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45 years ago, Carl Sagan beautifully explained the fourth dimension with just an apple

Sagan was the Mister Rogers of complex scientific concepts.

via Carl Sagan Planetary Society/Wikimedia Commons and John Finkelstein/Pexels

Carl Sagan used a sliced apple to perfectly explain the fourth dimension.

The concept of the fourth dimension seems beyond human comprehension. As three-dimensional beings, we are unable to see beyond a physical object's height, width and depth. What else could there be? Even if you understand the concept, it is almost impossible to picture it in your mind, which is bound by the limits and realities of the physical world around us.

Enter Carl Sagan, revered as one of the greatest science communicators of his time. Perhaps best known for his research into extraterrestrial life, he was one of the first people to demonstrate that life could have existed on Mars. Sagan possessed a unique gift for demystifying complex scientific concepts, making them accessible and thrilling for the general public. If you never had the pleasure of watching him on television, you could imagine him as something of a Scientific Mister Rogers. Friendly, a wonderful storyteller, and always able to distill difficult lessons into their simplest form.

In 1980, on Episode 10 of the groundbreaking PBS show “Cosmos,” Sagan embarked on a mission to explain the seemingly impossible fourth dimension.


carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein A great communicator and handsome, to boot. Giphy

Many of us have commonly heard of time being considered the fourth dimension. That's not so hard to understand — in order to locate an object in the universe, you'd need to know three dimensions of its spatial location and also the time during which it exists.

But there is also a more theoretical and harder to understand place, where all four dimensions are spatial. It is nearly impossible for any of us to comprehend... without the help of a gifted teacher.

What’s excellent about Sagan’s explanation is that he uses simple and relatable objects: an apple and a Tesseract, or a hypercube.

carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein Sagan explains that if an apple existed in a 2-dimensional space, anyone living in this "flatland" would only see a cross-section of it at a time. Giphy

"In discussing the large scale structure of the cosmos, astronomers sometimes say that space is curved. Or that the universe is finite but unbound," Sagan begins. "Whatever are they talking about?"

Yeah, this guy gets it.

Sagan then goes on to explain how a two-dimensional being living in a flat world would perceive a three-dimensional object like an apple.

Watch his full explanation here. It's hypnotic and entertaining and incredibly enlightening.

- YouTube www.youtube.com


“Imagine we live in this ‘Fllatland’/2-D plane with no concept of ‘up’ or ‘down.’ Then along comes a 3-D object like an apple. We do not even notice it until it crosses our plane of existence — and even then, we have no idea what the apple is,” Sagan explains. “We see only a fragment as it passes through our plane. There is no way we can comprehend the 3-D quality/dimension of the apple, because it is more than we can understand. We only have the evidence of what has passed through our plane.”

To further demonstrate, Sagan stamps the apple into an inkpad and then onto the surface in front of him, which represents Flatland and all of its inhabitants. Inside Flatland, the apple exists only as its points of contact on the paper; or four small dots. He adds that as the apple passes through the 2-dimensional Flatland, its cross-section changes. So someone living in that plane of existence would experience the apple as an ever-shifting and rearranging set of shapes or objects. Wild!

Sagan then related this two-dimensional experience of the third dimension to how we might try to understand the fourth. To do so, he used the Tesseract, a four-dimensional cube, to demonstrate how difficult it is for us to perceive or visualize dimensions beyond our own three.

carl sagan, cosmos ,4th dimension, 3-D, 4-D, 2-D, physics, theoretical physics, math, science, space, spacetime, einstein A tesseract can not exist in 3-dimensional space, but it can be approximated the same way a cube can be drawn on paper. Giphy

Sagan explains that the tesseract is a cube expanded into a 4th dimension, but "I cannot show you a tesseract because I, and you, are trapped in three dimensions." But what he can do is show us a 3-dimensional rendering of one. Just like a cube can be drawn and approximated (or cast a shadow) onto a piece of paper, a 4-dimensional tesseract can be imperfectly represented in 3-dimensional space. Still following?

At this point, Sagan is asking the viewer to expand their minds to understand the fourth dimension metaphorically. Though we cannot see it or even properly visualize it, that doesn't mean that the things we can see can't offer clues and lessons about the fourth dimension.

Studying 4-dimensional space can help in our understanding of the universe around us. Just because we see and experience only three dimensions doesn't mean that's all that exists. It's critical for physicists and mathematicians to be able to understand and map these theoretical spaces to better comprehend things we otherwise can not explain. Remember the ever-changing, rearranging set of shapes as the apple passes through Flatland?

