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You can tell this is another overly optimistic, Gee Whiz! future:

2058 - The Beatles' music catalogue enters the public domain

It'll never happen. Mickey Mouse will enter the public domain centuries before The Beatles do.

See http://futuretimeline.net/21stcentury/2019.htm#copyright . I have no doubt that when 2019 rolls around, if Disney et al. (I mention Disney specifically instead of the RIAA or anyone else because Disney seems to be the one really at the forefront of the copyright extension issue every time it comes up) are still around in any significant form (hopefully they'll have been thoroughly disrupted years before then, but you can't really predict the future, etc. etc.), they'll be pushing for another extension to copyright terms. However, there's no guarantee that said push would make it through Congress, especially given recent victories over legislation such as SOPA/PIPA and efforts to disrupt the industry. The website presents its predictions in light of current laws and trends, since anything else would end up being too complicated from all the possible "what-if" alternate timelines.
I would imagine, at some point, the compromise will happen that the old works are in the public domain, but newer trademark laws protect the characters from being used in other people's new works. That is their biggest fear anyway.
So you don't have copyright but yet you still have copyright rights on the characters? That would be a weird legal limbo, let's not go there.

The even simpler compromise is that older copyrights that do not have a current registration maintained fall into the public domain. Registrations must be refiled every few years to stay current.

This compromise would fit current interpretations of copyright, allow Steamboat Willie to continue to be effectively permanently copyrighted, without constantly rewriting copyright law. It would also allow the vast bulk of existing old copyrights to become public domain.

It is a compromise where each side gets most of what it cares about, and we don't need to have progressively worse laws passed.

Personally, I believe that any system allowing for indefinite copyright protection (even a system like the current one, that involves constantly changing the system to extend protection) is harmful in the long run, but your compromise is definitely far superior to the status quo, and would probably make for a pretty good bridge from now to future, far more sane copyright law.
2019 is a mere 7 years away. With the resources Disney has (IP, cash, mindshare, etc) they will still be going strong in 2019, even if only through momentum.
Even if they never made another dime, they'd last through 2019 without a problem. I think people underestimate just how much money these companies have.
Exactly. Consider how long SCO has stuck around as an obnoxious legal entity. Now give it billions of dollars.
Hahaha. It's funny that you think that prediction sounds so implausible compared to all these other crazy notions like genetically engineered designer babies.
All that hyper-technology and not one desalination plant. For that matter, I would guess before the USA ceded any territory to Mexico, we would try some geoengineering to bring the temperature down.
And while we have autonomous robot factories (being wasted uselessly on asteroids or whatever), we might as well, you know, cut the costs of manufactured goods by six orders of magnitude, bring about the end of economics, and maybe build some free infrastructure while we're there. Like desalination plants, but powerful enough to fill artificial rivers the size of Niles.
Whether it's geopolitics, technology, or social changes, it is next to impossible to predict further than 10-20 years down the road with any kind of accuracy.

Could people living at the height of the space race realistically predict the collapse of American space exploration? Could they see coming the subsequent rise of private space ventures?

We'll just have to wait until pschyohistory is invented.
(spoiler alert)

Not even psychohistory worked in the long run. It fundamentally could not predict the Mule.

A charitable way to read this site is to use it as a way of talking about current trends. For example, they say "Male and female salaries are reaching parity" in 2067. Who knows what'll happen, but it's a novel way of talking about just how far behind female salaries are and at what rate they're changing today. For another, projecting Moore's law out to 2083 is silly, but it is interesting to remember how transistors (and other computer parts) have been shrinking exponentially through the present.
Futuretimeline.net is an awesome website. Not awesome as in "cool", but as in something that literally inspires awe.

Sure, a lot of the predictions will turn out to be wrong/incorrectly timed. However, the point isn't in the details of the predictions or exactly when stuff will happen, but in the broad pictures it paints. Heck, even that may be wrong, but it certainly gives you a lot to think about..

2038

Older computers are at risk of experiencing major software malfunctions

The Year 2038 problem (also known as "Y2K38" by analogy to the Y2K Millennium bug) gains considerable public and media attention this year. It affects programs written in the C programming language. These were relatively immune to the earlier Y2K problem, but suffer instead from the Year 2038 problem. They use a library of routines called the standard time library. This takes a stored, 32-bit integer and interprets the current value as the number of seconds which have passed since 00:00:00 UTC on Thursday, 1st January 1970.

Because of the limited number of possible values that can be derived from this 32-bit integer, the farthest time that can be represented in this way is 03:14:07 UTC on Tuesday, 19th January 2038. Any times beyond this point will "wrap around" and be stored internally as a negative number, which these systems interpret as a date from 1901, rather than 2038. This is called integer overflow.

For older computers that still use this system, major problems begin to arise with file systems and databases, due to erroneous calculations. Fortunately, most systems have been upgraded by now, and little overall damage is done.

I thought that "bug" was patched by making a 64 bit integer included by default? Wouldn't they just have to recompile the program with the new library sometime during the next 26 years?
What happens if you have a file format, or network protocol, that stores timestamps in a 32-bit field?
It's not systems that can be updated that are the problem, it's embedder electronics. Desktops have no where near enough life span to be a problem, most servers will be updated before then due to advances in electronics.

Embedded electronics can usually only be updated by replacing the entire machine and are written to be as simple, so many systems could be vulnerable to this bug. When you think of things like cars and and even microwaves, this starts to become rather probable.

  Orbital solar power, since its introduction nearly 15 
  years ago, has grown considerably.** Various new stations 
  are now in place, able to provide continuous power to Earth.
Extremely doubtful.

http://physics.ucsd.edu/do-the-math/2012/03/space-based-sola...

  On a yearly basis, then, getting continuous 24-hour solar 
  illumination beats the California desert by a factor of 2.6 averaged 
  over the year, ranging from 2.0 in the summer to 3.5 in the winter. 
  One of my points will be that launching into space is a heck of a lot 
  of work and expense to gain a factor of three in exposure. It seems a 
  good bet that it’s cheaper to build three times as many panels and 
  stick them on the ground. It’s not rocket science.

  [...]

  At this level, our 3.6 km diameter collecting area would generate 
  about 40 GWh of energy in a day, at an assumed reception/conversion 
  efficiency of 70%. By comparison, a flat array of 15%-efficient PV 
  panels occupying the same area in the Mojave Desert would generate 
  about a fourth as much energy averaged over the year. So these 
  beaming hotspots are not terribly more concentrated than what the 
  sunlight provides already. Again, I find myself scratching my head 
  as to why we should go to so much trouble.
Solar's a great technology. Space based solar ain't.
I don't know... based on your excerpts, the main objection is that the cost of putting the panels in space exceeds the net benefit. The claim seems to basically be that, in 33 years, that objection will no longer apply because tossing a couple stations into space will no longer be a big deal, expense-wise.
And if we're mining asteroids at that point, there's no need to toss the stations into space. Just build them there.