Why is the Cross a Sign of Redemption?

I am not a Christian so I have to admit there are some basic things that I don't 'get.'  First and foremost, how did a torture instrument become a symbol of 'redemption'?  Imagine for a moment a convicted murderer sitting on an electric chair.  Those closest to him say he is innocent of all charges yet in spite of all of this he 'fries in the chair' as scheduled.  Leaving aside the question of whether anyone could imagine that this criminal was the 'Son of God' for a moment it would seem downright bizarre to say the least that the electric chair itself would become venerated as a symbol of redemption for mankind.

I think that I will keep looking up at artistic representations of the Cross and not 'get' what this has to do with redemption.  Nevertheless over the last couple of days I have made some progress.  If we take our cue from Justin Martyr, the Cross was certainly saltire, that is 'X shaped' as opposed to our familiar 'T shaped' variety.  Now I am not hear to argue the point.  Let's just let the point stand for now.

It is interesting that the Aramaic term for 'redemption' is peraqon, Syriac purqana.  Yet pereq means cross-shaped.  It is actually quite fascinating to go through Jastrow's Jewish Aramaic dictionary and see all the examples which seem to be rooted in Biblical Hebrew.  In Obadiah 1.14 we read:

Neither shouldest thou have stood in the crossway (hapereq), to cut off those of his that did escape; neither shouldest thou have delivered up those of his that did remain in the day of distress.

Not only is the crossroad cross-shaped but Jastrow notes that pereq is used to reference 'open scissors' (nithpael) among other cross-shaped items

The ancient Semitic root here goes back to the idea of 'separate.'  Clearly Jesus is understood as 'separated' on the Cross and thus 'redeeming' and perhaps 'redemption'?  The point is made in the Gospel of Philip albeit using parush which nevertheless arguably comes from the same biradical stem p-r