Last Words

https://commons.wikimedia.org/wiki/File:Spectacle_Reef_Light_Aerial_View.jpg

On April 8, 1959, when keepers arrived at the Spectacle Reef lighthouse in Lake Huron to prepare it for a new season, they discovered a note:

To Whom It May Concern:

At 1705 hours my plane went down 400 kilometers out at 035 to 050 degrees. I was one mile northeast of here at 5000 feet when my engine went quite dead. I tried to make it in but landed in the water. At that time there were large open areas of water. I did not try to land on the ice as it did not look thick enough. Also I wanted to get as close to this light as possible.

The plane went down in about two minutes after it landed. Before it did it floated close enough to a floe for me to jump. The ice was not over two inches thick. Another large body of water separated me from the light so I waited.

Suddenly the wind shifted to the northeast. The ice I was on started to move. At the very last moment one quarter of the ice ground against the ice packed around the light. My ice floe broke up fast so I ran for the light. I got ashore but was wet from falling in. My clothes froze before I could get the door open.

Once inside I used your towels and overshoes to keep from freezing.

About 2100 I got your stove lit. I hooked up the batteries and lit your warning lamp. The radio receiver worked but the transmitter was dead. I didn’t know enough about it to make it work. I have used the batteries until they are going dead. I sat up last night sending out SOS calls by blinking the main light.

Right now I am deliberating whether to stay here or cross the ice. From the chart I will have eleven miles to travel. There are large water holes, thin ice which had been broken into pieces by the wind yesterday. There is hardly any wind today. We have had two freezing nights, so I ought to make it in about four hours. I want to go now because it is nice weather.

Also I did not file a flight plan so no one will look for me another two or three days. The weather may be bad again.

I have made a mess of your building. I hope you will forgive me. I am going to take some equipment with me, binoculars, coat, hat, blankets, etc. I will turn them into the United States Coast Guard as soon as I get ashore.

Signed,

M.Sgt. William J. Wyman
USAF

The note bore no date. Wyman had departed Saginaw in a Piper Super Cruiser on Feb. 22, headed for the former Kinross Air Force Base near Sault Ste. Marie. He had never arrived. No trace of him was ever found.

(Thanks, Charles.)

| Death · Oddities

Observation

https://pixabay.com/photos/moon-full-moon-sky-night-sky-lunar-1859616/

Reading books in one’s youth is like looking at the moon through a crevice; reading books in middle age is like looking at the moon in one’s courtyard; and reading books in old age is like looking at the moon on an open terrace. This is because the depth of benefits of reading varies in proportion to the depth of one’s own experience.

— Chang Ch’ao

| Literature

“The Impossible Fact”

Palmstroem, old, an aimless rover,
Walking in the wrong direction
At a busy intersection
Is run over.

“How,” he says, his life restoring
And with pluck his death ignoring,
“Can an accident like this
Ever happen? What’s amiss?

“Did the state administration
Fail in motor transportation?
Did police ignore the need
For reducing driving speed?

“Isn’t there a prohibition
Barring motorized transmission
Of the living to the dead?
Was the driver right who sped … ?”

Tightly swathed in dampened tissues
He explores the legal issues,
And it soon is clear as air:
Cars were not permitted there!

And he comes to the conclusion:
His mishap was an illusion,
For, he reasons pointedly,
That which must not, can not be.

— Christian Morgenstern (translated by Max Knight)

| Poems

The Top Hat Illusion

https://archive.org/details/B-001-014-611/page/n69/mode/2up

A striking oddity from Matthew Luckiesh’s Visual Illusions, 1922. The height of this silk hat appears much greater than its width, but the two are the same.

