[Blog Post] Spatial Spread And Conditional Character Entropy Reduction

[pfeaster]

I'm not sure cards would make the game more interesting. 

I was just thinking there would need to be some way to assign players a specific text to encipher -- I don't see cards in particular as having any other advantage.

But whenever I pick up a history or survey of cipher techniques, it never seems to mention anything like this.  Does anyone have an explanation as to why?  ...

Nothing is known apparently. However they did play board games so the possibility existed that someone, just once, designed a cipher with rules similar to a board game, it isn't a big conceptual leap.

No, it's not.  And closely related to the gameboard is the counting-board used for mathematical calculations, which is another model I find intriguing, in part because it's something that was ubiquitous at the time but easy to overlook now.  There was, as I'm sure many here know, a gradual transition in the late medieval and early modern periods from working out problems with tokens on ruled boards (the old way) to working out problems on paper with Arabic numerals (the new way).  If later ciphers were designed to be solved "on paper," then, there's arguably some context for imagining an earlier period in which the cultural impulse could have been to design them to be solved by manipulating objects on boards instead.  There's also some context for imagining the latter approach falling into disfavor as philosophically "behind the times."

Coming at this from another direction:

I gather that at least a few of us have been drawn to gameboard-type ciphers in our efforts to come up with plausible explanations for the structure of Voynichese.  But ciphers like these also seem to have much to recommend them more generally: a method that would be fiendishly difficult to implement otherwise can become trivially easy when worked by (say) moving a few coins around a grid.

If we can think of ciphers like this, presumably other people can too: as you say, it doesn't take any big conceptual leap.  And yet it's not only the early 1400s for which documentation of such methods seems to be lacking.  I don't find anything comparable mentioned in popular-audience survey works like Helen Gaines's You are not allowed to view links. Register or Login to view. either.  It's not that gameboards aren't sometimes associated with ciphers, but when they are, they don't seem to be used mechanically *as* gameboards (e.g., the "chessboard/trellis" and "straddling checkerboard" ciphers).

So I'm unsure how to reconcile our sense that this approach shouldn't have taken a "big conceptual leap" in the early 1400s with the observation that it seems to have had so little impact on cryptological practices in general, even up to our own time.  Is there some factor that militates against the development of this kind of cipher process?

It really does appear to have its advantages.  Processes such as Anton's spatial spread of characters in different pools (especially if used in combination with a Polybius Square) might seem prohibitively cumbersome for a text as long as the VM is if we think about someone carrying out the encryption and decryption in their heads or straightforwardly on paper.  But the use of physical tokens might have streamlined such work in ways that are hard to appreciate without actual experience of doing it.  J. M. Pullan writes in The History of the Abacus (1969) about the processes used for reckoning on counting-boards:

These methods may look clumsy and slow to those of us who have become accustomed to Arabic figures and are proficient in using them for calculation, but when we consider that counter-casting was the normal method for dealing with accounts and calculations of all kinds for several hundred years it is evident that it must have been regarded as reliable and efficient.  
A little practice with counters on a simple board will show that this is indeed true; and anyone who will take the trouble to work a few simple calculations may be surprised at the ease with which they can be carried out once he has become familiar with the feel of the counters....
Actual practice with counters is necessary, too, for a full appreciation of the size, shape and layout of a counting-board and of the reasons for the kind of moves that are made, including a number of short cuts that one soon begins to use.  It is only by practice with counters that one realises why one should always push them from place to place and not attempt to pick them up; and one soon finds by experience what an advantage it is to have a low rim round the board.
When explaining the moves required for even a simple calculation detailed verbal or written descriptions tend, inevitably, to make the procedure seem longer and more complicated than it is in practice, and this is another reason why one should not rely upon merely reading about the abacus method, but should try it out for oneself. 

The same could go for seemingly "unwieldy" cipher methods.  It's worth bearing in mind that the people of the early 1400s had more powerful tools available to them for manipulating data than we might assume.  The publication below dates from 1542, but the methods being described were very old by then.