Origins of UDASSA

The everything-list

In January, 1998, Wei Dai sent out the following announcement and invitation:

Date: Thu, 15 Jan 1998
From: Wei Dai
Subject: ANNOUNCE: the "everything" mailing list

You are invited to join a mailing list for discussion of the idea that all possible universes exist. Some possible topics of discussion might include:

• What is the set of all possible universes?
• What is a reasonable prior/posterior distribution for the universe that I am in?
• Why do we believe that both the past and the future are non-random, but the future is more random than the past?
• Before observing anything about the universe, should we expect it to have (infinitely?) many observers?
• How can we/should we predict the future and postdict the past?

Here are some papers that can serve as a basis for the discussion:

• "Investigations into the Doomsday Argument", Nick Bostrom
• "A Computer Scientist's View of Life, the Universe, and Everything", Juergen Schmidhuber
• "Is ``the theory of everything'' merely the ultimate ensemble theory?", Max Tegmark

The "everything-list" has been active in the years since, with many discussions and ideas being tossed around. Much of the conversation has worked within the framework of two pioneers of multiverse models, Juergen Schmidhuber and Max Tegmark. Both of these men created theories in which our universe is just part of a larger structure called the multiverse, and in which the multiverse itself is fundamentally built out of information. The difference is that Schmidhuber uses a computational model in which the elements of the multiverse are considered to be the outputs of an abstract computer which simultaneously runs every possible computer program. Tegmark, in contrast, considers the multiverse to be composed of all possible abstract mathematical structures, where certain structures are so complex that they can contain what he calls "Self Aware Subsystems". In this way he sees universes as being made out of pure mathematics.

Wei Dai's invention

The concept behind what I am calling UDASSA originated in a posting to the everything-list by Wei Dai in January, 1999. The archive from those days is dead but here is a defunct link to the posting. And here is what Wei Dai wrote:

Let me be more specific and precise about my proposal. I propose that the measure of a conscious experience is related to the measure of the associated state information, and take this measure to be the universal a priori distribution.

The universal a priori probability of a string is inversely related to the length of the shortest program that outputs that string (the distribution actually takes into account all programs, but the shortest ones contribute most to the distribution). Now take an AI running on some computer, and consider its state at some given time. The shortest program (P1) that produces this state as output probably consists of two parts. The first part of the program simulates the physical universe (which let's say is a newtonian universe) which contains the computer running the AI. The second part of the program extracts the AI's state from this simulation.

Now if the *memory* elements containing the AI's state were doubled in size, that should allow the second part of the program to be shorter, since it would take less information to "find" the AI's state in the wavefunction simulation. The smaller program size implies a larger measure of the state.

If the AI were simultaneously running on two computers, there would be two shortest programs that produce the state as output (they would be identical in the simulation part but slightly different in the extraction part), and these two programs together would make twice as much contribution to the universal a priori distribution as P1, and again the measure of the state would be increased.

This is a highly insightful comment! Let me unpack it a bit and explore its ramifications.

First, Wei refers to the "universal a priori distribution" and probability. This is what I am calling simply the Universal Distribution, the UD of UDASSA. Wei's first paragraph is basically a capsule summary of the UDASSA concept, that the measure of a conscious experience is based on the Universal Distribution.

The second paragraph then discusses the key point, that in practice it is likely that the shortest program for a conscious experience consists of a part that simulates a universe that contains the conscious observer, and a part that then takes the output from the first part and extracts the information pattern of that conscious experience.

Wei then discusses one of the most counter-intuitive predictions of UDASSA, namely that larger implementations would have greater measure than smaller ones. It also follows from this that observers within small universes would tend to have greater measure than those within larger ones, for the same reason. He goes on to apply this to the question of whether exact copies of implementation add to measure, concluding that they do so.

Although Wei Dai invented the basic concept of UDASSA, he has, I believed, moved on in his conceptions on these issues. He has moved away from the computationally based Universal Distribution and its association with Schmidhuber's multiverse, and towards a more Tegmarkian notion of general mathematical structures as a foundation. And instead of a measure and associated ASSA based pattern of conscious perceptions, he now advocates a position that I do not understand very well. He suggests, I believe, that measure is fundamentally arbitrary and that each conscious observer is free to adopt whatever measure he likes for the various possible worlds and information patterns in the multiverse.

I prefer to work with the original UDASSA concept as it is approximately computable and provides the potential to make at least theoretically testable predictions. Plus, I understand it much better! I have built on Wei's work and managed to derive many interesting and surprising predictions and analyses, which are described on these web pages.