time trip on a mobius strip

January 16, 2021

The Timeless Journey of the Möbius Strip

After the disaster of 2020, let’s hope we’re not on a figurative one

By Serena Alagappan

Dimitri Otis Getty Images

If you were to trace both “sides” of a Möbius strip, you would never have to lift your finger. A single-sided surface with no boundaries, the strip is an artist’s reverie and a mathematician’s feat. A typical thought experiment to demonstrate how the three-dimensional strip operates involves imagining an ant on an adventure. Picture the insect traversing the Möbius band. One apparent loop would land the ant not where it started but upside down, only halfway through a full circuit. After two loops, the ant would be back at the beginning—but dizzy.

The figurative and narrative implications of the Möbius strip are rich : when you try to go forward, you ring sideways, when you try to circle in, you find yourself outside. It’s an apt allegory for losing control. We might ask ourselves after 2020, where are we? Have we spun around after so much chaos, and found our position stagnated, back where we started? Or are we at a new beginning?

The continuum of crossing a Möbius strip is emblematic of how we experience time in a nonlinear way. Artists and authors explore this phenomenon as well. One salient literary example is Gabriel García Márquez’s One Hundred Years of Solitude . Melding history, memory, and prophecy, the novel follows the Buendía family through cyclical patterns of behavior and emotion. An exchange between two family members illustrates this central theme: “Úrsula sighed. ‘Time passes.’ ‘That’s how it goes,’ Aureliano admitted, ‘but not so much.’”

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

The unorientable quality of the Möbius strip is perhaps its most distinctive. Orientability can be defined as “a continuous choice of local orientation.” A more colloquial explanation : “a space is orientable if you can choose ‘inward’ and ‘outward’ or ‘up’ and ‘down’ directions at every point on the surface that are compatible: you will never accidentally end up at the same point but with ‘up’ flipped to ‘down.’”

The Möbius strip was independently discovered by two German mathematicians in 1858. August Ferdinand Möbius was a mathematician and theoretical astronomer (and also the first to introduce “homogenous coordinates” into “projective geometry”). Johann Benedict Listing, a younger mathematician, coined the term “ topology ” for the study of surfaces, and in conducting that research, independently determined the properties of the Möbius strip. Though perhaps too neat a metaphor, it’s interesting to note that these two men arrived at the same conclusion, from different directions, at the same time.

You can make a model of the Möbius strip with just a rectangular piece of paper: give it an odd number of half-twists, then tape the ends back together. But the strip was long thought never to occur in the natural world. Because it has never been observed in our organic environment, it is sometimes referred to as an “impossible shape.” Practical applications of it abound in the world of human invention, however. For instance, Möbius strips are used in continuous-loop recording tapes, typewriter ribbons and computer print cartridges. In the 1960s, Sandia Laboratories also used Möbius bands in the design of adaptable electronic resistors . Conveyor belts use Möbius strips because they allow the entire surface area of the belt to receive an equal amount of wear, which makes it last longer.

The Möbius strip has also been tailored to various artistic and cultural products. Paintings have displayed Möbius shapes, as have earrings, necklaces and other pieces of jewelry. The green, three-arrowed universal sign for recycling also composes the Möbius band. There’s a depth to the image that reminds you to reduce, reuse and recycle. It is not just a circular action; it’s dynamic. The symbol seeks to represent the three interdependent aspects of a sustainable loop: the collection of materials to be recycled, the manufacturing of recycled materials into new products, and the purchase and use of the products made from recycled materials. Each arrow pleats and pivots itself, as all three arrows pursue and power one another.

The Möbius band is used in hardware and popular imagery, but the mathematical and scientific fascination with the Möbius strip has also endured for over a century. In 2005, Isaac Freund at Bar-Ilan University in Israel, proposed that light’s polarization could be twisted . Light’s polarization is a property that describes how its electric field moves. Polarization in physics is defined as “the action of restricting the vibrations of a transverse wave, especially light, wholly or partially to one direction.” A transverse wave means that light’s oscillations travel perpendicular to the direction in which its energy moves. Scientists can confine light to certain planes depending on its orientation in space. In other words, light can be coaxed into new shapes.

In 2015, Peter Banzer of the Max Planck Institute for the Science of Light in Erlangen Germany tested Freund’s hypothesis that light could be twisted. According to Katherine Kornei, writing at New Scientist, “Banzer’s team scattered two [polarized] green laser beams off a gold bead that was smaller than the wavelength of the light. The resulting inference introduced a polarization pattern with either three or five twists, giving it a Möbius-like structure.”

When I was in high school, my English teacher, Ms. Mulvihill, gave each of our classmates an individual question to answer for a final assignment. One of my peers was asked, “What is the shape of time in One Hundred Years of Solitude ?” He responded with a story: his family used to have a dog that would chase his tail. The dog drove himself crazy, running in circles, teeth bared, hunting his own hind legs. One day, racing after his tail, he bit it off. That’s the shape of time in One Hundred Years of Solitude.

In this year of solitude, disorientation and distance, we have been navigating what feels like misshapen terrain and time. But unlike the characters in Macondo, Márquez’s fictional town that is “exiled from the memory of men,” we continue to remember and discover. Even as we mourn the people we have lost, scientific innovation is thriving, and salving.

Darkness can seem like an endless, unbounded surface. We can walk it alone; we can walk it together. But we now know something else can be an infinite curl, a dizzying ground, an effervescent hypothesis confirmed: light. It only needs a little nudging.

ADMIN AREA MY BOOKSHELF MY DASHBOARD MY PROFILE SIGN OUT SIGN IN

Awards & Accolades

Google Rating

TIME TRIP ON A MOEBIUS STRIP

by Richard D. Lewis ‧ RELEASE DATE: Feb. 2, 2007

Trippy bit of indulgent storytelling, readable in short bursts.

A scientist enters another dimension through a giant seashell and meets a cast of historical characters.

Marine biologist Philip Grieg had a magical, if unsettling, experience as a child. Growing up on the beaches of Padre Island, Texas, he was accustomed to strange artifacts washed ashore by the Gulf of Mexico. But none matched the wondrousness of a ten-foot-high shell, one so large that the young Philip could walk inside. There, he heard an eerie voice that would haunt him into adulthood. Twenty-five years later, Philip is a prominent scientist, with the specter of the seashell still lingering over him. He looks up a friend, professor Moebius at Harvard, and asks for help in resolving the mystery of the otherwordly shell. The professor has a secret weapon at his disposal: His great-grandfather was Dr. August Moebius, who discovered the Moebius strip, a geometrical and physical oddity with two edges but only one surface. It is said that traveling along the strip is akin to traveling between dimensions. Thus, Philip and Moebius, with the help of the beautiful M.D. Elaine Rogers, work to lay a track of Moebius strip down inside the spiraling, symmetrical shell, aiming to gain access to the supernatural properties it possesses. Using vehicles to speed around the strip, they soon confirm their suspicions and enter another dimension, one that exists between the living and dead. The space is populated by noteworthy historical characters, all dead or presumed missing. The protagonists meet John Dillinger, Amelia Earhart, Jimmy Hoffa, Glenn Miller and George Leigh Mallory, among others. There, the plot unravels and forward motion ceases, literally and figuratively, as each of the notorious figures tells their story, and Philip looks for a common thread. The stories become episodic and unlinked, causing the narrative to suffer. The mishmash of history and pseudoscience don’t do the story any favors; while interesting, readers may doubt its accuracy. There is too heavy a reliance on historical information throughout, and not enough focus on realistic dialogue or narrative development. Literary audiences, however, will enjoy Lewis’ tribute to Walt Whitman’s Leaves of Grass, and how he ties it into the plot.

Pub Date: Feb. 2, 2007

ISBN: 978-0-7414-3797-6

Page Count: -

Publisher: N/A

Review Posted Online: May 23, 2010

Review Program: Kirkus Indie

SCIENCE FICTION | GENERAL SCIENCE FICTION | GENERAL SCIENCE FICTION & FANTASY

Share your opinion of this book

Our Verdict

New York Times Bestseller

by Max Brooks ‧ RELEASE DATE: June 16, 2020

A tasty, if not always tasteful, tale of supernatural mayhem that fans of King and Crichton alike will enjoy.

Are we not men? We are—well, ask Bigfoot, as Brooks does in this delightful yarn, following on his bestseller World War Z (2006).

A zombie apocalypse is one thing. A volcanic eruption is quite another, for, as the journalist who does a framing voice-over narration for Brooks’ latest puts it, when Mount Rainier popped its cork, “it was the psychological aspect, the hyperbole-fueled hysteria that had ended up killing the most people.” Maybe, but the sasquatches whom the volcano displaced contributed to the statistics, too, if only out of self-defense. Brooks places the epicenter of the Bigfoot war in a high-tech hideaway populated by the kind of people you might find in a Jurassic Park franchise: the schmo who doesn’t know how to do much of anything but tries anyway, the well-intentioned bleeding heart, the know-it-all intellectual who turns out to know the wrong things, the immigrant with a tough backstory and an instinct for survival. Indeed, the novel does double duty as a survival manual, packed full of good advice—for instance, try not to get wounded, for “injury turns you from a giver to a taker. Taking up our resources, our time to care for you.” Brooks presents a case for making room for Bigfoot in the world while peppering his narrative with timely social criticism about bad behavior on the human side of the conflict: The explosion of Rainier might have been better forecast had the president not slashed the budget of the U.S. Geological Survey, leading to “immediate suspension of the National Volcano Early Warning System,” and there’s always someone around looking to monetize the natural disaster and the sasquatch-y onslaught that follows. Brooks is a pro at building suspense even if it plays out in some rather spectacularly yucky episodes, one involving a short spear that takes its name from “the sucking sound of pulling it out of the dead man’s heart and lungs.” Grossness aside, it puts you right there on the scene.

