Q:

What was the context of Queen Juliana's "I can't understand it" quote?

I came across a quotation in that piqued my interest.

I can't understand it.  I can't even understand the people who can understand it.
— Queen Juliana of the Netherlands.

I'd like to know the context of this quote. What was she talking about? Was it in a personal interview? A written memoir? Is it a translation from, say, Dutch? Is there, in fact, any serious evidence she said or wrote such a thing?

What I've found so far
The earliest mention I can find of the quote is from 1987. Juliana of the Netherlands abdicated in 1980, age 71, but the quotation is attributed to "Queen" which suggests that the utterance occurred while she was still on the throne.
Quote databases
The influential Unix fortune cookie program, and the databases that accompanied it, have been particularly popular among the science and technology crowd, although the topics of the quotes are certainly not restricted to those topics.
The quote in question appears to have entered the Unix fortune cookie database around somewhere between 1988 and 1995. Specifically, it was not in Berkeley Unix BSD4.3 (1988) but was in BSD4.4 (1995). I also found evidence that the quote was being passed around online as far back as 1987. The filename was different then, but the wording and punctuation seem to be an exact match for the modern version.
It seems to have originated from the same Berkeley sources that would later become BSD4.4. The first part of that 1987 archive begins with a note:

[This is the latest and most uptodate version of Ken Arnold/
       Berkeley's fortune program and data base.  Thanks to Ken
       Arnold for sending this to me.   -br]

Another quotation database, QuotationsPage.com, contains an entry for this quote. The site describes Michael Moncur's (Cynical) Quotations, the relevant collection as "a collection of quotes which I (Michael) have been adding to since 1985."
Outside quote databases
The most formal reference I've found is an essay in a 1988 policy advice book (Schmitt, p. 309). In this case the quote is said to be spoken, and also specifically about computers.

... many politicians ... undoubtedly feel sympathy for Queen Juliana of Holland, who was heard to exclaim, "I don't understand computers. I don't even understand the people who understand computers."

Next steps
I don't speak Dutch, but I wonder if I might have more luck searching Dutch books and newspapers for reports of Juliana alongside words like begrijp and mensen (which apparently mean 'understand' and 'people', respectively).
Then again, I'm not used to historical research, so it's possible I've missed an obvious approach.
Help me, History.SE! What did Juliana not understand?

References
Schmitt, R. W. (1988). Federal policies for academic research. In Golden, William T. (Ed.), Science and Technology Advice to the President, Congress, and Judiciary. Elmsford, NY: Pergamon Press.
[Google books]

A:

Well, this appears to predate most of the 80's thoughts.  The 60's versions of this quote give us a location at least, that she gave this quote while watching a demonstration of either an 'electronic computer', or an 'electronic data processing machine'. The oldest report I find is 1958:

Personally, I share the opinion of Queen Juliana of the Netherlands
who, watching the demonstration of an electronic data-processing
machine, said, “I can't understand it. I can't even understand the
people who can understand it.”
AMA Management Report - Issues 5-8 - Page 93 1958 -

The quote appears a couple of times during the sixties:

Above him on the lintel of the machine, was the proud motto of the
National Programer's Union, originally a remark by Queen Juliana of
the Netherlands: "I can't understand it. I can't even understand the
people...
World's Best Science Fiction - Page 79 -1965

and

Even Queen Juliana of the Netherlands voiced the same objection when
she was watching a demonstration of an electronic computer at an
Amsterdam exhibition. "I can't understand it," she complained "I can't
even understand the people who understand it."
Financial Executive - Volume 35 - Page 24, 1967

(All emphasis mine)
So we can see this event occurred sometime in the late 50's to early sixties. Since these are all snippit view search entries, (I can't verfy for sure that the dates listed on periodicals aren't first publication dates.) The statement seems to have occurred during some sort of demonstration taking place in Amsterdam, pre 1958 if the first publication date is accurate. There are a couple of more entries,

Catholic World, 1965
Books and Bookmen - Volume 12 - Page 11- 1966

which basically repeat the same info, that the quote was about computers she was observing at a demonstration.

A:

The best I could find with a fair bit of searching was your same Schmitt reference from 1988. It was introduced there as "was heard to exclaim". The implication there is that this wasn't a prepared remark, but rather a conversational one.
If the part about it being something she said in a conversation is accurate, there can never really be a definitive source (or even form) for the quote. It was not said in a venue where one would expect it to have been authoritatively recorded. So it seems quite likely that is the best you are going to find.
And then of course there's the likelyhood it isn't accurate. Schmitt was just using it as a colorful anecdote, not as a central part of his argument that had to rely on bulletproof sourcing. At the time it would have been said, Schmitt was an executive at GE (or before that, a researcher), so it seems unlikely he was moving in the kind of social circles to have even heard this second-hand. On the other hand, as director of the GE R&D Center until 1986, it seems quite likely he was exposed to the Unix "fortune" program.
The 1987 "fortune" find shows the other form of the quote was at least co-existent with Schmitt's. So in the absence of any other earlier written source he could have gotten it from, it seems most likely Schmitt read it from "fortune", and inserted "computers" because he was using one of those newfangled computer thingies when he read it, so he assumed that's what she was talking about.

