On fantasy and discount rates

…some method for discounting future and distant consequences is necessary. It is possible, perhaps, that the degree of discounting would exactly correspond to the increasing degree of uncertainty that goes with predicting remote events. But there is no simple formula that relates time or distance to uncertainty—some events a year from now or 5,000 kilometers from here may be much more predictable than other events only one week from now or 100 meters away.” (Wallach & Allen, Moral Machines)

This bit made me think. Wallach & Allen state correctly that the relation between (physical or temporal) distance and uncertainty is not a simple one, and some things which happen far away are more predictable than some things that happen nearby. But in what kind of a universe would that statement be incorrect? If it always made sense to consider events happening a week from now 20% more predictable than events happening a year from now, or events happening 100 meters away 20% more predictable than 5,000 kilometers away, regardless of the type of the event, what would that imply of the world one lived in?

It seems to me that this would have to be a world where the laws of nature were highly local. Things such as the speed of light and the boiling point of water would have to vary smoothly, depending on where and when you were. Actually, whether the universe had things such as “light”, “water”, or “boiling” in the first place would also vary by location. There are some things that we probably need to keep constant in order to avoid a logical contradiction, though. For instance, since we stipulated that events happening 100 meters away should be 20% more predictable than events happening 5,000 kilometers away, the geometry of the universe should not change as to make the concept of distance meaningless, nor should the axioms of arithmetic be changed at random.

Would it be possible to live in such a universe? Certainly if the discount rate was high enough, the universe would be so chaotic as to make all advance planning pointless. Not to mention the fact that organisms wouldn’t live for very long if their blood might literally begin to boil at any time. But let’s stipulate that the rate of change was slow, and that the organisms living in the universe were generally changed in such ways as to not outright kill them or drive them insane. Note that we are now again forced to introduce some predictability that is not a direct function of distance.

Things would perhaps get easier if we dropped the bit about change over time. The laws of nature would be spatially local, so traveling 5,000 kilometers would get you to a place where things worked quite differently, but things wouldn’t change if you stayed put. For this, we’ll obviously have to limit ourselves to laws of physics which allow for time and space to be separated in such a way. Now we don’t need to protect the organisms living in this universe from its changes anymore – organisms in different regions will simply evolve to exploit their local laws of nature, and to avoid going into places where they cannot survive anymore.

Some of the regions in such a universe would be teeming with life (though whether we’d recognize it as life is another matter), while other regions would be desolate, incapable of supporting any kind of complex structure. Journeying far from your home would let you see things that were literally impossible back at your place of birth, but to travel far enough would mean a certain death. Although you could never directly witness the wonders of the regions that were too different from yours, you might find creatures that lived at the borders of such regions. They could travel farther away than you, although they could not come to the place you were from; and if you could find a way to communicate, the two of you might be able to swap tales. You could tell them of the things you had seen, and in turn, be told of wonders you could imagine, but never quite comprehend.

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