The idea of turning manmade constructs (made up stuff) into mathematical formulas has been the key ingredient in almost every advancement in technology throughout history. Recent advancements in the process of turning written language into mathematical formulas, has allowed computers to calculate human language and ideas in amazingly constructive ways.
Character codes aka numerical representations of a single character. This is a little different than the 1s and 0s that make up the actual character, but the concepts are related because the numbers are made up from bits anyway.
“a” = 97
“A” = 65
Numerical representations of whole words.
“animal” = 97, 110, 105, 109, 97, 108
“animals run wild” = 97, 110, 105, 109, 97, 108, 115, 32, 114, 117, 110, 32, 119, 105, 108, 100
The mathematical calculation of vectors applies to thoughts by simply calculating multiple sentences and the vectors of each word.
However, it goes further. You also have to calculate the vectors for all the words in the definitions of each of those words. You have to take into account how the words can have different meanings based on the way they are used.
Here is where you get into “cognitive computing” as talked about in the media. This is a far more thorough and advanced approach. It calculates the vectors of every single layer mentioned above, but it includes synonyms, antonyms, grammar and even the history and origin of the words.
When you calculate all of these together you can create a mathematical formula for representing an actual complex concept. This is where the real advancements in machine learning are coming from such as IBM Watson, Siri, Google Brain and others.