Kudos

“Did you hear what Howells once said to a boring author who was trying to wring a compliment out of him? ‘I don’t know how it is,’ said the author, ‘I don’t seem to write as well as I used to do.’ ‘Oh, yes you do — indeed you do. You write as well as you ever did;– But your taste is improving.”

— From a letter from John Jay Chapman to Margaret Chanler, Nov. 30, 1911

Applied Geometry

George Wither wrote this “rhomboidal dirge” in 1622:

                        Ah me!
                    Am I the swain
              That late from sorrow free
          Did all the cares on earth disdain?
      And still untouched, as at some safer games,
  Played with the burning coals of love, and beauty's flames?
Was't I could dive, and sound each passion's secret depth at will?
And from those huge o'erwhelmings rise, by help of reason still?
    And am I now, O heavens! for trying this in vain,
        So sunk that I shall never rise again?
          Then let despair set sorrow's string,
              For strains that doleful be;
                    And I will sing,
                        Ah me!

                        But why,
                      O fatal time,
                Dost thou constrain that I
          Should perish in my youth's sweet prime?
      I, but awhile ago, (you cruel powers!)
  In spite of fortune, cropped contentment's sweetest flowers,
And yet unscornèd, serve a gentle nymph, the fairest she,
That ever was beloved of man, or eyes did ever see!
    Yea, one whose tender heart would rue for my distress;
        Yet I, poor I! must perish ne'ertheless.
          And (which much more augments my care)
                  Unmoanèd I must die,
                    And no man e'er
                      Know why.

                      Thy leave,
                    My dying song,
                Yet take, ere grief bereave
            The breath which I enjoy too long,
        Tell thou that fair one this: my soul prefers
    Her love above my life; and that I died her's:
And let him be, for evermore, to her remembrance dear,
Who loved the very thought of her whilst he remained here.
  And now farewell! thou place of my unhappy birth,
      Where once I breathed the sweetest air on earth;
            Since me my wonted joys forsake,
                And all my trust deceive;
                    Of all I take
                      My leave.

                        Farewell!
                  Sweet groves, to you!
                You hills, that highest dwell;
              And all you humble vales, adieu!
          You wanton brooks, and solitary rocks,
      My dear companions all! and you, my tender flocks!
Farewell my pipe, and all those pleasing songs, whose moving strains
Delighted once the fairest nymphs that dance upon the plains!
        You discontents, whose deep and over-deadly smart
          Have, without pity, broke the truest heart.
              Sighs, tears, and every sad annoy,
                That erst did with me dwell,
                    And all other joys,
                        Farewell!

                          Adieu!
                    Fair shepherdesses!
                  Let garlands of sad yew
              Adorn your dainty golden tresses.
        I, that loved you, and often with my quill,
    Made music that delighted fountain, grove, and hill;
I, whom you loved so, and with a sweet and chaste embrace.
Yea, with a thousand rather favours, would vouchsafe to grace,
        I now must leave you all alone, of love to plain;
            And never pipe, nor never sing again!
              I must, for evermore, be gone;
                  And therefore bid I you,
                      And every one,
                          Adieu!

                        I die!
                    For, oh! I feel
              Death's horrors drawing nigh,
            And all this frame of nature reel.
          My hopeless heart, despairing of relief,
    Sinks underneath the heavy weight of saddest grief;
Which hath so ruthless torn, so racked, so tortured every vein,
All comfort comes too late to have it ever cured again.
    My swimming head begins to dance death's giddy round;
        A shuddering chillness doth each sense confound;
            Benumbed is my cold sweating brow
                A dimness shuts my eye.
                  And now, oh! now,
                        I die!

In 1968, conceptual artist Douglas Huebler used small bits of self-sticking paper to mark the vertices of two giant imaginary hexagons in Boston and New York. “The world is full of objects, more or less interesting; I do not wish to add any more,” he wrote later. “I prefer, simply, to state the existence of things in terms of time and place.”

Unquote

“You may be sure that when a man begins to call himself a ‘realist,’ he is preparing to do something that he is secretly ashamed of doing.” — Sydney Harris

“When a stupid man is doing something that he is ashamed of, he always declares that it is his duty.” — George Bernard Shaw

Harmony

https://commons.wikimedia.org/wiki/File:Handshake_problem_visual_proof.svg
Image: Wikimedia Commons

By CMG Lee, a pleasing visual proof that the number of possible handshakes among n people is the (n-1)th triangular number.

The first pair shake hands, and each new arrival shakes with everyone already present. The cumulative total counts every possible handshake.

