fans flames of sheer with gossamer notes
burn dark bright through seared clear words crisp
lick searching for hell's deep heights of
verse parches air thin burning with
a yearning melody leaves shivering all
it warms sighs crying elegies fierce
flashing flaring fiery forms
doomed desperate winged pleadings pierce
In speaking to other mourners, I have noticed that people’s recollections of their deceased loved ones differ widely. Some people seem to remember only the most loving and tender of moments, whereas others recall a wider range of experiences. (I’ve also met widows who only spoke of dark and painful memories after their husbands passed away, even after decades of living peacefully with their spouses’ shortcomings.)
I miss Papa more than my words can express, but not all of my memories of him are positive. On one hand, I don’t want to besmirch Papa’s good name; on the other hand, I don’t think that focusing exclusively on my good memories does him any real honor.
If we’re being honest, I think all of us inevitably learn two ways from our parents – 1) we observe certain choices and ways of theirs that we hope to emulate, and 2) there are others that we consider less than ideal, which we deliberately attempt to approach differently than they did.
We empower ourselves and our children to best learn and improve ourselves by honestly reflecting upon our collective pasts.
A particular memory
After graduating from college, I lived at home for several years while my brother Eli was yet a child. One memory that has stayed with me to this day is that of babysitting him on a particular afternoon while our parents were away. The details are hazy in my mind, but I remember losing my patience with him, and I remember him bursting into tears (he was only four or five at the time).
I also remember myself immediately feeling terribly guilty and attempting to comfort the little boy, apologizing to him for my unreasonably irritable outburst. A thought followed, soon after I had calmed him down: “Oh, God. That’s the way Papa acts.”
Papa, you see, tended to be irritable and impatient with me, leading me to often approach him with hesitancy. It was a trait of his that I had never fully developed the tools to content with, other than to avoid him.
Just to be clear!
What I’ve written above bears clarification.
My Babushka (Mama’s mother), who very much adored my father (as did all of my mother’s family), no less than she might have adored her own son, put this to me in a way that rang deeply true. My Papa, as Babushka explained to me on more than one occasion, could be irascible (вспыльчивы), but he never stayed angry for long and never bore any grudges. He was irritable, yes, true, but he was also incredibly forgiving, and one of the kindest men to have ever lived.
Human beings are all so complicated, aren’t we?
Me, myself, and I
The memory I shared with you above is one of my own impatience, and it’s one which I have been trying to grow from in all the years since.
Nevertheless, the reality is that despite my best efforts to subdue this particular character trait of mine, my irritability still manages to occasionally find its way to the fore. I have been impatient at times with both my wife and my daughter, and that is not something to be proud of in the slightest. Such episodes have always left me feeling ashamed. Thus, it is my own limitations, rather than Papa’s, which have led me to write this blog post.
Reflecting upon this, I have decided to explore some traditional Jewish texts and lessons on patience and attempt to create something positive: another article for my ‘ethical will’.
Still waiting for the Messiah
The first thing that immediately strikes me regarding Jewish theology is that we Jews are still waiting for the Messiah’s arrival. Obviously, that’s not to say that all Jews believe in the Messiah, but, still, that’s the official party line: we have been praying for Redemption for thousands of years; and, even today, even with the establishment of the modern Jewish State of Israel (from which we were exiled for nearly two millennia), we continue to pray for the eventual coming of the Messianic Age.
I believe with perfect faith in the coming of the Messiah; and even though he may tarry, nonetheless, I wait every day for his coming.
The mostclassic example of Jewish impatience
My second thought relates to the classic Biblical case of the Jewish people’s impatience. Stories of our collective impatience abound in our TaNaKh (Jewish Bible), but most people would agree that the story of the Golden Calf represented our greatest failure.
As the story goes, the Israelites were impatient for the return of their leader Moses from Mount Sinai after he ascended to receive the Torah from God. They felt he was tarrying too long. The Torah describes this impatience as the cause of the Israelites’ unrest, which ultimately resulted in their demand for a Golden Calf.
Descending from Mount Sinai, Moses witnessed the Israelites worshipping their Golden Calf. He became enraged and hurled the Ten Commandments, which he had just received from God, down to the ground. The stone tablets shattered into fragments. God then told Moses that he intended to destroy all of the Israelites (Exodus 32):
10 Now therefore let Me alone, that My wrath may wax hot against them, and that I may consume them; and I will make of thee a great nation.’
