(CNN) "I don't want to be a flat Earther," David Weiss says, his voice weary as he reflects on his personal awakening. "Would you wake up in the morning and want everyone to think you're an idiot?"

But Weiss is a flat Earther. Ever since he tried and failed to find proof of the Earth's curve four years ago, he's believed with an evident passion that our planet is both flat and stationary -- and it's turned his world upside down.

"I absolutely freaked out," Weiss tells CNN in a phone interview. "It literally whips the rug out from underneath you."

Now, Weiss finds it tedious to associate with the majority of people -- though he "unfortunately" still has some friends who believe in a round Earth. "I have no problem with anybody that wants to believe we live on a ball. That's their choice," he says. "It's just not something I resonate with."

Weiss' preferred community is those who share his life-altering belief.

And that community is vast.

This week, the businessman attended the third annual Flat Earth International Conference, held at an Embassy Suites hotel in suburban Dallas, Texas. Organizers told CNN that about 600 others went too.

Previous conferences have taken place in Raleigh and Denver -- while Brazil, Britain and Italy have also held flat-Earth conventions in recent years.

The event's schedule resembled any corporate conference, with some fairly noticeable twists. Speakers gave presentations including "Space is Fake" and "Testing The Moon: A Globe Lie Perspective." Awards for the year's best flat Earth-related videos were handed out. And believers reveled in an opportunity to meet several of the movement's most influential minds.

A merchandise stall at last year's Flat Earth International Conference in Denver, Colorado.

"We've all been communicating online (but) this brings us together so we can shake hands and give each other hugs," says Weiss. "We can collaborate, we can make new friends. Because guess what, our old friends... we lost a lot of friends."

On a clear day, the curvature of the Earth can be seen from an airplane window. But remarkably, the hundreds of flat Earthers at the Dallas gathering were just a small portion of the movement.

People in every pocket of this spherical planet are rejecting science and spreading the word that the Earth is flat.

There's no clear study indicating how many people have been convinced -- and flat Earthers like Weiss will tell you without evidence there are millions more in the closet anyway, including Hollywood A-listers and commercial airline pilots -- but online communities have hundreds of thousands of followers and YouTube is inundated with flat-Earth content creators, whose productions reach millions.

A YouGov survey of more than 8,000 American adults suggested last year that as many as one in six Americans are not entirely certain the world is round, while a 2019 Datafolha Institute survey of more than 2,000 Brazilian adults indicated that 7% of people in that country reject that concept, according to local media.

The flat-Earth community has its own celebrities, music, merchandise -- and a weighty catalog of pseudo-scientific theories. It's been the subject of a Netflix documentary and has been endorsed by figures including the rapper B.o.B

Each year, more flat-Earth events fill the calendar, organizers say.

"I've never seen anything grow this fast," says Robbie Davidson, the founder of the Dallas conference. "I would say that within 10 years, the numbers are going to be astounding... next year, there's going to be a conference in every major country in the world."

But experts are wondering if the movement is really harmless -- and whether we're even approaching the edge of its influence.

Falling off the edge

When Davidson first heard that people really do believe in a flat Earth, "I just laughed and said, 'they've got to be the stupidest people ever.' Who in their right mind could believe something so dumb?"

A couple of years later, Davidson was setting up the first international flat Earth conference. Like most of the speakers at the event CNN spoke to, he was convinced after he decided he couldn't prove the Earth's roundness.

For Davidson, a born-again Christian, the most logical explanation for the conspiracy of the millennium goes like this: "Let's just say there is an adversary, there is a devil, there is a Satan. His whole job would be to try to convince the world that God doesn't exist. He's done an incredible job convincing people with the idea that we're just on a random speck in an infinite universe."

A digital illustration of a flat earth.

The reality, says Davidson, is that the flat Earth, sun, moon and stars are contained in a "Truman Show"-like dome. From there, pitfalls can be easily dismissed -- like photos of the Earth from space, which flat Earthers believe are photoshopped. "This all goes away if they put a 24/7 camera feed on the moon," he adds.

And Davidson quickly found a large online community believing the same thing. "I thought doing a conference would just take it to the next stage where the media and the world will look at it and say, 'wait a minute -- something must be going on. This is not just some internet fad, or a bunch of crazy people online. They're now meeting in buildings.'"

He has a few things he wants to make clear to a flat-Earth novice. Firstly, and most importantly -- "none of us believe that we're a flying pancake in space." The community merely believes that space does not exist, the world sits still and the moon landing was faked. The jury is out on gravity -- but as Davidson notes, no one has ever seen it.

Secondly -- no, you won't fall off the edge. While flat Earthers' views of the world vary, most believe the planet is a circular disk with Antarctica acting as an ice wall barrier around the edge.

And thirdly, modern flat Earthers have little in common with the Flat Earth Society, a group that has existed for decades and has more than 200,000 followers on Facebook.

Samuel Shenton, founder of the International Flat Earth Research Society (IFERS), in 1967.

That organization, some speakers told CNN, is a government-controlled body designed to pump out misinformation and make the flat-Earth cause sound far-fetched to curious minds. Davidson calls their theories "completely ridiculous."

The Flat Earth Society told CNN: "We are not a government-controlled body. We're an organization of Flat Earth theorists that long predates most of the FEIC newcomers to the scene."

