CLOSE

Super Mario World + Quantum Physics = Lots of Fun

I have a soft spot for Super Mario Brothers videos, and am particularly intrigued by a series of hacked versions of various Mario games that have hit the net in the past few years. In these hacked versions, the levels have been rearranged to make them more difficult, requiring players to repeat levels over and over to figure out the way past each little section. Videos appear on YouTube showing supergamers running through the hacked levels, performing seemingly impossible feats of timing and precision -- but also dying a lot.

An anonymous blogger/gamer wanted to take this to the next level -- he wanted to make a video of one level of Kaizo Mario World (which he describes as "the most evil Super Mario World hack ever") showing all his mistakes, but without all that time to reload and restart the level after each death. He had to hack his Super Nintendo emulator to support his goal, and the results are bizarre and wonderful -- from one Mario come many Marios, but only one Mario survives. Just watch it:

After the jump, we'll hear a bit about how this video illustrates some principles of quantum physics.

The anonymous blogger/gamer explains:

...tiny quantum events can create ripples that have big effects on non-quantum systems. One good example of this is the Quantum Suicide “experiment” that some proponents of the Many-Worlds Interpretation claim (I think jokingly) could actually be used to test the MWI. The way it works is, you basically run the Schrödinger’s Cat thought experiment on yourself– you set up an apparatus whereby an atom has a 50% chance of decaying each second, and there’s a detector which waits for the atom to decay. When the detector goes off, it triggers a gun, which shoots you in the head and kills you. So all you have to do is set up this experiment, and sit in front of it for awhile. If after sixty seconds you find you are still alive, then the many-worlds interpretation is true, because there is only about a one in 1018 chance of surviving in front of the Quantum Suicide machine for a full minute, so the only plausible explanation for your survival is that the MWI is true and you just happen to be the one universe where the atom’s 50% chance of decay turned up “no” sixty times in a row. Now, given, in order to do this, you had to create about 1018 universes where the Quantum Suicide machine did kill you, or copies of you, and your one surviving consciousness doesn’t have any way of telling the people in the other 1018 universes that you survived and MWI is true. This is, of course, roughly as silly as the thing about there being a universe where all the atoms in your heart randomly decided to tunnel out of your body.

But, we can kind of think of the multi-playthrough Kaizo Mario World video as a silly, sci-fi style demonstration of the Quantum Suicide experiment. At each moment of the playthrough there’s a lot of different things Mario could have done, and almost all of them lead to horrible death. The anthropic principle, in the form of the emulator’s save/restore feature, postselects for the possibilities where Mario actually survives and ensures that although a lot of possible paths have to get discarded, the camera remains fixed on the one path where after one minute and fifty-six seconds some observer still exists.

By the way, if said anonymous blogger/gamer wants to reveal him or herself to the world, please leave a comment!

(Via Kottke.org.)

nextArticle.image_alt|e
iStock
arrow
fun
If You Can Solve This Math Puzzle, You Might Be a Genius
iStock
iStock

by Reader's Digest Editors

Do you think of yourself as a secret mathematician? This math brainteaser has even the biggest number nerds scratching their heads.

People’s Daily, China tweeted out this math puzzle in which each picture represents a number.

These algebra problems might seem easy at first glance, but hold on. People’s Daily was nice enough to give away the answer before you began. If you didn’t get 16, you did something wrong. Take a closer look at the pictures—you probably missed a few key details.

Still stumped? We’ll walk you through it. For the sake of the explanation, we’ll call the shoes S, the cat C, and the whistle W.

The first equation sets up the whole math puzzle. Three pairs of shoes added together equal thirty. S + S + S = 30, so divide 30 by three. Each pair of sneakers represents the number 10. Easy enough.

 
See Also...

The Town Located at the Center of North America Has the Absolute Perfect Name
*
Take a Sneak Peek Inside Largest Starbucks Store in the World
*
Why Airlines Don't Tell You How Long Flights Really Are
 

Now the second equation is clearer. Sub the shoes out for a 10, and you’ll find out 10 + C + C = 20. Subtract 10 from each side, so C + C = 10. Each cat must represent the number 5.

Look closely at the next equation before you jump into it. In the third equation, there are two whistles in each line, but the final one only has one whistle. So 5 + 2W + 2W = 13. If 4W = 8, then each whistle represents the number 2.

OK, so that clears up a bit of the next equation—until you plug the numbers in. Sub S + C x W for 10 + 5 x 2. Remember your order of operations? Multiply first, then add. So 10 + 10 = 20. What went wrong?

The key is in the cat’s clothes. In the second and third equations, the cat has a whistle around its neck—but not in the last one.

No need to go back and redo all your hard work. Just change the last equation to S + (C – W) x W. Now plug the numbers in: 10 + (5 – 2) x 2. Work your way through it. The equation goes to 10 + (3) x 2, then 10 + 6. Finally, you get 16—problem solved!

nextArticle.image_alt|e
Hulton Archive/Getty Images
arrow
science
6 Priceless Documents That Reveal Key Moments Early in Einstein's Career
Hulton Archive/Getty Images
Hulton Archive/Getty Images

You've probably seen it before on coffee mugs, crocheted pillows, or personal journals. It's one of Albert Einstein's most famous quotes: "I have no special talent, but am only passionately curious."

