At the equator an mountain range ringed the planet. The lowest pass was over 30,000 feet. While the existence of another hemisphere had been postulated for centuries, it could not be confirmed. Even with the invention of air travel, the prop planes could not be controlled as they approached the mountains due to the extremely powerful updrafts and constant thunderstorms on the slopes of the range.
For ages past, skeletons, well preserved corpses, and the occasional insane, haggard man were found on the slopes of the mountains. It was postulated that there were villages high in the mountains, filled with strange creatures. Those who found them often died of strange and painful diseases, and in Medieval times armies were sent to locate and destroy the source of the plague. Every decade or so, explorers attempted to climb the mountains. Few expeditions returned, and those who failed and came back often returned only to be sent to asylums, reduced to vegetables by hypoxia and cerebral edema. Bulky air tanks and other supplies were destroyed in freak accidents - but expeditions continued.
Mines were established in the mountains to locate rare metals needed for industry. These were used as refueling stations for the explorers as the deep mines had more air than the surrounding area. Some attempts were made to tunnel through the mountain, but miles of tunnels were met with no sign of an end, and the rapid geological changes caused frequent cave ins. Measurements of seismic activity suggested that the mountains did end (it wasn't all a plateau), but more than 200 miles of tunnel would be needed to reach the other side.
The first contact had been accidental. It was inexplicable interference on the wireless telegraph - at first attributed to atmospheric perturbations, and later determined to have a pattern. It took decades to establish 2 way communication because of the intense lightning storms in the vicinity of the mountains - eventually, it was determined to use a series of repeaters around the planet to bounce messages off of the upper atmosphere at sunset. Over time, both sides learned the others' language, and departments were set up in governments on both sides to establish relations with "the other side." Treaties led to information sharing to help the unseen allies, and wars one side led to diplomatic actions and even open fighting (see the French and Indian War in our own world).
The discovery that there was habitable land on the other side of the mountains, and that it was habited by people similar to them led to an immediate race for allies. A complex information-sharing system developed, where allies would research projects together and use espionage to tip the balance of power. A highly efficient technical pidgin developed, using simple electromagnetic pulses to encode information for allies on the other side. Doctors looked at schematics of devices sent across and determined that those on the other side were the strange mountain creatures of old.
[... Stuff happens ...]
Someone managed to develop a proxy to link the two internets. Super nerds developed the stack and began to form professional relationships. Facebook adapted easily, as most relationships were between people who had never met anyway...
[... more stuff ...]
Eventually it was determined that technologies had advanced enough to allow representatives of the two sides to meet in relative safety. It had been put off until the mid 21st Century (relatively speaking of course) because scientists were aware of the health risks of contact with such an alien species. The governments of two of the leading powers on each side determined to send a representative in space flight on a one-way trip to the other side, to become a permanent ambassador. This was scheduled to take place on the solstice, and the ambassadors would be monitored carefully by medical staff to determine what further contact was possible.
While perfect peace was impossible, the fragmented nations of both sides meant that local wars kept the peoples fighting those of their own kind, with technical assistance to allies on the other side. The ability to move any kind of fighting force across the divide would not be developed until manned space flight became cost effective. By that time, both sides possessed the technology to easily eliminate each other, so peace was the general rule.