Can we say that programmers changed the world ?

Answer 1

In technology, yes.

Answer 2

Yes, in lot of ways.
Since every hardware with a PCB needs a software for the user to instruct for the working of that particular system.
Every minute of the day we are surrounded by something or other with a software in it which took atleast 1-2 years for a team of software designers to make and implement.

Answer 3

Yes, in different ways, both technologically and mindwise. By mindwise i mean, programming have set a higher cap for things that seem "miraclous" or impossible to an average person, but at the same time produced more speculations and theories on how reality works and what we are and information is.