Originally published on 5 September, 2012
1. Formulation.
Any given piece of historical data will eventually be completely lost.
2. Proof.
Premises of the theorem:
-time does not stop
-human memory capacity is limited
-human lifetime is limited
-during the run of civilization nothing happens that makes at least one of the first three premises false
-civilization runs for long enough period of time relative to a piece of historical data in question
Because time does not stop, historical data will always be generated, thus increasing the total volume of historical data available for study. At the same time, human memory capacity is limited, just as human lifetime is. Thus, an individual always has to choose what to study and what not to. Eventually any historical data, no matter how important to the generations of today, will be replaced with records of newer events and be completely squeezed out of the active historical awareness of a civilization.
3. Scope.
The theorem stresses the contrast between the non-stopping inflow of events and limited human resources. Obviously, although this theorem is true for any human civilization in principle, it will manifest itself for every historical fact only if a civilization runs indefinitely. If a civilization runs for finite periods of time, not every piece of historical data will fall into oblivion during the lifetime of a civilization.
Since we live in a universe that displays only finite processes, the theorem can be reformulated in this manner: after a certain point in the future any present-day historical fact will be lost.
Whether civilization survives to that point or not is an independent issue.
4. Possible counter-arguments.
4.1. Technology.
Counter-argument: digital technology or any other type of recording possibilities will allow for eternal preservation of data.
Response: while this may be true, this does not address the limitation of human memory and human lifetime. Thus, even if a given historical event exists in the records, eventually it will escape any significant attention as nobody will choose to study it. While it is possible that a scholar, randomly reading old data, might discover an event, long ago forgotten, he would have very little chance of drawing any attention to it.
However, more fundamentally, any technology has limitations and any library, no matter how sophisticated, does require maintenance, which in turn has a cost. Eventually, the amount of data will reach such a size that it will become too expensive to maintain a library and some data would have to be erased. It is against the nature of the world we live in, as we understand it today, to have a technology that will allow for eternal data preservation in a literal sense.
Additionally, when you have such an enormous volume of information, you have a problem of searching through it. The cost of search for an event of distant past might be too high and lower practical usefulness of the library to almost zero.
And, finally, digital technology allows not only for recording data of the past, but extends greatly the opportunity to register more events of the present. Thus, the more sophisticated digital recording is, the more new historical data it will archive, thus decreasing the active lifetime of older archived data.
4.2 Large population.
Counter-argument: in the future human population may rise to huge numbers. This increases audience receptive to various information of the past.
Response: more population will in turn generate more events in the present and eventually neutralize any advantage of a possible diverse historical interest.
4.3 No wars.
Counter-argument: if a civilization grows to not have wars, the last war will be remembered.
Response: this touches on the counter-intuitive aspect of the theorem - no matter how important the event seems, eventually all historical data concerning it will be completely lost. Although there might theoretically be no wars and people would place an emphasis on remembering the last war, eventually it will still be forgotten, small details at first, more important things next, until only the name remains. And when this name gradually turns into a symbolic "last war", with no personalities, dates and specifics, it would be inappropriate to call it "historical data".
4.4 Art.
Counter-argument: some historical data can become part of an artwork and survive indefinitely in that form.
Response: It is true that art has a chance to survive indefinitely, however, historical data in it does not. If a book, movie or song contain some accurate historical data, eventually future generations will not be able to tell what part of it is fiction and what is not without reference to historical studies, which would be long gone by that time.
It could be argued that a good artwork may regularly interest people in the historical data, however, it is a very unlikely scenario. In fact, very often good plot based on history turns into mythology, meaning that the plot itself is left intact, but stripped of all of the historical data. Many times the older historical context is replaced with a contemporary one, thus keeping the story up to date.
There is also considerable difference between the popular interest and scholar interest. Various examples show that popular interest can considerably distort facts rather than preserve accurate historical data. For instance, interest in World War II has created so many movies, video games and books which mix in accurate data with errors and fiction, that for a non-scholar it is quite difficult to separate fact from fancy, although the event is fairly recent by historical standards.
5. Does the theorem apply to other types of information?
Shortly speaking, no.
To expand on the answer, let us look at what these other types of information are and to what extent the theorem is applicable to them.
Other types of information may include cultural data (art) and knowledge.
5.1 Art.
The theorem is very likely to work for most cultural artifacts, but there could be exceptions. So, for art the theorem could be rephrased to say that any given artwork is likely to be completely lost, but such a statement would not carry logical necessity. The difference between cultural and historical data is seen in that it is usually more abstract and thus can stay relevant by slightly changing form but not the content. This is more true for some art forms and less true for others. A musical composition certainly has more chances of making it as opposed to a sculpture. So, the more abstract the art form is, the more chance it has for eternal survival.
Any historical data about a given art piece would necessarily be lost though. For instance, we can safely say that any given work of art, if survives, eventually becomes anonymous. In fact, with the advent of digital distribution we can see that process happening right before our eyes, when creations get distributed, remixed, remade and distributed further, often without attribution or with attribution confused. And, as stated above, even if we do retain the name of the author, it can hardly be considered "historical data" in any meaningful sense - we may very well put any name at that point.
5.2 Knowledge.
The theorem works even less for knowledge than it does for cultural data. Reason for it is that knowledge is very specific kind of data.
First of all, some of knowledge can be generalized - new discoveries and advancements in our understanding of the world do not necessarily increase the volume of information. In fact, an opposite can happen, when, for instance, a new law of physics becomes a generalization of some other laws and so preserving just this general law is enough to then deduce the rest from it, thus in effect reducing the amount of information vital for transmission - and even for study. Descriptive data does increase in volume with time. However, advancement of natural sciences can make it easy to observe it directly, for instance, by using sophisticated measurement devices, and thus making preservation of records of descriptive data not necessary. Nevertheless, there is definitely a probability for descriptive knowledge to be lost.
Second, knowledge is practically useful, in some cases vital, and thus is usually prioritized over other types of information. And while knowledge can be lost, due to a catastrophe that kills many people and/or destroys most libraries, in such a case it would be fair to say that this particular civilization has ceased and a new one started to develop from its ashes, whereas the theorem works for a civilization continuously running.
Just as with cultural data, any historical information regarding knowledge will also be lost. To supply an example, if this theorem makes it into mainstream attention at all and is considered important enough to be studied, in the distant future no person will know who the author of the theorem was. And even if I put my name on and name it Louigi Verona Theorem, at some point there will be no data available to future generations to verify whether that name is accurate and whether such a person really existed and was indeed connected to the theorem in question.