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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, einsteinA 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, einsteinSagan 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.

- YouTubewww.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, einsteinA 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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Science

Can't comprehend the 4th dimension? Carl Sagan explains it with an apple in this classic clip.

Sagan was a master science communicator.

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

Carl Sagan and a sliced apple

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?

Enter Carl Sagan, revered as one of the greatest science communicators of his time. He possessed a unique gift for demystifying complex scientific concepts, making them accessible and thrilling for the general public. In 1980, on Episode 10 of the groundbreaking PBS show “Cosmos,” Sagan embarked on a mission to explain the seemingly impossible fourth dimension.

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

Sagan began by discussing how a two-dimensional being living in a flat world would perceive a three-dimensional object like an apple.

“Imagine we live in this ‘flatland’/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.”

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. At this point, Sagan is asking the viewer to expand their minds to understand the fourth dimension metaphorically.

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 with thought-provoking visuals.


This article originally appeared last year.

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Science

Carl Sagan's irrefutable 1990 argument for using all U.S. resources to fight climate change

He was way ahead of his time and his logic stands now.

via IslandPalm14/YouTube

Carl Sagan's keynote address at the 5th Emerging Issues Forum at NCSU.

Carl Sagan, the legendary astrophysicist and science communicator, was best known for his incredible ability to express complicated concepts in a way that the everyday person could understand. He did so most notably as host of PBS’s groundbreaking “Cosmos: A Personal Voyage" from 1980 to 1981.

Sagan was also a brilliant futurist who was way ahead of his time. In 1961, he predicted that the clouds of Venus might be home to life, an idea that has gained traction over the past few years. He also predicted many of America's current problems in 1995 and correctly claimed that one day AI would be used for psychotherapy back in the '70s.

He was also ahead of his time when sounding the alarm about Climate Change, evidenced by a 1990 speech he gave at the 5th Emerging Issues Forum. In the keynote address, he said that America should treat the climate crisis as seriously as it did the Cold War. Sagan’s speech was delivered a year after the fall of the Berlin Wall, which concluded the icy, 5-decade conflict between the U.S. and the Soviet Union.

For some context, in 1990, only 30% of Americans were worried about global warming or the greenhouse effect. Today, 54% describe climate change as a “major threat” to the country’s well-being.

- YouTubeyoutu.be

“The amount of money that the United States has spent on the Cold War since 1945 is approximately 10 trillion dollars,” Sagan says, adding that with that amount of money, one could own everything in the country, minus the land.

“How certain was it that the Russians were going to invade? Was it 100% certain? Guess not since they never invaded. What if it was only, let’s say 10% certain? What would advocates of big military buildup have said? We must be prudent. It’s not enough to count on only the most likely circumstance," Sagan continues.

“I ask my friends who are comfortable with that argument, including the editorial page of the Wall Street Journal, why doesn’t that same argument apply to Global Warming? You don’t think it’s 100% likely? Fine. You are entitled to think that. If it’s only a small probability of it happening since the consequences are so serious, don’t you have to make some serious investment to prevent it or mitigate it? I think there’s a double standard of argument working and I don’t think we should permit it.”



Sagan would then list the steps we can take to mitigate the effects of climate change, including eliminating CFCs (chlorofluorocarbons), increasing fuel efficiency in cars and trucks, seeking out new alternative energy sources, dealing with the global population crisis and planting trees. "A tree is an engine for taking carbon dioxide out of the atmosphere and it does it. It’s not the only thing a tree does, but that is one of the things that trees are good for and it's especially relevant to this issue,” Sagan says.

Sagan’s solutions are the same ones we discuss today, although fears of a global population crisis have waned over the years.

Sagan concluded his address by comparing the dangers of global warming to those faced by the U.S. during the Cold War and making an argument that many support today: fighting climate change is also good economic policy.

"So, what I say to those who complain that it is too uncertain–beyond pointing out the standards that were applied to the Cold War ought to be applied here–I say look, every one of these steps makes good sense, makes good economic sense,” Sagan says. “And think of all of the industries that are implied by what I have just said, especially alternative energy sources. There is money to be made in developing a technology which will appropriately address greenhouse warming."

You can watch the entire address here:

- YouTubewww.youtube.com

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Politics

Carl Sagan's answer when Ted Turner asked if he's a socialist is a roadmap for rebuilding America

Carl Sagan really had all the answers, didn't he?

via David Grinspoon / YouTube

In 1989, CNN founder Ted Turner asked iconic astrophysicist and science communicator Carl Sagan about his political leanings.

Surely, someone with such a deep understanding of the universe and a passion for humanism would have important insights into how we organize ourselves politically.

"Are you a socialist?" Turner asked Sagan. "I'm not sure what a socialist is," he replied.

While it seems unlikely Sagan was unfamiliar the concepts of socialist political theory, he was smart to sidestep the loaded term.

Socialism is such a broad concept that, in the modern era, it could be applied to numerous countries of varied economic development from Cuba to Canada. Conservatives tend to see it as a malignant political idea and point to Venezuela as a failed socialist state.

While many liberals point to Democratic Socialist countries in Europe such as Denmark and Germany where people have a standard of living that is comparable and, in some ways superior, to the United States.

Back in the '80s "socialist" was used by the U.S.S.R. to describe its totalitarian communist regime, so Sagan was smart to distance himself with any association with the bloc.

Ted Turner asks Carl Sagan if he is a socialist.www.youtube.com

So Sagan provided his own definition.

"But I believe the government has a responsibility to care for the people," he said.

"I'm talking about making people self-reliant, people able to take care of themselves," he continued. "There are countries which are perfectly able to do that. The United States is an extremely rich country, it's perfectly able to do that. It chooses not to. It chooses to have homeless people."

He also noted that in 1989 we were 19th in infant mortality. "We are 19th in the world in infant mortality. Eighteen other countries save the lives of babies better than we. How come?" Sagan asked, rhetorically.

Sadly, things have only gotten worse over the past 31 years. The U.S. is currently ranked 47 infant mortality.

"They just spend more money on them," said Sagan. "They care about their babies more than we care about ours. I think it's a disgrace."

Sagan also believed that the U.S.'s priorities are completely mixed up. We have a hard time helping our most vulnerable citizens, but we still have enough money to pay for high-priced weapons systems.

"Just look at what something like 'Star Wars,'" Sagan said, pointing to a costly '80s defense program. "We've already spent $20 million on it. And if these guys are permitted to go ahead, they will spend a trillion."

31 years later, things haven't improved, we're near an all-time high in military spending at a time when the world has never been more peaceful.


"Think of what that money could be used for: to educate, to help, to bring people up to a sense of self-confidence," Sagan added.

"To improve not just the happiness of people in America, but their economic standing, to improve the competitiveness of the US compared to other countries. We are using our money for the wrong stuff."


This article originally appeared on 10.5.20

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