Maybe our consciousness is multidimensional but it needs a tool to manisfest itself on a given dimension.  That tool, in the third dimension, is the brain.  When the brain dies, we cannot maisfest ourself here in the same way.  Maybe a different way or maybe not at all.

So the brain is like a computer.  Our consciousness is us.  Our memories are the programs in the computer.  When the computer gets old and slow (like a Windows machine) we scrap it and get something else.  We may be able to take our programs (memories) with us to some other computer (like running a Windows program on a Mac).  Except that in this analogy, the Mac is the tool used in another dimension.  So we may have some knowledge of our life in the third dimension.  Kinda like playing Call of Duty with strangers on the internet and then switching to Medal of Honor on the internet and those strangers switched also and then they meet you and then they're like, "Oh I remember your sorry ass from COD, you SOB!!!" before blasting you with a bazooka.

But I digress...

Or maybe we get another Windows machine and a newer version of COD and continue paying.  And maybe those strangers on the internet did the same thing and meet you in this new version of COD and then they're like,  "Oh I remember your sorry ass from the previous version of COD, you SOB!!!" before blasting you with a bazooka.

Which is why I hate COD ;)