Can't change, won't change, can't learn

The first thing I think when someone tells me that "people can't change" is the person speaking can't learn.

A simple example is math.  Suppose a person consistently makes a mistake adding 2+2 and makes it always equal to 4 even though we are working in a base 4 system where the number 4 does not exist.

Okay, maybe I lost some of you.

Suppose a person constantly writes down 2+2=5.  If we sit down with that person and we explain that the numbers are abstract representations of fingers and we count fingers the person will change what they write, 2+2=4 (in any base greater than 5).

The person has changed because they learned.

As children we make almost no choices about how or what we learn.  As we become older we create a ton of filters which influence our ability to learn.  Some people build walls instead of filters becoming incapable of learning, thereby becoming incapable of change.

If a person is capable of learning a person is capable of change.

I could blather on for a few thousand words giving more examples, but, I'm not going to bother today.  Usually I enjoy vomiting out verbiage into the void, but, today I am just going to make a point and say "later".