Archive for the ‘Articles’ Category.

Chicago Bridge Nationals July 2023

I went to Chicago Nationals to play in the Spingold with Farley Mawyer and teammates Larry Gordon and Steve Siegel, who had just placed second in Grand National Teams B. We lost in the first match to the Overdeck team against Norberto Bocchi and Leonardo Fruscoloni. Roberto can deal at ten times the normal speed. Leo bet me that you can get a review of the bidding any time during the play, and paid up $1. In the MiniSpingold we qualified the first day but then lost to the team that won the whole thing.* I also played with Victor Xiao (father of the precocious Eric and Jeff) and off-duty pro Alamiro Pinoargote from Equador. But no victories until Bob Cole and I won the final open pairs side game. Hand 25 at 4 Spades looked hopeless after the Diamond finesse failed, as I would have to keep Clubs to a single loser. I led low from South’s dummy and West erred by rising with the Ace. Now I could lead the J from hand, smothering the T.

*Martin Harris, Chicago IL; Miriam HarrisBotzum, Orefield PA; Mark Kinzer, New Berlin WI; Bob Marheine, Waukesha WI.

Jorge Luis Borges

When a first-year student at MIT, I went to hear Jorge Luis Borges speak at Tuft University on April 9, 1971.

Two secretaries read Borges’s poetry in English and Spanish. Borges followed the readings with excellent explanation.

I found the poetry, much of which dealt with blindness and age, dramatically impressive, sensitive, and moving.

Some Comments by Borges

  I awake to despair in the realization of my human identity, “Borges, the overrated writer.”

The dream poem I dreamt and wrote at my mother’s insistence. My enemy’s cane falls from view as objects fall from dreams. I never knew Treatise on Dreams; I selected the name from Encyclopedia Britannica.

    Eternity is not the sum total of yesterdays, todays, and tomorrows stretching on forever; it is all time at once. In my poem on John xx:xx, I attempt (and of course fail) to write from eternity into time.

“Israel” a gift of inspiration, which no doubt came to many that week. Others, I hope, have written it better.

Forgiveness and revenge, I cannot understand. They are both the same.

“Cain and Abel:” the nameless star just sets the story in antiquity. Logical error: Abel’s ghost should meet Cain. But this would be a literary error.

Blind man in library autobiographical. Note early use of sense-impressions, casual mention of blindness. Happiness comes unreasonably; just enjoy it. Blindness can be an avenue of happiness.

Praise to darkness. Darkness has two meanings. Blindness simplifies, abstracts. I used to employ every moment (e.g. reading on bus), but now time flows differently. Simplification and abstraction. A sleepless night is not necessarily an unhappiness. Intimately personal poem.

Afterward, Borges autographed books, answered questions. I felt that he was not well enough befriended and taken care of and respected. His secretaries on stage whispered behind him even as he explained his poetry. People mobbed him before he could sit down, “I am tired.” He deserves respect.

A very humble man. He explains he is not completely blind, and demonstrates by distinguishing forms and colors accurately.

Amazing Play at Cape May Bridge Club

I fell to an amazing play by Harriet Walcott partnering Baby Vistenzo on Board 6 at the Karen Sylvester’s Cape May County Duplicate Bridge Club March 30, 2023. Declaring 4H in the North I won the Diamond lead with the J, led a Spade to the Ace, a Club to the King, and ruffed a Spade. As West popped the King, I could now turn my attention to trumps. A Heart to the King lost to the Ace. West returned a small Spade, I discarded a small Club, and Harriet smoothly discarded a Club, convincing me that West held the remaining Hearts (and even if not, Harriet held the guarded Jack). I confidently led the Heart 10 for a finesse, Harriet won the Jack, and led a Diamond for a ruff by her partner’s remaining Heart 7. They still had two Club tricks for down 2 and a top.

Continue reading ‘Amazing Play at Cape May Bridge Club’ »

An Impossible 3NT in Lebhar IMP Pairs at Nationals

Made the following impossible 3NT playing with Mark Blanchard at the national Lebhar IMP Pairs in New Orleans March 12, 2023. As North I dealt and passed, East opened 1S, Blanch overcalled 2D, I raised to 3D, Blanch bid 3H, and I bid 3N. When dummy comes down, it is apparent that the opponents can cash at least 5 Clubs and the SA. On the lead of the S8 I have eight top tricks, but where is the ninth? The Heart finesse seems unlikely. So I need East to lead a Heart or a Spade. I desperately lead the CQ from dummy. When the expert East wins with the CK, it is “obvious” that I have CAJ as well as the SK, that his partner has the HA, and that his best shot is to lead to his partner’s HA and get a Spade back through me. His Heart play gives me my ninth trick. He was astounded when he realized what had happened.

I loved the New Orleans Nationals, with one sorry exception: the literary quality of the limericks. To remedy this unfortunate situation, I hereby submit the following (featured on the May 4, 2023, Sorry Partner podcast):

While trying my hand at Pairs Silly*
I suddenly brought out Gazilli.
Pard jumped to a grand
With no Ace in his hand;
I guess I’ll just have to Ask Billy.

*term for the Silidor Pairs, courtesy Adam Grossack.

See also TV clip (opening with the back of my head) from Good Morning New Orleans.

