Infinitely-sided dice produce a surprising result.
Here’s the challenge. You have three infinitely-sided dice. When you roll one of these dice, you get a Real Number between0and1. So when you roll three of these dice, you get a Real Number between0and3.Capish?
Here’s the question. You roll the three dice. You square the outcome of each die.
What are the odds that the sum of the three squares will be less than or equal to 1?
These examples should clarify:
In the first example, we roll 0.98, 0.35 and 0.72. (We’ll stick to rational numbers to keep things clean.) The sum of the squares (0.98²+0.35²+0.72² =1.6013) is greater than 1, so this is a fail.
In the second example, we roll 0.89, 0.21 and 0.37. The sum of the squares (0.89²+0.21²+0.37² =0.9731) is less than 1, so this is a win.
Now, roll those magical mathematically perfect dice. How likely are you to win?
So you don’t accidently scroll down and see a spoiler, I will place this photo of my cat here.
Solution
Represent the space of possible outcomes within a 3-D cube.
Each point in this 3-D space takes the outcome of the dice as its x, y, z coordinates. Point A is (0.89, 0.21, 0.37). Point B is (0.98, 0.35, 0.72).
Now, let us include our condition: x²+y²+z²≤1.
Our condition — that the sums of the squares be less than 1 — gives us the set of points on the surface of, or contained within, a sphere of radius 1.
We can reframe our question as follows.
Given a random point within a 1×1×1 cube, what is the probability that it will fall within a sphere of radius 1, with a centre at one of the cube’s corners?
We need the volume of that chunk (an eight) of the sphere, and the volume of the cube. Divide one by the other, and we’re done.
The odds are slightly in favour of the result being less than 1.
Isn’t it awesome that those infinitely-sided dice — which would each be spherical — produce πin this way?
Edgar A. Poe landed in Philadelphia in 1838. He had been raised among the elite of Richmond, Virginia, but in Philadelphia he was an impoverished outsider seeking recognition and stability as a professional writer. Strikingly, Poe’s first publication in Philadelphia—and the one that sold the most in his lifetime—was a scientific textbook.
When Poe arrived with his teenage wife (and first cousin) Virginia Clemm and her mother Maria, they were “literally suffering for want of food,” living on “bread and molasses for weeks together.” Poe’s friend James Pedder, well situated at a sugar manufacturer’s, purifying the raw goods delivered from Caribbean slave islands, came to their aid; his daughters, Bessie and Anna, visited with gifts for “Sissy” and “Muddy.” Pedder was also editor of The Farmers’ Cabinet, publicizing techniques for improving soils and raising crops—the kind of practical, commercially oriented publication in which much of the era’s natural science was reported and discussed. Pedder had studied the beet industry in France and was scheming to introduce beet sugar to the States.
Pedder helped Poe find odd jobs. His old friends in Baltimore, Nathan Brooks and Joseph Snodgrass, published his occasional pieces in The AmericanMuseum of Science, Literature, and the Arts. Hoping for a government post, in July 1838 Poe wrote to the novelist James Kirke Paulding, who had become Van Buren’s secretary of the navy; he longed to “obtain the most unimportant Clerkship in your gift—anything, by sea or land.” No luck.
By September 1838 the Poes had moved to a small house on Locust Street, with a garden suitable for the pet fawn that a friend offered as a gift for Virginia: “She desires me to thank you with all her heart—but, unhappily, I can not point out a mode of conveyance.” He had to content himself with imagining “the little fellow … already nibbling the grass before our windows.” Pedder offered a more useful gift: an introduction to a natural historian in need of a writer’s help.
Thomas Wyatt, a lecturer and schoolteacher based in Delaware, had published a large textbook on conchology—the classification of shells—with Harper & Brothers. Wyatt’s textbook relied on previous works by the French biologists Lamarck and Blainville. He also received assistance from Isaac Lea, the Philadelphia publisher and naturalist.
