Comparison of the Merits/Demerits of the Linear B, Greek & Latin Numeric Systems:

Linear B:

As can be readily discerned from the Mycenaean Linear B Numeric System, it was quite nicely suited for accounting purposes, which was the whole idea in the first place. We can see at once that it was a simple matter to count as far as 99,999. Click to ENLARGE:

Mycenaean Linear B Numeric System and Alpha

In the ancient world, such a number would have been considered enormous.  When you are counting sheep, you surely don't need to run into the millions (neither, I wager, would the sheep, or it would have been an all-out stampede off a cliff!)  It worked well for addition (a requisite accounting function), but not for subtraction, multiplication, division or any other mathematical formulae. Why not subtraction, you ask?  Subtraction is used in modern credit/deficit accounting,  but the Minoans and Mycenaeans took no account (pardon the pun) of deficit spending, as the notion was utterly unknown to them. Since Mycenaean accounting ran for the current fiscal year only, or as they called it, “weto” or “the running year”, and all tablets were erased once the “fiscal” year was over, then re-used all over for reasons of practicality and economy, this was just one more reason why credit/deficit accounting held no practical interest to them. Other than that, the Linear B numeric accounting system served its purpose very well indeed, being perhaps one of the most transparent and quite possibly the simplest, ancient numerical systems.

Of course, the Linear B numerical accounting system never survived antiquity, since its entire syllabary was literally buried and forgotten with the wholesale destruction of Mycenaean civilization around 1200 BCE (out of sight, out of mind) for some 3,100 years before Sir Arthur Evans excavated Knossos starting in early 1900, and successfully deciphered Linear B numerics shortly thereafter. This “inconvenient truth” does not mean, however, that it was all that deficient, especially for purposes of accounting, for which it was specifically designed in the first place. 

Greek:

Greek alpha-numeric
On the other hand, the Greek numeric system was purely alphabetic, as illustrated above. It was of course possible to count into the tens of thousands, using additional alphabetic symbols, as in the Mycenaean Linear B system, except that the Greeks were not anywhere near as obsessive over the picayune details of accounting, counting every single commodity, every bloody animal and every last person employed in any industry whatsoever.  The Minoan-Mycenaean economy was hierarchical, excruciatingly centralized and obsessive down to the very last minutiae. Not surprisingly, they shared this zealous, blinkered approach to accounting with their contemporaries, the Egyptians, with whom the Minoan-Mycenaean trade routes and economy were inextricably bound on a vast scale... much more  on this later in 2014 and 2015, when we come to translating a large number of Linear B transactional economic and trade records.

However, we must never forget that the Greek alphabetic system of numeric notation was the only one to survive antiquity, married as it is to the universal Arabic numeric system in use today, in the fields of geometry, theoretical and applied algebra, advanced calculus and physics applications. Click to ENLARGE:

geometry with Greek and English algebraic annotation 
It would have been impossible for us to have made such enormous technological strides ever since the Renaissance, were it not for the felicitous marriage of alphabetic Greek and Arabic numerics (0-10), which are universally applied to all fields, both theoretical and practical, of mathematics, physics and technology today. Never forget that the Arabians took the concept of nul or zero (0) to the limit, and that theirs is the decimal system applied the world over right on through to computer science and the Internet.

Latin (Click to ENLARGE):

Latin 1-1000

When we come to the Roman/Latin numeric system, we are at once faced with a byzantine complexity, which takes the alphabetic Greek numeric system to its most extreme. Even the ancient Greeks and Romans were well aware of the convolutions of the Latin numeric system, which made the Greek pale in comparison. And Roman numerics are notoriously clumsy for denoting very large figures into the hundreds of thousands. Beside the Roman system, the Linear B approach to numerics looks positively like child's play. Thus, while major elements of the alphabetic Greek numeric system are still in wide use today, the Roman system has practically fallen into obscurity, its applications being almost entirely esoteric, such as on clock faces or in dating books etc. And even here, while it was still common bibliographic practice to denote the year of publication in Roman numerals right on through most of the twentieth century, this practice has pretty much fallen into disuse, since scarcely anyone can be bothered to read Roman numerals anymore. How much easier it is to give the copyright year as @ 1998 than MCMXCVIII. Even I, who read Latin fluently, find the Arabic numeric notation simpler by far than the Latin. As for hard-nosed devotees of Latin notation, I fear that they are in a tiny minority, and that within a few decades, any practical application of Latin numeric notation will have faded to a historical memory.

Richard