Sagan’s demonstration of the fourth dimension isn’t just a wonderful explanation of a scientific idea that many of us find difficult to comprehend; it’s also a great example of how to teach complex ideas by combining clear explanations, everyday concepts everyone can understand, and brilliant storytelling.

This article originally appeared last year. It has been updated.

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Carl Sagan once easily debunked flat Earthers with just a piece of cardboard

The science doesn't lie.

Image via YouTube

Carl Sagan on 'Cosmos'

Over the past few years, there has been a growing number of people who believe the Earth is flat. A 2019 YouGov survey of more than 8,000 Americans found that as many as one in six are "not entirely certain the world is round."

Flat Earth Theory has, surprisingly, gained a lot of traction. A 2021 study published in the National Library of Medicine posited that the theory is buoyed by "the cognitive tendency to interpret, favor, and recall information in order to strengthen one's personal beliefs" or, in other words, confirmation bias. Though the "how" and "why" of Flat Earth Theory and its popularity is fascinating (and troubling, to be honest), the scientifically proven truth is that the Earth is round. It is a globe. It is spherical.

Of course, the knowledge that the Earth is round is not new. Ancient Greek philosophers across centuries studied and found evidence that the Earth is indeed round thousands of years ago. Way back in the 6th century BC, Pythagoras first proposed the Earth was round from observing the shape of the Moon. In the 5th century, Empedocles and Anaxagoras noticed evidence of the Earth's true shape by observing its curved shadow during lunar eclipses. In the 4th century, Aristotle argued the Earth was round after noting how ships disappear "hull-first" over the horizon line. In the 3rd century, Eratosthenes actually calculated the Earth's circumference using geometry and shadows with shocking accuracy.

earth, globe, sphere, flat earth, skeptics, scienceWe've got the whole (round) world in our hands. Image via Canva

Naysayers remain skeptical, and there's probably no changing their minds, but to this day, experts insist the Earth is round and back it up with cold, hard science. NASA posted this video just days ago. Watch:

- YouTubewww.youtube.com


Here's where Carl Sagan comes in.

Sagan hosted the original version of TV's Cosmos: A Personal Journey in 1980-81. According to PBS, Cosmos would become "one of the highest-rated programs in the history of public television" largely due to Sagan's ability for "reinterpreting intricate scientific jargon into elegant and memorable statements that the common person can easily conceptualize and appreciate." The show would be revived in 2014 with astrophysicist Neil deGrasse Tyson at the helm.

In the first episode of Cosmos, Sagan easily proved the Earth was a sphere using a piece of cardboard, some sticks, and the work of none other than the ancient Libyan-Greek scholar, Eratosthenes. Watch:

- YouTubewww.youtube.com

"How could it be, that at the same moment, a stick in Syene would cast no shadow and a stick in Alexandria, 800 km to the north, would cast a very definite shadow?" Sagan asked. "The only answer was that the surface of the Earth is curved," he concluded. "Not only that, but the greater the curvature, the bigger the difference in the length of the shadows."

Considering the distance between the two cities and the lengths of the shadows they produced, Eratosthenes was able to determine that the Earth had a seven-degree curve. He used that calculation to speculate the Earth was 25,000 miles in circumference.

These days, we know that the earth is 24,901 miles in circumference, which means Eratosthenes was less than 100 miles off. Didn't we say his accuracy was shocking? Not bad for over 2,000 years ago.


This article originally appeared five years ago.

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The U.S. Air Force concocted a serious plan to nuke the moon in the 50s as a show of power

A young Carl Sagan was one of the scientists on the team that planned it.

Photo credit: Canva

The moon nearly had a man-made crater on it.

Over the past 70 years, scientists have created detailed maps of the entire surface of the moon in minute detail, right down to every crater and rock formation. But those maps almost looked a lot different, considering the fact that the United States wanted to detonate a nuclear bomb on the surface of the moon a decade before we sent the first humans there.

That's right, Project A119 (which might as well have been called Project Nuke the Moon) was a real U.S. Air Force project to send an atomic bomb to the moon and detonate it in a spot where the explosion would be seen from Earth. Why? Because we could, and because we wanted the Kremlin to see that we could, in a nutshell.

That team of scientists working on the project included a young graduate student named Carl Sagan. Yes, that Carl Sagan, who became one of the most famous and beloved cosmologists and science communicators of all time. If you're wondering whether he thought nuking the moon was a whackadoodle idea or not, apparently he was at least somewhat on board with it. He thought it might reveal information about possible microbes or organic compounds on the moon.

