In most of the connected multiverse, Octover 29 1962 is not a particularly important date. On a small band of 61 worlds, it stands out as quite possibly one of the most important ones of history, since on that day in 61 different worlds a strange anomaly appeared on the horizon on 12:00 AM GMT. The difference between these worlds, as discovered through intra-universal communications is which second of that minute the mirror cube appeared in Earth's sky from 11:59:59 to 12:00:60.
Following phone calls or other notifications, the leaders of nations on 61 earths turn their eyes skyward to the mirrorcube. This is just in time to see the shock as reflections of radios and satellite signals from other, seemingly mirror versions of earth arrive once the orbital.
Even now, this cube remains in the orbit of these 61 worlds, doing nothing besides serving as a conduit for transworld communications.
* * *
The histories of these 61 worlds vary in many particulars, but there are commonalities despite these differences. Given their origin one might compare these differences to a pallet-swap or a sprite recolor. In the multiversal scheme of things, the differences are outweighed by the similarities. Even though the butterfly effect is in operation, these 61 worlds show various broader trends and averages. Besides just serving as an example for various social experiments, you have crossworld communications providing people with advice that they may or may not decide to take("y'know, you might want to pass a civil rights act" or "Leave the rhodies alone. They're bad but look good compared to ZANU or ZAPU" "don't get involved in land wars in east asia"). Some changes are constant to all or almost all worlds while others are on mere majorities or 2/3s of worlds.
One of the most notable commonality of all of these worlds is the post-1962 detente -- part of it is the cuban missile crisis that had just ended with the other part being the mirrorcube's existence as an out of context problem that put the issues of East and West in context. The detente at bare minimum started off 10-15 years long, and in a few actually led to the full normalization of relations between East and West with the cold war ending in the mid 1970s. At minimum this period led in most worlds to the Red Chinese being allowed into the UN, the Cuban Embargo being ended(Florida wasn't a swing state then and the missiles *were* just removed) among a few other things.
The other characteristic both of the early years, and to an attenuated degree even the present is a significant interest in space. Yes, it's taken hits from seeing the maintenence bills for Moonbase Alpha and Lunagrad along with cost projections for either asteroid mining or mars missions, but quite a few worlds have gone beyond the minimum of orbital hotels and 2-3 powers with lunar bases to mars expeditions. There are even a couple martian colonies now across the 61 worlds -- this ranges from a ramshackle base of 700 people for one mars to a functioning small city of 5,000 on another, more advanced world. Asteroid mining, due to it's risk is only done by three of the 61 worlds but is proving to be a literal goldmine.
After the first decade or so, the world's politics settled into business as usual in most of the worlds for good or for ill. On the positive side of things, this included increasing economic integration of the more functional bits of the third world into the world economy. On the downside, this included things like the energy crisis that hit 2/3 of the worlds anytime from 1967 to 1985.
The next major set of unexpected changes that hit were the decline of communism throughout these worlds -- in the years from the mid 80s to the late 2000s, 70% of all Soviet Unions either experienced partial or full collapse of one sort or another(This can mean your russias or a greater or lesser flavor or gorby-style liberalized USSRs or other, different states). In fact, by the present year of 2015, 96% of all Warsaw Pacts had either melted down fully or partially.
Meanwhile, as the communist blocs were all either ossifying then imploding or doing desperate reforms the west enjoyed tech booms of varying strength -- OTL's tech boom would have been middle of he road, with one lucky world managing to time it so that it also got to experience concurring booms in the space and biotech sector.
Recent years appear to be seeing the start of a new era of instability both international and domestic. America is either declining or deciding to slowly withdraw from world governance as great powers either rise to handle their regional issues or in worse cases become either competition or reviving old competitions. Meanwhile, economies are dealing with increasing automation, adjusting to higher energy prices, the effects of the internet and other technological shocks.
On the other side of things, there have been some unusual disasters in about 2/3 of these worlds. These range from the mundane issues of governance failure within a big power like the economic system simply 'bricking' and being locked into a depression-followed by stagflation-type pattern that takes a decade or two to fix at all(OTL since 2008) -- this has happend to about a third of the United States sometime between 1984 and the present. Other relatively mundane problems include the second energy crises that 40% of worlds have experienced sometime between 1995 to now thanks to energy(and often other resource ) producers noticing rising demand. Then there are the more unusual disasters such as in one world an extremely anti-piracy software company releasing a virus designed to enforce DRM that ended up bricking enough systems to lead to a billion people dead by the time everything settled down(copyright is gone) or Mexican collapse dragging in the US in another, different world. On the upside, no world has had any nuclear wars or outright collapses of civilization -- people credit both luck and the ability to look. After all, without the ability to hear about other worlds' economic policies would all 61 of the known versions of the United States have experienced economic crashes instead of merely a third?
