I've done some figuring on Message 4, and these are tentative conclusions, with some speculation and head-scratching thrown in. The 'a#b#a' construct is pretty easy to figure out. It's essentially scientific notation: 'a times ^b' (where  is of course 6 decimal). The TCs are pretty explicit about this in the last ## sentence: G QXQ L QX#Y#XQ L QBABQ 5Y5 QBABQ G If we're right about what L means, this says 'The number X#Y#X is the product of X and  to the power of Y.' The numerical examples that come before prove this out. There may be a transcription error in the next segment of Message 4. The released message shows 'n' but the strings of B's and A's seem to refer to hex-matrix images, rather than square-matrix images. Given previous assumptions (and images), we would expect 'o' rather than 'n' in these phrases. Be that as it may, I think these images suggest that '@' may mean 'length' or 'spatial dimension'. The paired V-W sentences seem to say 'The @ of nBn is 1; the @ of nBBAABAAn is 3; the @ of nBBAABAA BAAAAABAAAAAn is 5.' If the 'n'-phrases are taken as hex-matrix images, they depict a single dot, a line of length 3, and a line of length 5. The next V-W pair is particularly interesting. It seems to be addressing the '@' of '0' -- and we have tentatively concluded that '0' means an individual Tau Cetian itself. Are they trying to say that their length/height/spatial dimension is '!@!QBEBQ!@!'? If so, what exactly does the phrase '!@!' mean? (The 'QBEBQ' is the number . i.e., 10.) I am trying to work out whether the '!-!' phrases could signify measuring units of some sort, in which case the '@' of a Tau Cetian would be  @-units. (As you can see, here we are deep into speculation.) The '%' and '!' tones are a mystery to me at the moment. We have four sentences: G % P !%! QBDBQ !%! P % G '% = !%! ' (9 dec) G % P !%! QECEQ !%! P % G '% = !%! ' (26 dec) G % P !%! QBBCBBQ !%! P % G '% = !%! ' (44 dec) G % P !%! QBEDEBQ !%! P % G '% = !%! ' (63 dec) If the '!-!' phrases are units of some sort, I have no idea what these mean. (Actually, I have no idea what they mean period.) Also interesting is the V-W pair regarding '!Q!': G V !Q! V G G W !Q! pQBQp !Q! W G If 'p' is a mistranscription for 'P' then this is '!Q! = 1'. Otherwise, it seems to say '!Q! is a radius of 1 (or a circle of radius 1)' assuming the gloss of 'p' as 'radius of a circle' is correct. My vote is for an error in transcription, but I may be way off. The other phrase that bugs me is: G !@! e P !$! P e !%! G This may require an adjustment in the gloss for 'e' (currently standing at 'rightward directional ratio'). The use of 'e' and 'P' together is odd. I've just had a thought. Suppose I'm right that '!-!' means units, and that '@' means 'distance'. Would it make sense for '!%!' to mean 'time'? Then the above sentence could mean (again, using 'e' as a rightward ratio) '!$! is !@! (distance) divided by !%! (time)' -- making '!$!' mean 'speed' or 'velocity'. This might lead to a translation of the last sentence of Message 4 giving the value of '*' as a velocity with a very large number,  (which I have hand-calculated as 702,767,143 decimal). Could '*' signify the speed of light in Tau Cetian space and time units? OK, now I leave it to the rest of you to pick this apart. Whaddya think, sirs?