This definition of causality doesn’t seem to work, since the universe clearly doesn’t generate future values independently of each other. Consider the following story:
On Monday I decide to buy 2 windows of the same mass. Suppose I want to buy the biggest windows I can afford, and I have money in two bank accounts that I can use for this purpose. On Tuesday a couple of cute little vandals break both of my windows. Some of the glass falls inside my home, and rest outside. Now let:
L1 = how much money I had in bank 1
L2 = how much money I had in bank 2
M1 = mass of window 1
M2 = mass of window 2
R1 = mass of glass that fell inside my home
R2 = mass of glass that fell outside my home
Intuitively it seems pretty obvious that the arrow of causality runs from left to right, but if you use the definition Eliezer gave, you’d get the opposite result. Quoting Eliezer:
Then we can guess causality is flowing from right to left.
Well, P(M2|L1,L2) ≠ P(M2|M1,L1,L2) because M2 depends on the price of glass as well as L1 and L2, but knowing M1 gives us the precise value of M2 (remember that I wanted to buy 2 windows of the same mass). P(M2|R1,R2) = P(M2|M1,R1,R2) since M2=(R1+R2)/2 and M1 doesn’t give any more information on top of that.
This definition of causality doesn’t seem to work, since the universe clearly doesn’t generate future values independently of each other. Consider the following story:
On Monday I decide to buy 2 windows of the same mass. Suppose I want to buy the biggest windows I can afford, and I have money in two bank accounts that I can use for this purpose. On Tuesday a couple of cute little vandals break both of my windows. Some of the glass falls inside my home, and rest outside. Now let:
L1 = how much money I had in bank 1 L2 = how much money I had in bank 2 M1 = mass of window 1 M2 = mass of window 2 R1 = mass of glass that fell inside my home R2 = mass of glass that fell outside my home
Intuitively it seems pretty obvious that the arrow of causality runs from left to right, but if you use the definition Eliezer gave, you’d get the opposite result. Quoting Eliezer:
if we see:
P(M2|L1,L2) ≠ P(M2|M1,L1,L2) P(M2|R1,R2) = P(M2|M1,R1,R2)
Then we can guess causality is flowing from right to left.
Well, P(M2|L1,L2) ≠ P(M2|M1,L1,L2) because M2 depends on the price of glass as well as L1 and L2, but knowing M1 gives us the precise value of M2 (remember that I wanted to buy 2 windows of the same mass). P(M2|R1,R2) = P(M2|M1,R1,R2) since M2=(R1+R2)/2 and M1 doesn’t give any more information on top of that.