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The first thing that came to my mind reading your question certainly is data storage and retrieval. History often is a lot of documents. Databases can be immensely helpful for storing, accessing, and cross-referencing large piles of (historical) data, and complex algorithms can be used to analyze such data. Computer analysis can also be very helpful in decoding forgotten writing systems and languages.
Another common application is algorithms helping archaeologists to do their work. For example, algorithms are used to analyze satellite images to identify likely spots to find artifacts (the remainings of old settlements are often small hills), or create 3D models of settlements, palaces, and temples. (Contrary to popular believe, archeology doesn't only deal with prehistory, but is also concerned with finding proof of what can be found in old texts.)
Quite a daring application is the extrapolation of the future from the history. Meadows/Meadows/Randers/Behrens did that in the Club of Rome's The Limits to Growth study in the early 70s (and in the 90s with the sequel Beyond the Limits):
The results are, basically, a prediction of the future, based on which mankind could perform corrective actions.
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sorry for my poor english. I've been searching for computer applications in history in particular too. I read a lot of papers and some books about. Recently to sitematize that material, under a historic criterium (i.e.), organize the material in a way to document the computting applications in history trough the tiem. The first work that I collect about was the work authored by Edward Porter "The Computer and Historian"(1971). Porter describes some tips (obviously outdated) to apply in the treatment of historical sources. Later he describes some applications. In 70's, a journal called "Historical Methods", gathered applications of computer softwares and quantitative techniques. In mid 90's, the Association for History and Computing published a newsletter and a series of parpar in the same spirit. The papers are still on line. Recently, the computing applications are encompassed under the umbrella term "Digital Humanities", embracing applications far beyond database development. In 2013, Universidade de São Paulo USP sponsored a international seminar about the Digital Humanities. Hope that help you. PS. Actually I working in a digitaion project of historical sources in Brazil.
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Using imagine techniques to reveal lost codex of Archimedes underneath the text written much later on tom of it is IMHO a nice example how computers can help historians.
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Intelligent agents and modelling of society. As a history nerd and programmer this is the sort of stuff that fascinates me.
some links to at least abstracts to give the Idea of some projects in these field.
http://jasss.soc.surrey.ac.uk/16/4/11.html
https://ddd.uab.cat/record/127995
http://ieeexplore.ieee.org/document/4740679/
https://link.springer.com/chapter/10.1007/978-90-481-8927-4_5
https://link.springer.com/chapter/10.1007/978-90-481-8927-4_16
https://link.springer.com/chapter/10.1007/978-3-319-14627-0_11
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It's a fascinating question. One of the greatest contributions of computer science to the study of history is the fact that people created computer science, which is based on logic. There is quite a long process between the invention of logic, and it's encoding into the physical realm through machine logic. This fact sheds a bright light on your search for an algorithm.
I suppose you would expect to find something meaningful from such an endeavor? Perhaps you think that if you succeeded at finding these algorithms that "mankind could perform corrective actions" as it says in your accepted answer. These 'corrective actions' could have profound effects on history. Might that be the purpose of your search?
But the thing you search for negates and obviates the very purpose of your search.
There is a logical error in the purpose of your search, because the computer algorithms you search for would not be able to account for the fact that man's actions are purposive. In fact such purpose would 'break' your algorithm.
Imagine your algorithm trying to account for the fact that you thought you could find an algorithm of history, thought you had found it, and then performed "corrective action". Then imagine that there are millions of other people, with millions of other even wilder ideas also trying to perform corrective actions using their own computer or other types of algorithms.
For further analysis of this fascinating problem you should probably read "Theory and History" by Ludwig von Mises: http://mises.org/th.asp. It is a theory of history which includes the fact that when we act we act with purpose, which would be why you are asking the question in the first place.
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Attempts to produce quantitative history, ie cliometrics within Economic history; may make more computationally intensive demands than traditional text interpretation. This kind of economic history is not viewed as a core element of the discipline. The computational requirements are probably computationally boring from a theoretical perspective; and, replication from an applied perspective.
Regarding history par history, historians regularly require the service of information professionals:
we can probably add a couple here,
But this is very much a service relationship, with the profession of semantically oriented computer scientists serving the needs of historians, much like archivists serve the needs of historians but are a profession unto themselves.
Obviously solving AI will solve history—if the AI is cheaper than training historians. But that isn't really a "problem" specific to history; it is the specific implementation of a general problem.
We can reverse this—historians could well serve computer science through an analysis of the conduct and engagement of the discipline. I've read a decent monograph on scale and funding waves and the development of multiple distinct types of computing company. It suggests that old models retain their utility in domains where old funding structures and old systems-of-problems remain.
There's no real transdisciplinary space; but maybe there is room for project level interdisciplinary cooperation. From what I've generally seen of the concept of "Digital Humanities" it appears to be an ark to save literary criticism from institutional execution; and the few historians who participate participate more as information professionals than as historians.
ymmv.
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I'll separate my answer into two: ancient history and modern history.