Books and Movies 2022


Friends with Money (Netflix)

Troy (Paris killed Achilles killed Hector killed Menalaus, Breseis killed Agamemnon killed Priam; Netflix)

We Were Soldiers (Mel Gibson, Vietnam, Netflix)

The God Committee (pig heart, Kelsey Grammar, Netflix)

The Sound of Music: From Fact to Phenomenon (1994) – Julie Andrews, Christopher Plummer, Robert Wise (YouTube)

Continue reading ‘Books and Movies 2022’ »

Progressive Squeeze in Phoenix

I had this progressive squeeze at Phoenix Nationals playing with Farley Mawyer in the 10K IMP Pairs. I was E playing in NT. South led the S10. I won the Q, unblocked the K, and led the HQ. North took the Ace and played Diamonds. I won the third one and cashed two Hearts and two Spades. On the last Spade, North holding — 10 Q K5 was squeezed and discarded the DQ. Now on the D9 he was squeezed again, and graciously threw in his cards.

The second day I picked up KT9 AKQ62 AKQ63 —. I opened 2C, planning an auction such as 2C 2D 2H (Kokish) 2S (forced) 3D …, ending in 6H or 6D. But my partner’s response to 2C was a surprise 2S. So I just bid 7S. When the lead of D5 wasn’t ruffed, partner could claim.

Frank Morgan Library Dedication

Dedication of the Frank Morgan Library in the Department of Mathematics and Statistics at Williams College, November 19, 2022.

Cutting the ribbon (video).

















My remarks (click for video): Thank you. Mihai asked about this tiling discovered by students here. I had a paper with 8 students on the best unit-area pentagonal tile, where best means shortest perimeter. Of course the best triangular tile is the equilateral triangle, the best quadrilateral tile is the square, and for six or more sides, the regular hexagon is best of all.  Unfortunately the regular pentagon does not tile. The best pentagon is a tie, between the prismatic tile here which looks like a house, and the Cairo pentagon which I’ve seen on the streets of Cairo. Successive students discovered that you could mix the two types as in this beautiful tiling you see here and in Colin Adams’s new book on tilings.

Now some deeper history. When  I first came to Williams I found in the old Bronfman a wonderful, distinctive math-stats library, with faculty offices around the perimeter opening onto the library. Those who went before, such as Guil Spencer, who served as chair for 18 years, had paid careful attention to every detail of the plans. For our students it was a favorite place to study, and we’d continually meet and greet them and each other there, sharing mathematics and statistics and often pulling a book from the shelves.

When the old Bronfman was knocked down it seemed that this space would be lost. But thanks to the persistent efforts of faculty, staff, and students, including the remarkable Students of Mathematics and Statistics Advisory Board, SMASAB, this library space as well as prominent classroom space has been preserved and enhanced. What a joy it is to look out today and behold all of that and more, to see all of you who have contributed to that spirit (I see the Horns of Horn Hall) and who have contributed to this place, and who are continuing that communal mission we all love and share. To me it’s the very essence of Williams: the community of faculty, students, and staff working together as colleagues to advance understanding. May Williams never lose that identity, through community such as you and spaces such as this.

Many thanks to Paul Collins, Joey Horn, Margaret, and Ellen Kennedy for photos and videos.

My Game with Zia

In a drawing for the monthly NewTricks bridge tournament September 27, 2022, I won the chance to partner with Zia. Basically he just consistently plays good bridge. He generously emailed me three times about our convention card. We came in 3/20 with 63%, despite 5.6% for 6H-1 on a finesse and 22% when the opponents made 3N by a smart deep finesse in Hearts (Board 17 below). Zia made some of his characteristic deceptive plays, such as leading 2 from A962 in dummy’s Heart suit against 3D, leading 6 from QJ63 in dummy’s suit against 3N, and playing K from KQJ752 on my lead against 4C to make Declarer think his points were elsewhere. In my favorite example, Zia was playing 6C on Board 16 below. How to play the Spades? After drawing trump he immediately discarded the SJ on the HA and called for a low Spade from the Board. Of course his RHO, now imagining Zia with the stiff K and not wanting to hesitate (and realize if Zia started with doubleton KJ he would thrown both on the Hearts), would pop up with the A if he had it, saving Zia from the guess. Otherwise Zia could let the 9 ride. Of course on this particular layout, he couldn’t go wrong.


You can watch our whole match with expert commentary at

And my NewTricks “Challenge an Expert” Peter Crouch


Continue reading ‘My Game with Zia’ »

Lucky 6H at Cape May

Had a lucky 6H on Thursday June 17, 2022, at the festive Father’s Day game at the Cape May County Duplicate Bridge Club of the amazing Karen Sylvester. As North I opened 1H. My partner responded with a game-forcing 2C instead of showing 4-card support by Jacoby 2N or more accurately 3H with this 12-count. We soon arrived at a unpromising 6H. The DK lead gave a glimmer of hope if East also held the SK and I could locate the CQ, now probably with West. After drawing trump and clearing Clubs, I put East in with a Diamond. Afraid of giving up a ruff-discard by leading Clubs or Diamonds, East returned a Spade, giving me the SQ and the slam.

Lawlor proves equal-volume triple bubble conjecture.

In a talk at Columbia University today (April 15, 2022), Gary Lawlor announced and described his proof that the standard triple soap bubble in R^3 is the least-perimeter way to enclose and separate three equal volumes.

Update 5/19/22: Milman and Neeman post proof of general triple and quadruple bubble conjectures in R^n and S^n See my review at and the beautiful Quanta article by Erica Klarreich.

Update 7/18/23: Milman and Neeman post proof of quintuple bubble conjecture as promised