Language can be defined as a sequences of signals (whether visual, aural or any other type of signal). A signal is any physical expression of information.

So what does defining those concepts accomplish for us? Thinking of language as sequences of information allows us to chunk our used language down to the basest character or blip and scale up until we reach novels, libraries or the theoretical limit of all information in existence. This allows us to have endless sets of data contained within another, discrete and overlapping. For example a “book” is a discrete set of data which may contain subsets such as chapters, which contain paragraphs, which contain sentences, which contain words, which contain characters. There can be discretely separate sets (such as a paragraph which contains the only instance of a certain sentence) or overlap (such as the letter “a” belonging to multiple words in the book).

Sequences (sets with an indexed order) can have fun and unique properties. For example a sequence that is the same forward and backward is a palindrome. This is a type of symmetry, since one side is mirroring the other. There may be further symmetries in the sequence, especially if you use monospace, or cell block typesetting. Some characters are themselves geometrically symmetrical around the central vertical axis(A, M. V) or around the central horizontal axis (I, D, K) or both (O, H. X) ; I call them spinners since you can spin them around the center (using depth) and they’ll end up the same.

Sometimes characters are not symmetrical geometrically symmetrical due to what I call a “jinx”, or a mark that breaks something that would otherwise have a symmetry (“m” jinxed on the left side with a vertical line, “y” jinxed by the right side continuing past the center down to the left). Sometimes there exists two different jinxes on the same basic shape (“b” and “d” or “p” and “q”). This allows for us to make a geometrically symmetrical sequence that is NOT a palindrome; “bod” is reflectionally symmetrical around the central vertical axis of the “o”, but lacks rotational symmetry, “pod” is reflectional around either axis running through the center of the “o” at 45 or -45 degrees and has rotational symmetry but lacks a reflection around the central vertical axis.

Another type of sequence symmetry is aural symmetry. Take the word “Ava” for example. If you pronounce it “Ah-v-Ah you have an audible symmetry, the “Ah”s surrounding the central “v”. It is also a spelling symmetry, or palindrome, since it is written the same forward and back. Palindromes are very powerful since they relay the same information twice in the same number of cell blocks. Palindromes can exist in sub-sequences of larger sequences, i.e. not the whole word. For example, “Amazing” starts with the three letter palindrome “ama” and the word “mama” contains “mam” as well as “ama”. It is worth noting that any 1 character or double character (e.g. JJ) forms a one and two letter palindrome respectively.

The method used to create and express sequences also plays a role in the symmetries one can create or find. Consider the words “XOX OXO XOX”. When it is displayed as we just did there is a three word palindrome, containing three single word palindromes as well as four palindromes of lengths 1 to 11 characters long. If you remove the spaces it becomes a single word 9 character palindrome “XOXOXOXOX” containing seven 3-character palindromes and five 5-character palindromes and three 7-character palindromes. Just deciding whether to add spaces between the words or not drastically changes its symmetries. It is worth noting that in both of our examples all palindromic symmetries are also rotational symmetries around the central character’s center, and reflectional around the any central character’s horizontally central axis. “XOX OXO XOX” only has 3 vertical axis around which palindromes can be observed while “XOXOXOXOX” has 7 different vertical axes of symmetry.

But that’s not all we can do in terms of making modifications in how we display sequences. We could also seperate with line breaks instead of spaces.

XOX
OXO
XOX

This introduces vertical and diagonal symmetries which are not usually found in examples of English text. In this representation we have our three 3-character palindromes, but we can also combine two or all three of the lines and still have an axis of symmetry running down the center of the center characters. Also because of the characters’ symmetry, any line drawn horizontally or vertically through a 3 letter sequences center will be an axis of reflectional symmetry, and the center of any vertical or horizontal sequence is a point of rotational symmetry. Additionally any line drawn from the bottom most diagonal corner to its opposite is an axis of reflectional symmetry. Finally the center of the central “X” is a point of rotational symmetry of the 4th degree. There are some additional one character wide diagonal axes of reflectional symmetry as well but we won’t get into them. Note that many of these symmetries require monospaced typefacing, or “cell block font”.

So as you can see, treating written/spoken language as sequences as large as necessary composed of sub-sequences as small as necessary. We can find palindromic symmetries in one dimensional strings of characters, and with monospaced “cell block” fonts we can expand the types of geometric and palindromic symmetries we can find by introducing a second dimension and all the angles in between. We can use symmetrically cell blocked characters to create larger geometric symmetries, and we can even pull some symmetries from “jinxed” characters. I call these two concepts “linguistic symmetry” and “representative symmetry”. Linguistic symmetry would include palindromes, both at the single character level as well as with larger sub-sequences. All of the geometrical symmetries we explored would fall under representative symmetry since they depend on geometrically expressed characters to form symmetries.

This is just scratching the surface of what sequential and set analysis can uncover or express within our everyday lives. The more aware you are of a concept the more powerful it becomes, so give it a shot.