Einstein wrote this self-effacing description on March 11, 1952 in a letter—seen below—to his biographer Carl Seelig. (The original German: Ich habe keine besondere Begabung, sondern bin nur leidenschaftlich neugierig.) The letter is one of some 200 priceless documents of Einstein's that are held in the library archives at ETH Zurich, the university where the scientist got his undergraduate degree in 1900.

einstein letter to seelig 1952
ETH Zurich

As was directed in his will, Einstein's papers went to Hebrew University in Jerusalem, which holds tens of thousands of his documents. In conjunction with Caltech and Princeton University, Einstein's professional home for 20 years, Hebrew University has made some of these documents searchable (and some viewable) online.

The collection at ETH Zurich is composed of letters and postcards he wrote to friends and colleagues, which were either donated or acquired from private collections, along with university papers associated with his days as a student and teacher there. These papers give us an intimate look at some seminal moments of his famed life long before he became fixed in the public mind as a wild-haired genius.

Mental Floss got to see some of these documents firsthand at the ETH Zurich Library. They're almost never on display, but are kept in a vault under lock and key. You can, however, see much of the collection online.

We've chosen six documents to highlight. For insight about each, we spoke to Michael Gasser, the library's director of archives.

1. EINSTEIN GETS PERMISSION TO TAKE AN EXAM HE'S NOT QUALIFIED FOR … AND FAILS.

letter about einstein from hertog to maier
ETH Zurich

When Einstein was 16, his family moved from Munich, Germany to Milan, Italy to start a business, and he dropped out of school. "He was just living in Milan for a year," Gasser says. "He didn't go to school there, he studied at home."

He then decided he wanted to go to college at the Federal Polytechnic Institute in Zurich—now known as ETH Zurich. But he wasn't 18 and lacked a diploma; both were required by the university. A well-connected friend of the Einstein family, a banker named Gustav Maier, wrote a letter on his behalf to Albin Herzog, the university director, asking that Herzog let Einstein, whom Maier called a wunderkind, take the entrance exam anyway. His plea worked: In the September 25, 1985 reply to Maier, above, Herzog writes that despite his misgivings about a wunderkind, Einstein can take the exam.

Einstein picked up his pencil in October 1895—and failed. He did fine on the mathematics and natural sciences sections but was deemed "insufficient" on language and history. Back to high school Einstein went. He got his diploma a year later at a school in Aargau, near Zurich. There was one upside: While Einstein was still in high school, Friedrich Weber, a physics professor at the university, let Einstein attend his lectures.

2. EINSTEIN IS A NO-SHOW AT ONE OF HIS CLASSES … AND BOMBS IT.

einstein's failing grade
ETH Zurich

Einstein did eventually get into Polytechnic/ETH Zurich, attending from 1896–1900. He did not impress his professors. "He was a strong-headed student in the sense that he attended some courses and skipped others. He was interested in some subjects and fields—especially [theoretical] physics—that were not taught at ETH Zurich at the time. He preferred to read papers at home," Gasser says. "This is clearly reflected in the student file he has. In his third term, he got the worst mark he could get in Switzerland: a 1, for a course on practical physics, from Jean Pernet. He was reprimanded by the head of the school."

Who wrote that thick black 1, above, is a mystery; Gasser says it likely wasn't Pernet himself but someone in the registrar's office. But whoever marked the grade seems to have had strong feelings about it. "It does look like an angry 1," Gasser says. "It stands out. It's not something you find often in such files."

There's also a remark about Einstein's scholastic habits written in his student file that Gasser says is hard to translate, but it essentially accuses him of "laziness."

3. EINSTEIN GRADUATES … BUT ISN'T OFFERED A JOB.

einstein's failing grade
ETH Zurich

In Einstein's department, there were five students (above). Of the four who passed the final exams, Einstein had the lowest mark and was the only one who wasn't offered a job as an assistant teacher at ETH Zurich. The fifth student, and only woman, was his girlfriend (later wife) Mileva Maric, who failed.

When it came to cramming for tests, the diffident student Einstein often leaned on the meticulous notes kept by his classmate and close friend Marcel Grossman, who got the second highest exam score. After graduation, as Einstein struggled to find teaching work, Grossman, with the help of his father, hooked him up with a job as a clerk in the Swiss patent office in Bern in 1902. Grossman became a renowned mathematician. Einstein turned to his friend again when refining the math of one of his seminal works. "Grossman helped Einstein with some mathematical problems in the General Theory of Relativity," Gasser says.

Grossman died young, in 1936, after a slow and painful deterioration, likely from multiple sclerosis. "It was kind of a sad story," Gasser says. "Einstein kept in touch with some of his friends and former fellow students till the very end. He was a very loyal friend."

