Hi John E. Franklin (2);

I have a question:

What has happened to John E. Franklin 1?

7. did he start with for example, sampling and digital and then eventually worked into analog ideas and how did he bridge the gap, supposing this is what he did.

That is exactly what he did. In their notes you find that most people start by experimenting with small examples. The classical mathematicians leave all of that out when they write the paper and the experimental ones hurry to put it in.

As far as I can understand Newton generalized it all with the question of what happens when there are an infinite number of small pieces. This led to the concept of the limit and what you call analog.

I remember attending a lecture of a famous physicist often seen on television. Half way through the lecture I woke up only to hear that he claimed he never worked with numerics or discrete examples. He claimed he came up with his ideas by thinking in 9 dimensional space. As the rest of the audience began to nod knowingly, I went back to sleep.