It was only upon Moses pleading with Him that God finally relented:
יד וַיִּנָּחֶם, יְהוָה, עַל-הָרָעָה, אֲשֶׁר דִּבֶּר לַעֲשׂוֹת לְעַמּוֹ.
14 And the LORD relented on the evil which He said He would do unto His people.
In fact, the Torah does not even suggest that God forgave the people for their impatience and lack of faith. Rather, it was Moses’ beseechment that moved Him, and the prophet’s plea to the Master of the Universe appealed only to A) God’s concern with His own reputation, and B) The promises He’d made to the patriarchs Abraham, Isaac, and Israel (Jacob).
One can only imagine how differently the Jewish story might have unfolded if the Israelite people had exhibited faith in God and His chosen messenger.
Verses on wisdom
Beyond the above “big picture” examples, the TaNaKh, as one would expect, is very direct about the virtue of patience. Such verses include the following:
29 [He who has] long patience is of great understanding; but [he that is] hasty of spirit exalteth folly.
לב טוֹב אֶרֶךְ אַפַּיִם, מִגִּבּוֹר; וּמֹשֵׁל בְּרוּחוֹ, מִלֹּכֵד עִיר.
32 [He who has] long patience is better than a hero; and [better] he that ruleth his spirit than he that taketh a city.
These three verses speak to my point so I won’t belabor it any further, but a cursory review of Jewish source texts reveals others as well.
Patience… with myself
If I were to list my most self-destructive traits, impatience would rank in my Top 5. As much as I am drafting this ethical will of mine piece by piece for my daughter and future children, I find that it is also helpful to me to collect my thoughts and do some much needed introspection and self-work.
Coming from a traditional Jewish context, writing about patience is almost too easy because it stands out as a primary theme that is splattered all over the scored and stitched leather sheets of our Torah scrolls.
In this vein, I’ve been encountering a personal conflict in compiling my ethical will… some principles and values are so self-evident to me that I hesitate to write about them at all. Do I really need, I have asked myself, to write posts about being kind, being appreciative, being generous, etc.? Shouldn’t we naturally appreciate the truth and fundamentality of these values?
It seems to me that I must work on being more patient with myself.
‘We are teachers to our grandchildren’, a d’Verse prompt
He was supposed to teachher math and now
he fucking won't because he's ~
We? What 'We'? Is this the
'We who take being alive
for granted' or
'We who are not to live again
salute you - No - justkidding! We're ~
He was supposed to teach her math!
He was supposed to
be here. Today.
He was supposed to
wish me a happy birthday.
He was not
to be ~
I grew a longer beard after Papa
is a Jewish
mourning tradition, you know
And it makes me look
(Good - because I am!)
I have some white
hairs in it; some day
they will all be white
and I hope
buried that way
when I am ~
Don't tell me that Papa
is teaching her
through me. He's not.
He's not teaching
he's not teaching
anything -because he's fucking ~
It's my birthday and -
The tall blonde’s thin cotton skirt swished as she walked by the loquat trees not far from the edge of the sidewalk. Behind her the sun continued its descent towards the distant Mediterranean, its beams piercing through the branches. The Star of David hanging from the her tanned neck sparkled.
Osnat trained her lens upon the Star of David, noting the small beads of sweat glistening on the young woman’s bronze skin. She seemed a wistful beauty, a perfect subject for Osnat’s new sunset photo series. Zooming in and out as the blonde glided around the corner, the older woman let her camera do the work, capturing the pinks and purples of the sky behind the young lady as she made her way to the nearby Jerusalem bus stop. Yosef would have so appreciated the girl’s air of pensiveness…
The middle aged woman traced the camera’s edges with her fingers, remembering how her husband had once held his beloved instrument, one hand under the lens, the other steadily gripping it along the side. In the years before his death, Yosef had taken such pride and pleasure in his hobby, presenting his work at local fairs and framing his favorites for friends and family. In those later years, he was hardly ever without his camera, always looking for graceful birds in flight or unsuspecting children at play. His photography still remained, lining the walls of their house.
After Yosef’s abrupt death, Osnat had taken to emptying out his bedroom and office, unable to gaze at his bookshelves and assorted tchotchkes without sobbing. It was thus she came upon his camera equipment in the office closet. At first, she couldn’t bear look at it, but as the weeks had gradually turned into months, Osnat eventually found herself laying Yosef’s many camera lenses, tripods, flashes and more out on her husband’s bare desk. The bird photographs on the walls looked at her.