In the 1830s, geology was one of the most hotly pursued branches of science, not least because of the growing industrial importance of coal. Geology and conchology were closely linked: Knowing which shells and rocks went together made it possible to line up geological strata as successive chapters of the long history of the Earth. Lea, whose passion for natural science was stoked by his friendship with the geologist Lardner Vanuxem, wrote that geology and conchology, “its sister science,” revealed “objects of the highest importance, a thorough knowledge of our cosmogony,” or the origin of the universe. In a more radical vein, the poet and naturalist Erasmus Darwin had taken for his family’s emblem the phrase e conchis omnia—“Everything From Shells.”
Lea’s eyes were opened to the wonder of creation when he first examined a crate of shells from China and Ohio: He “did not know what it was to live on God’s earth before.” Lea published “Description of Six New Species of the Genus Unio”—shells of freshwater mussels—for the American Philosophical Society and became, along with Samuel Morton, a leading light of Philadelphia’s Academy of Natural Sciences, founded in 1812 as a less formal, more inclusive scientific society than the patrician American Philosophical Society.
In 1832, like many Americans of his generation pursuing scientific topics in depth, Lea took a tour of Europe. In Paris, Lea was given access to the library of the legendary naturalist Georges Cuvier; he acquired part of Jean Baptiste Lamarck’s shell collection and met the anatomists of the Jardin des Plantes, who reclassified the museum’s Unio shells according to Lea’s system. On his return Lea published a large folio with full-color prints, Observations on theGenus Unio.
Thomas Wyatt built on Lea’s classifications in his conchology textbook, merging them with others to form a more comprehensive overview of all known shells. Yet as Wyatt gave lectures on the lyceum circuit, his book proved too large and expensive for his listeners, many of them women and children. He needed a handier, more affordable volume but could not publish a similar work without infuriating his publisher, the mighty Harper & Brothers, by undercutting their sales. He needed a new edition: shorter, cheaper, and signed under another author’s name.
Enter Poe, newly arrived and eager for work. Thanks to his work on his only novel, The Narrative of Arthur Gordon Pym of Nantucket and reviews he had written, Poe had a proven record on scientific topics. Fluent in French, he could work through the relevant volumes by Cuvier, Lamarck, Blainville, and naturalist Étienne Geoffroy Saint-Hilaire, all available for consultation in the Library Company on Locust Street—an august space overlooked by a giant bust of Athena.
Published in 1839, The Conchologist’s First Book by Edgar A. Poe was slim, portable, and inexpensive, with several plates of engraved shells. The preface and introduction were lifted from Wyatt’s book and from Thomas Brown’s Elements of Conchology, which openly acknowledged their own debts to French precursors. Though later wags accused Poe of plagiarism for this book, all “new” systems of natural history depended on earlier systems, which were in turn the product of an enormous collective and largely anonymous labor by observers, collectors, and taxonomists around the world. In his preface, Poe thanked Isaac Lea for his “valuable public labors” and for “private assistance” in preparing the book.
Poe introduced important improvements. The biologist Stephen Jay Gould pointed out the book’s “progressive, even innovative, arrangement of material.” Brown’s book had followed the order of description of Lamarck, presenting the shells descending from those taken as most advanced or perfect to the lower, more “primitive” types, but Poe adopted a more widely practiced convention, ascending from “lower” shells upward.
Poe’s subtitle, A System of Testaceous Malacology, announced a more significant advance. “Malacology,” taken from the Greek word for “soft,” is the study of small, soft creatures, while “testaceous” means having a shell. Previous works of conchology, Poe wrote, “appear to every person of science very essentially defective, inasmuch as the relations of the animal and shell, with their dependence upon each other, is a radically important consideration in the examination of either.” He saw “no good reason why a book upon Conchology (using the common term) may not be malacological.” Rather than a study of the ruins left by dead creatures, Poe described both shells and their squishy inhabitants, raising conchology “from artificial description to integrative biology.” Poe’s book was not just shorter and cheaper but more complete, with innovations that surpassed its predecessors.