4. EINSTEIN PROPOSES "MODIFICATIONS" TO THE CURRENT THEORY OF SPACE-TIME … AND CALLS HIS FRIEND A "FROZEN WHALE."

einstein letter to harbicht
ETH Zurich

"This is probably the most famous letter in all of ETH Zurich," Gasser says. It dates to May 15, 1905, when Einstein was employed at the Swiss patent office but in his spare time was plugging away at "very high-level work," including his doctoral thesis for the University of Zurich (which he dedicated to his pal Grossman). This letter is to mathematician Conrad Habicht, a close friend with whom he'd formed a small group called Akademie Olympia that discussed physics and philosophy over food and drink, usually in Einstein's Bern apartment. In the letter, Einstein is in high spirits, teasing Habicht about missing him on Easter, asking for Habicht's dissertation, and mentioning that he is working on four papers.

"Dear Habicht,

"Such a solemn air of silence has descended between us that I almost feel as if I am committing a sacrilege when I break it now with some inconsequential babble. But is this not always the fate of the exalted ones of the world? So what are you up to, you frozen whale, you smoked, dried, canned piece of soul, or whatever else I would like to hurl at your head, filled as I am with 70% anger and 30% pity! You have only the latter 30% to thank for my not having sent you a can full of minced onions and garlic after you so cravenly did not show up at Easter.

"But why have you still not sent me your dissertation? Don’t you know that I am one of the 1.5 fellows who would read it with interest and pleasure, you wretched man? I promise you four papers in return. The first deals with radiation and the energy properties of light and is very revolutionary, as you will see if you send me your work first. The second paper is a determination of the true sizes of atoms …

"The third proves that bodies on the order of magnitude 1/1000 mm, suspended in liquids, must already perform an observable random motion that is produced by thermal motion. Such movement of suspended bodies has actually been observed by physiologists who call it Brownian molecular motion. The fourth paper is only a rough draft at this point, and is on the electrodynamics of moving bodies which employs a modification of the theory of space and time."

What Einstein so casually refers to as a "rough draft" featuring a "modification" of the theory of space and time we know by a different name: the Theory of Special Relativity. He also got his Ph.D. in 1905, which would go down in history as Einstein's annus mirabilis, or miracle year.

5. EINSTEIN BECOMES A PROFESSOR … BUT HE'S NOT REALLY INTO TEACHING.

classes einstein taught at ETH zurich
ETH Zurich

After 1905, Einstein became famous in his field virtually overnight, Gasser says. In 1909, the University of Zurich created a new professorship for theoretical physics, and Einstein was its inaugural professor. Other universities competed for him, including the German University of Prague.

Einstein was a good teacher. When his students at the University of Zurich learned that he was being lured away to Prague, they signed petitions to raise his salary, hoping to keep the rising star. "I think he had a good relationship with his students," Gasser says, but "he didn't want to invest much time in teaching."

After a couple years in Prague, he returned to Zurich in 1912 as a full professor at ETH. Above are some of the course offerings in the math and physics department for the winter term of 1912–1913. Einstein taught analytical mechanics, thermodynamics, and a seminar in physics. "It was seven hours per week," Gasser says. "That was a normal teaching load for the time."

But research remained his main interest. At the time he was working on the problem of gravitation; once again he collaborated with Grossman, now his fellow professor at ETH. This work would eventually play a role in his General Theory of Relativity.

When Berlin's Friedrich Wilhelm University offered him a professorship with no teaching obligations, Einstein couldn't resist, and in 1913 he left Zurich for Germany.

6. EINSTEIN WORKS OUT SOME EQUATIONS … AND MAKES SOME MISTAKES.

einstein letter to weyl 1916
ETH Zurich

In 1915, Einstein published The Formal Foundation of the General Theory of Relativity. One of its earliest and most enthusiastic proponents was a geometry professor and former colleague of Einstein's at ETH Zurich named Hermann Weyl, who sought to express the theory using mathematical formulas different from Einstein's. The letter above, dating to November 23, 1916, is Einstein's take on a lecture Weyl gave in which he proposed these other formulas. Einstein says his ideas are interesting and plays around with the equations. "He’s working out the math as he’s writing," Gasser says. "It’s very technical."

For us non-geniuses, one appeal of this letter lies not in its far-reaching intellect but in its scribbles and crossouts. It's consoling, somehow, to know that even Einstein made mistakes.

That notion wouldn't be lost on him, Gasser says: "He doesn’t describe himself as a solitary genius. He really believed in cooperation and was actively seeking help at some stages. He relied on excellent mathematicians, and this letter really illustrates this."

Two years later, in 1918, Weyl published his seminal work Raum, Zeit, Materie (Space, Time, Matter), which explained general relativity in more elegant mathematical terms than Einstein himself ever had. Einstein was greatly impressed. 

SECTIONS

arrow
LIVE SMARTER
More from mental floss studios