It was then that Osnat had decided to teach herself photography. Their son Ephie’s daily kaddish recitation for his father at shul brought her great comfort, knowing that Yosef would have expected and wanted that traditional honor, but she, as a woman, felt out of place among the stern, bearded prayer-goers. Osnat would honor Yosef’s memory through the lens of his own camera.
* * *
Mincha, the afternoon prayer, ended with the recitation of the mourner’s kaddish, which Ephie always stood for. Even after he’d completed his year of kaddish, the young man had continued coming to shul, just as his father had done before him. Ephraim wasn’t much of a believer, but he respected those who somehow managed to find and hold on to faith, including his Abba who had continued attending services long after he’d completed his year of mourning for his father.
He glanced out the window at the sky as its pinks and oranges darkened to purples. Eema was probably out with her camera somewhere, looking for new subjects to capture for her new Jerusalem Sunset series. He knew that she didn’t feel entirely comfortable at shul because of its male-centeredness, which bothered him also. That’s why she’d been so glad that he’d been the one to recite kaddish for Abba.
Of course, some ladies did occasionally come to services to recite kaddish for their parents from the women’s section in the back, but they were hard to see, seated behind the deliberately tall latticed mechitza that separated them from the men’s section. Also, many were self-conscious about their secondary role in the gendered public prayer space and didn’t recite their kaddishes loudly enough for the men to hear them and respond. They were largely unheard and invisible.
Since completing his own year of kaddish, Ephie had come to feel very strongly, as Yosef had before him, about supporting other mourners in the community with a firm, resounding response to their kaddishes; and his seat happened to be in the back, just in front of the women’s section.
Conscientiously, the young man always made sure to time his response with the female mourners behind him: “Yehe shmeh rabba mevarakh leʻalam ulʻalme ʻalmaya!”
* * *
Osnat stood and stretched her legs as the young woman’s bus drove off.
Ephie would soon be praying ma’ariv, the evening prayer service. His Abba’sshul had practically become a second home to him, ever since Yosef died. It pained her to see that the young man was still grieving so deeply, but he had to know that no amount of kaddishes would ever bring Abba back. “At some point,”she sighed, “we all have to start living again.” The old men at shul were undoubtedly kind souls, but how would Ephie ever meet a young lady if he couldn’t leave the past behind him?
Quietly, Osnat turned in the direction of the Old City, seeing the Western Wall in her mind. “Hashem, I’m not a religious woman, but surely You know my heart. Please – help my Ephie heal… it’s already been four years since his Abba died. Please – help my baby move on from his Abba’s death. Please. Please, my Lord. Help him.”
* * *
The young man completed his prayers and glanced around the sanctuary. Were there any mourners present to recite the kaddish? No, it seemed not, he thought sadly. Ephie always felt a sense of incompleteness when no mourners were available to recite the kaddish after services. Somehow, he felt that tradition had actually intended people’s personal kaddishes for the entire community, including the souls of Abba and Saba.
Suddenly, the sound of a door swinging at the back of the women’s section caught his attention, and Ephie made out the sound of somebody walking quickly, nearly running, towards the mechitza. Through the latticework, he could barely make out a female worshipper and heard her clear her throat nervously. Softly, she began reciting the kaddish, muffled through her tears.
None of the other men had noticed the woman’s entrance, and they were too far away to hear her… the necessary prayer quorum was already dispersing!
Ephie stood in place, seriously, deliberately, and intoned his response loudly for all the rest to hear: “Yehe shmeh rabba mevarakh leʻalam ulʻalme ʻalmaya!” The elderly petitioners stopped and looked around the room, trying to figure out whom Ephie was responding to. Through the stillness, they finally heard the woman’s kaddish and crying. Collectively, the men moved closer towards the mechitza to better hear her kaddish.
“B’rich hu,” they responded together, and then: “Amen; Amen!”
The mourner completed her recitation, and the men smiled at Ephie as they threw on their jackets and headed for the exit. The sexton patted Ephie on his shoulder; “Tzaddik,” he whispered.
Ephraim shrugged shyly and returned his siddur to the bookshelf, before reaching for the light switch. As he made his way down the corridor, he heard a woman’s voice behind him: “Excuse me? Were you the one standing next to the mechitza?”