Pub Date: June 16, 2020

ISBN: 978-1-9848-2678-7

Page Count: 304

Publisher: Del Rey/Ballantine

Review Posted Online: Feb. 9, 2020

Kirkus Reviews Issue: March 1, 2020

GENERAL SCIENCE FICTION & FANTASY | GENERAL THRILLER & SUSPENSE | SCIENCE FICTION

More by Max Brooks

BOOK REVIEW

by Max Brooks

More About This Book

BOOK TO SCREEN

THE THREE-BODY PROBLEM

From the remembrance of earth's past series , vol. 1.

by Cixin Liu ; translated by Ken Liu ‧ RELEASE DATE: Nov. 11, 2014

Remarkable, revelatory and not to be missed.

Strange and fascinating alien-contact yarn, the first of a trilogy from China’s most celebrated science-fiction author.

In 1967, at the height of the Cultural Revolution, young physicist Ye Wenjie helplessly watches as fanatical Red Guards beat her father to death. She ends up in a remote re-education (i.e. forced labor) camp not far from an imposing, top secret military installation called Red Coast Base. Eventually, Ye comes to work at Red Coast as a lowly technician, but what really goes on there? Weapons research, certainly, but is it also listening for signals from space—maybe even signaling in return? Another thread picks up the story 40 years later, when nanomaterials researcher Wang Miao and thuggish but perceptive policeman Shi Qiang, summoned by a top-secret international (!) military commission, learn of a war so secret and mysterious that the military officers will give no details. Of more immediate concern is a series of inexplicable deaths, all prominent scientists, including the suicide of Yang Dong, the physicist daughter of Ye Wenjie; the scientists were involved with the shadowy group Frontiers of Science. Wang agrees to join the group and investigate and soon must confront events that seem to defy the laws of physics. He also logs on to a highly sophisticated virtual reality game called “Three Body,” set on a planet whose unpredictable and often deadly environment alternates between Stable times and Chaotic times. And he meets Ye Wenjie, rehabilitated and now a retired professor. Ye begins to tell Wang what happened more than 40 years ago. Jaw-dropping revelations build to a stunning conclusion. In concept and development, it resembles top-notch Arthur C. Clarke or Larry Niven but with a perspective—plots, mysteries, conspiracies, murders, revelations and all—embedded in a culture and politic dramatically unfamiliar to most readers in the West, conveniently illuminated with footnotes courtesy of translator Liu.

Pub Date: Nov. 11, 2014

ISBN: 978-0-7653-7706-7

Page Count: 400

Publisher: Tor

Review Posted Online: Oct. 4, 2014

Kirkus Reviews Issue: Oct. 15, 2014

SCIENCE FICTION

Please select an existing bookshelf

Create a new bookshelf.

We can’t wait for you to join Kirkus!

Please sign up to continue.

It’s free and takes less than 10 seconds!

Already have an account? Log in.

Trouble signing in? Retrieve credentials.

Almost there!

Industry Professional

Welcome Back!

Sign in using your Kirkus account

Don’t fret. We’ll find you.

Magazine Subscribers ( How to Find Your Reader Number )

If You’ve Purchased Author Services

Don’t have an account yet? Sign Up.

Time Trip on a Moebius Strip › Customer reviews

Customer reviews.

Time Trip on a Moebius Strip

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

There was a problem filtering reviews right now. Please try again later.

From the united states.

There was a problem loading comments right now. Please try again later.

Amazon Newsletter
About Amazon
Accessibility
Sustainability
Press Center
Investor Relations
Amazon Devices
Amazon Science
Sell on Amazon
Sell apps on Amazon
Supply to Amazon
Protect & Build Your Brand
Become an Affiliate
Become a Delivery Driver
Start a Package Delivery Business
Advertise Your Products
Self-Publish with Us
Become an Amazon Hub Partner
› See More Ways to Make Money
Amazon Visa
Amazon Store Card
Amazon Secured Card
Amazon Business Card
Shop with Points
Credit Card Marketplace
Reload Your Balance
Amazon Currency Converter
Your Account
Your Orders
Shipping Rates & Policies
Amazon Prime
Returns & Replacements
Manage Your Content and Devices
Recalls and Product Safety Alerts
Conditions of Use
Privacy Notice
Consumer Health Data Privacy Disclosure
Your Ads Privacy Choices

The Mathematical Madness of Möbius Strips and Other One-Sided Objects

The discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology

David Gunderman and Richard Gunderman The Conversation

You have most likely encountered one-sided objects hundreds of times in your daily life – like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles.

This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on Sept. 26, 1868.

Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician named Listing actually described it a few months earlier, but did not publish his work until 1861.) Möbius seems to have encountered the Möbius strip while working on the geometric theory of polyhedra, solid figures composed of vertices, edges and flat faces.

A Möbius strip can be created by taking a strip of paper, giving it an odd number of half-twists, then taping the ends back together to form a loop. If you take a pencil and draw a line along the center of the strip, you’ll see that the line apparently runs along both sides of the loop.

The concept of a one-sided object inspired artists like Dutch graphic designer M.C. Escher , whose woodcut “ Möbius Strip II ” shows red ants crawling one after another along a Möbius strip.

The Möbius strip has more than just one surprising property. For instance, try taking a pair of scissors and cutting the strip in half along the line you just drew. You may be astonished to find that you are left not with two smaller one-sided Möbius strips, but instead with one long two-sided loop. If you don’t have a piece of paper on hand, Escher’s woodcut “ Möbius Strip I ” shows what happens when a Möbius strip is cut along its center line.

While the strip certainly has visual appeal, its greatest impact has been in mathematics, where it helped to spur on the development of an entire field called topology .

A topologist studies properties of objects that are preserved when moved, bent, stretched or twisted, without cutting or gluing parts together. For example, a tangled pair of earbuds is in a topological sense the same as an untangled pair of earbuds, because changing one into the other requires only moving, bending and twisting. No cutting or gluing is required to transform between them.

Another pair of objects that are topologically the same are a coffee cup and a doughnut. Because both objects have just one hole, one can be deformed into the other through just stretching and bending.

The number of holes in an object is a property which can be changed only through cutting or gluing. This property – called the “genus” of an object – allows us to say that a pair of earbuds and a doughnut are topologically different, since a doughnut has one hole, whereas a pair of earbuds has no holes.

Unfortunately, a Möbius strip and a two-sided loop, like a typical silicone awareness wristband, both seem to have one hole, so this property is insufficient to tell them apart – at least from a topologist’s point of view.

Instead, the property that distinguishes a Möbius strip from a two-sided loop is called orientability. Like its number of holes, an object’s orientability can only be changed through cutting or gluing.

Imagine writing yourself a note on a see-through surface, then taking a walk around on that surface. The surface is orientable if, when you come back from your walk, you can always read the note. On a nonorientable surface, you may come back from your walk only to find that the words you wrote have apparently turned into their mirror image and can be read only from right to left. On the two-sided loop, the note will always read from left to right, no matter where your journey took you.

Since the Möbius strip is nonorientable, whereas the two-sided loop is orientable, that means that the Möbius strip and the two-sided loop are topologically different.

When the GIF starts, the dots listed off clockwise are black, blue and red. However, we can move the three-dot configuration around the Möbius strip such that the figure is in the same location, but the colors of the dots listed off clockwise are now red, blue and black. Somehow, the configuration has morphed into its own mirror image, but all we’ve done is move it around on the surface. This transformation is impossible on an orientable surface like the two-sided loop.

The concept of orientability has important implications. Take enantiomers. These chemical compounds have the same chemical structures except for one key difference: They are mirror images of one another. For example, the chemical L-methamphetamine is an ingredient in Vicks Vapor Inhalers. Its mirror image, D-methamphetamine, is a Class A illegal drug. If we lived in a nonorientable world, these chemicals would be indistinguishable.

August Möbius’s discovery opened up new ways to study the natural world. The study of topology continues to produce stunning results. For example, last year, topology led scientists to discover strange new states of matter . This year’s Fields Medal, the highest honor in mathematics, was awarded to Akshay Venkatesh , a mathematician who helped integrate topology with other fields such as number theory.

David Gunderman, Ph.D. student in Applied Mathematics, University of Colorado and Richard Gunderman, Chancellor's Professor of Medicine, Liberal Arts, and Philanthropy, Indiana University

Get the latest Science stories in your inbox.

THE MOBIUS STRIP

"It is widely believed that spacetime must be both orientable and time-orientable. Arguments are that there is no evidence of a lack of orientability and that a nonorientable spacetime would be incompatible with the observed violations of P (parity) and T (time reversal invariance)."

ORIENTABILITY OF SPACETIME THE MATH OF NON-ORIENTABLE SURFACES HAWKING: LARGE SCALE STRUCTURE OF SPACE TIME BACKWARD CAUSATION THE TWIN PARADOX TIME TRAVEL: MEETING YOURSELF (please click) TIME PARADOX ONE TIME PARADOX TWO TIME PARADOX THREE TIME PARADOX FOUR TIME PARADOX FIVE TIME PARADOX SIX

"There had to be in existence two of me at the same time, albeit occupying separate spaces. One of me quite possibly knowing my mother died, the other still having a mother alive."

