Science Forums 2

[Doctordick]

Hi modest, you are clearly confused over an issue that seems quit clear to me. As I know you are well aware, I have had great difficulty communicating the central issue of my numerical labels x_i. I have just finished reading The Rosetta Stone The Decipherment of the Hieroglyphs, by Robert Sole, Dominique Valbelle and W.V.Davies (or rather, a translation into English by Steven Rendall). Perhaps an example cast as an analogy to Champollion's translation of the Egyptian Hieroglyphs would make the issue clearer.

To put the problem in a nutshell, the Rosetta stone (it was found in Rosetta Egypt in 1799) had three inscriptions on it. One in Greek which could be read by the finder, Pierre Bouchard (a French army officer under Napoleon) and two others he could not read. The clue to its importance was in the last sentence of the Greek inscription: “This decree shall be inscribed on stelae of hard rock in sacred characters, both native and Greek, and they shall be erected in each of the temples of the first, second and third category, next to the image of the king living eternally”. No known person had been able to read Egyptian Hieroglyphs for more than one thousand four hundred years. (As an aside, the last document known to be written in hieroglyphs was written around 394 AD. The Byzantine emperors had prohibited the practice of pagan cults. The last Egyptian temple was actually closed around 551 AD.)

So there was the problem, they had a text (the English translation of the Greek runs roughly eight pages of type written composition) written in three different languages Greek, Coptic and Egyptian which claimed to say the same thing. Now, let's cast the problem in an abstract form which I hope you can follow. The Greek inscription is the explanation (what it says is really unimportant; what is important is that it can be understood). The Coptic I will lay aside for the moment; its real value is pronunciation as the inscription is essentially a cursive representation of the hieroglyph language about the time of Alexander.

The problem then is to associate each and every significant element of the Greek inscription (our explanation) to each and every supposed significant element of the Hieroglyph inscription (what we are trying to explain). First, let us take every element of the Greek inscription (every letter, every word, every phrase, every sentence: every element to which we can assign a meaning) and assign a numerical label to that element (those numbers are analogous to my index “i”). Secondly let us examine the Hieroglyphic inscription and lay out each and every distinct feature of that inscription we can recognize and assign a numerical label to that element (those numbers are analogous to my index “x”). Note that we have no proof that any of those specific features are significant nor can we be sure any one of them actually was intended to convey a meaning but we do know that we have included all features capable of communicating meaning (because any we have not labeled can not be seen as different).

Now, our problem is to establish an association between the collection of i indices and the collection of x indices. If we can do so, we have solved the translation problem. How we do that is totally immaterial here; the point is that the solution can be expressed by that collection of numbers called x_i. Note that I have totally thrown away those numbers (both i and x) for which no connection can be made. It is possible that some of my “i” indices serve no purpose: i.e., perhaps there are ideas in Greek which cannot be expressed in Hieroglyphs. Likewise, it is possible that some of those “x” indices serve no purpose: i.e., perhaps there are features of the Hieroglyphs which convey no meaning (say like the angle of a particular line in a specific glyph which is somewhat different in two similar glyphs).

The important thing here is that the solution of the problem is in that collection of numbers called x_i. Now, suppose one finds another bilingual document and one does the same thing with that document. Let us call our first solution (x_i)₀ and our solution for the second (x_i)₁. This additional index is to allow changes in the meanings of some glyphs from one document to another (think in terms of context; certainly you must include the possibility of changes). Changes in “i” can certainly also exist; however, those are known (because that is the language the translator understands).

The whole object here is to have a way of representing any flaw-free solution of the problem of translating some unknown information into an explanation of that information.

Let me know if this analogy clarified anything for you.

Have fun -- Dick