Reality doesn’t always compute. Certain images only make sense under the influence of dreams, drugs or Dali.

A rainforest thriving in Antarctica. A speck in the sky (Polaris) that’s 67 times larger than the sun. Madonna working at a Dunkin’ Donuts in Midtown Manhattan.

Aaron Rodgers graduating from high school without one scholarship offer from a Division I program.

“He would write all these letters himself, and the schools would write back and say, ‘No, you’re not good enough,’” said Craig Rigsbee, Rodgers’ former coach at Butte College. “But they never came up and saw him in person. They didn’t know how good he was.”

Illinois got a glimpse at a camp in Champaign, but coach Ron Turner couldn’t see past Rodgers’ underwhelming size. Other coaches wouldn’t waste their time trekking to a supposed talent wasteland 85 miles north of Sacramento, where the future Hall of Famer kept each of his rejection letters. Purdue produced the pièce de résistance, writing, “Good luck with your aspirations in college football.”

Rodgers took a detour to a community college roughly 15 miles from his home in Chico, Calif. Before he watched Brett Favre from the bench and sat behind Reggie Robertson at Cal, the Jets quarterback was an unheralded true freshman at Butte, projected to play behind third-year quarterback Bryan Botts.

“We had our quarterback already,” offensive lineman Joaquin Echuari said. “It was [Botts’] turn. He’d waited for it. Then comes this scrawny 18-year-old kid who was getting rides from his mom.”

The training-camp battle was competitive, but it was obvious which quarterback had greater potential, a greater understanding of the game, an ability to unleash a picturesque 50-yard dart during the team’s second practice.

It just wasn’t clear who would be named QB1.

“They were battling neck and neck, and I asked everybody on our staff to give me an opinion, ‘Who should be the starter?’” Rigsbee said. “Every one of them said the other guy. They said, ‘Well, he’s been here, he’ll be more ready,’ and I said, ‘No. [Rodgers] is better than him now, and he’s only been here two weeks. In another week, he’ll be 10 times better.

“Sure enough, Aaron came in the first game and threw four touchdowns and caught one [the only receiving touchdown of his career]. After a couple games, the other kid quit.”

Botts’ mother sent Rigsbee — a former offensive lineman — a “scathing letter.” The coach made a mistake, she said, and he would regret it.

“It was about the worst letter I ever got,” Rigsbee said. “She said, ‘You were a lineman. You can’t judge quarterbacks. You don’t know anything.

“‘This other kid, he’s never gonna amount to anything.’”

Ed Rodgers’ Hail Mary fell incomplete.

Aaron’s father was an offensive lineman at Chico State who played for a semi-pro team in California and earned multiple CFL tryout invitations before settling down with his wife and three sons.

Aaron was the middle child, a late bloomer like the rest.

The four-time NFL MVP was a 5-foot-3 high school freshman, who barely topped 100 pounds. Growth came steadily, but slowly, with him reaching 6-feet tall and 175 pounds as a senior.

Before the 2005 NFL Draft, teams called the Pleasant Valley High School athletics office, flummoxed at how the potential top pick went ignored by colleges just four years earlier.

“One organization calls me about five days before the draft and says, ‘What’s the scoop on this kid? Drugs? Alcohol? Trouble with the law?’” said Ron Souza, Rodgers’ former high school quarterback coach. “I’m like, ‘Wait, what? That’s not the case. Great kid. Very conservative. Family’s religious. Kid doesn’t drink.’ The guy says, ‘No. Nobody misses kids like this. They don’t just fall out of the sky. By the time they’re 15 years old, we know who has this kind of potential.’

“I said, ‘You missed him because when he was 15, he was probably 5-foot-3, 105 pounds. We’ve got guys like that all over our campus. Come on down.’”

Rodgers didn’t need a scholarship to attend most of the schools on his wish list. He had a 3.9 GPA and scored 1310 on the SAT.

He also had been drawing football plays since he’d learned to write, using G.I. Joes to run patterns. He knew his beloved 49ers’ formations by age 5, and later met with coaches before classes to discuss schemes he saw on TV.

