Every week in The Magnet I’ll write about tips I find useful, recommendations of things that interest me, what I've learned, interviews, recipes, quotations, and more. I’ll also i...
Every week in The Magnet I’ll write about tips I find useful, recommendations of things that interest me, what I've learned, interviews, recipes, quotations, and more. I’ll also i...
The Magnet 0003Confounding dice, forcing functions, pan-fried miso-encrusted tofu, a music broadcast for extraterrestrials, and more
Welcome to the third issue of The Magnet! A big thank you to everyone who has subscribed, especially when I’m just getting started. It means a lot.
If you’re a non-paying subscriber, this will be your final free full issue. After that, you’ll get occasional public posts but will miss out on a lot of exclusive subscriber content. If you like what you’ve seen so far, I hope you’ll subscribe to support the creation of this newsletter. You can get a yearly subscription to The Magnet at a 30% introductory rate by clicking the button below: MIND BOGGLERMy fascination with these confounding dice
Jack Vance’s Tales of the Dying Earth trilogy is set billions of years in the future when our sun is a red orb on the verge of blinking out. Earth’s few thousand remaining inhabitants practice different kinds of magic, including a “strange abstract lore” called “mathematics”:
Nontransitive dice feel like magic to me. I first heard mention of them in William Poundstone’s 2005 book Fortune’s Formula, where he recounted a 1968 meeting between Warren Buffet and the mathematician/hedge fund manager Edward O. Thorp:
That was all Poundstone had to say about them, but I was intrigued and looked them up. At first glance, nontransitive dice look like ordinary dice, but you can see how they are numbered differently:
What makes these dice special? Here’s a scenario that reveals their surprising property:
Show your friend three colored dice. Point out that they are not like regular dice.
Ask your friend to select a die. If they choose black, pick red. Roll the dice 20 or 30 times and keep score. You will win about ⅔ of the rolls.
Now give your friend a chance for a rematch. Your friend will probably ask for the red die since it beat the black die. Give it to them, and select the yellow die for yourself. You’ll win about 7/12 of the rolls.
There’s nothing remarkable about this so far. But what happens next is the part that “confounds most people's ideas about probability.”
Your friend will likely think, “If the red die beats the black die, and the yellow die beats the red die, then the yellow die must be the strongest die.” They will choose yellow and you’ll select the black die. And once again, you will win about 7/12 of the rolls.
Red beats black. Black beats yellow. Yellow beats red!
In fact, no matter which of the three dice your friend picks, you can always pick one that will beat it! It’s like playing Rock Paper Scissors and knowing in advance which one your friend will use. How can this be possible?
Take a look at the figure above. It shows the outcomes for all 36 possible rolls between each pair of dice. Red beats black 25 out of the 36 possibilities. Yellow beats red 21 out of 36. Black beats red 21 out of 36. Even though this figure explains why the dice behave as they do, they still feel like magic to me.
I made a 3D model of the dice and printed them on my 3D printer (they are in the photo at the top). You can also make your own using square craft cubes or order pre-made sets online.
Many different kinds of nontransitive dice have been invented over the years. Wikipedia has a good article describing them.
(Portions of this were adapted from my book, Maker Dad) NEWSLETTER HIGHLIGHTS
Every issue of the Lifehacker newsletter has at least one or two tips I find useful. The 13 Aug issue links to Claire Lower’s article about a versatile, cheap kitchen tool — a brick wrapped in foil:
Maker Mind is a weekly neuroscience-based newsletter about decision making, continuous learning, thinking, creativity, and productivity. The 20 Aug issue discusses the Planning Fallacy (the tendency to underestimate the time it takes to complete a project, even when you take the Planning Fallacy into account) and 5 ways to overcome it. The 5 ways include taking an outside view, defining your priorities, questioning your motivations, managing your time, and performing a pre-mortem:
Designer Jonathan Hey’s Sketchplanations explains one thing a week as simple hand-drawn sketches. Hey’s 20 Aug sketch explains “forcing functions,” which are design features that keep us from doing something wrong or dangerous:
RECIPEPan-fried miso-encrusted tofu
Over the past several months, I’ve been experimenting with ways to cook tofu. So far, everyone in the family likes my pan-fried miso-encrusted tofu recipe the best. But we don’t agree on one point — whether or not the tofu should be frozen and thawed in advance. Years ago I learned you can add a lot of chewiness and texture to a block of tofu if you freeze it for 24 hours, let it thaw, and gently squeeze out most of the water. I prefer it this way. My wife and daughter would rather eat this dish using unfrozen tofu. But either way I make it, everyone at the table eats every last crumb.
Ingredients:
Instructions:
Tofu retains heat for a long time so be careful when taking your first bite! LONGSHOTSJohn Shepard spent 30 years trying to contact aliens
After John Shepherd was abandoned as a child by his parents, he moved in with his grandparents in rural Michigan, converting their home into a laboratory for contacting aliens. For 30 years he DJ’d a nightly radio show for extraterrestrials, treating them to Afropop, jazz, and1970s German electronic music, transmitted into deep space using a wondrous assemblage of electronic equipment scavenged over decades. Shepherd is the subject of an engrossing 15-minute documentary by Matthew Killip, called “John Was Trying to Contact Aliens,” which won Sundance’s “Short Film Jury Award: Non-fiction” in 2020. The last few minutes of the film are a joyful surprise. Watch the trailer here.
QUOTE“It is as easy to deceive oneself without perceiving it as it is difficult to deceive others without their perceiving it.” — François duc de La Rochefoucauld, Maximes (1664) François VI, duc de La Rochefoucauld (1613-1680) was the most famous writer of maximes, defined by Britannica as a “French literary form of epigram that expresses a harsh or paradoxical truth with brevity.”
The Magnet is written and produced by Mark Frauenfelder and edited by Carla Sinclair. |