Why category thoery is fundamental yet hard to understand

Category theory is mathematical theory about mapping. Some call it the foundation of mathematics.

According to my understanding of math as reproducible mental object, this is not supprising. As all the brain does is doing mapping. Or in Plovian's words: conduction. Signals going from one set of neuros to another.  Understanding mapping is fundamental obviously.

Now category is billed the hardest to understand branch of mathematics, also known as "abstract nonsense". 

In programming world, functional programming is considered hard. Object Oriented Programming, the world of "nouns", despite of its limitations and actual complexity, is considered easier to understand.

The reason is the same.

Brain does not feel pain when touched or even lesioned. Similarly, the actual processing itself of the brain is hard to be perceived by brain itself. The results of the processing, often the nouns, are easier to be feeled. Hence property (nouns) are easier, mapping (verbs) is harder to conceputalize.

However, mapping is still more fundamental, in term of governing the laws of mental operation.

Training and education is the key. Cannot just cater to what feel easier.


Post new comment

The content of this field is kept private and will not be shown publicly. If you have a Gravatar account associated with the e-mail address you provide, it will be used to display your avatar.
  • Allowed HTML tags: <a> <em> <strong> <cite> <blockquote> <code> <ul> <ol> <li> <dl> <dt> <dd> <div> <h1><h2><h3><sub><sup><b><i><u><font><img>
  • You may post code using <code>...</code> (generic) or <?php ... ?> (highlighted PHP) tags.
  • Lines and paragraphs break automatically.

More information about formatting options

To prevent automated spam submissions leave this field empty.
Nice place