“A pole or a tree is generally appraised as of greater length when it is standing than when it lies on the ground. This illusion may be demonstrated by placing a black dot an inch or so above another on a white paper. Now, at right angles to the original dot place another at a horizontal distance which appears equal to the vertical distance of the first dot above the original. On turning the paper through ninety degrees or by actual measurement, the extent of the illusion will become apparent.”

| Oddities · Science & Math

“The Worst of All Puns”

https://blog.le-miklos.eu/wp-content/HabeMortemPraeOcculis.jpg

At Nuremburg a wolf’s tooth was shown to travellers … on which an Abbé is represented lying dead in a meadow, with three lilies growing out of his posteriors. This is not only the worst pun that ever was carved upon a wolf’s tooth, but the worst that ever was or will be made. The Abbé is designed to express the Latin word Habe. He is lying dead in a meadow, … mort en pré; this is for mortem præ; and the three lilies in his posteriors are to be read oculis, … au cu lis. Thus, according to the annexed explanation, the whole pun, rebus, or hieroglyphic, is Habe mortem præ oculis.

— Robert Southey, Omniana, 1812

In other words, the French phrase Abbé mort en pré au cul lys (“Abbot died in a meadow with lilies in his rump”) sounds like the Latin phrase Habe mortem præ oculis (“Keep death before your eyes”). This joke appears to be referenced in Hieronymus Bosch’s 1504 triptych The Garden of Earthly Delights:

https://commons.wikimedia.org/wiki/File:The_Garden_of_earthly_delights.jpg

| Art · Humor · Language · Oddities

Cameo

Western Illinois University mathematician Iraj Kalantari published an unusual puzzle in Math Horizons in February 2019. A sphere B of radius 150 is centered at (150, 150, 0). A sphere M of radius 144, centered on the z-axis, lies entirely below the (x, y)-plane so that the volume of its intersection with B is 1/2. “Can we find a sphere S of radius 73 that has its center on the circle (x – 73)2 + (y – 73)2 = 1502 in the plane z = 73 so that the volume of B minus its intersections with M and S equals the volume of M minus its intersection with B plus the volume of S minus its intersection with B?”

The answer is no, because Vol(B – (M ∪ S)) = Vol((M – B) ∪ (S – B)) if and only if Vol(B) = Vol(M) + Vol(S), and that’s the case if and only if r_{B}^{3} = r_{M}^{3} + r_{S}^{3} , where rB, rM, and rS are the radii of the three spheres. “[A]nd because the radii are integers, this equality is impossible by Fermat’s last theorem!”

The placement of the spheres and the fact that the values differ by 1 are red herrings.

(Iraj Kalantari, “The Three Spheres,” Math Horizons 26:3 [February 2019]: 13, 25.)

02/28/2026 UPDATE: In my original statement of the problem I left out a vital phrase in Kalantari’s presentation: The sphere S should have its center on the circle (x – 73)2 + (y – 73)2 = 1502 in the plane z = 73.

I’d omitted the last phrase, a condition that guarantees that S lies above the xy plane and so does not intersect sphere M, which is required to deduce the equation involving the volumes. Many thanks to reader Francesco Veneziano for pointing this out.

| Science & Math

Devotion

A “prayer to the local deities” offered by Socrates in Plato’s Phaedrus:

Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul; and may the outward and inward man be at one. May I reckon the wise to be the wealthy, and may I have such a quantity of gold as a temperate man and he only can bear and carry.

“Anything more? The prayer, I think, is enough for me.”

| Society

Down Under

https://commons.wikimedia.org/wiki/File:La_rotondit%C3%A9_de_la_Terre,_Image_du_monde_(cropped).jpg

How is it with those who imagine that there are antipodes opposite to our footsteps? Do they say anything to the purpose? Or is there any one so senseless as to believe that there are men whose footsteps are higher than their heads? Or that the things which with us are in a recumbent position, with them hang in an inverted direction? That the crops and trees grow downwards? That the rains, and snow, and hail fall upwards to the earth? And does any one wonder that hanging gardens are mentioned among the seven wonders of the world, when philosophers make hanging fields, and seas, and cities, and mountains?

— Lactantius, Institutiones Divinae, 303

| History · Science & Math