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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.

via Richard Patterson / Flickr

A spyware company has developed an easy way to take over any Apple computer, watch, or iPhone so the software giant is asking everyone to update their devices. The malicious software attacks Apple devices through the iMessage app.

"It's absolutely terrifying," said John Scott-Railton, a senior researcher at The Citizen Lab, the company that discovered the hack and reported it to Apple.

What's scary about the hack is that it doesn't require the victim to download or click on anything to take effect. A device can be taken over by simply receiving a message. In the cybersecurity industry, it's known as a "zero-click" exploit.


People who have been attacked by the hack are extremely unlikely to know anything happened. "The user sees crickets while their iPhone is silently exploited," Scott-Railton said. "Someone sends you a GIF that isn't, and then you're in trouble. That's it. You don't see a thing."

The Citizen Lab says the hack has been around since February. It was created by NSO Group, an Israeli company that sells its hacking software to "vetted" customers across the world for counterterrorism and law enforcement purposes.

After the attack was discovered by The Citizen Lab and reported to Apple, it created a fix that's available to users in its latest iOS or Mac OS updates. However, most users shouldn't be too concerned about the hack unless they believe they're being targeted by a government that uses NSO's software.

"This will prevent you from being infected with this exploit going forward," Scott-Railton said. "But what we know is NSO is always trying to find other ways to infect people's phones, and they may turn to something else."

Apple thanked The Citizen Lab for notifying them of the hack. "Attacks like the ones described are highly sophisticated, cost millions of dollars to develop, often have a short shelf life, and are used to target specific individuals," Ivan Krstić, Apple's head of Security Engineering and Architecture, said in a statement.

The hack was developed by NSO Group to deploy Pegasus, the spyware it sells to governments around the world to surveil suspected criminals or terrorists. NSO Group claims that the software is only used for those purposes but it's been found on devices belonging to human rights activists, dissidents, and journalists.

The hack was discovered by The Citizen Lab on the phone of a Saudi dissident. "In this case, it's pretty clear that this person was targeted for being an activist and not for any other reason," Bill Marczak, a Citizen Lab senior research fellow, said according to Today.

The company insists that it can't be used to target Americans' phones. Facebook has accused NSO Group of hacking over 1,400 mobile devices using WhatsApp. NSO has disputed the accusation.

How to update your iPhone:

  1. Plug your device into power and connect to the internet with Wi-Fi.
  2. Go to Settings > General, then tap Software Update.
  3. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now.





For years, a homeless encampment has been growing on Apple property in San Jose, California, and the company is taking some unusual steps to remove it.

According to The Mercury News, dozens of people experiencing homelessness have set up shelter in broken down vehicles, RVs, and makeshift wooden structures on a vacant lot where Apple's North San Jose campus will be built. Apple has been working with local government and non-profit organizations to figure out what to do about the camp.

The company has taken a hands-on approach by making each resident of the encampment an offer on the company's dime: Nine months in a motel room plus 12 months of services to manage addiction, mental health, and long-term housing plans. The move is costing Apple millions of dollars, according to Andrea Urton, CEO of the non-profit HomeFirst, which has been working with Apple to help relocate the residents.

"I think the level of Apple's involvement is amazing, to be quite frank," Urton told The Mercury News. "They could just kick these people off, throw away their belongings and displace them. That's not what they chose to do."


For people who don't want to leave their RVs or other vehicles, an emergency safe-parking site will be provided by the city. Residents were also offered space at Boccardo Regional Reception Center, Santa Clara County's largest homeless shelter.

A few residents have refused all of the offers, but 53-year-old Frank Pacheco told The Mercury News that his new motel room provided by Apple is "the best thing I could ever have."

Pacheco has lived in an RV at the encampment for two years, after a work-related head injury impacted his job as a mechanic.

"It's a wonderful thing that Apple's doing for us," he said. "They don't have to do anything for us. They could just kick us off the property. They could just feed us to the wolves."

Urton said that Apple's funding also will provide residents with clothes, food, dental care—whatever they need—in the hopes that after nine months of housing and services some of them will be ready for employment. However, the cost of living in the area is one of the highest in the nation. While Apple contributing some of its substantial resources to directly address its local homelessness issue is admirable, it's just one piece of a large, complex puzzle that's going to require more long-term, sustainable solutions.

Long-term solutions to the homelessness crisis in the Bay Area and around the nation are not simple, however. Even the temporary solutions offered by Apple are not without controversy. According to the San Jose Spotlight, there have been an assortment of complaints regarding treatment of the homeless population during the clearing of the site, protests from local residents about individuals from the Apple site moving into their neighborhoods. Additionally, some activists are critical about Apple's timeline for clearing the camp before the city had provided the safe parking area for those with vehicles to move to.

In 2019, Apple made a $2.5 billion pledge to address the housing and homelessness crises in the Bay Area, and had promised to make some of the land for its North campus available for affordable housing. However, progress has been slow on that front, which is unsurprising considering the upheaval of the COVID-19 pandemic.

The issue of homelessness is multi-layered and multi-faceted, and Urton points to Apple as a shining example of what companies can do for their part to contribute to solutions.

"If every company took responsibility for what's happening with homelessness in their neighborhood," Urton told The Mercury News, "I think we'd nail it."

Crews Clear North San Jose Homeless Encampment on Apple Propertywww.youtube.com

Photo by Tyler Lastovich on Unsplash

The hardest words to say are, "I'm sorry," but Apple (surprisingly) doesn't have a problem saying them after a whistleblower revealed that human strangers were listening to your private conversations. Apple commendably went a step further and actually fixed the issue that makes it feel like your phone is eavesdropping on you.

The unnamed whistleblower told The Guardian that Siri records conversations as a form of quality control called "grading." The purpose was to allow Apple to improve Siri, but it ended up feeling like one huge privacy violation.

It turns out, Apple's voice assistant could be triggered accidentally, even by muffled background noises or zippers. Once triggered, Siri made audio recordings, some of which included personal discussions about medical information, business deals, and even people having sex. The percentage of people yelling out, "Hey Siri!" while getting it on is probably very small.


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Apple ensured that these recordings wouldn't be linked to data that could identify you, but the recordings were linked to user data that showed location, app data, and contact details. So, yeah, they could actually identify you.

To make things worse, the recordings were listened to by third-party contractors, not Apple employees. "[T]here's a high turnover. It's not like people are being encouraged to have consideration for people's privacy, or even consider it. If there were someone with nefarious intentions, it wouldn't be hard to identify [people on the recordings]," the whistleblower told The Guardian.

Apple did the right thing and apologized for the practice. "We know that customers have been concerned by recent reports of people listening to audio Siri recordings as part of our Siri quality evaluation process. We realize we haven't been fully living up to our high ideals, and for that we apologize," Apple said in a post.

Not only that, they changed their policy to address the concerns revealed in The Guardian article. Now, Apple will no longer record conversations as a default. If you want to share your conversations with Apple so they can make improvements on Siri, you have to specifically opt in. Apple will also stop using third-party contractors to listen to the recordings. Quality control will be left to Apple employees who will review computer-generated transcripts instead of recordings. Any accidental recordings will be deleted.

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Technology has made our lives easier, but it's also ushered in a whole slew of privacy concerns. It's hard not to feel like your phone is your own personal telescreen from "1984," but worse because at least telescreens didn't have addictive Snapchat filters. Why should privacy be the trade-off just because we want the convenience of being able to say, "Hey Siri, what's the difference between a dolphin and a whale?" It's nice to have the peace of mind that we can make robots do our bidding without feeling like they're spying on us – at least when it comes to our iPhones.