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 Quote by James S Saint Okay, so you are saying there, that “if Einstein could have seen a clock at the stop-button, that clock would have been reading [-9.815] at Einstein’s t=0 because he would see a distance of [19.630] and was traveling at .5c.”
No, that's not what I'm saying. We are not now talking about clocks that are at rest in the station frame but clocks that are at rest in Einstein's frame which are traveling with respect to the stop-button, or more precisely, the stop-button is traveling past a whole bunch of Einstein's coordinate clocks.
How is Einstein's "coordinate clocks" any different than "what Einstein would see of the other clocks"? It seems to be the same thing to me. If there is a difference, I seriously need to know what that is.

 If you want to calculate how Einstein determines what the time was on the stop-clocks when the button was pressed, you need start with the event of Einstein being colocated with the stop-button. In the station frame this event is [34,17] and transforms to [29.445,0] in Einstein's frame. The delta between this time and the event of the button press in Einstein's frame is 29.445-6.351=23.094. Dividing this by gamma gives us 20. Now we subtract 20 from 34 and we get 14. Do you see the significance of the 6.351?
I had asked for the derivation of the 6.351. Your explanation of its "significance" makes it seem like merely a number injected so as to justify the chosen conclusion. How did you calculate it?

..and btw, my method for getting to the conundrum is much simpler. I am looking for anything that would indicate what my error might be.