- YouTubewww.youtube.com

Let's step back for a minute here. This was the 1950s, a time when much of our scientific advancements and nearly all of our space research was inextricably linked to the Cold War. Support for science was largely dictated by political and military aims, which left scientists to mold their own goals and aims around the projects the government wanted to explore.

If the military wanted to create an explosion on the moon big enough for the Kremlin to see it and feel intimidated, scientists would make the most of the opportunity to learn what they could from it. Some of the team were interested in what the detonation would reveal about the chemical makeup of the moon. Others were interested in studying the seismic effect of the blast on the moon's subsurface structure.

The top-secret project, known by the benign title "A Study of Lunar Research Flights," was launched in 1958 and led by physicist Leonard Reiffel, who would eventually become deputy director of NASA's Apollo Program. To his credit, he did try to explain to the government why nuking the moon might not be such a great idea, scientifically speaking.

"I made it clear at the time there would be a huge cost to science of destroying a pristine lunar environment," Reiffel told The Observer. "But the US Air Force were mainly concerned about how the nuclear explosion would play on Earth."

The plan was to detonate a bomb on the Terminator Line, the border between the light and dark side of the moon, which would be the location most visible from Earth. And as asinine as it might sound to us now, the goal of this enormous undertaking really was just to flex our muscles—to show Russia that we could best them in both the space and the arms race.

"It is a pretty interesting window into the sort of American mindset at that time," Alex Wellerstein, a historian of science and nuclear technology, told the BBC. "This push to compete in a way that creates something very impressive. I think, in this case, impressive and horrifying are a bit too close to each other."

Reiffel himself told The Observer in 2000, ‘It was clear the main aim of the proposed detonation was a PR exercise and a show of one-upmanship. The Air Force wanted a mushroom cloud so large it would be visible on Earth."

Would it have even worked, though? According to Reiffel, they could have gotten the bomb within two miles of where they wanted it and could have detonated it, creating a big enough flash bang to see from here. However, there wouldn't have been a mushroom cloud, since there's very little atmosphere on the moon. Without the resistance of a dense atmosphere, the dust and debris from the explosion would just keep expanding outward; it wouldn't curl back inward into any kind of formation like it would on Earth.

Ultimately, nuking the moon didn't happen, though the reasons the project was scrapped are classified and have never been revealed. Thankfully, we went ahead with sending humans to the moon instead of our most notorious weaponry. Can you imagine how much bombing the moon would have changed our approach to space exploration?

astronaut, moon, NASA

As British nuclear historian David Lowry said according to The Guardian, "It is obscene. To think that the first contact human beings would have had with another world would have been to explode a nuclear bomb. Had they gone ahead, we would never have had the romantic image of Neil Armstrong taking 'one giant step for mankind.'"

It was "one giant leap for mankind," actually, but who's counting? Let's all just be grateful we got that giant leap instead of a big ol' nuclear crater that would forever change the way we see the moon, literally and figuratively.

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In his last interview, Carl Sagan warned that America will be taken over by a 'charlatan' political leader

Sagan never would have believed in a fortune tellers but dang this is prescient.

via PBS

Astronomer Carl Sagan was the original host of "Cosmos" back in 1980 and it became most watched show in public television history. Few science communicators have been able to match his talent for stoking wonder about the universe.

Shortly before his death in 1996, he appeared on "Charlie Rose" and made a dire warning about how the average Americans' lack of skeptical, scientific thinking could lead to disastrous consequences.

Today, we can see the problems that are happening due to America's anti-science streak whether it's anti-vaxxers, conspiracy theories or climate change deniers.

Sagan was right, America will suffer due to a lack a lack of scientific skepticism.


Carl Sagan and Government_ Charlie Rose.wmvwww.youtube.com


"We've arranged a society on science and technology in which nobody understands anything about science and technology, and this combustible mixture of ignorance and power sooner or later is going to blow up in our faces," he told Rose. "I mean, who is running the science and technology in a democracy if the people don't know anything about it?"

He then warned that our lack of critical thinking leaves us vulnerable to those who wish to exploit our ignorance.

"Science is more than a body of knowledge, it's a way of thinking," he says. "If we are not able to ask skeptical questions to interrogate those who tell us something is true to be skeptical of those in authority, then we're up for grabs for the next charlatan political or religious who comes ambling along."

Sagan believes that a democracy cannot function without an educated populace.

"It's a thing that Jefferson lay great stress on. It wasn't enough, he said, to enshrine some rights in the Constitution and the Bill or Rights, the people had to be educated and they have to practice their skepticism and their education," he says. "Otherwise, we don't run the government, the government runs us."


This article originally appeared five years ago.

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