Just curious about all this. Coming from the perspective of a perpetual student with quirky learning differences and someone that is interested in learning differences generally -- for instance, helping other people and working with their differences.

I have always had trouble with arithmetic -- the pencil and paper of math. Today I was reading about Golomb ruler's. Looking at the tables, the "rulers", I realized how much trouble I have understanding the "distances" between numbers.

For instance, I understand that the technical distance between "0" and "1" is infinite. But that aside, what is the distance between, say, "4" and "9"? To me it is 4 (5, 6, 7, and 8). Arithmetically though, it is 5.

That may seem very simple, but for whatever reason, even though I "know" the difference, I can't get away from the 4 unless I take a long time to work the details. Then I can get confused.

If I follow my intuition and include the infinite distance between "4" and "5" and count that as 1 then take the same between "8" and "9" (to be politely symmetrical) and count that as 1 I get: 1 + 1 + 4 = 6. Arithmetically. But the distance between "4" and "9" is not 6. It is supposed to 5. Right?

Imagine doing that every time simple math comes up. Then try to pass college algebra.

In the mix is knowing about different number basses (from computer programming -- 2, 8, 16, 32, 64, etc...). About the "distance" between ASCII "4" and ASCII "9". And the computer memory distance between two variable with the respective values of 4 and 9 as: "characters", longs, ints, floats and doubles, etc.....

Imagine the numbers 4 and 9 written out in six bits, in binary (000100, 001001). Think of the pattern differences here. And what about rotating each "0" and "1" by, say, four bits to the left. It is still the accumulations of 1's and 0's, same just different patterns. And so on...... (Yes, I know about base-to-base conversions -- the value of place, so to speak)

What about all the different distances between any particular 4 and any particular 9 in, say, any given set of 10 books.

That all is not meant to be a play of semantics or whatever. It is actually what happens when I have to deal with numbers. For real. All the time.

Now imagine trying to teach simple arithmetic to someone looking at a "4" and a "9" on a page of math lessons. One difference, for example, being that they see those numbers in relation to all the other numbers on the page/s or things in the room. In other words, they see the numbers in their broader context's -- different pages of different lessons on different days at different times in different places. Essentially, for them, totally different numbers.

Where do you go with that?