"(U)nknown to me, my mother was no longer at home, having become totally unable to care for herself, so much so my dad placed her into a full care sanatorium-like hospital in Santa Barbara, California on an around the clock basis. Before my dad had a chance to respond to the couple, the couple, knowing full well that my mother was in a sanatorium, without my father's grace, took me to India, simply sending him a note saying that in the end I had changed my mind about going. While I was gone my mother died. I missed the funeral and by the time I got back my family had disintegrated, my two brothers and myself all going separate ways, my dad disappearing into the countryside heavy into alcohol." SRI RAMANA MAHARSHI: The Last American Darshan

"Everything in my life from before entering Laos to Chiang Mai to my eventual return to Rangoon and beyond, time-wise, led up to, overlaid and bracketed my stay at the monastery as outlined in Doing Hard Time In A Zen Monastery . Within that bracketed period of time at the monastery I came in contact with (the) woman at the farm house, ending up in Tiruvannamalai circa 1944 and the Ramana ashram. It was embedded inside that same period of time in Tiruvannamalai that the three hours sitting before the Maharshi in the ashram transpired. Added together, the whole of the whole episode that unfolded, at least outside of the monastery walls it would seem, and how time is typically constituted consensually by those in the Samsara world, was enveloped in the broader sense by the calendar year 1964." (source)

"There had to be in existence two of me at the same time, albeit occupying separate spaces. One of me quite possibly knowing my mother died, the other still having a mother alive." (see)

THE SPIRITUAL ELDER AND THE SANTA FE CHIEF

He came over and sat next to me and asked if my dad was in the war. I told him no that he worked in the shipyards. Asking if I liked comic books he opened his suitcase and pulled out one called Blue Bolt. All the while he was thumbing through the pages like he was looking for something he was telling me he had a son in the war and that his son was a pilot. After he reached a certain spot he folded open the pages and pointed to a story about a group of American pilots that shot down 77 German planes in one outing. Then, carefully reading the story page by page and pointing to the different pictures he told me that his son was one of the pilots. My uncle told me with that I took the book from the man's hands completely fascinated, so much so I read the story over and over without stopping or setting it down. The man, seeing how much I appreciated the comic and the story, said I could have it. After that my uncle said I continued to read it again and again all the way back to California and months afterwards." THE GOOSE SHOOT

The POW escape is recorded as having transpired on January 14, 1943. The Goose Shoot happened in the skies over Tunisia, North Africa three months later on Sunday, April 18, 1943. The story I showed the POWs of the Goose Shoot was in BLUE BOLT , Issue Number 6, which wasn't even published until January, 1944, one full year after the POW escape --- even though I had the comic book with me at the time of their escape.

"Once through the main portal the time associated within the walls of the monastery and the land beyond flowed like the surface of a Mobius Strip, non-orientable." "What is not known with any amount of certainty is when passing through the portal from the outside into the monastery, is the measurable distance from the outside to the inside more than the thickness of the doors' front to back, or once in the monastery is the inside and all of the surrounding countryside beyond the thickness of the monastery doors actually somewhere else?" Shambhala, Time, and the Langoliers

"The question arises, did showing up at the ashram in the past affect or change the future, and if so, how?"

"The Zen master's intent, as I have extrapolated it in hindsight, was for me to bypass any potentially powerful Mara induced impediments by coming in on the side of time in front of them, that is before they happened. Thus in a sense, after which returning into the present forward, maintaining in place any 'mental barriers that had been reduced to nothingness' before the impediments were set into motion. As events seemed to unfold in my life such does not seem to be the case, that is, the Zen master missed his mark."

RESTITCHING THE HOLE IN THE FABRIC OF SPACE-TIME

The thing is, even though I was drawing from history that hadn't even happened yet, they were in the process of putting into place what would happen that would eventually lead to that history, so they thought, knowing what they did from there own time, there was no way I could know what I knew if I wasn't one of them.

When I met Kaufman in Calcutta he was ten years younger than he was when I met him at my merchant marine friend's home in Redondo Beach.

RETURN TO THE MONASTERY

Two-way thermodynamics: could it happen, large scale structure of space time, the zen master misses his mark.

As to the subject of donations, for those of you who may be interested in doing so as it applies to the gratefulness of my works, I invariably suggest any funds be directed toward THE WOUNDED WARRIOR PROJECT and/or THE AMERICAN RED CROSS .

Footnote [1]

"That is to say, if the past and the future exist in the physical way that the present does, we have no way of knowing it, because we only experience the present. And yet, if the past and future don't exist, then what exactly are we measuring when we measure time?" AN ANALYSIS OF THE CONCEPT OF TIME OF ST. AUGUSTINE, linked below

TIME TRAVEL

Mobius strip time loop, analogies in time and place, on time travel and visiting the past, enlightenment and time: nagarjuna's concept, an analysis of the concept of time of st. augustine, mobius strip, the liverpool letter.

"My mother died when I was quite young. However, even before her death, because of her illness my father continued to have to work more and more hours to pay for mounting medical expenses. Through it all he found it extremely difficult to care for my two brothers and myself and work the hours he did. At first he dealt with it with regular day-to-day babysitting, then overnight and weekends with my grandparents and neighbors. Along the way a couple that just happened to be visiting our next door neighbors for Thanksgiving dinner, and of which we were invited to, offered to help by taking one of us kids fulltime. A few days later I was selected and basically fostered out, moving away from my brothers and family even before my mother passed away." BUCK ROGERS: HIS HISTORY AND EVOLUTION

"There I was, a young boy barely even closing down on six or seven years of age, not long returned from India, without a mother, having missed both her final days and her funeral as well." THE LAST AMERICAN DARSHAN

THE BALCHOWSKY PARADOX: A SPACE-TIME CONUNDRUM

Subscribe or renew today

Every print subscription comes with full digital access

Science News

An enduring möbius strip mystery has finally been solved.

A mathematician’s journey to prove how short the loops can be had some twists and turns

An illustration of a green Möbius strip, a loop of paper with a half-twist in it.

A Möbius strip (one shown) is a loop of paper with a half-twist in it. A mathematician has now proven the shortest possible Möbius strip for a given width.

MirageC/Moment/Getty Images Plus

Scientists find a naturally occurring molecule that forms a fractal

An image of grey numbers piled on top of each other. All numbers are grey except for the visible prime numbers of 5, 11, 17, 23 and 29, which are highlighted blue.

How two outsiders tackled the mystery of arithmetic progressions

A predicted quasicrystal is based on the ‘einstein’ tile known as the hat.

The produce section of a grocery store with lots of fruit and vegetables on sloped displays

Here’s how much fruit you can take from a display before it collapses

Here are some astounding scientific firsts of 2023

An image showing 1+1=2 with other numbers fading into the black background.

‘Is Math Real?’ asks simple questions to explore math’s deepest truths

A photo of a variety of different colored textiles with adinkras, used in Ghana's Twi language to express proverbs, stamped in black ink.

Non-Western art and design can reveal alternate ways of thinking about math

A 1934 photo supposedly of the Loch Ness Monster.

Seen Bigfoot or the Loch Ness Monster? Data suggest the odds are low

Subscribers, enter your e-mail address for full access to the Science News archives and digital editions.

Not a subscriber? Become one now .

Screen Rant

Avengers: endgame's time travel explained (properly).

Your changes have been saved

Email Is sent

Please verify your email address.

You’ve reached your account maximum for followed topics.

8 Recent Box Office Flops I Think Will Be Cult Classics In The Future

Matt damon & ben affleck's next movie together is a first in their 35-year history, 10 ways edgar wright's the running man remake will be different from schwarzenegger's version.

WARNING: Major spoilers for Avengers: Endgame .

Avengers: Endgame brings time travel to the fore of the MCU and, as predicted, it's really rather complicated. Time travel isn't a totally new concept to the Marvel Cinematic Universe . Doctor Strange made use of the Time Stone in his solo movie to defeat the Dark Dimension's Dormammu by trapping him in a time loop, and Ant-Man and the Wasp teased that the Quantum Realm had "time vortexes". Avengers: Endgame takes that latter thread and runs with it.

After Thanos has destroyed all the Infinity Stones and been killed by Thor, the Avengers are lacking the means to undo the effects of the snap. A get around comes five years later in the form of Scott Lang, whose time in the Quantum Realm felt like only five hours; he rationalizes that, because time moves differently, it would be possible to leave and enter at different points across the timeline. A plan is formulated, leading to the entire second act of Avengers: Endgame (and a fair bit of the third) being concerned with time travel.

Related: Every Marvel Cinematic Universe Movie, Ranked (Including Endgame)

Time travel is hard . As something theoretically possible on a quantum mechanics level but physically impossible from a human vantage point (unless you count Planet of the Apes ' use of relativity to move forward at a fast rate), it functions in fiction entirely on stated logic within the story at hand. There is no true rule to time travel, which means every movie can create new ideas. However, only a handful - The Terminator (just the first), Looper , Primer - follow their rules religiously. That's not a problem if the story a movie is telling is entertaining (see Back to the Future , which is impossible to track yet so exciting it doesn't matter), but it can still leave audiences scratching their heads.

Avengers: Endgame , as expected, doesn't make total sense . It pulls from multiple different ideas of time travel, using them all at once for different ends. This is all in service of the characters and their fight against Thanos - you can't get Captain America's incredibly satisfying ending without fudging things a bit - but it can mean making sense of what's going on a little tricky. And so here we'll explain every question you could possibly have about Avengers Endgame 's time travel.

First, though, here's a glossary of the four different types of time travel that will be important in this discussion.

Linear timeline (with time loops): whatever happened, happened. Going into the past can't change the past because it already happened, you simply enable it to happen. Example: Twelve Monkeys , The Terminator (just the first)
Grandfather paradox: if you go back in time and kill your own grandfather, then you can't have existed to go back and kill him. Example: Surprisingly few, Donnie Darko comes close. Many others (such as Looper ) subvert the idea.
Butterfly effect: any small change in the past will have massive impacts on the future. Example: The Butterfly Effect
Fluid timeline: a mixture of all of the above where what changes have an impact is decided based on in-story logic. Example: Back to the Future , Terminator 2: Judgement Day

How Avengers: Endgame's Time Travel Works

The justification of time travel is fundamental to Avengers: Endgame 's second act, with characters repeatedly questioning its possiblity. Of course, Tony Stark's scientific explanation - its perils are rooted in quantum chromodynamics theory, Scott turned into a baby and old man because of the EPR paradox and Deutsch proposition, the wrist devices derive from the eigenvalue of a particle field accounting for spectral decomposition under his Mobius strip configuration - glances with genuine theory but one without any real application. Yes, Mobius strip time travel is a pre-existing idea (it's at the heart of the grandfather paradox), but it's not how the film presents time travel.