“At a very young age we gave him packages where he could check the line of scrimmage, change the protection, and most importantly, he knew why,” Souza said. “Aaron Rodgers is about the ‘why.’ Why it works. Why something doesn’t. What creates an advantage? He learns entirely differently. It’s what makes him tick. It’s not just football. It’s how he is with everything in life. That’s how he operates. He could just see the game so clearly. It’s like ‘A Beautiful Mind.’

“I know he’s short on patience at times, but believe it or not, he’s got a lot more patience than he used to. His frustration was that kids didn’t understand the game the way that he did. But who could?”

Rodgers spent two years as the varsity starter, setting the school’s single-season record for passing yards (2,303) as a senior in 2001 while earning his second All-Section selection.

His most interested suitors came from Division III programs, including Lewis & Clark College, Occidental College and Claremont-Mudd-Scripps.

“Back then, people didn’t know who you were if you were up north,” Rigsbee said. “That was before [the online recruiting video tool] Hudl. We still had these big tapes you had to mail around the country.”

It was winter, and Rodgers didn’t know his plan for the fall. He considered quitting football. He considered studying law. Souza asked him to consider baseball, even though Rodgers hadn’t played since the eighth grade.

On the mound, the right-hander forgot his frustrations with football. On the rubber, winning mattered most again.

“I think it changed his life,” said Souza, who was also the school’s baseball coach. “He was very demoralized, but baseball got his competitive juices going again. He just loves being part of a team.

“He was very talented, throwing 95 [mph] consistently. He was capable of hitting 97, 98. When he was with the Packers, the Brewers could’ve signed him and made him their closer. He was that good. He did consider it, but his heart was in football.”

Butte gave Rodgers the chance to keep his dream alive. Selling the quarterback on community college proved easier than convincing his mother, Darla, to take the detour.

“I knocked on his door and she said, ‘Hey, good to meet you, but no kid of mine is going to community college,’ because he was really smart and had really good grades,” said Rigsbee, who coincidentally lived around the corner from Rodgers. “I said, ‘I’m gonna tell you, the War of 1812 still happened in 1812 at Butte. You still gotta get ‘x’ by itself in algebra. I don’t care if you go to Cal-Berkeley, it’s the same thing. Those classes will transfer and you’re gonna get your degree from somewhere else and it’s not gonna have an asterisk that you went to community college.’

“She liked that and we laughed and we had a good talk and she gave me some cookies.”

Rodgers was confident he could transfer to a D-I school after one year. He would commit to Butte — under one condition.

“I started telling him we had a really good quarterback coming back and he stopped me and he said, ‘I don’t really need to hear that. The only promise I need you to make to me is you’re gonna give me a legitimate chance to play for you,’” Rigsbee said. “I almost started laughing. You haven’t been recruited by anybody.”

Replace Rodgers with Keanu Reeves and you get “The Replacements.”

Butte’s new quarterback was an ‘A’ student, surrounded by teammates whose poor grades prevented them from playing at four-year schools. Rodgers, who lived roughly 20 minutes from campus, was joined by players from Canada, Hawaii, Texas and Florida. He was an 18-year-old freshman, playing alongside dozens of 20-somethings — including his 25-year-old center — who had served time in the military and in prison and worked as truck drivers.

Second and final chances cost $200 tuition per semester at a school where a single-wide trailer served as an office and the head coach was required to raise money for bus fuel and uniforms.

“It was a cast of characters and Aaron was significantly younger than all those guys, but it was a good growing experience for him,” said Jeff Jordan, the Roadrunners’ former offensive coordinator. “At first I’m sure they were thinking, ‘Who is this little pimple-faced guy?’ But his actions spoke loud. He carried himself with that swagger. He was very confident in himself. To be quarterback, that’s what you need.”

In 2002, Rodgers set numerous program records while leading the Roadrunners to a 10-1 record, a conference championship and a No. 2 national junior college ranking. He finished with 2,408 passing yards, 28 touchdown passes and four interceptions.

