Making meaning: Association

Our goal in this class is to help you develop your skills in solving complex problems: figuring out the answer to a new question using things you know, often in new combinations. Two of the mantras that you will hear over and over again are that we "need to be sense making" and that we can "use our math to make meaning." These are rather handwaving requests. What does it mean to "make sense"? What does it mean for something to "be meaningful"?

To get some idea of what we're trying to do, think about how you might go about finding the meaning of a word that you don't know. Of course what you would do today is Google it and read a definition. But just to get a cleaner sense of what's going on, imagine you don't have the web available but only have a (paper) dictionary. Well, you would look the word up and read its definition.

Suppose, however, that you weren't looking up an English word, but at this one:

Some of you might recognize this and know its meaning, but I do not. I suspect that it's Arabic, since it's written in what I recognize to be Arabic letters. 

If I had an Arabic dictionary (NOT an Arabic-English one!) I might be able to find this word, especially if I knew that Arabic is written right to left instead of left to right. 

The word would then be defined in terms of other words. Found it! Success! Nope. Problem! Those words are all in Arabic and I still don't know Arabic. I could look up each of those words again and find them again, but I'm still skunked. If I know neither my starting words nor any of the words being used to explain it, I'm stuck.

This toy model shows the situation inherent in any dictionary: it is necessarily circular. Words are defined in terms of words.

The only way you can understand what the word being defined means is if at some point in the circular chain you come across a word or words you already know and have ultimately learned in some other way than from definitions. Starting from infancy you begin to associate words with object, events, processes, and feelings. From that base you can combine words with contexts to create the meaning that you know and feel and that you associate with language.

Just as memory is reconstructed, meaning is constructed by links to other kinds of knowledge,
associations with things you know and are comfortable with.

You can create the appearance of knowledge by memorizing and parroting back terms that have no meaning for you. This becomes especially problematic when you are learning something new and have to pick up and make sense of many new terms (and perhaps ways of thinking). 

You can think about the mathematics we're learning in this class as a new language. When math is done in a math class the focus is on mathematical structures. (See The disciplines.) When math is done in a science class, the meaning is made through associations of mathematical symbols with physical quantities.

One of our goals for this class is to help you learn to build rich connections and associations, not just memorized terms and equations, learning "the meaning of physics and of the math of physics". 

Joe Redish 7/6/18