The young man turned to see a beautiful blonde with tear stained cheeks standing before him. “I’m Nechama,” she told him, “And I just wanted to say ‘thank you.’”
Did you know that according to traditional Jewish law, no rabbi is necessary for the performance of a Jewish wedding? That’s right: Jews don’t need rabbis to get married.
Okay, so what are the essentials?
The groom gives the bride something of at least a certain minimum value(usually a wedding ring that he puts onto his bride’s right index finger) and then makes a formulaic proclamation about her now being consecrated to him, all of which must be performed before two kosher witnesses;
A ketubah(wedding contract outlining the husband’s obligations to his wife) is signed by two kosher witnesses (not necessarily the same ones) prior to the wedding ceremony and then given to the bride during the ceremony.
Now, there are various ways to give honors to family and friends at a Jewish wedding, and I would say that no honor is considered greater than serving as one of these kosher witnesses. After all, it is they, rather than the officiating rabbi, whose roles are required by Jewish law.
Theoretically, if one of the kosher witnesses is revealed to be unkosher (not living up to certain religious standards) that would invalidate his testimony as a witness and render the wedding illegitimate.
Okay… so what?
Well, when my wife and I were planning our wedding, we really delved into the [religious] details of the ceremony and celebration.
We thought about how to strike a balance between Jewish tradition and feminism; how to ensure the comfort of our ultra-Orthodox wedding guests at our modern minded ceremony; how to make Jewish tradition accessible to our many secular friends and family members; whom to give which honors to…
My wife and I each assigned a witness to sign the ketubah and observe the ceremony beneath the chuppah (wedding canopy). Understanding the fundamental significance of these two kosher witnesses, and wanting our marital union to be religiously ironclad, each of us picked the most pious, God loving people that we knew. My wife picked the father of her adopted Israeli family, and I picked one of my Torah instructors, Rabbi Meir:
I starkly remember a rabbinic panel on prayer, held at the Pardes Institute. One devout rabbi (a teacher of mine whom I had specifically asked to sign our ketubah out of awe at the earnestness and intensity of his relationship with God) explained that he felt closer to God than he ever did to other people. He related that he would pour his heart out to God in prayer every single day in a way that he couldn’t with others. Upon hearing this, a second rabbi shed tears before the other panelists and demanded, “How do you get that way?”
I hadn’t seen this rabbi in more than half a decade when I read that his wife had very unexpectedly died.
She was such a lovely woman; I had been to their home for Shabbat several times over the years and would also chance to speak with her every year at our community retreats. Truly, I cannot say enough good things about her; she was incredibly humble and gentle. While both had been born only children, together they raised a gorgeous family of nine in Israel.
Nobody expected her death.
Malka had led an active life and suddenly she found that walking up the stairs was presenting a challenge… The doctors were shocked, given her healthy lifestyle and outward appearance, that she needed to undergo triple bypass surgery. Over the course of several days following that surgery, Malka fought and then faded. And then- she was gone.
Visiting the rabbi
In Jewish tradition, mourners accept guests to comfort them for seven days following the funeral. These seven days are called the ‘shiva’, which is derived from the Hebrew word ‘sheva’, meaning ‘seven’.
Based upon my own experience as a mourner, it has become very meaningful to me to show support for others in mourning, particularly those who are dear to me. Thankfully, a friend [with a car] who had also studied with Rabbi Meir proposed that we visit him at the shiva together.
Beyond wanting to show my support to my teacher, I was curious to see how a man of iron faith such as Rabbi Meir might deal with the unexpected death of his wife of fifty years. He spoke of Malka and shed tears before his visitors (something I had never imagined I’d see him do); and, somehow, through it all, he continued to exude that deep grace and dignity, which he is known for. He was shattered, but his faith in God remained unassailable.
Rabbi Meir shared that he had just retired after more than forty years of teaching Torah, and they had been discussing how they would spend their years together after the COVID-19 insanity settled down. Malka died very shortly after his retirement.
Split screen in my mind
Writing about Papa is difficult for me, but perhaps writing about Mama is even more so because she is alive. After all, Papa doesn’t have to live with the consequences of what I write about him.
My parents had been planning on selling their home (the house where my younger brother grew up) and moving to North Carolina. With him permanently out of the house and me far across the ocean, they no longer needed their large house. They hadn’t found a buyer for the house yet, but that was their goal.