The Other Half

Hungarian playwright Ferenc Molnár was almost never awake until afternoon. Once when he was forced to get up early in the morning because of jury duty, he looked unbelievingly at the people crowding the Budapest streets and asked, ‘Are they all jurors?’

— Shirley Motter Linde, The Sleep Book, 1974

Balloon Balance

https://commons.wikimedia.org/wiki/File:Balloon_balance_puzzle.svg
Image: Wikimedia Commons

Richard Garfield, creator of Magic: The Gathering, offered this innovative problem at the Ninth World Puzzle Championship in 2000:

“Add the weights and balloons to the diagram so that the entire mechanism is in equilibrium. As with normal balance puzzles, the total torque at each fulcrum must be zero.” The weights and balloons can be attached only at the designated blue points. Each beam is graduated, though that can be a bit hard to see here — click to enlarge.

The solution is here.

Roundabout

Poet Alastair Reid arranged unusual words into “garlands,” rings that end where they began:

What is a Tingle-Airey?

A tingle-airey is a hand organ, usually played on the street by the turning of a handle, and often decorated with mother-of-pearl or piddock shells.

What are Piddocks?

Piddocks are little mollusks which bore holes in rocks and wood, or in the breastsummers of buildings.

What is a Breastsummer?

A breastsummer is a great beam supporting the weight of a wall, and sometimes of a gazebo above.

What is a Gazebo?

A gazebo is a round balcony with large windows looking out on a view, often of ornamental gardens and cotoneasters.

What is a Cotoneaster?

A cotoneaster is a kind of flowering shrub, a favorite of mumruffins.

What is a Mumruffin?

A mumruffin is a long-tailed tit which often visits bird tables in winter for its share of pobbies.

What are Pobbies?

Pobbies are small pieces of bread thrumbled up with milk and fed to birds and baby animals.

What is Thrumbled?

Thrumbled is squashed together. Ants thrumble round a piece of bread, and crowds in streets thrumble round gongoozlers.

What is a Gongoozler?

A gongoozler is an idle person who is always stopping in the street and staring at a curious object like a tingle-airey.

Once you’ve traversed the list twice or thrice, he says, “you will be able to use them whenever you wish.”

Things to Come

https://archive.org/details/the-strand/The%20Strand%20v26%201903/page/678/mode/2up

H.G. Wells’ predictions for the “house of the future,” made in 1903:

  • Chimneys will be obsolete, replaced by an electric heater in the center of each apartment. The absence of chimneys will also permit roof gardens.
  • Air will be circulated by an electric fan “and will come in through a proper shaft and filter” communicating with the roof.
  • No longer required for ventilation, windows may take any shape and will be positioned for lighting and for aesthetic effect.
  • Labor-saving appliances will include dustless sweepers, self-making beds, and “neatly-mounted electric cooking things.”
  • Walls and floors will meet in a curve rather than at right angles, to prevent the accumulation of dust.
  • Walls will be soundproof, doors will be framed in metal, artificial stone floors will be clad in linoleum, and all will be fireproof.
  • “In the end our present houses may come to be thought singularly squat, massive, and dark beside these elegant new comers.”

He also thought that single-family homes would become rare in urban areas, replaced with “a wide forest of buildings in which many families may live,” sharing common restaurants, children’s playgrounds, and the like. “The scope for ingenuity and for invention in planning such places is enormous.”

O Loving Hate!

In 1988, Harvard mathematician Steven Strogatz hit on a new way to teach differential equations. Juliet loves Romeo, but Romeo is fickle: The more she warms to him, the colder he becomes, but when her interest wanes his feelings grow. She, on the other hand, tends to echo his feeling for her, returning love for love and hate for hate:

dr/dt = –aj, dj/dt = br,

where

r(t) = Romeo’s love/hate for Juliet at time t
j(t) = Juliet’s love/hate for Romeo at time t.

Positive values of r, j signify love, negative values signify hate, and the parameters a, b are positive, to be consistent with the story.

“The sad outcome of their affair is, of course, a neverending cycle of love and hate; their governing equations are those of a simple harmonic oscillator. At least they manage to achieve simultaneous love one-quarter of the time.”

The same idea can be pursued in other variations. He adds, “the term ‘many-body problem’ takes on new meaning in this context.”

(Steven H. Strogatz, “Love Affairs and Differential Equations,” Mathematics Magazine 61:1 [February 1988], 35.)

Checkmate

A puzzle by A. Savin, from the July-August 1996 issue of Quantum:

A mother, her brother, her daughter, and her son take part in a family chess tournament. Two of the four are twins. At the end of the tournament, the winner and the “loser” (the player in last place) are found to be the same age, and the winner is the opposite gender to the loser’s twin. Who won the tournament?

Click for Answer