Random Thought #124

Isomorphism. That's that new word I learned this week. Actually, I've been noticing new concepts in books and articles I read that explain habits I have which I was aware of but didn't really know that there was a word or concept for it. Let me provide an example. Let's define isomorphism. Isomorphism is basically being able to represent something in two different ways without changing the content via some form of mapping axiom. For example, abc and 123. These say the exact same thing assuming you have a mapping in place that says a=1, b=2, and c=3. I've basically said the same thing but two different ways. How does this relate to a habit of mine? Well without really knowing it, whenever I'm driving, I look at people's license plates as I go by them or pull up behind them. Most traditional license plates have a grouping of 3 numbers or letters followed by another grouping of 3 numbers or letters. I would simply compare the first grouping to the second grouping by developing some sort of mapping axiom. It was a fun game to play. Since that time, license plates have gotten a little more complicated. The first grouping could have a combination of letters and numbers as could the second grouping. I've even seen some license plates that have a grouping of 3 and a grouping of 4, both mixing letters and numbers and so I start trying to solve algebraic equations. For example, if I setup a certain mapping axiom such that letters have certain numerical volumes, what would the extra letter have to be in the grouping of 4 to make both sides equal. Its how I'm able to remember a multitide of license plates so well. That actually brings me to another point. Isomorphism is how we assign meaning to things. We take a known formal system (alphabet or whole number system) and try to take an unfamiliar system or pattern and map it to our known system. When we are able to do this, we make that unfamiliar system familiar to us via the linkage of the developed mapping axiom. Its quite amazing and a core fundamental of how we solve problems and recognize patterns, which partially leads to intelligence. Anyways, I know it may seem weird but I found it quite fascinating and hope you at least learned a little something too