First, please don't carry out extended discussions in comments. Comments are intended to allow readers to request clarifications or provide complements or objections related to a post. Long discussions detract from the generally-useful comments. And especially do not carry out extended discussions in comments on a non-participating user's post: the poster gets an inbox notification for each comment that you make on his post.
There is a place that is intended for discussions: chat. If you feel that a chain of comment replies is going to keep going, please switch to chat (leave a last comment like
Let's continue in [chat](http://chat.stackexchange.com/rooms/2710/computer-science).). You might even see an automated message suggesting going to chat, but don't wait for that automated message (it doesn't trigger in all circumstances where it would be warranted).
Each Stack Exchange site has a associated main chatroom; ours is Computer Science. You can take the discussion there. The main chatroom is open to pretty much anything (with the usual proviso to be nice — in theory, discussions are expected to be at least vaguely related to the site's topic, but this is only enforced in a few dedicated room.
If one of the participants in the discussion has at least 100 reputation (totaled over the whole Stack Exchange network), xe can create a new room instead.
You need 20 reputation and a registered account to participate in chat. If one of the participants has less than 20 reputation, xe can be invited by a moderator or room owner. So the best course of action if you have more than 100 rep and the other user has less than 20 rep is to create a room, grant explicit write access to the other user on the “access” tab of the room's info page, and leave a last comment inviting the user to join you in that chatroom.
If you need assistance with chat and none of the site moderators are around, try the Assembly. All Stack Exchange site moderators are moderators on chat, regardless of where the room is associated (except Stack Overflow and Meta Stack Overflow which have their own chat).