There are two scenes in Avengers: Endgame where time travel is explained. First is Banner ahead of Hawkeye's test mission. Responding to Rhodey's suggestion of killing Thanos in the crib (an adaptation of the " kill Hitler " time travel theory), Bruce dismisses most time travel examples from popular culture ( Back to the Future especially, but Star Trek , Terminator , Time Cop , Time After Time , Quantum Leap , Somewhere In Time , Hot Tub Time Machine and Bill and Ted's Excellent Adventure are all mentioned), stating " if you travel to the past, that past becomes your future and your former present becomes the past, which can't now be changed by your new future. " The basic implication is that you can't change the past because you've existed in the future; no matter what you do, the end result is the same. Even if you were to try and kill baby Thanos, the future you have must be unchanged.

Later, when Bruce is attempting to get the Time Stone from the Ancient One, she talks to him and elaborates on his idea further: " The Infinity Stones create what you experience as the flow of time. Remove one of the stones and that flow splits. " This suggests that, while the post-Decimation future the Avengers have come from will be there when they return, their actions in the past can impact the timeline to the point that new timelines are created (which, due to the lack of Stones, are much more fraught). While it's possible any change could do this, it's only explicitly stated that it occurs when an Infinity Stone is removed from the timeline, which Bruce proposes can be fixed if they " return each one to its own timeline at the moment it was taken so chronologically, in that reality, it never left. "

Related: Every Returning Character in Avengers: Endgame

In short, the Avengers can't change their own timeline as it already happened, so going into the past doesn't affect their own reality. However, removing the Infinity Stones from an earlier point does, creating darker timelines. To correct this, the Infinity Stones need to be returned to their original place in the timeline after use.

Now, both of these exposition characters are shown in Avengers: Endgame to not have full knowledge of the situation - Bruce is enlightened by the Ancient One, who is herself later corrected by Doctor Strange's plan involving giving up the Time Stone - but given these are the film's prime exposition beats regarding time travel, they can be assumed to be intended as accurate by the filmmakers. The ambiguity comes with what is a big enough change to alter the timeline: taking an Infinity Stone creates a branch, but returning it would essentially uncreate it; but what does that mean of the interactions the future Avengers have with their past selves, or the full-on diversion with Thanos?

What The Avengers' Time Travel Plan Is In Endgame (& How It Goes Wrong)

The Avengers intend to go back in time to takes the Infinity Stones to attach to their own, new Infinity Gauntlet. They split into four teams: Iron Man, Captain America, Ant-Man and Hulk to New York during The Avengers to get the Tesseract, Loki's Scepter and Mind Stone; Thor and Rocket to Asgard during Thor: The Dark World to remove the Aether from Jane Foster; War Machine and Nebula to get the Power Stone from the Morag at the start of Guardians of the Galaxy ; and Hawkeye and Widow to retrieve the Soul Stone from Vormir.

There's a question of why they needed to go to the events of the movies - while the Battle of New York makes sense due to the three Infinity Stone argument, the Aether was in the Collector's museum since Thor: The Dark World and the Power Stone on Xandar following Guardians of the Galaxy , situations with fewer timeline implications. Of course, that would make for a much less interesting film and is argued away in-universe as requiring characters' knowledge of events.

Related: Every Marvel Movie Releasing After Avengers: Endgame

The plan goes awry in multiple cases. Clint gets the Soul Stone but has to lose Natasha (which doesn't break the timeline). Thor talks to Frigga moments before her death, getting the goodbye he was robbed and a speech about being a hero, before taking Mjolnir . War Machine gets the orb, but Nebula is stopped from traveling back to the present by 2014 Thanos. Captain America gets the scepter after a tussle with his past self and Hulk the Time Stone (as well as knowledge of the timeline issues above) but Tony and Scott fail to secure the Tesseract, which Loki uses to teleport out; they instead go to 1970 to get it from Camp Lehigh in New Jersey, as well as more Pym Particles for the return journey.

Most Of The Infinity Stones (And Mjolnir) Create A Simple Time Loop

There's a lot to break down here, so let's first look at the most simple case. The major wrinkle of taking the Infinity Stones creating multiple timelines is addressed at the end of Avengers: Endgame , with Steve Rogers returning them - along with Mjolnir - back to their original time periods. Assuming Cap does this correctly (as implied), that means the actions surrounding the Reality Stone in Thor: The Dark World , the Space Stone in 1970, the Mind Stone in The Avengers , the Time Stone in 2012 and the Soul Stone in 2014 are all reverted to normal: he erases the timelines created by their removal. The question of how exactly Steve returned the Soul Stone, or his reaction to Red Skull being its guardian, is left to audiences' imaginations.

What that does leave is a pretty startling implication: this always happened. Rocket always stole the Aether from Jane, Howard Stark always bumped into grown-up Tony on the day of his son's birth, the Ancient One always talked to Banner four years before her death. It's a linear timeline and all of this was going on in the background of the MCU all along. While that's a retcon by anyone's reasoning, it is rather tight; none of the mentioned past-future interactions directly contradict the timeline.

Loki Created A New Timeline?

The first true break (or diversion) of the Marvel timeline in Avengers: Endgame is regarding the Space Stone in 2012. Tony and Scott intend to give 2012 Tony an arc reactor failure when he meets Secretary Pierce (something that presumably always happened), allowing them to remove the Tesseract briefcase from the equation. An angry 2012 Hulk complicates matters and the Space Stone is attained by Loki , who teleports out of New York.

Related: The Tesseract Timeline (Including Captain Marvel)

Following the rules laid down by the Ancient One (and the fact that the film puts focus on the Loki moment), this a clear and intended break in the Marvel timeline that is not resolved by the time Avengers: Endgame comes to an end. In this reality, Loki escapes capture at the Battle of New York with the Tesseract.

The knock-on effects of this are serious: directly, Loki is still working for Thanos at this point so may give him the Space Stone years earlier; from a movie perspective, he isn't there for the events of Thor: The Dark World or Ragnarok , meaning Odin is never replaced and, possibly, Asgard may not be destroyed and Thor never loses Mjolnir; the Avengers also haven't completed their first mission, likely keeping them together longer and impacting solo movies up to and beyond Captain America: Civil War . The extent of all of this is speculation, sure, but the very immediate potential is massive. This would also mean that everything that happens subsequently in this time period is not part of the prime MCU universe: Steve Rogers didn't always fight his future self because he was never looking for Loki.

Practically, this is a get around of Loki's death at the start of Avengers: Infinity War . Thanos declared " no resurrections this time " and he was right, from a certain point of view. Loki is dead in the MCU going forward, yet a version of him is alive and well for new adventures at his most malicious in another timeline, which is a topic that will surely be explored in the Tom Hiddleston-starring Disney+ Loki show .

Thanos Breaks Avengers: Endgame's Time Travel Logic

The one Infinity Stone we've not accounted for yet is the Power Stone. Already, this was a weird case as Nebula and War Machine directly interfered with the opening of Guardians of the Galaxy , although it could be explained Star-Lord being knocked out always happened, meaning Steve returning the stone at the end maintained continuity.

Related: How Much Did Avengers: Endgame REALLY Cost To Make?

But it's the impact of Nebula being in the past that breaks things. Due to her conscious network, the past and future Nebula are connected, which alerts a Guardians of the Galaxy -era Thanos to the Avengers' mission: he swiftly learns about his victory in Avengers: Infinity War , subsequent death and an attempt to undo it via time travel. And here's where it gets actually complicated: intercepting future Nebula, Thanos time travels the Sanctuary II to the post-snap world in a bid to stop the Avengers undoing his dead future self's work. His plan is now to reclaim the Infinity Stones, wipe out all life and build a new world with him as de facto God. In the end, though, Thanos from 2014 and all his forces are dusted by Iron Man's snap .

The temporal issues here are massive. In Guardians of the Galaxy , Thanos was sat in his throne letting minions do his bidding and yet to have a single Infinity Stone in his grasp. Avengers: Endgame gives him full knowledge of the future, takes him into the 2020s and kills him. With no Thanos or threat, the entire MCU after Guardians of the Galaxy is different, up to there not even being an Infinity War (at least not against the Mad Titan - we know the Collector is also coveting the Infinity Stones).

It's possible that this is all a result of Loki's Tesseract grab, which has already happened in the " present " of some of the future Avengers, but there's little to back that up. Conversely, it may be that Steve returning the Power Stone resets all of this timeline to make this Thanos essentially exist on a separate stream. But the most logical explanation using the film's rules is that something the Avengers changed in 2014 altered the past. This would be unrelated to an Infinity Stone, making the Ancient One's advice wrong, and mean all these smaller changes the Avengers were making in the past do have an impact, butterfly effect-style, leading to an infinite number of alternate timelines.

However, any of those assumptions go well beyond what's laid down explicitly by Avengers: Endgame , making big assumptions and attempting to consolidate multiple forms of time travel (linear timeline, butterfly effect, alternate dimensions) into one. The important thing is that this Thanos who learns beyond his time is defeated at the end.

Related: Thanos' MCU Introduction Doesn't Make Sense - Here's How We'd Fix It

How Can Nebula Kill Her Past Self?

A subset of the Thanos concern is Nebula. The notion of both versions being connected is actually rather logical by itself; think of it like taking a phone to the past - which one receives calls and messages? But when things are taken through to completion, it gets confusing.

