Knowledge is expanding exponentially, as humanity fills the galaxy and then some. But advances in physics (which Draper describes in fictional mathematical terms) are able to keep up with the storage problem, until all of human knowledge, for all time to come, is packed into one drawer. Of course, there is one wee problem. Retrieval is ultimately macroscopic. And so the indexes grow. And when they get miniaturized, the indexes to the indexes grow. And so on, which then leads to a higher-order index of the iterated indexes, and then so on again. All this is spelled out in some detail.
The neverending recursion, while threatening to grow to Ackermann-like proportions, is still manageable. But when a spontaneously generated Gödelian self-reference is discovered in the indexing system, the whole lbry, and with it all of human civilization, collapses overnight. . .
By William E. Emba
What puzzled our research teams was the suddenness of collapse and the speed of reversion to barbarism, in this multigalactic civilization of the biped race. Obvious causes like war, destruction, plague, or invasion were speedily eliminated. Now the outlines of the picture emerge, and the answer makes me apprehensive.
Part of the story is quite similar to ours, according to those who know our own prehistory well.
On the mother planet there are early traces of *books*. This word denotes paleoliterary records of knowledge in representational and macroscopic form. Of course, these disappeared very early, perhaps 175,000 of our yukals ago, when their increase threatened to leave no place on the planet's surface for anything else.
First they were reduced to *micros*, and then to *supermicros*, which were read with the primeval electronic microscopes then extant. But in another yukal the old problem was back, aggravated by colonization on most of the other planets of the local Solar System, all of which were producing *books* in torrents. At about this time, too, their cumbersome alphabet was reduced to mainly consonantal elements (thus:
Next step was the elimination of the multitude of separate
This building, twenty-five miles square and two miles high, was buried in one of the oceans to save land surface for parking space, and so our etymological team is fairly sure that the archaic term liebury (
The fundamental advance, at least in principle, came when the representational records were abandoned altogether in favor of *punched supermicros*, in which the supermicroscopic elements were the punches themselves. This began the epoch of abstract recs — or
The great breakthrough came when Mcglcdy finally invented mass-produced *punched molecules* (of any substance). The mass of
(1) Getting below matter level, Shmt began by notching quanta (an obvious extension of Kwlsk's work) but found this clumsy. In a brilliant stroke he invented the *chipped quantum*, with an astronomical number of chips on each one. The
(2) Shmt's pupil Qjt, even before the master's death, found the chip unnecessary. Out of his work, ably supported by Drnt and Lccn, came the *nudged quanta*, popularly so called because a permanent record was impressed on each quantum by a simple vectorial pressure, occupying no subspace on the pseudo-surface itself. A whole treatise could be nudged onto a couple of quanta, and whole branches of knowledge could for the first time be put in a nutshell. The
(3) Finally — but this took another yukal and was technologically associated with the expansion of the civilization to intergalactic proportions —
All the
To understand the nature of these misgivings, we must now turn to a development which we have deliberately ignored so far for the sake of simplicity but which was in fact going on side by side with the shrinking of the
First, as we well know, the
Secondly, a process came into play of which even the ancients had had presentiments. According to a tradition recorded by Kchv among some oldsters in the remote Los Angeles swamps, the thing started when an antique sage produced one of the paleoliterary
These were the innocent days before the problem became acute. Later, Index runs were collected in Files, and Files in Catalogs — so that, for example, C3F5I4 meant that you wanted an Index to Indexes to Indexes to Indexes which was to be found in a certain File of Files of Files of Files of Files, which in turn was contained in a Catalog of Catalogs of Catalogs. Of course, actual numbers were much greater. This structure grew exponentially. The process of education consisted solely in learning how to tap the
Another type of Index, the Bibliography, also nourished, side by side with the C-F-I series of the
On the other hand, the first History of Histories of Bibliographies came much later, and this H-prime series always lagged behind. It goes without saying that the B-H-H series (like the C-F-I series) had to have its own indexes, which in turn normally grew into a C-F-I series ancillary to the B-H-H series. There were some other but minor developments of the sort.
All these Index records were representational; though proposals were made at times to reduce the whole thing to pizzicated quanta, reluctance to take this fateful step long won out. So when the
Under the stress of need, resistance to abstractionizing broke, and with the aid of the then new process of cospatial nudging, the entire mass of
Now this drawer (D1) itself had to be activated by indexed code numbers. More and more scholars turned away from research in the thinner and thinner stream of discoverable knowledge in order to tackle the far more serious problem: how to thread one's way from the
The inevitable happened in the course of a few yukals: The
Then it was the old familiar story: The liebury filled up, the ASS's filled up. Around 10,000 yukals ago, the first artificial planet was created, therefore, to hold the steadily mounting agglomeration of
This tragic story can be told with some historical detail, thanks to the work of our research teams.
It began with what seemed a routine breakdown in one of the access lines from D57x103 to D42x107. A Bibliothecal Mechanic set out to fix it as usual. It did not fix. He realized that a classification error must have been made by the ariadnologist who had worked on the last pseudosolar system. Tracing the misnudged quanta involved, he ran into:
"See C11F73I15."
Laboriously tracing through, he found the note:
"This
Tracing this through in turn, he found that they led back to the original C11F73I15!
At this point he called in the district Bibliothecal Technician, who pointed out that the misnudged sequence could be restored only by reference to the original
Without hesitation, His Bibliothecal Excellency pressed the master button on his desk and queried the
To his stunned surprise, the answer came back: "See also C11F73I15."
Frantically he turned dials, nudged quanta, etc., but it was no use. Somewhere in the galaxy-size flood of Ix drawers was the one and only drawer of
A desperate physical search was started, but it did not get very far, breaking down when it was found that no communication was possible in the first place without reference to the knowledge stored in the
The final result you know from my first report. Rehabilitation plans will be
sent tomorrow.
Yours,
Yrlh Vvg
Commander
This report received L-43-102. File it under M42A8E39. - T.G.
You must be mistaken; there is no M42A8E39. Replaced by *W-M23A72E30 for duodenomattoid reports. - L.N.
You damfool, you bungled again. Now you've got to refer to the Rx to straighten out the line. Here's the correction number, stupid: