How long after Charles Babbage's death were new ideas for a programmable computation device conceived?

The choice indicating that new ideas for a programmable computation device were conceived 100 years after Charles Babbage's death is correct due to the historical context of computing advancements. Babbage, often referred to as the "father of the computer," passed away in 1871. It wasn't until the mid-20th century, particularly around the 1940s and 1950s, that the foundational concepts of modern programmable computation began to take shape.

In this time frame, major developments such as the creation of electronic computers and the formulation of programming languages emerged. Notably, the first fully electronic programmable computer, the ENIAC, was completed in 1945, positioning this period as a significant leap in computing technology that drew on principles that could be traced back to Babbage's initial ideas.

The gap of approximately 100 years between Babbage’s death and the bloom of practical programmable devices highlights the slow progression of technology and theoretical understanding that was required to realize the complexities of computation as we know it today.