During the present-day battle in Avengers: Endgame 's finale, future Nebula convinces past Gamora to join her (a reversal of their arc in Guardians of the Galaxy Vol. 2 ), which leads to a showdown in which future Nebula kills her past counterpart. Common time travel logic would make this a grandfather paradox - Nebula can't exist to kill herself - but there's no slow fade away. This is further evidence that whatever is happening after Thanos comes to the future is from its own existent timeline, although any further exploration - or even an acknowledgment of what's happened from Gamora or Hawkeye - isn't forthcoming.

Captain America Goes Back To The Past (And Was Always There?)

The end of Avengers: Endgame has one final big time travel reveal. When Steve Rogers goes back in time to replace all the stones and, as the movie tells it, correcting every potential issue, instead of returning to the present, he uses the Pym particles to jump to the 1940s to be with Peggy. He gets that date, that dance, that life that he was forever robbed from by his duty. This is confirmed by an appearance of a much older Steve just after he leaves, saying he was happy with the life his chose and passing the shield to Falcon.

Related: Every Captain America Movie, Ranked

Thematically perfect and tear-inducingly delivered, this moment nevertheless creates even more complications thanks to, once again, borrowing from multiple forms of time travel. Captain America has inserted himself into the past, becoming Peggy Carter's husband.

It's notable that Marvel movies have been avoiding giving much of Peggy's post- Agent Carter background even as they teased Steve's eventual fate. The only proper mention of her husband came in Captain America: The Winter Soldier where, in an archived video at the Captain America Smithsonian exhibit, she explained how he was someone Steve saved during World War II; Agent Carter was canceled before the show could reveal his identity as promised and pictures on her bedside further showed only her children. It's distinctly possible that this ambiguity was intended to hide that it was really Steve Rogers all along.

This line of thinking comes with its own problems, many explainable. Steve and Peggy would have had to hide his return from the outside world, likely seeing him live under an alias. As spies, this would be well within their remit, and if the focus was on living a life together, a worthy sacrifice. It would also explain the now-incongruous fact that Peggy has a photo of young Steve on her desk; she's covering for him. It also doesn't make the Sharon Carter love story (too) disgusting as Steve wouldn't be her blood relative.

Of course, that would directly work against what happened to Guardians of the Galaxy -era Thanos; following that logic, Steve's return would have started a new chain of events that would surely butterfly into a totally different, possibly Avengers-less future. This solution here would that old Steve turning up straight after his disappearance isn't just him simply revealing himself but having traveled across from another reality using Pym particles for a proper goodbye.

Related: The Evolution Of Captain America In The MCU

Frankly, the time loop where Captain America was always in the past makes the most sense, with the Thanos problem a product of twisty time travel storytelling.

What About The MCU Timeline?

From all we've discussed, Avengers: Endgame leaves the MCU timeline pretty much as it is, with only one major branch thanks to Loki and the Tesseract and a closed loop with 2014 Thanos. And, for the most part, the implication is that the timeline of the MCU as has been told for the past decade hold true. No movies have been retconned or removed from continuity, just events added just off-screen.

But, as any Marvel fan knows, the MCU timeline isn't perfect. From Phase 1, which altered along with the original Avengers plan , there were always noticeable plot holes that make nailing down a proper order of events tricky: Spider-Man: Homecoming 's "eight years later" claim is the most well-known, but complications run through the movies, from confusion over when Iron Man is set, to a very weird post- Civil War build-up to Infinity War .

Avengers: Endgame doesn't really concern itself with addressing any of these. Avengers: Infinity War already corrected the Homecoming mistake , and the movies revisited were all set in their release years. However, the ending does leave a question. Avengers: Endgame begins in 2018, the aftermath of Thanos' snap, then jumps forward five years to 2023. This is the baseline time for the Avengers, where the final battle occurs and when the snap victims return to. This means that, from an outside perspective, half the population disappeared for five years, then everything returned to normal... sort of. Half of the population will have mourned and aged five years, while another has been thrown back into a new world. This would be upsetting for families, friends, jobs and schools.

Related: Avengers: Endgame's Ending & Marvel Movie Future Explained In Detail

Indeed, while Peter Parker's return to Midtown High and reuniting with Ned is played as happy, this ignores that surely half of his class are now college age. This poses some major implications for Spider-Man: Far From Home - it surely must be a prequel set before Avengers: Endgame , otherwise the film will have to take place in a near-miss-dystopia 2023. It's further notable that 2020's MCU releases - Black Widow and The Eternals - are both prequels to the rest of the MCU, meaning the effects of the Infinity War don't need to be explored directly.

Time Travel's Future In The MCU After Avengers: Endgame

With Hank Pym returned, there's an unlimited amount of Pym particles, meaning the Avengers are technically able to travel into the Quantum Realm as much as they so wish. But is that something to actually expect in the MCU's future? The plot device was rather specific to Avengers: Endgame and an opportunity to revisit previous movies in a send-off Captain America and Iron Man, so it's unlikely to be immediately returned to in future Avengers movies . Time travel can be a narrative-breaking device (as we've already seen) and worth putting to bed.

However, there will still be several potential impacts of the time meddling. The most pressing is, of course, Loki. His Disney+ series will at the very least deal with the fractured timeline he created when stealing the Tesseract, although whether it's resolved (or how) is up in the air. It's also suggested that Star-Lord still hopes to find Gamora, hinting at his arc in Guardians of the Galaxy Vol. 3 ; it's also unclear where 2014 Gamora has gone, meaning there could still be a survivor of that confusing time loop.

Related: Every Marvel TV Show Coming To Disney+

Captain America's ending also leaves open a rather tantalizing possibility: Steve Rogers' eventual return. While he gets his happy life with Peggy, nothing says he doesn't get called on again to help fight another reality-threatening foe at some point down the line. Already, Chris Evans' portrayal of Captain America has reached classic status, and in 5-10 years, audiences would no doubt be excited to see him return (think the original Star Wars cast in the sequel trilogy).

For now, though, Avengers: Endgame 's final moments seem intended to put a resolute end to all the temporal meddling. Thanos is defeated, the timeline is safe, Captain America got a happy ending. Just don't overthink it.

Next: Every Marvel Movie Releasing After Avengers: Endgame

Key Release Dates

Spider-man homecoming 2.

SR Originals
Avengers: Endgame (2019)

Mobius Strips: So Simple to Create, So Hard to Fathom

Share Content on Facebook
Share Content on LinkedIn
Share Content on Flipboard
Share Content on Reddit
Share Content via Email

The mathematics of otherwise simple-looking objects can be surprisingly perplexing. There's likely no greater example of this than the Möbius strip.

It's a one-sided object that can be made by simply twisting a piece of paper and connecting the ends with some tape. If you were to follow the loop around with your finger, you'd eventually end up right back where you started, having touched the entire surface of the loop along the journey. This simple creation, the Möbius strip, is fundamental to the entire field of topology and serves as a quintessential example of various mathematical principles.

One of these principles is nonorientability , which is the inability for mathematicians to assign coordinates to an object, say up or down, or side to side. This principle has some interesting outcomes, as scientists aren't entirely sure whether the universe is orientable.

This poses a perplexing scenario: If a rocket with astronauts flew into space for long enough and then returned, assuming the universe was nonorientable, it's possible that all the astronauts onboard would come back in reverse.

In other words, the astronauts would come back as mirror images of their former selves, completely flipped. Their hearts would be on the right rather than the left and they may be left-handed rather than right-handed. If one of the astronauts had lost their right leg before flight, upon return, the astronaut would be missing their left leg. This is what happens as you traverse a nonorientable surface like a Möbius strip.

While hopefully your mind is blown – at least just slightly – we need to take a step back. What's a Möbius strip and how can an object with such complex math be made by simply twisting a piece of paper?

The History of the Möbius Strip

Practical uses for the mobius strip, how do you create a möbius strip.

The Möbius strip (sometimes written as "Mobius strip") was first discovered in 1858 by a German mathematician named August Möbius while he was researching geometric theories. While Möbius is largely credited with the discovery (hence, the name of the strip), it was nearly simultaneously discovered by a mathematician named Johann Listing. However, he held off on publishing his work, and was beaten to the punch by August Möbius.

The strip itself is defined simply as a one-sided nonorientable surface that is created by adding one half-twist to a band. Möbius strips can be any band that has an odd number of half-twists, which ultimately cause the strip to only have one side, and consequently, one edge.

Ever since its discovery, the one-sided strip has served as a fascination for artists and mathematicians. The strip even infatuated M.C. Escher , leading to his famous works, "Möbius Strip I & II" .

The discovery of the Möbius strip was also fundamental to the formation of the field of mathematical topology , the study of geometric properties that remain unchanged as an object is deformed or stretched. Topology is vital to certain areas of mathematics and physics, like differential equations and string theory.

For example, under topographical principles, a mug is actually a doughnut . Mathematician and artist Henry Segerman explains it best in a YouTube video : "If you take a coffee mug, you can sort of un-indent the place where the coffee goes and you can squish out the handle a little bit and eventually you can deform it into [a] symmetrical round doughnut shape." (This explains the joke that a topologist is someone who can't see the difference between a doughnut and a coffee mug.)

The Möbius strip is more than just great mathematical theory: It has some cool practical applications, whether as a teaching aid for more complex objects or in machinery.

For instance, since the Möbius strip is physically one-sided, using Möbius strips in conveyor belts and other applications ensures that the belt itself doesn't get uneven wear throughout its life. Associate professor NJ Wildberger of the School of Mathematics at the University of New South Wales, Australia, explained during a lecture series that a twist is often added to driving belts in machines, "purposefully to wear the belt out uniformly on both sides." The Möbius strip also may be seen in architecture, for example, the Wuchazi Bridge in China.