I was rocked by Papa’s death, but I didn’t have to physically face its reality on a daily basis if I didn’t want to. After all, I was still living with my wife and daughter far away in Israel and working at the same job. That surreality of returning to “normal” was, in large part, what prompted me to recite kaddish for Papa every day, as well as to pursue my Skeptic’s Kaddish writing project during my year of mourning.
For Mama, everything changed dramatically. Where would she live? What would she do with the rest of her life? Whom would she do it with? Clearly, she still had to sell her too large house, but then– what?
That was another reason why I started blogging about my mourning experience – I wanted to feel closer to Mama and Eli, and I aspired to helping them feel closer to me, despite the more than ~9,000 kilometers between us.
As I sat at that shiva several weeks ago, listening to my dear teacher crying over the unexpected and sudden loss of his beloved wife Malka, part of my mind found itself with Mama on the other side of the Atlantic Ocean…
no doors in walls to Keep out fear
just: Look and See, but no walls there...
once structures, now Convulsing lines
there's Is, there's Was, less timeless rhymes
no what, no I, but only Am
Am Flail for textures; Whisper, "damn..."
unbearable, Am's Feels Are Galled
Walled in, Crawling, no space at all!
nouns swiftly Twisting into verbs
Think straight! no theater left to Be absurd
Am Think, Think Knows, and on it Goes...
and then: Am Start. "Do Are Suppose?"
Are Could Aid Am by Opening...
the... the... constantly Creaking th...ing?
Are Know... what... Am... Am Trying to Say...
dear, Grab the Turns and Pull that... way...
Hope Looks; Look Sees; See Steps; Step Lands-
Am find myself in Are's... dear hands?
hands warm... Hands firm, Hands' Form confirms
Convulsions slow; Walls' Lines conform...
are... You... am I... I... feared I'd die
before I... held You one last Time...
I... want... to say... I've come to see...
That... You and I... We'll al...ways... be...
One of the things that I reflected upon after Papa died was a series of coincidences that preceded his death. In November 2018, I wrote the following (emphasis mine):
I’m not one to assign meanings to coincidences, but the timing of particular events before my father’s death was uncanny. In no particular order:
⦿My father completed the manuscript for his first (and ultimately only) book, which will be published in 2019.
⦿My daughter awoke two days before he died, thinking that Dedushka Shurik was with her in the apartment. My wife explained that it was a dream, and she tried calling my father in America so that our little girl could speak with her grandfather, but he had already gone to bed. Learning of this, my father glowed with love and pride for what turned out be his final two days in this world, telling everybody that he spoke with that his granddaughter had dreamed of him.
⦿My brother, who had been living away from home that summer, returned to live with my parents due to problems with campus housing. He was present at the hospital when our father passed away.
⦿ On the night before he passed away, my father, usually averse to crowds and parties, decided to go with my brother and mother to a friend’s home on the shore to watch a brilliant, beautiful fireworks display. It was the last thing he would see before waking up with shortness of breath the following morning.
⦿Several days before my father died, and after three years of soulful struggling with being unable to pray, I had begun praying again privately in my home. I had no inkling that I would soon be reciting kaddish every day for my father, but my gates of prayer had already been unbolted when the time came; I didn’t feel forced into prayer by kaddish.
Well, it is now nearly 2021, almost 2½ years after Papa died, and his book has finally been published. I am very proud of my father for completing this intensive project and very thankful to all of the brilliant people who took his work all the way to publication following his death.
Foremost among those who I am thankful for is my father’s friend Nassim Nicholas Taleb, of Black Swan fame. It was he who encouraged my father to write a book, and it was he who suggested a subject. Dr. Taleb was very fond of my father, and he offered to write a foreword for the book, which, ultimately, he penned after Papa had died.
Foreword for Cut the Knot: Probability Riddles by Alexander B.
How do you learn a language? There are two routes; the first is to memorize imperfect verbs, grammatical rules, future vs. past tenses, recite boring context-free sentences, and pass an exam. The second approach consists in going to a bar, struggling a little bit and, out of the need to blend-in and integrate with a fun group of people, then suddenly find yourself able to communicate. In other words, by playing, by being alive as a human being. I personally have never seen anyone learn to speak a language properly by the first route. Also, I have never seen anyone fail to do so by the second one.
