Hypervector Analysis of the Voynich Manuscript

[Alin_J]

That is right, but PCA only gives you two the first two of 10,000 dimensions, and it should then be clear that one has to be very careful about drawing conclusions from only these two dimensions.

René, I have to correct you on this one. It is not true that PCA only gives you the first two of the 10 000 dimensions. The two first principal components in any n-dimensional set gives two directions, as a 2-dimensional projection, of the directions in the n-dimensional set along where the two largest co-variances are found (these are the directions of highest correlation in the data). You have to look at the percentage of variance explained by the components in each individual case to determine if this is high enough. But it's completely possible to have 10 000-dimensional data with the first two components together explaining 99% or so of the variance/co-variance in PCA. 

In this case where the correlation in data is made up to be fully random for most of the possible pairs of the dimensions being compared it is even probable that the vast majority of dimensions will not make any difference (that of all the co-variances being evaluated, most will be very close to zero).