First, let me start by saying I am by no means an accountant, an economics expert, or even a particularly well informed amateur. That said, what I've looked into leads me to conclude:
While the numbers may be correct, they are also meaningless.
I'll take each question in order.
What is it?
First of all, I can't find any sources which discuss "infinite horizon" accounting that don't relate to social security or other government debt. That leads me to believe that either A) it's a political pseudo-accounting term which real accountants would shake their heads at, B) it's a real accounting term that has no practical value, so is almost never used, or C) it's a term borrowed from another branch of math/science that doesn't belong in accounting (like complex numbers).
I also can't find any sources which define it clearly for a layman, which is another red flag for me. The closest definition I could find which wasn't related to the debate was way over my head in math. Another source which is slightly more approachable explains:
Markov Decision Models with infinite horizon can be seen as an approximation of a model with finite but large horizon. Often the infinite horizon model is easier to solve and its optimal policy yields a reasonable policy for the model with finite horizon.
Reading further, I think your guess of doing something like limits in calculus and subtracting one infinity, future proceeds, from another, future expenditures is close in concept. Regardless, if it has meaning in accounting, its a term which has a very specific definition that doesn't mean what laypeople think it does.
The official report which used the infinite horizon model said:
Another measure of trust fund finances is the infinite horizon unfunded obligation, which takes account of all annual balances, even those after 75 years. The extension of the time period past 75 years assumes that the current-law OASDI program and the demographic and economic trends used for the 75-year projection continue indefinitely.
...
The $24.9 trillion infinite horizon open group unfunded obligation is equivalent to 4.1 percent of taxable payroll or 1.4 percent of GDP. These relative measures of the unfunded obligation over the infinite horizon express its magnitude in relation to the resources potentially available to finance the shortfall.
The summarized shortfalls for the 75-year period and through the infinite horizon both reflect annual cash-flow shortfalls for all years after trust fund reserve depletion. The annual shortfalls after trust fund reserve depletion rise slowly and reflect increases in life expectancy after 2033. The summarized shortfalls for the 75-year period, as percentages of taxable payroll and GDP, are lower than those for the infinite horizon principally because only about three-quarters of the years in the 75-year period have unfunded annual shortfalls, and annual shortfalls within the 75-year period represent a smaller share of taxable payroll and GDP than do the shortfalls in later years.
In short, they plugged a bunch of current numbers and assumptions into the model, ran it out past 75 years until it reached some kind of stability, and reported that number.
How about the "fiscal gap" itself?
The fiscal gap is much more understandable when not carried out to the infinite horizon... but it's also much less useful to discuss. The linked article describes it as "the difference between our government’s projected financial obligations and the present value of all projected future tax and other receipts". Discounting the extreme long term, this is the same measure as most budget projections: Projected income vs expenditures.
There is validity to the concept of "off book" debt, and it's true that Social Security payments don't show up in standard accounting projections, but debates about government debt already factor that in. This article says:
Andrew Biggs, a scholar at the American Enterprise Institute and
former principal deputy commissioner of the Social Security
Administration, explains it this way:
Budget experts use two main measures of the budget deficit: the
"on-budget" balance, which includes everything except Social Security
and the postal service, and the "unified budget," which merges the on-
and off-budgets.
The unified budget approach is by far the most common for budget
experts and the media -- and when the Obama White House talks about a
2013 budget deficit of $901 billion, it's the unified budget deficit
that's being cited.
On a unified budget basis, when Social Security's financial position
worsens, the budget deficit grows. Social Security contributes about
$53 billion to the budget deficit.
Is it valid?
So, is it valid? This article (unsourced, emphasis original) says:
In a letter to the Social Security trustees in December 2003, the American Academy of Actuaries, the leading professional organization of actuaries, warned that infinite-horizon projections "provide little if any useful information about the program's long-term finances and indeed are likely to mislead anyone lacking technical expertise in the demographic, economic, and actuarial aspects of the program's finances into believing that the program is in far worse financial shape than is actually indicated".
Economic projections decades into the future can fluctuate dramatically in response to small changes in assumptions about economic growth, demographic predictions or technological changes. Expanding these projections to an "infinite horizon" greatly exacerbates the impact of these small errors in predicting the future.
It goes on to make what I find the most telling point against this kind of thinking:
They point out that changes which took place over the last 75 years were unforeseeable to actuaries in 1928, such as the Great Depression or the baby boom, and therefore have no reason to expect that unforeseeable changes will not occur in the future.
75 years ago (from 2015), Nazi Germany was expanding all over Europe, Walt Disney had just released his second animated film, McDonalds was about to open its first restaurant, Roosevelt was president, his New Deal was still new, and the first electrical digital computer was revealed. Any economic predictions made back then, including those based on the 5-year-old Social Security program, would be completely unable to account for everything that has happened since. There's no reason to think that any predictions made now would be any more likely to be right about what the situation will be like in 75 years.
Can it be fixed?
In the short term, any solutions would be the same as for addressing the deficit in the first place. I won't address whether that can be "fixed". In the long term, we shouldn't try. That doesn't mean the government shouldn't look to the future, but there's no sense making drastic policy decisions based on extreme long-term projects with huge amounts of uncertainty. Trying to do so is a recipe for disaster.
The children of the Great Depression grew up dealing with the decisions of government in the Roaring Twenties. The Baby Boomers grew up dealing with the decisions of government in the Great Depression. We're dealing with decisions made for the Baby Boomers. Our kids will have to deal with decisions made for us. That's the way things go, and while we should leave things in as good a state as possible, there's no way to tell just what ideas that seem good now will be really bad ones later on.