Unlike Wyatt—but like Lea—Poe also included natural theological reflections: “To an upright and well regulated mind, there is no portion of the works of the Creator, coming within its cognizance, which will not afford material for attentive and pleasurable investigation.” He quoted the German naturalist Carl Bergmann, who wrote that shells are “medals of the Creation”—lasting records of God’s design.
The first edition sold out; a second, published the same year, added “more recently discovered American species,” noting that the work had been adopted by several schools. In three editions, the book sold more copies than any other Poe published in his lifetime. It brought him at least $50, putting food on the table. It also gave him a crucial contact with Isaac Lea, whose Philadelphia publishing house would print Poe’s first collection of stories. And the success of The Conchologist’s First Book gave him something to crow about as he put his skills up for sale.
In addition to his three poetry collections, at age 30 Poe was the author of two very different books: his playful, sensational, mysterious novel Pym, full of empirical detail and psychological insight but denounced as an “attempt at humbugging the public,” and The Conchologist’s First Book, a widely read scientific textbook, adding to the best established research of the day, extending a rational classification over a significant domain of nature.
In Philadelphia, a vast public hunger for entertaining novelties was matched by projects to standardize knowledge and ban the speculations of quacks. Standing at the intersection of these two currents, Poe would be right at home.
Jordan Peterson and the Tragic Story of the Man-Child
What women despise in men
Canadian psychologist Jordan Peterson made a recommendation for the best documentary he’s ever watched. This was the documentary “Crumb.”
I don’t know if it’s the best — but it’s certainly the most unforgettable.
It tells the story of a successful cartoonist named Robert Crumb, who escaped his mother’s obsessive oedipal control that consumes both his brothers' lives.
Crumb’s brother Charles lives at home obsessing over his high school yearbook, masturbating four to five times a week, and admits to his brother that he can’t get an erection anymore.
Charles killed himself shortly after the documentary was filmed. The final cut reveals that bit of information for the audience at the end. It’s horrifying.
Crumb” came out in 1995, but its message has multiplied. Men are children, and it’s killing us.
Today’s men can barely ask out a girl let alone work at a competent enough job to move out of their parent’s basement. I’d be remiss, however, not to point out that the oppressive arm of neo-feminism and post-modernism certainly doesn’t help.
Regardless, Peterson took me down this road, and now I wanted to see what women on internet forums like Reddit, Quora and YouTube had to say about man-children. Here are some things to avoid, men —
Strings attached to everything and unwritten contracts
I have a friend like this. He’s a man-child.
He’ll make arrangements with you in his head and never disclose this information out loud. Once you’re in his web of deceit he’ll hold you accountable to these unfair imaginary standards.
Contrary to what Marx argues in the Communist Manifesto, everything isn’t about power. Life is about reciprocity. You don’t always have to be selfish and create social contracts that benefit you and you alone.
Man the fuck up and learn to speak out about what you want.
Owns various books on “get rich quick” schemes (or videos)
“The Secret” by Rhonda Byrne
“The Power of Positive Thinking” by Norman Vincent Peale
Man-children won’t read anything that demands too much time or attention. Man-children want total entertainment forever. They won’t wash their dishes or do laundry. And they enjoy bad junk food, video games 24/7 and YouTube videos with all-caps titles LIKE THIS!!
A disciplined man invests time in his future and doesn’t expect results on the first day.
Man-children often create the illusion of wit, competence, and hygiene but in reality are king of the lost boys, as Peter Pan was. They’re all talk with nothing of substance to do or say.
Moreover, they’re distracted by an illusion when a real woman is right in front of them. Peter Pan wasn’t interested in Wendy, he was distracted by Tinker Bell who represents male fantasy.
Tink is a stripper, prostitute, or porn. Take your pick.
A liberal arts degree turns men into Peter Pans. They make little over minimum wage, accumulate loads of debt, and like to talk as though they can solve the world’s problems; yet they still live at home.
Always remain humble or you’ll become king of the lost boys.
