In this photo taken by a neighbor July 16, Harvard professor Henry Louis Gates Jr., center, is arrested at his home in Cambridge, Mass. Cambridge police officers attending include Sgt. James Crowley, right, and Sgt. Leon Lashley, front right.

Henry Louis Gates Jr. felt the hairs on the back of his neck stand up as he looked across the threshold of his home at Sgt. James Crowley. Looking back at Gates, Crowley worried about making it home safely to his wife and three children.

Fear was the only thing the white police officer and black scholar had in common. Soon their many differences would collide, exploding into a colossal misunderstanding.

How could things go so wrong? How could two by all accounts decent men start a fire that drew comparisons to the O.J. Simpson case and knocked President Barack Obama off his racial tightrope?

Part of the answer lies in the truth seen through each man’s eyes during the episode, which ended with one of the most influential men in America charged with disorderly conduct.

If this really is to become a “teachable moment,” as Obama hopes, then we have to examine what they saw, according to their public statements — and why they saw it that way.

• • •

It’s early afternoon on Ware Street in Cambridge, Mass., a few blocks from the campus of Harvard University. Gates and his car service driver, a large black man, are trying to force open Gates’ jammed front door. Lucia Whalen, a 40-year-old white woman who works up the street at the Harvard alumni magazine, is passing by and calls 911.

According to Crowley’s police report, he arrived to find Whalen standing on the sidewalk in front of the home. She told Crowley that “she observed what appeared to be two black men with backpacks on the porch … her suspicions were aroused when she observed one of the men wedging his shoulder into the door,” the report says.

No one is blaming Whalen, who has not spoken publicly since the story broke.

“It wasn’t her fault,” Gates said.

We don’t know how she sees the world, what types of experiences color her vision.

But had she shared just one or two different details with Crowley — or if the sergeant had gleaned something else from their conversation — things might have happened differently.

Gates, 58 and gray-haired, says he was dressed in a blazer and walking with a cane. He says his driver was wearing a black suit jacket and matching pants. After they forced open the door, Gates says, the driver carried Gates’ luggage into the house, then drove off in the vehicle.

None of that was on Crowley’s mind when he walked up the steps to Gates home.

“Witnesses are inherently reliable,” he said later. “She told me what she saw.”

• • •

Crowley is on the porch, alone; Gates is inside his home. They apparently notice each other through the front door window at about the same time.

Crowley sees the unknown: “I really wasn’t sure exactly what I was dealing with,” he said later.

The sergeant is 42, a decorated 11-year police veteran who grew up attending diverse public schools in Cambridge. All three of his brothers work in law enforcement. He’s an instructor in a police academy class on how to avoid racial profiling.

He asks Gates to step outside.

“I was the only police officer standing there, and I got a report that there was people breaking into a house. (The request) was for my safety, because first and foremost I have to go home at night, I have three beautiful children and a wife who depend on me,” he said later.

“So I had no other motive other than to ensure my safety, because this gentleman either could have been one of the people breaking in, or he could have been the homeowner who was unaware that there were people in his house unauthorized. I just didn’t know.”

Gates, meanwhile, is a renowned scholar of black history who has spent most of his life literally cataloguing the sins of the past in volumes like “Africana: The Encyclopedia of the African and African American Experience.”

“I know every incident in the history of racism from slavery to Jim Crow segregation,” he said recently.

He knows some of it firsthand. About 1989, hired by Stanley Fish to teach at Duke University in Durham, N.C., “one of the first things Gates did was buy the grandest house in town,” Fish wrote in a recent blog on The New York Times’ Web site.

“During the renovation workers would often take Gates for a servant and ask to be pointed to the house’s owner. The drivers of delivery trucks made the same mistake.”

“The message was unmistakable: What was a black man doing living in a place like this?” Fish wrote.

So when Gates hears Crowley ask him to step outside, he sees history. How could he not?

“All the hairs stood up on the back of my neck, and I realized that I was in danger,” Gates said later. “And I said to him no, out of instinct. I said, ‘No, I will not.'”

• • •

Crowley asks Gates to prove he lives there.

Looking out his front door, Gates sees someone who should be asking, “Is everything all right, sir?” He sees someone who would not doubt that a 58-year-old, gray-haired Harvard professor lived in this home — if he were white.

Gates sees a racist.

Gates leaves the front door to get his identification. Crowley follows him inside. Gates says he provided a driver’s license with the address of the home they were standing in; Crowley’s police report only mentions a Harvard ID.

“Now it’s clear that he had a narrative in his head,” Gates said. “A black man was inside someone’s house, probably a white person’s house, and this black man had broken and entered, and this black man was me.”

Gates demands that the sergeant provide his identification.

Crowley sees someone who should be grateful, but instead is yelling and falsely accusing him of being a racist. He sees a problem — “something you wouldn’t expect from anybody that should be grateful that you’re there investigating a report of a crime in progress,” he said.

Neither man understood what the other one saw.

• • •

Gates continues to demand that Crowley provide his name and badge number.

Crowley said in his report that he had already told Gates his name, twice, but Gates was yelling too much to hear him. Gates said Crowley ignored his demands.

Gates doesn’t let up. Crowley says he’ll talk to Gates outside. Then he says something Crowley understands perfectly, boiling down his 2,095 pages of “Africana” down into one cry of resistance:

“I’ll speak with your mama outside,” he said, according to the police report.

Gates denies making the remark.

Should Gates have realized that you can’t antagonize the police? Should Crowley have understood what it means to suspect a black man of breaking into his own home? Arguments will persist for years.

Once Obama recovered his balance, backing off his statement that Crowley acted “stupidly,” the president assumed his traditional position of racial referee and said that both men overreacted.

“My hope,” the first black president continued, “is that as a consequence of this event, this ends up being what’s called a teachable moment, where all of us, instead of pumping up the volume, spend a little more time listening to each other … and that instead of flinging accusations, we can all be a little more reflective in terms of what we can do to contribute to more unity.”