Dr. Edward English Jr ., middle school math teacher and former optical engineer, says that as when he first learned about the Möbius strip in grade school, his teacher had him create one with paper, cutting the Möbius strip along its length which created a longer strip with two full twists.

"Being intrigued by and exposed to this concept of two 'states' helped me, I think, when I encountered up/down spin of electrons," he says, referring to his Ph.D. studies. "Various quantum mechanics ideas weren't such strange concepts for me to accept and understand because the Möbius strip introduced me to such possibilities." For many, the Möbius strip serves as the first introduction to complex geometry and mathematics.

Creating a Möbius strip is incredibly easy. Simply take a piece of paper and cut it into a thin strip, say an inch or 2 wide (2.5-5 centimeters). Once you have that strip cut, simply twist one of the ends 180 degrees, or one-half twist. Then, take some tape and connect that end to the other end, creating a ring with one-half twist inside. You're now left with a Möbius strip!

You can best observe the principles of this shape by taking your finger and following along the sides of the strip. You'll eventually make it all the way around the shape and find your finger back where it started.

If you cut a Möbius strip down the center, along its full length, you're left with one larger loop with four half-twists. This leaves you with a twisted circular shape, but one that still has two sides. It's this duality that Dr. English mentioned helped him understand more complex principles.

If you cut a bagel along the path of a Möbius strip , you'll be left with two connected bagel rings. Not only that, but the surface of the cut will be larger than just cutting the bagel in half, allowing you to spread more cream cheese on the bagel to eat.

Frequently Asked Questions

What impact has the concept of the möbius strip had on modern mathematics and physics, how are möbius strips used in practical applications outside of mathematical theory.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

Woman admiring Escher's "Metamorphosis III"

The Inventory

Support Quartz

Fund next-gen business journalism with $10 a month

Free Newsletters

The quantum mechanics of “Avengers: Endgame,” fact-checked by scientists

Many of the concepts in “Endgame” are connected, at least in name, to recent scientific theory.

Spoiler alert: This story contains details of the plot of Avengers: Endgame.

At the end of Avengers: Infinity War half the people (including heroes and villains) in the universe were gone in the snap of a finger from Thanos (Josh Brolin).

So how can Avengers: Endgame try to bring them back?

Well, with that tried and tested movie plot device: time travel. Plus a surprising amount of scientific jargon thrown in, including quantum mechanics , Deutsch propositions , eigenvalues , and inverted Möbius strips .

But don’t think that everything you hear during the movie was created in the minds of some crazy screenwriter. Many of the time-travel concepts in Endgame are connected, at least in name, to recent scientific theory, simulation, and speculation.

Let’s dive into the science of quantum time travel and discuss whether eigenvalues can really save the universe.

Time travel 101

The key premise of the movie is that the only thing that can reverse the deaths of half the universe are the things that caused those deaths in the first place: the powerful Infinity Stones .

Problem is, Thanos destroyed these in the present day, so the stones are only available in the past. Retrieving them will require a convoluted journey back in time to multiple locations by the remaining Avengers.

Is time travel actually possible? We’ve known since Albert Einstein posed his Theory of Special Relativity more than 100 years ago that traveling forward in time is relatively easy.

All you need to do is move at close to the speed of light and you can theoretically travel millions or even billions of years into the future within your lifetime.

But could you get back again? This feat appears to be much more difficult. Here are a few challenges and possible solutions.

The grandfather paradox

Traveling back in time can cause apparent logical inconsistencies in reality, like the well-known grandfather paradox .

If you went back in time and killed your grandfather when he was young, then you could never be born, but if you weren’t born, then how did you go back and kill him?

Scientists have several theories about these time loops (physicists call them closed timelike curves ). Some theories state that such loops are just physically impossible and therefore traveling back in time can never happen.

But we know, also thanks to Einstein, that spinning black holes can twist up both space and time , which is why one side of the black hole is brighter than the other in the first picture ever taken of one .

Time travel in Endgame

In the movie, the characters first make fun of many other time-travel movies such as Back to the Future and the Terminator series where changing your own past and future is possible.

Instead, Endgame goes with the alternative reality idea, where any changes back in time cause a whole new universe to be created, a so-called splitting or branching off of multiple timelines. In physics, this idea is called the Many Worlds Theory .

To avoid this problem, the Avengers plan to borrow the stones from past timelines, use them in the present day, but return them to exactly the same moment once they have finished with them. But will it work?

Enter quantum mechanics

Quantum mechanics is mentioned a lot in the movie and there are in fact many emerging theories about quantum time travel , including some that potentially solve the grandfather paradox .

In quantum mechanics, atomic particles are more like indistinct waves of probability . So, for example, you can never know both exactly where a particle is and what direction it’s moving. You only know there is a certain chance of it being in a certain place.

A British physicist named David Deutsch, who is mentioned in the movie, combined this idea with the Many Worlds theory , and showed that the grandfather paradox can disappear if you express everything probabilistically .

Like the particles, the person going back in time only has a certain probability of killing their grandfather, breaking the causality loop. This has been simulated successfully .

This might seem strange, and while some of the jargon used in the movie may seem a little over the top, you can be sure that real quantum science is even stranger than movie makers could ever imagine. It’s clear that even scientists are struggling to make sense of the implications of quantum theory.

Terminology for effect

The time-travel theory scenes (of which there are several) are filled with technical jargon, some out of place and some in the right ballpark.

Here are a few of the terms we hear in the movie concerning time travel:

Eigenvalues

In discussing their approach to time travel, characters Tony Stark and Bruce Banner mention eigenvalues . This is most likely an example of movie math talk for effect, as eigenvalues are a fairly low-level (basic) concept in linear algebra.

Verdict: A case of the math mumbles

Planck scale

The Planck scale is all about very small things. Planck length, time, and mass are base units used in physics. A Planck length is 1.616 × 10 −35 m. That’s very small.

It is the distance that light travels in one unit of Planck time—which is also a very small amount of time. Given the movie is about quantum mechanics-based time travel, chatting Planck scales don’t seem too far off topic.

Verdict: Planck has a point.

Inverted Möbius strip

The time-travel jargon also discusses inverting a Möbius strip. A normal Möbius strip is a surface with only one side. You can create one easily by taking a strip of paper, twisting it once, and then sticking it together.

Although a Möbius strip has a range of interesting mathematical properties, its technical relevance to time travel is tenuous, beyond some high-level attempts to explain the grandfather paradox.

Verdict: Twisting theory a little.

From a scientific perspective, it’s intriguing to have a new movie with such a heavy plot foundation in time travel, and the movie doesn’t pull many punches in diving straight into both the jargon and implications of various time-travel scenarios.

While some of the mathematical terminology is clearly there for effect, the plot makes a reasonable effort to adhere to current high level-thinking about time travel—to a point.

Time travel is one of those captivating scientific concepts that is perhaps furthest from implementation by scientists, and so its pivotal role in a movie about superheroes who can fly, go subatomic, destroy universes, and change reality is perhaps particularly apt.

This article is republished from The Conversation under a Creative Commons license. Read the original article .

📬 Sign up for the Daily Brief

Our free, fast, and fun briefing on the global economy, delivered every weekday morning.

an image, when javascript is unavailable

Demi Moore on Full Frontal Nudity With Margaret Qualley in ‘The Substance’: ‘A Very Vulnerable Experience’ but I Had a ‘Great Partner Who I Felt Very Safe With’

CANNES, FRANCE - MAY 19: Demi Moore and her dog Pilaf attend a photocall at the 77th annual Cannes Film Festival at the Carlton Cannes Hotel on May 19, 2024 in Cannes, France. (Photo by Pascal Le Segretain/Getty Images)

Demi Moore ‘s new film, the feminist body horror “ The Substance ,” sees her bare it all, with several scenes featuring full nudity. At the Cannes Film Festival press conference for the film on Monday, the 61-year-old actor discussed the “vulnerable experience.”

“Going into it, it was really spelled out — the level of vulnerability and rawness that was really required to tell the story,” Moore said. “And it was a very vulnerable experience and just required a lot of sensitivity and a lot of conversation about what we were trying to accomplish.”

More from Variety

Zhang yimou to direct ‘three-body problem’ movie, is netflix about to turn into a franchise factory, china box office: ‘be my friend’ opens ahead of ‘furiosa’ and ‘civil war’ on dragon boat holiday weekend, ‘deadpool & wolverine’ to incur only ‘minimal cuts’ ahead of confirmed china theatrical release, new bundles point to broadband’s growing power in svod packaging, china box office: ‘doraemon the movie: nobita’s earth symphony’ wins opening weekend, ahead of ‘garfield’, more from our brands, taylor swift brings travis kelce onstage at london eras tour show, lewis hamilton: the spanish grand prix usually tells you how good your car is, espn seeks more ratings gold with clark-reese showdown, the best loofahs and body scrubbers, according to dermatologists, doctor who boss: yes, that star wars film inspired finale’s ruby twist, but there are ‘more revelations to come’, verify it's you, please log in.

Share full article

A young man in a sepia-toned photograph wearing a Chinese military uniform.

In Search of My Father’s Frontier: His Years in Mao’s Army

For nearly a decade, I worked in China as a Times correspondent and bureau chief. But it wasn’t until researching for a book that I uncovered the full story of my father’s role in Communist rule.

Yook Kearn Wong, then a member of the Chinese military, in 1953. Credit...

Supported by

By Edward Wong

Edward Wong is a diplomatic correspondent in Washington and the author of the new book “At the Edge of Empire: A Family’s Reckoning with China,” from which this article is adapted.

June 23, 2024 Updated 5:52 p.m. ET

I didn’t have much time. I was in the remote town of Altay in China’s far northwest region of Xinjiang, on the mountainous border with Russia, Mongolia and Kazakhstan, thousands of miles from my base in Beijing as a bureau chief for The New York Times.

