Shifted version:
1-2+3-4+5-6 ...
1-2+3-4+5 ...
sum: 1-1+1-1+1-1 ...
Multiplied version:
2-4+6-8+10-12 ...
The multiplied version shifts between +(2n) and -(2n). Following the logic that S_1 = 0.5, because that is the average between 0 and 1, I would argue that the multiplied version of S2 should equal 0, as that is the average between a postitive constant and its negative (but the variance is going to be infinite. Doesn't that have a say?). Triple shifted version:
1-2+3-4+5-6+7-8+9 ...
1-2+3-4+5-6 ...
sum: 2-3+3-3+3-3+3 ...
Look! now 2・S2 is equal to 2!
Right now I am looking at:
Havoc low profile[1], because it is mechanical and low
Surface Ergonomic Keyboard[2], because it is basically an ergonomic windows version of what I had.
Can anybody weigh in on these?
[1] https://www.prohavit.com/products/hv-kb390l-low-profile-mech...
[2] https://www.microsoft.com/en-us/surface/accessories/surface-...