"It probably goes without saying that we find no joy in this sectarianism, or the elevated emotions that surround some of our disagreements," the group added in response to criticism from speakers at the conference. "We wish the Flat Earth International Conference organizers all the best, but we remain steadfast in our own convictions."

But flat Earthers don't pretend to have all the answers. "People don't really know 100% what (the Earth) is, we're just questioning what we're being told it is," Davidson explains.

Several members of the community have carried out their own experiments, like bringing spirit levels onto airplanes, that have supposedly proved their thesis.

They haven't. To be absolutely clear, the Earth is not flat -- as NASA explains in a fact sheet aimed at fifth to eighth graders.

But most adherents say they're just curious, as all good scientific minds should be. "We love science," Davidson insists.

'It's difficult to break out of that mindset'

Still, most adherents demonstrate plenty of anti-scientific tendencies. It's hard to find a flat Earther who doesn't believe most other conspiracies under the sun; a flat-Earth conference is invariably also a gathering of anti-vaxxers, 9/11 truthers and Illuminati subscribers, to name a few.

It's that hyper-skeptical mindset that helps flat earthers answer the big questions -- like who's hiding the true shape of the planet from us?

"The ruling elite, from the royal family to the Rockefellers, the Rothschilds ... all of those groups that run the world, they're in on it," says Weiss.

Two women at a Flat Earther meet-up in Orange County, California, in 2017.

But "once you get into flat earth, the other (conspiracy theories) get knocked down into another tier," says Mark Sargent, a filmmaker and stalwart of the movement who was featured in the 2018 Netflix documentary "Behind the Curve."

"Everybody here, they've got their top 20 conspiracies -- and you could walk around door to door and those top 20 would differ from person to person. But everybody's number one is always flat Earth," he tells CNN.

It helps that the group has a mutual target. "Most of our ire is pointed towards NASA. That's our bread and butter," Sargent says of the agency flat Earthers believe is ultimately behind the conspiracy.

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But why, and how, could people believe a conspiracy theory so out of this universe?

"People, in essence, are just trying to understand the world," says Daniel Jolley, a senior lecturer in the psychology of conspiracy theories at the UK's Northumbria University. "And they're looking at the world in a gaze where they're biased in their thinking."

"They may have distrust towards powerful people or groups, which could be the government or NASA, and when they look towards evidence that makes sense to them ... this world view (is) endorsed," he says. "It's difficult to break out of that mindset."

Scientists have also noted that a social motive draws people to conspiracy theories -- the desire to "maintain a positive view of the self and the groups we belong to," as social psychologist Karen Douglas of the University of Kent says.

And few groups have as strong a community as flat Earthers.

"This (conference) is an outlet for a lot of people that might otherwise get ostracized by friends and family and co-workers. When they come here, they know it's absolutely a safe space," Sargent says of this week's event.

Timothy John at last year's conference.

But perhaps the most important driver is an underlying need for power and control. "People want to feel safe and secure in the world," Douglas says. And power comes from knowledge -- no matter how questionable it may be.

"When you find out the Earth is flat ... then you become empowered," Weiss says.

That feeling helps believers to understand the world better, as they see it. "You feel like you've got a better handle on life and the universe. It's now more manageable," adds Sargent.

'It's not going to harm anyone'

Sargent could arguably be regarded as the godfather of the modern flat-Earth movement. "If you got into flat Earth, there's a really high chance you read into my stuff first," he tells CNN.

But he had help -- it was the advent of YouTube that gave him a platform to spread his own views, which he says the movement "wouldn't exist without."

"Flat Earth was a binge watch on YouTube," he adds, aided by algorithms and personalized recommendations that turned flat earth research into a never-ending rabbit hole.

Earlier this year, YouTube started burying those videos and reducing recommendations of "borderline content," but video makers like Sargent feel it no longer makes much difference. "Anything on social media is always going to be helpful if it goes viral, right?" adds Davidson. "Well flat Earth has gone viral."

CNN has contacted YouTube for comment.

But the alleged rapid growth of a movement so enthusiastically rejecting fundamental scientific beliefs does have some worried.

"It seems that increasingly, people don't trust scientists and experts, or their motives," Douglas says. "More research needs to be done in this area, and I'm sure there are some positive consequences to believing in conspiracy theories, but early indications suggests that they are more harm than help."

A medieval engraving of a scientist leaving the world, representing the change in conceptions of the world in the 16th century.

"I don't say this often, but look -- there is a downside," admits Sargent, reflecting on the movement he helped encourage. "There's a side effect to flat Earth ... once you get into it, you automatically revisit any of your old skepticism."

"I don't think they're just linked," Sargent says of flat Earthers and populists. "They kind of feed each other ... it's a slippery slope when you think that the government has been hiding these things. All of a sudden, you become one of those people that's like, 'can you trust anything on mainstream media?'"

For Davidson, the next stage is to debate leading members of the scientific community, but "they just laugh at us and say, 'you guys are dumb.'"

But he's not deterred.

"It's touching everyone ... it's not going away, and it's not going to slow down," Davidson says of the movement. "This thing is out of the can."

This story has been updated to include a response from the Flat Earth Society.