In this case, my mission was personal: I was seeking records in Altay’s Civil Affairs Bureau on my father’s service in a Chinese army unit six decades earlier. I knew police officers would soon be trailing me, as they did whenever foreign journalists turned up in Xinjiang.

It was 2014. President Xi Jinping had begun enacting much harsher policies in the region, home to Uyghur and Kazakh Muslims. For centuries, control of the area, a vast land of people from myriad ethnic groups living among mountains, deserts and high steppe, has been central to Chinese rulers’ conception of empire .

I knew that finding anything about my father, Yook Kearn Wong, was a long shot. But at the Civil Affairs Bureau, I struck up a conversation in a second-floor office with Wei Yangxuan, a young woman who happened to be an army veteran and helped organize activities for military retirees. I asked her if she knew anything about an old army base of mostly Kazakh cavalry soldiers, where my father and a few other ethnic Han soldiers had served in 1952.

She shook her head no.

I knew I probably wouldn’t return to Altay, and that I had only this one chance. Suddenly I realized it was just past 7 a.m. in suburban Virginia, where my parents had lived for decades. Maybe if I called from my cellphone, Dad could tell Ms. Wei about the Kazakh base.

He answered. I told him I was in Altay.

“You’re where?” he said. He sounded incredulous.

A woman riding a horse herds sheep in a dry, mountainous landscape.

I asked him to describe the Kazakh base to Ms. Wei, then handed her the phone.

They talked for a few minutes. I looked out the window. On the plaza below, I saw two parked police trucks. Around each vehicle stood a few policemen in black uniforms and riot gear — helmets, batons, body armor. I thought I saw one of them look up at the window. I quickly backed away.

Ms. Wei handed the phone back to me.

Dad sounded confused, and a bit concerned. “I just told her about the Fifth Army’s base,” he told me, referring to the unit of Kazakh and Uyghur soldiers in which he had worked. “Now you tell me why you’re in Altay.”

The Uniform

My father rarely talked about China when I was growing up in Alexandria, Va. On nights he came home early, he didn’t sit on the edge of my bed regaling me with stories about his life. In that way, he was like many Asian immigrant fathers of his generation, those men who were intent on building something new for their families and focusing only on what was in front of them.

He had only Sundays off from his job at a Chinese restaurant, Sampan Cafe. On some of those days, we watched American football, and we looked at my math textbooks, algebra or geometry or calculus. He knew numbers. I would learn later that he had studied engineering after the army.

Sometimes I watched him put on a red blazer and black pants to go to work at the restaurant. For decades, this was the only uniform I associated with him.

But one day, while I was visiting from graduate school and starting to ask my parents about their upbringings in southern China, Dad showed me a photograph of himself from his days in the Communist army.

It had been taken in northwest China in 1953. My father’s eyes glimmered, and his skin had none of the lines of age. He wore a plain military uniform and a cap. I ran a finger over a darkened spot in the hat’s center. A shadow there. That was where the red star had been, he said. The symbol of the People’s Liberation Army of China. Dad had sent the photo to Hong Kong, where his parents were living at the time, and his father had rubbed out the star, fearful of what the British colonial authorities might do if they saw it.

I learned more about my father’s past after 2008, the start of nearly nine years I spent as a Times correspondent in China. I traveled to Guangdong Province in the far south, where both my father and mother had grown up. That prompted deeper conversations with them and with my father’s older brother, Sam.

My father was born in Hong Kong in 1932 but was forced to move to his family’s home village in Taishan County in southern China after the Japanese army occupied the British colony in 1941. He graduated from high school in the spring of 1950, the first full year of Communist rule, then entered university in Beijing that fall. He had been intent on going to school in the ancient city that Mao Zedong had chosen as a capital because he embraced the Communist cause, believing the new leaders would rejuvenate China after the ruinous policies and corruption of the Nationalists, or Kuomintang.

There he marched with other university students in a parade in front of Mao in Tiananmen Square. China had entered the Korean War to fight the American military, and he soon dropped out of school to join the new air force. He was proud to do his part to defend the motherland against what party leaders said was an inevitable invasion of China by the American forces once they triumphed on the Korean Peninsula.

His plans were dashed, however, when Chinese officers abruptly ordered him to abandon his training in Manchuria and deploy with the army to the northwest, and ultimately to the frontier with Central Asia. Dad’s offense, he suspected, was that his father was a merchant and had returned to Hong Kong with his mother, while Sam was studying in the United States. Because of that, he was being sent into exile.

It was here that the details of my father’s story remained shrouded in mystery. On that trip to Altay in 2014, I hit a wall: The police officers had indeed found me and followed me until I drove out of town. And in any case, Ms. Wei hadn’t given me any information. There were limits to what more I could learn in China.

But when I moved to Washington in 2018 as a diplomatic correspondent for The Times and began working on a book about my family and the arc of modern China, I returned to the subject of Altay and Dad’s other work in Xinjiang. I spent dozens of hours interviewing him in my childhood home, and reading letters he had written to Sam after his military service.

I was fascinated by the details of his role in how Mao and Xi Zhongxun , the father of Mr. Xi, had established military control of the northwest, a crucial moment that few people alive today can speak about. It laid the groundwork for Communist rule over Xinjiang and the quashing of independence movements there, and it presaged more recent efforts by Beijing at repressing Uyghurs and Kazakhs through the internment camp system, forced labor and mass surveillance.

Dad witnessed firsthand the early forms of control that have evolved into what we see today, and was a participant in it. The more I talked to him about his past, the more I realized the value in recording his memories, especially those of his time on the northwest frontier.

Mission to Altay

As my father told it, his trip from Manchuria to the far reaches of Xinjiang took half a year. He rode with other Han soldiers in the open back of army trucks that rumbled along the length of the Great Wall and beyond. He was filled with dread about what awaited him, but he was also struck by the beauty of a China he had never seen.

Heading west from Xi’an, the capital of Shaanxi Province, he remembered the persimmons, plump and smooth and the color of burned copper, hanging low from the trees in the autumn light. How sweet it would be to bite into one. Dust trailed the truck as it continued down the dirt road. He was heading into a vast and sere land, a place of ancient paths and towns, many now long gone. A frontier. The warriors who came before them, also gone.

By the time he reached a sensitive area north of the Tian Shan mountains, near the borders with the Soviet Union and Mongolia, snow covered the ground. In the town of Burqin, Kazakhs rode through the streets on horses. To my father and the other Han soldiers, it was a new world, wilder than any they had imagined existed in China.

He finally arrived at the base outside Altay on Jan. 27, 1952, the Lunar New Year, the start of the year of the Water Dragon. There were 1,000 Kazakh soldiers there. His mission, it turned out, was indoctrination.

Each morning, my father told me, Kazakh soldiers gathered in a hall. The Han Chinese political commissar, who was also the highest-ranking officer, sat at the head of the room, and the other Han soldiers sat near him. He did all the talking. With the help of an interpreter, he ran through the party’s lines of propaganda.

He talked about the Communist revolution and how it was ushering China into a new era. He talked about the end of the old feudal society and the elimination of classes. He talked about the leadership of Mao and the proletarian struggle and the need to resist imperialist powers, especially the United States.

Mao’s revolutionary vision was rooted in an uprising of peasants, like the Kazakh nomads here, and not just in the struggle of workers in cities, the officer said. Though the Han were the dominant ethnic group in the heartland, the officer said the native ethnic groups of the west and the Han had equal stakes in the future of China, and the party respected the cultures, beliefs and autonomy of all the peoples.

The routine was the same every day. In the morning sessions, my father sat quietly and listened to the officer. He thought he couldn’t talk about the party yet with others, to teach its doctrines and its ideas. The party was a mysterious beast, something unknowable for now, and he understood it would take time to learn its ways.

In the afternoons, the visiting Han soldiers huddled in their room, putting their hands near the coal stove to stay warm. It was so cold that the hunks of beef and sheep and horse meat that the soldiers arranged in piles by the wall stayed frozen. Every now and then, outside of the formal sessions, Dad tried speaking with one of the Kazakh soldiers and soon began to learn a few words of their language.

My father told me that relations between the Han and people of other ethnicities in Xinjiang were calm, but I found a darker assessment in a letter he sent to Sam on May 12, 1963, years after he had left Xinjiang. He wrote that the 15 or so ethnic groups he observed had one thing in common, which was “a deep hatred of the Han people.”

Dad described how after 1946, when the Nationalist general Zhang Zhizhong became governor, “the Han were violent and aggressive, actively oppressing the various ethnic peoples, which led the three main regions of northern Xinjiang (north of the Tian Shan) to rise up in revolt.”

As my father began his postings in those volatile northern areas, he hoped the People’s Liberation Army would be able to win the trust of the local groups. Surely Communist governance would be different from the earlier conquests, he thought.

But there were episodes of bloodshed from the start of military rule. In early 1951, a year before my father arrived in Altay, Han soldiers captured a Kazakh insurgent leader, Osman Batur, who had fought for years for nomad autonomy. They executed him by hanging that April. Hundreds of his compatriots fled across the Himalayas into India and eventually ended up in Turkey. Osman became a symbol of Kazakh nationalism.

The Labyrinth

After Altay and a couple of postings in the fertile Ili Valley, my father was sent to the town of Wenquan , near Soviet Kazakhstan, to work on one of the first military farming garrisons set up to control Xinjiang. Senior army officers recommended him for party membership, which filled him with hope.

In 1957, he got the chance to return to interior China and enroll in university in Xi’an to study aerospace engineering. But he soon discovered that he would likely never become a party member. Some officials still harbored suspicions of him because of his family background.