* * *
Researching the mirrorcube is the most obvious focus of these worlds. Despite the collective application of some of the brightest minds on all 61 worlds extremely little is known about it in practice since investigation appears impossible -- the entirety of knowledge that's agreed upon by all 61 worlds is the following: it emits low-energy neutrinos at a rate of one per second, it emits tachyons at the same rate, it orbits in geostationary, it acts as a transmitter for radio/satellite/television communications between the worlds, it's 144 meters in diameter and it's impossible to physically interact with it(probes have touched it to grab nothing but space, firing lasers to try producing a spectrum gets nothingm etc). The little information they've gotten, combined with the results of the experiments has produced entire schools of science and led to 120 scientists having severe enough breakdowns to being institutionalized.
Sicence itself has benefitted surprisingly little in spinoffs. Perhaps it'd be immediately useful if we were in the part of the galaxy where faster than light travel was even possible, but as things go the level of undersranding of the best and brightest is is like showing a post-singularity faster than light drive to a monkey. Not even a gorilla or chimp, but a baboon. On the other hand, the larger budgets given to scientists both in physics or in other areas have produced more results. Materials science, synthetics, computing, telecommunications, biotech, medicine and lastly to a lesser degree aerospace are the main beneficiaries of this windfall. Besides the windfall, science has gained a boost from interworld collaboration and information exchange. The least advanced world is 7 years ahead technologically on average, while the most is a full 20. The average is 13-14 years ahead with worlds sometimes lagging in areas or excelling in other, different areas.
Besides the theory, applied science is doing well. Companies collaborating with their counterparts in other worlds has led to larger R&D plans, since they're able to spread the costs over multiple worlds by passing data through. The fact they're able to test what works and what doesn't also helps.
Obviously, science fiction is both more popular and respectable than in OTL. Besides having a larger audience, the talent pool is larger as people who in one world or another heard of their counterparts or made money off of local royalties of their altergangers decide to get involved. There being much more money in it leads to all sorts of positive dividends; less rehashing of 30s-50s tropes, more fresh blood, more media adaptations, longer-lasting TV shows(Star Trek in all worlds lasts at least to 1970, with 95% of worlds having either a Star Trek: Phase II spinoff or a final sendoff with a big-budget movie or both), more series and a less ghettoized genre. These days, some of the more wealthy authors, or those with loyal fanbases who can donate for the connection fees(H. Turtledove, S. Stirling, J. Ringo, J. Pournelle) actually compare notes with their altergangers via crossworld e-mail and thus manage to do a crossworld "division of labor"(OK, Stirling-1 you write those novels with the world losing all technology and magic returning, I've got ideas for the third Draka trilogy, Stirling-3's doing his "Mirrorcube appears in 1940" book, Stirling 4's working on an outline of the 4th ISOT trilogy, Stirling 5's working on that third book in the Red Death trilogy, Stirling-6 is collaborating with Tom kratman on the third world war book, Stirling-6 is working with Charlie Stross on a one a one-off novel about Israel ISOT to 1944....", concluding with "Let's check back with each other in 3 months, k?". AS a result of the collaborative efforts, the lucky authors who are able to get more than one book done at once all get far more released. You also have a trend of famous authors managing to live at worse 6 months longer than OTL with many lasting several years more due to swapping notes on their health. There have also been hissyfits between altergangers, alas(Neofascist!Charlie Stross and social democratic!Charlie Stross predictably didn't get along well).
Alternate history is as to be expected quite a big genre in this world with lots of living reasons to be interested in it. The quality ranges from works as good as any seen in our world's SHWI multipart timelines to schlock like Nixon!(An ABC series taking place in an alternate 1990s where an aging Richard Nixon runs America as a bad 1984 clone). With more datapoints to work with alternate historians are more confident both with post-1962 PODs, and thanks to having a much larger pool of discussion pre-1962 PODs. The collective alternate history community of at last count 33 timelines has funded the creation of archives for the various discussion lists/fora/bulletin boards to be spread around the multiverse. There are less successful efforts by these same people to try convincing authors to release their works to the public domain. At least they've had a limited degree of luck as opposed to none.
Popular culture is one of the most altered by this change and has experienced a renaissance. More cynically, part of this efflorescence may be explained by the trend for copyright terms to lenghten being reduced(at minimum, you have world #00
where the situation is OTL pre-bono copyright extension act and you have to pay for each DMCA takedown. At most, you have a world that due to an incident involving botnets created to enforce their game's DRM that led to the deaths of a billion people before everything settling down with most nations outright scrapping IP law.