It is a not well-known fact that mathematics can also be learned by playing –just watch the private correspondence, discussions and pranks of the members of the august Bourbaki circle. Some of us (and it includes this author) do not perform well on tasks via “cold” approaches, unable to muster the motivation to do boring things. But, somehow we upregulate when stimulated or when there is play (or money) involved. This may disturb many people married to cookie-cutter pedagogical methods that require things to be drab, boring, and bureaucratic for them to be effective –but that’s reality.
It is thanks to Maestro Alexander B. that numerous people have learned mathematics by the second route, by playing, just for the sake of entertainment. He helped many to make it their hobby. His mathematical website cut-the-knot has trained a generation –many seemingly approached the problem as hobbyists then got stuck with it. For, if you liked mathematics just a little bit, Maestro Bogomolny made it impossible for you to not love it. Mathematics was turned into a frolic.
I discovered his riddles on social media. (Alexander B. does not like the word “problems”. I now understand why.)
* * *
Social media brings out the best and the worst in people. He was rigorous yet open-minded, allowing people like me (who did some mathematical economics and finance) to cheat with inequalities by using the various canned methods for finding minima and maxima. He even tolerated computerized mathematics, provided of course there was some rigor in the process. I initially knew nothing about him but could observe rare attributes: an extraordinary amount of patience and a remarkable sense of humor. One summer, as he was in Israel, I informed him that I was vacationing in Lebanon. His answer: “Walking distance”. He always had a short comment that makes you smile, not laugh, which is a social art.
Alexander B. created a vibrant community around his Twitter account. He would pose a question, collect answers and patiently explain to people where they were wrong.
I, for myself, started almost every day with a puzzle, with the excitement of unpredictability, as it took from 5 minutes to 4 hours to complete –and it was usually impossible to tell from the outset. For a couple of years, it was the first thing I looked at with the morning coffee. There was some mild competition, mild enough to be entertaining but not too intense to resemble an academic rat race. Once someone got a proof, we had to look for another approach so it paid to wake up early and beat those with a time zone advantage.
In the two years since he left us there has been no Saturday morning –104 of them –that I did not solve a riddle randomly selected on the web in his memory. But, without him, it is not the same.
* * *
How did Alexander Bogomolny get there?
I met him in an Italian restaurant in New Jersey. I was surprised to see a mathematician who looked much more like a maturing actor than someone in a technical specialty: tall, athletic, jovial, and with a charismatic presence. But, as he had warned me, he had a severe hearing problem, the result of a medical treatment for the flu.
This explained to me his veering away from an academic career to get involved in computer pedagogy. His hearing was worsening with time. It is hard to imagine being a professor with reduced auditory function in one ear (in spite of a hearing aid) and none in the other.
There was something fresh and entertaining about him. He was happy. One could talk and laugh with him without much communication.
He was neither interested in money nor rank –something refreshing as I was only exposed to academics who whether they admit it or not, are obsessed with both. When I asked him about commercializing his website cut-the-knot his answer was “I have two pensions. Next year I turn seventy”. He wasn’t interested in poisoning his life for more money.
Why did I start nicknaming him Maestro? Because it was pretty much literal: he played math like a master would with a musical instrument –and mostly to himself. He was physically bothered by a sloppy derivation or an error, as if he heard a jarring note in the middle of a sonata. It was a joy to see someone so much in sync with his subject matter –and totally uncorrupted by the academic system.
* * *
Now, probability. In one conversation, I mentioned to him that probability riddles would be very useful for people who want to get into the most scientifically applicable scientific subject in the world (my very, very biased opinion). What I said earlier about play is even more applicable to probability, a field that really started with gamblers, used by traders and adventurers, and perfected by finance and insurance mathematicians. Probability applies to all empirical fields: gambling, finance, medicine, engineering, social science, risk, linguistics, genetics, car accidents. Let’s play with it by adding to his feed some probability riddles.
His eyes lit up. Hence this book.
* * *
I thank Marcos Careira, Amit Itagi, Mike Lawler, Salil Mehta, and numerous others who supported us in this project.
And a special gratitude to Stephen Wolfram, Jeremy Sykes and Mads Bahrami for ensuring that Cut-the-Knot stays alive and that this book sees the day. Additional thanks to Paige Bremmer, Glenn Schloebo, and other members of Wolfram Media for editing the manuscript.
Cut the Knot: Probability Riddles, by Alexander Bogomolny, published by Wolfram Research in collaboration with STEM Academic Press, $19.95. On Amazon.