At the same time, Mao threw China into turmoil. During the famine that resulted from Mao’s failed economic policies of the Great Leap Forward, my father had barely enough food on campus to subsist and grew gaunt, with rib bones in sharp relief. His feet became swollen, and he could barely walk. He was one of the lucky ones: Historians later estimated that 30 to 40 million people perished in the famine between 1958 and 1962.

As the famine ebbed, he realized he had to escape China. He managed to flee in 1962 to the Portuguese colony of Macau and then reunite with his parents in Hong Kong. He moved to the Washington area in 1967 with his grandmother to join Sam.

My father managed to avoid the violence of the Cultural Revolution, which Mao ignited in 1966. He told me he likely would have been persecuted by Red Guard zealots, given his family background, and might not have survived. Other family members were not so lucky: A younger cousin who had been a childhood playmate and who was working as a scientist in Shanghai was wrongly accused by Red Guards of being a C.I.A. agent. He killed himself in 1969, leaving behind a wife and two sons.

Decades later, another cousin of his who had grown up in very different circumstances, Gary Locke, would serve in Beijing as the U.S. ambassador to China while I was living and working there.

I marvel at the ways my family’s story has looped like a Möbius strip around multiple generations and around the history of China. Twice, I have stood in Tiananmen Square watching Mr. Xi wave to a military parade, just as my father looked for Mao atop the crimson imperial gate while marching there in 1950.

By moving to Beijing as a Times correspondent, I became a proxy for that immersion in the People’s Republic of China that my father ended in 1962. In a letter to his brother more than four months after returning to Hong Kong, he wrote, “When I think back on these dozen years, it is as if I have gained nothing — a thought that makes me quite melancholic. Normally when I speak to others about this journey, I hide the fact that I was in the army, or that I ever tried to join the party.”

My father turns 92 next month, and he looks back on his years in China now with clear eyes but without that earlier bitterness, having built a life over nearly six decades in America. He even talks about that period with some nostalgia, saying that at least he was part of something larger then, part of a moment when most citizens embraced a sense of national duty and collective purpose.

One afternoon last year, when I was still writing my book, he told me that the Communists had been necessary for China, for reviving it after the war with Japan and the corrupt rule of the Nationalists.

But the party had fundamental flaws. While my father had done everything he could to demonstrate his loyalty, to show he wanted to work for the future of China under the new rulers, even going to the frontier for them, party officials would not bring him into their fold. Mired in their fears, in their ideas of power, in the labyrinth of their own making, they had no reserves of trust or faith or generosity.

Their leaders were no exception, he said.

Years ago, as we sat together in my childhood home after dinner, he told me he still remembered the words to “The East Is Red,” the anthem that most Chinese citizens learned by heart in the 1960s. He cleared his throat and sang the words in Mandarin with no hesitation, even though it had been decades since he had last done this.

The east is red, the sun is rising

From China comes Mao Zedong

He strives for the people’s happiness

Hurrah, he is the people’s great savior!

After he finished, he sat back on the couch and gave me a faint smile. At that moment, he was again the young man in a tan uniform with a red star on his cap riding a horse through the high valleys of the northwest, there at the edge of empire.

Edward Wong reports on global affairs, U.S. foreign policy and the State Department. He is the author of the book “At the Edge of Empire: A Family’s Reckoning with China.” More about Edward Wong

The Great Read

Here are more fascinating tales you can’t help reading all the way to the end..

A Red State Weatherman: Chris Gloninger said he was hired by a Des Moines television station to talk about global warming in his forecasts. That’s when things heated up .

What Trump Learned From Don King: For more than three decades, the boxing promoter and Donald Trump have shared an enduring friendship. They also share some defining similarities .

Murray Hill’s Showbiz Dream: For years, the comedian wowed ’em in the clubs with his drag-king lounge act. Now, against all odds, he’s breaking out .

Pregnant With Nowhere to Go: As the war in Gaza killed all hope around her, a Palestinian woman fought to bring a new life into the world .

Smelling Parkinson’s: A woman first noticed the disease’s scent on her husband. Now, her abilities are helping unlock new research in early detection .

COMMENTS

Time Trip on a Moebius Strip
Time Trip on a Moebius Strip is a science fiction mystery novel about sixteen famous people of history who disappeared and are presumed dead. In the novel they all find themselves lost in another dimension. The main character is a marine biologist who enters this other dimension by way of a vehicle riding upon a Moebius strip inside of a giant ...
The Timeless Journey of the Möbius Strip
Melding history, memory, and prophecy, the novel follows the Buendía family through cyclical patterns of behavior and emotion. An exchange between two family members illustrates this central ...
Here's The Actual Science Behind That Huge Plot Point in Avengers
The time-travel jargon also discusses inverting a Möbius strip. A normal Möbius strip is a surface with only one side. You can create one easily by taking a strip of paper, twisting it once, and then sticking it together. ... Time travel is one of those captivating scientific concepts that is perhaps furthest from implementation by scientists ...
Time Travelling Using Mobius Strip
Is time travel possible by applying the Mobius Strip principle? Video segment explaining the "Grandfather Paradox" by courtesy of Andrew Campfire.A Mobius St...
Time Trip on a Moebius Strip by D. Richard Lewis
Read reviews from the world's largest community for readers. Time Trip on a Moebius Strip is a science fiction mystery novel about sixteen famous people of…
TIME TRIP ON A MOEBIUS STRIP
A scientist enters another dimension through a giant seashell and meets a cast of historical characters.
"TIME TRIP ON A MOEBIUS STRIP" by D. Richard Lewis (The Sci-Fi Novel)
http://moebiustripper.blogspot.com The author of "Time Trip on a Moebius Strip" discusses his science fiction mystery novel.
Möbius strip
A Möbius strip made with paper and adhesive tape. In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE.
Amazon.com: Customer reviews: Time Trip on a Moebius Strip
Find helpful customer reviews and review ratings for Time Trip on a Moebius Strip at Amazon.com. Read honest and unbiased product reviews from our users.
The Mathematical Madness of Möbius Strips and Other One-Sided Objects
This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a ...
The Mobius Strip & Time Travel
BLUE BOLT. TIME PARADOX THREE: "Once through the main portal the time associated within the walls of the monastery and the land beyond flowed like the surface of a Mobius Strip, non-orientable." "What is not known with any amount of certainty is when passing through the portal from the outside into the monastery, is the measurable distance from ...
An enduring Möbius strip mystery has finally been solved
An enduring Möbius strip mystery has finally been solved. ... The optimal paper Moebius band. arXiv:2308.12641. Submitted August 24, 2023. ... We are at a critical time and supporting climate ...
What Is a Möbius Strip?
Having trouble visualizing the Mobius strip? Don't worry! A lot of people have a hard time getting the unique surface of the Mobius strip straight in their minds when they first learn about it. To help, head to the Internet to view an illustrated, moving Mobius strip. Does this help you get a better idea of what the Mobius strip looks like?
Mobius strip
topology. Möbius strip, a one-sided surface that can be constructed by affixing the ends of a rectangular strip after first having given one of the ends a one-half twist. This space exhibits interesting properties, such as having only one side and remaining in one piece when split down the middle. The properties of the strip were discovered ...
Avengers: Endgame's Time Travel Explained (Properly)
Yes, Mobius strip time travel is a pre-existing idea (it's at the heart of the grandfather paradox), but it's not how the film presents time travel. There are two scenes in Avengers: Endgame where time travel is explained. First is Banner ahead of Hawkeye's test mission. Responding to Rhodey's suggestion of killing Thanos in the crib (an ...
The Mobius Strip and The Möbius Strip
The Mobius strip--the common sense-defying continuous loop with only one side and one edge, made famous by the illustrations of M. C. Escher-leads us to some of the strangest spots imaginable. ... 39-60 Tegmark, Max, 132 Thalidomide, 54 Three-torus, 128-130, 140 Time travel, 182-183 Tissandier, Gaston, 3 Topology, xvi, 61-84 Torus eversions, 79 ...
Möbius Strip -- from Wolfram MathWorld
The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving one of the two ends thus produced a half twist, and then reattaching the two ends (right figure; Gray 1997, pp. 322-323). The strip bearing his name was invented by Möbius in 1858, although it was independently discovered ...
Neil deGrasse Tyson Explains the Möbius Strip
What is a Möbius strip? If you've never heard of it, that's alright. Neil deGrasse Tyson and comic co-host Chuck Nice are here to explain what exactly is goi...
PDF The Möbius strip
The Möbius stripis formed from a rectangular strip by gluing the short ends together with a half twist. One unusual property of this surface is that it is one-sided and not two -sided like most of the familiar surfaces in 3 -dimensional space like the sphere. Two -sidedness means that one can define a continuous unit vector valued ...
Mobius Strips: So Simple to Create, So Hard to Fathom
It's easy to make a Möbius strip. Creating a Möbius strip is incredibly easy. Simply take a piece of paper and cut it into a thin strip, say an inch or 2 wide (2.5-5 centimeters). Once you have that strip cut, simply twist one of the ends 180 degrees, or one-half twist. Then, take some tape and connect that end to the other end, creating a ...
The time travel of "Avengers: Endgame," explained by scientists
Inverted Möbius strip. The time-travel jargon also discusses inverting a Möbius strip. A normal Möbius strip is a surface with only one side. You can create one easily by taking a strip of ...
Paradox of the Möbius Strip and Klein Bottle
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you...
Demi Moore on Full Frontal Nudity in 'The Substance'
Demi Moore's new film, the feminist body horror "The Substance," sees Demi Moore bare it all, with several scenes featuring full nudity.
A Times Reporter on His Father's Years in Mao's Army in China
On that trip to Altay in 2014, I hit a wall: The police officers had indeed found me and followed me until I drove out of town. ... By the time he reached a sensitive area north of the Tian Shan ...