Everyone has some understanding of the number line. I do not know if people just simply remember what they have been taught in grade school or if they intuitively have this uncanny understanding of the number line. Somewhere in between we humans know how to count using the number line. My question is about counting. Can you count without knowing numbers? If I ask you to count to 100 you can easily do this.
What if I tell you to do the same thing again but do not use the base 10 decimal system. In fact don't use any number based system other than unary. Can you count now? Sure you can. But you will soon loose track of where you are if you try to use your brain's short term memory or if you eat to much MSG. You will know not if you are getting close to the original number that I requested you to count to. You will not know if you have passed this number.
In this context, we have a new phenomenon. The number line is basically still there but we do not have any more reason to call it a number line. Let us call it a "counting line."