What does it mean when someone says "Would you please indulge me for a couple of minutes?"? [closed]

What does it mean when someone says "Would you please indulge me for a couple of minutes?"?

The context in which I heard it makes it seem self-evident, but I may be wrong. Somebody was talking to another person, and the person being addressed was asked by the lecturer to please indulge him. The lecturer went so far as to say, 'I beg your indulgence.' What does this mean? I thought indulgence meant 'something enjoyed as a special pleasure': Good food is my only indulgence.

Solution 1:

An indulgence is also permission to do something which ordinarily might be considered in violation of some rule, such as a rule of etiquette. It is also used as permission to act or speak under the assumption that something that is ordinarily considered true or false is, for the purpose of discussion in that moment, the opposite.

In a discussion of astronomy, I might ask for the indulgence of my interlocutor to assume temporarily that something we both know is true, for example, that the earth orbits the sun, is false - that the sun orbits the earth.

It might also be taking the liberty of going off on a tangent in a discussion or lecture, covering material that doesn't relate to the topic at hand. For example, I might ask my audience's indulgence to depart from my advertised topic of central processor design to reflect upon the problem of disposal of waste material generated from the process of manufacturing computer chips.