of the children had to give up and drown. My oldest boy, John Fulton, kept his head above the water as long as he was able. At last he said: ‘Mother, you always said Jesus would help. Will he help us now?’ What could I do but answer that Jesus would be with him, whether in this world or the brighter one beyond the skies? He thought we might get out into the open air. We could not force a way through the wall of the ceiling, and the poor boy ceased to struggle. What I suffered, with the bodies of my seven children floating around me in the gloom, can never be told.

She gave birth to a baby girl a few weeks later, but the child did not survive.

From the flood museum website and the National Park Service.

| History

Reflections

http://www.sxc.hu/photo/698003

Aphorisms of German physicist Georg Lichtenberg (1742-1799):

  • “Passionate ambition and suspicion I have invariably found to go together.”
  • “It is in most cases more difficult to make intelligent people believe that you are what you are not, than really to become what you would appear to be.”
  • “True, unaffected distrust of human power in general is the surest sign of mental ability.”
  • “I am convinced that we not only love ourselves in others, but hate ourselves in others too.”
  • “Where moderation is a fault indifference is a crime.”
  • “I suppose there never was a man of any great mark who was not slandered; or hardly any blackguard who never directed a slander against some man of merit.”
  • “Mankind loves company, even if it is no more than that of a burning candle.”
  • “It is a fact that there are numbers of people who read merely that they need not think.”
  • “With most people unbelief in one thing is founded upon blind belief in another.”
  • “What is very rare seldom remains long unexplained. What is inexplicable is usually no longer rare, and has perhaps never been so.”
  • “The commonest opinions and the things that everybody takes for granted often the most deserve examination.”
  • “That in advancing years we should grow incapable of learning has some connection with age’s intolerance of being ordered about, and a very close connection, too.”
  • “I have looked through the list of illnesses, and did not find cares or sad thoughts mentioned among them. That is a mistake, surely.”
  • “Saints in stone have done more in the world than living ones.”

“Has anyone, I wonder, ever dreamt of odours, without an external cause to give rise to the impression? — dreamt, for instance, of the smell of roses, when there was no rose or rosewater in the vicinity. With music this is certainly the case, and with light too; but feelings of pain in a dream usually have some external cause. As regards odours I am uncertain.”

| Quotations

“Man and Bird”

A Man with a Shotgun said to a Bird:

‘It is all nonsense, you know, about shooting being a cruel sport. I put my skill against your cunning — that is all there is of it. It is a fair game.’

‘True,’ said the Bird, ‘but I don’t wish to play.’

‘Why not?’ inquired the Man with a Shotgun.

‘The game,’ the Bird replied, ‘is fair as you say; the chances are about even; but consider the stake. I am in it for you, but what is there in it for me?’

Not being prepared with an answer to the question, the Man with a Shotgun sagaciously removed the propounder.

— Ambrose Bierce, Fantastic Fables, 1899

| Literature