The Man-Child talks a lot about what they want but never puts in any effort
“Man cannot discover new oceans unless he has the courage to lose sight of the shore.” — Andre Gide, Nobel Prize winning author
Man-children don’t like to fail. They’d rather do nothing than try. Failure is a major blow to their ego — which was of course bolstered by their worthless liberal arts degree.
They’ll talk talk talk until they’re blue in the face. Likely what they say, however, will contradict itself or parrot someone from a video they heard online.
Like a California forest, they’re full of deadwood.
Decorates apartment with scantly clad models and/or Scarface movie posters
I’m no interior decorator myself, but there are certain standards to what goes inside my apartment. There are no —
Iron words with cliche motivational sayings (Live, Love, Laugh)
Excessive pop art (with the exception of this Andy Warhol)
Scarface posters, nude girl pics, sports paraphernalia or anything else that belongs in a douchey frathouse
If you’re not good at decorating then consider living like a minimalist. It’s your life and personality, but Jesus get some fucking taste.
“I can’t exercise, I ran a mile once and it didn’t do anything.”
Navy Seal David Goggins is the master of overcoming your inner-bitch.
Here’s an exercise he created: record yourself the next time you don’t want to do a few push-ups or go for a short walk and/or run. Record all the thoughts inside your head and hear them played back to you.
You’ll hear how much of a bitch you sound like.
It’s only 20 minutes to an hour of light exercise; less than 1% of your day. You can do it. Stop bitching.
“I can’t ask out a girl, I got rejected once and it hurts bad.”
Girls can be a guys’ greatest fear. I’ve seen this before too.
It’s normal to have anxiety over a woman you’re attracted to, but being paralyzed with fear is classic man-child behavior.
The worst that can happen is you get rejected and move on from your life. It’s very unlikely, however, that you’ll find any worthwhile woman by saying nothing and going home to jerk off.
Stop looking at porn and delete your Tinder. Dating apps are saturated with Onlyfans girls now anyway.
You don’t even have to meet women solely at bars. Go to a farmers market, a park, fuck it, go to church and you’ll meet deeply interesting down to Earth women. You’ll find a keeper.
Punches inanimate objects when mad
You look like a moron and are most likely a closeted sociopath.
Let your anger and energy out on something productive. Go to the gym. Ride a bike. Get some form of exercise on a weekly basis. Your body will thank you later.
As literary critic William Hazlitt once said, “it’s better to have a weak mind in a sound body than a sound mind and a weak body.”
Seriously — stop punching inanimate objects.
They’re always broke to pay for rent, but have money for weed and/or video games
Hedonism will always be your greatest regret in life.
You ate like shit, destroyed your lungs with vapes and weed, never worked out, always had your mom do things for you, never read a book past the age of 20, and never invested your money wisely. Fuck, what a life.
Once people find out who you really are — a man-child loser — they won’t want to hang around you anymore.
Flipping out over menstrual cycles
Maybe it’s because I grew up with sisters but this always seemed like a pathetic thing to complain about.
Women are different. Get over it.
The fact they have to deal with monthly pain and we actually don’t hear about it more is honestly shocking to me.
Dostoyevsky once said that if you looked hard enough you’d find that every woman is interesting in some form or fashion, but the same cannot be said about men. I agree. Especially when it comes to man-children.
Destroys controllers when they lose a video game
I’ve seen this firsthand and it’s so pathetic that everyone who even watched feels shamed.
I get it. Michael Jordan raged when he lost. Tom Brady rages when he loses. Hungrybox (the number one smash player) rages when he loses. But you’re none of them. You’re not a pro. You’re probably not even that good in the first place.
Even so, those celebrities are often shamed too for being divas
Sure, take the game seriously. Blood sweat and tears and all that good stuff. But if you enact real-world violence after losing a video game — you need help.
All of this isn’t to say that your story has to end with you as a man-child.
But the day you decide to change yourself will be the most painful one of your life. Making a change at 30 is fucking brutal. Making a change at 40 or 50 is something like the suffering Jesus experienced on the cross.
Either way, you will suffer whether you want to or not.
The ones who choose to suffer willingly and choose discipline are men. The ones who push it off are man-children.