In the numberfile video he doesn't explain the way he calculates 2・S_2. He says he shift it, but doesn't explain why that is valid. Shifted version:

In the numberfile video he doesn't explain the way he calculates 2・S_2. He says he shift it, but doesn't explain why that is valid. 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?). What if we triple shift? 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!