Personally, I think the most interesting and very "new" field is the use of DNA analysis to study ancient human migrations. See for example the Wikipedia article Models of migration to the New World and Mitochondrial Eve. This field uses information that has survived up until today (sort of like archaeology) but that is too complex and numerous to understand simply by "looking at it" (there is also some applications in archeology more directly, as discussed in a different answer here) and where there are no written sources. I am no biologist but if I was 19 again this field is something I would have seriously considered aiming for. Think about it: for most of the history of humans we have no written or sources - no names of empires, wars, kings or anything - only what we can dig up, what we can infer from language relationship (another possible field! See computational linguistics though I don't know if that article has any historical applications) and from genetics.
No idea about how the actual practical research works but I imagine it has to have a lot of algorithms and computation... some references to research papers are in the Wikipedia article and in other articles linked from those.
For more modern periods, there is a lot of data that is complex and needs algorithms to be made sense of. This is not only the case for the last decades; rich census data is available for some countries from at least the mid-1800s and has to a large extent already been digitized. See for example the data sets at http://www.ipums.org/. For more recent periods, most aspects of economic history can involve some sort of computation, in particular if there is a lot of data. Google "cliometrics", "econometrics" and look into economic history in general. A lot of this might be more statistics than computer science, though.
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I have degrees in Informatics and Cognitive Sciences (which is a mixture of sciences but traditionally not yet the "history faculty"). I had this discussion 15 years ago with persons from the history faculty and the first thing I think of is ofcourse Asimov and Harry Seldon)
I read this as "can we pull the history faculty in cognitive science"
I think this is because just "pure history + it" will result in answers as above "finding algorithms in data", which will be of less use. So what is missing is the human itself as indicated above.
Luckily we have a thirds batch of sciences: the social behavioural sciences along with neurophysics which more and more conclude that the behind the complexity of humans there is actually a system and possibly only a system and no "strange undetermined something attached".
So i suspect now that "social network sciences" are becoming more mature (e.g. how does communication flow in a network, how do humans networks work) and if we can analyze human networks and how information and memes flow between humans based on data archives like e.g. http://kranten.kb.nl/ (all newspapers since 1616)(*) where we correlate human behaviour and group behaviour (the latter which simpler than 1 human) to flow of information between humans within a certain cultural context we will make some nice steps.
I also agree that it will not be a science that will influence since these group behaviours are difficult to steer. However analyzing and predicting human groups behaviour based on historical material and finding new social history patterns seems a pretty logical next step.
(so summary: especially include the behavioural science faculties including cognitive science and the new social network sciences to create this new science).
Where somewhere at the end of this discussion the "free will" discussion takes place (but probably that is key to every behavioural science department) (and yes cliche)
(*) I suspect we need sentences and words by people used of different kinds of groups that lead to group behaviour as found in newspaper interviews and reports. I think data archives with pure statistical data are of less use. (but obviously including cultural context, dna, mathematics, it algorithms, and lots of other sciences combined though humans are key) or as Asimov / Harry Seldon has put: Psychohistory.
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It is a little surprising to me that what I think is currently the relevant example has not been mentioned so far (this may be due to the fact that what has been called a "breakthrough" in the press happened well after the OP):
It will not be possible for me to summarize what this is about in detail, yet I think it is highly relevant to the OP. Very briefly: the papyri are many, many of them tightly rolled, many of them charred or decayed, yet computer science can help to read them. And there is much left to do. I just cite from the current Wikipedia article:
In September 2016, a method pioneered by University of Kentucky computer scientist W. Brent Seales was successfully used to unlock the text of a carbonized scroll found on the western shore of the Dead Sea.[18] According to experts, this new method devised by Dr. Seales may make it possible to read the carbonized scrolls from Herculaneum.[18]
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As sbi noted, relational databases can be used for analyzing historical data. A specific example comes from the scholarly work The First Crusaders, 1095-1131 by renowned crusade scholar Jonathan Riley-Smith. This book focuses on studying the first generation of crusaders. In the introduction Riley-Smith explains how he used an Oracle database to store basic information about men and women associated with crusading, pilgrimage, and settlement in the Holy Land during this period. The system provided a way to produce family trees, identify points of contact between groups of people, and identify trends in the data.
Aside from relational databases, history and computer science can intersect in entertainment, such as historical video games. Many games take place in a historical setting, and historical knowledge would be useful for producing such games. Some games, such as The Falklands War 1982, clearly attempt to make historical accuracy one of their selling points.
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Although I'm not an expert in the field, it is my understanding that we would not be able to reach much of the Dead Sea Scrolls without modern image processing. (And in the absence of digitization the documents would be available to a far smaller group of scholars).
And only recent image processing has revealed the secret of the subject smear, which is a kind of neat insight into Jefferson's thoughts while drafting the Declaration of Independence.
Of course we wouldn't know that we had found Richard III without computer facilitated DNA comparision.
Computers were used in Bayseian analysis of the Federalist papers to determine authorship. Second source with more details. This was an early effort, so the effort was combined digital/manual; subsequent efforts have used far more digital techniques. This may fit your "super OMG" category.