Square Matrix

12 May 2016

Charles Dodgson wrote this poem. He is better known as Lewis Carroll for writing Alice and Wonderland and Through the Looking Glass. Dodgson was also a mathematician who pioneered how to find the determinant of a square matrix; essentially, he found whether a solution to a system of linear equations existed.

Notice that this poem fits in a 6x6 table. It’s a square. Also, notice that the poem can be read both horizontally (through the rows) and vertically (through the columns). For example, see the bolded text above.

Personally, this is fascinating if you use linear algebra to consider the poem as a matrix. So, then you can see that a12 = a21; in this case, “often” = “often”. When the columns and the rows of a matrix are interchanged, then we get the transpose of that matrix. In this case, A= AT. By a further set of proofs (A-1AT = I), we can see that our matrix A is invertible. Yes, linear algebra deals with numbers (integers, floats). However, Dodgson shows that you can also look at words (strings)!

Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic. - Tweedledee