The Textual Work of August Walla, mentally disabled artist

[Alin_J]

I also studied the intra-word relationships in Walla's invented words using Principal Component Analysis. For each word in the vocabulary, the first character to the next to last's transition to the next-following character was counted (bigram frequencies of all the bigrams in the words, so that if a word is spelled "abc..." the first bigram of this word is "ab", the next "bc" and so on. These bigram frequencies of all different word-types were summed together and arranged in a matrix where a row stands for the first character in the bigram, and a column the second character. Next, all the matrix elements were normalized by dividing each matrix element with the frequency sum for the corresponding row, resulting in a transition-probability matrix that expresses the transition-probability given character i, to character j if i is the row index and j is the column index, normalized also as the sum-average of each word in the vocabulary. Only the characters which had frequencies above 0.5% of the total character count was included into the matrix. For Walla's text all upper-case characters were converted to lower-case before frequency counting and analysis. Principal components (PC) analysis on this matrix revealed the following score scatter plot:

   

The first character in the bigram (observation point) label is prefixed by "f-" and the second character in the bigram (original variable vectors, represented by green lines) labels are not prefixed at all, simply labeled by its character. Each principal component is a linear combination of all the original variable vectors and these vectors are hence also here summed for PC1 and PC2 and projected into the plots.

The plot showed, as is usual for natural languages, a pretty clear separation of vowels and consonants, where most of the vowels show up on one side along PC1 and the consonants along the opposite side of the 0 value of PC1. Also typical for natural languages is the similar division of the vowel/consonant original variable vectors (green lines) along opposite sides of the PC1 0 value, where the vowel-vectors are on the same side as the consonant observation points and vice versa. This is because natural language words often alternate between vowels and consonants. This is also present in Walla's words. There does not seem to be much additional groupings, and this also appears to be typical for natural languages. Sometimes however in natural languages there is a certain bigram that is very frequently used, for example "sh" in English, a digraph representing a single phoneme. These types of digraphs would often reveal themselves as outliers in a separate direction (along the variable line representing the second character in the bigram). 

The first (most significant) two components had the following eigenvalues and % of covariance explained:


PC Eigenvalue % variance
1  0.0251165  41.497
2  0.00849664 14.038


The % variance of the first PC is usually much larger than the second (and all the rest) in natural languages, because in natural languages PC1 is mostly governed by the vowel-consonant alternation which results in much larger covariance than what any other types of common grammar rules/frequent syllable characteristic, etc would result in, even taking language's frequent uses of certain digraphs into account. So, these values would also be quite typical for natural languages.

The following two plots and tables show the corresponding results for VMS languages A and B in respective order. Note that this was made using the 101 transliteration. Note also that in this case the observation point labels are prefixed with "_" (not "f-").

   

VMS Language A


PC Eigenvalue % variance
1  0.0475643  38.251
2  0.0274967  22.113


   

VMS Language B


PC Eigenvalue % variance
1  0.0477088  29.021
2  0.035866   21.817


For the VMS the separation along PC1 is not as dominant as separation along PC2, particularly for language A, three pretty distinct directions are evident, one along the lower left quadrant, one in the upper part along PC2 and one more along PC1. PC1 is not as dominant as PC2 which is shown by their % variance values which do not decrease as much going from PC1 to PC2.

The possibilities for more in-depth analysis and discussions are many, but for now I don't have anything more conclusive than this. But in answer to the original question in this thread, if any analysis results of the same analyses on VMS as on Walla's text would be similar, for this analysis then they do not seem to be very similar in that Walla's text behave more like natural language than the VMS do.