A formal measure of subjective experience

From: Matt Mahoney (matmahoney@yahoo.com)
Date: Sun Mar 09 2008 - 14:15:41 MDT

I propose the following formal measure of subjective experience. The
experience of an agent observing event X is K(S2|S1) where S1 is the state of
the agent before observing X, S2 is the state afterwards, and K is Kolmogorov
complexity. In other words, the subjective experience is measured by the
length of the shortest program that inputs a description of S1 and outputs a
description of S2.


Humans are said to have subjective experience, meaning that:

1. You can recall that X happened (episodic memory).
2. After observing X, you assign a higher probability of observing X again in
the same context (procedural memory).
3. If X has nonzero utility, you change your behavior to increase your
utility, to seek or avoid X (reinforcement learning).

All of these result in a change in mental state. On the other hand, if you
were unconscious or someplace else when X happened, then none of these changes
would have taken place.

The existence of subjective experience has not been proven. For example, a
philosophical zombie is claimed to have no subjective experience but otherwise
behave identically to a human (e.g. say "ouch" but not feel pain). However a
rationalist would reject this view because there is no test to distinguish a
zombie from a human.

Assume humans have subjective experience. This experience must occur in the
brain. If you put a brain in a vat and stimulated its sensory nerves, it
would experience a sensation. If you replaced the neurons one at a time with
equivalent functional devices (Chalmers' fading qualia argument), then there
would be no change in behavior and presumably no loss of subjective
experience. If you replaced the brain with any equivalent Turing machine
(implementing the same function), then it must have subjective experience. If
we assume further that there are things that don't have subjective experience
(for example, rocks or dead humans), then subjective experience must be a
nontrivial property of Turing machines.

Conditional Kolmogorov complexity is therefore one possible measure. As
further motivation, consider experiencing two events, X and Y. This will
result in more to be recalled (greater complexity with respect to episodic
memory), greater adjustment of probability (procedural memory) and greater
change in behavior (reinforcement).


Some people believe that it is unethical to harm (kill or decrease utility of)
agents that have subjective experience. I do not take a position on this
issue, but if we assume it is true, then:

- Teleportation (making a copy of a person and destroying the original) is
ethical because K(S2|S1) = 0 (no change in mental state).

- Torture followed by reprogramming the brain to erase the memory of it is
ethical for the same reason.

- Killing animals to save humans is ethical because humans have bigger brains,
and therefore a greater capacity for subjective experience. (One could argue
that killing humans for the benefit of superhuman intelligence is ethical for
the same reason).

- There is no subjective experience of death because K({}|S1) = 0.

However, this ethical view also leads to the conclusion:

- Creating and then killing a person regardless of what happens in between is
ethical because K({}|{}) = 0. (But one could argue that killing is unethical
because of its negative utility on survivors).

A data compression program like zip has subjective experience in all 3 modes
that humans do. A compressor accepts a sequence of symbols from an unknown
source and has the task of predicting future symbols so that it can assign
shorter codes to the most likely symbols. It has procedural memory because
after each event (observing symbol X in some context), it raises the
probability that X will occur next time the same context is observed. It has
episodic memory because decompression recalls the exact sequence of events.
It undergoes reinforcement learning with a utility function equal to the
negative of the length of the compressed output. So even if you accept that
only one mode of learning is required for subjective experience (say, episodic
memory), then you have to conclude that if humans have subjective experience
then so do data compression programs.

The human brain has a capacity for subjective experience K(S2|{}) from birth
between 10^9 bits (Landauer's estimate of long term memory, see
http://www.merkle.com/humanMemory.html ), and 10^15 bits (the number of
synapses). A data compression program together with its output could
therefore have as much subjective experience as an adult human from birth if
its input is large enough.

-- Matt Mahoney, matmahoney@yahoo.com

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