“He made average wide receivers into superstars,” Echuari said. “He got a lot of guys college scholarships. He spread the wealth, throwing 50-, 60-yard bombs. He kept plays alive and turned bad plays into touchdowns. You would forget that he was 18 years old.”

There was his six-touchdown performance against rival Shasta College (he recited all six in order during a 2016 interview). There were his 465 passing yards and 165 rushing yards against Fresno City College in the team’s lone loss.

There was the game that Butte trailed at halftime, 19-6, and the coach put Rodgers in charge of the offense.

“He called every play and, s-t, we scored 40 points,” Rigsbee said. “He was like a coach on our team when he was 18 years old. I think he knew the offense better than me.”

There was the time the Roadrunners blew a huge lead against Foothill College and needed a touchdown to win. Less than two minutes remained. The ball was at their 2-yard line.

“Half of the guys in the huddle were scared s—tless, like, ‘How did we blow a lead this big?’” center Rob Christie said. “Aaron walks into the huddle, and he was so calm. He was so cool. He was so confident. We marched 98 yards to score, all based on Aaron calling every single play that entire drive.”

Rodgers was confident, but quiet; a leader, but a loner.

“Outside of football, he was a shy kid,” Echuari said. “We were in Chico, [the location of] Playboy’s No. 1 party school in the college edition, but he didn’t really come out with us on Saturday nights after the game.”

Christie said, “He was down-to-earth, reserved, very serious academically. He blended in campus really well. He just looked like a regular student who did his own thing. The guy had a goal. He wasn’t there to party or socialize. He was on a mission.”

In his final game at Butte, Rodgers led the Roadrunners to a 37-20 win over Delta College in the Holiday Bowl. After falling behind by 14, Rodgers’ 42-yard pass to Bobby Bernal tied the game in the second quarter. In the fourth quarter, Rodgers sealed the win with a 61-yard dime to Mark Onibokun.

“He comes running off, I’m fired up, we do a hip bump, and I say, ‘Hey, are you gonna get me tickets?’” Rigsbee said. “He goes, ‘For what?’ I said, ‘When you go to the NFL, are you gonna get me tickets?’”

Rodgers set records. He won all but one game. He won over a skeptical roster.

And D-I coaches still played a familiar tune.

Rodgers’ big break only came after Butte tight end Garrett Cross, who had 10 touchdowns that season, attracted the attention of Cal. When Cross was asked to send over game tapes, he included a pair of unremarkable performances in which his quarterback shined.

“I wanted them to see Aaron,” Cross said. “For me to put my name on that and endorse him, for them to look at someone else, it was a little bit of a bold move as a recruit, but I developed a very strong respect for him as a player and a leader. It was the right thing to do.

“Being from Chico, too, and going through that experience of knowing you have the potential, but not ever really getting the opportunity for someone to see it, we looked out for each other. He just needed a look.”

Cal coach Jeff Tedford was floored by the film. He called Rigsbee and asked who else was recruiting Rodgers. “No one,” Tedford was told.

The next day, the Cal coach made the 150-mile drive to Butte. He watched practice, telling Rigsbee that Rodgers was the “best JC quarterback” he had ever seen. During the return trip, Tedford called Rodgers, offering the quarterback his first D-I scholarship.

“It was the road less traveled, but it was the road he needed to take,” Rigsbee said. “It’s the road that led him to where he is now.”

More than two decades later, the potential Jets savior remains close with his community college coach. He wears Butte shirts to NFL press conferences. He acts as if it’s his alma mater during Sunday Night Football introductions.

It doesn’t make sense. But it doesn’t have to.

“That was the most important year of my young football career,” Rodgers said days before winning the Super Bowl MVP in 2011. “I learned a lot about myself that year, being an 18-year-old playing with guys from all over the country and different countries. We had a 25-year-old center, we had guys who had been to prison, guys who were bouncebacks from Division I …

“Trying to figure out a way to lead them, I learned a lot about leadership and I also got my confidence back because I had a real good season.”