I like the idea that the Gs are block delineators, i.e. that a block must start and end with G, as in G<statement>G. That would explain the single G at the beginning, the single G at the end, and the double Gs everywhere else. Also, I've noticed that the Hs come in statements like BHBBHB, or BBHBBBHB, or BHBBBHBB. It seems consistent that the number of Bs in between the Hs must be the sum of the number of Bs on both the right and left sides. Thus the H is an addition symbol, but not as we normally think of it. The addition doesn't read from left to right, but rather reads from outside to inside. It's like writting 4 (=9) +5, when the aliens write BBBBHBBBBBBBBBHBBBBB. Similarly, the I's come in patterns with BIBIBB and BBIBIB. Here the idea seems to be subtraction, but in the same outside to inside format, and without sign distinctions between positive and negative. I don't like that part at all. I'd much rather have the aliens understand the concept of a negative number. Maybe position is important? Could numbers on the left (or right) of the expression be positive, while numbers on the other side be negative? If the symbol I indicates subtraction, then there should be a distinction between writing 3 - 1 = 2 and writing 1 - 3 = 2, shouldn't there?