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> SUMMARY OF UDASSA
> 
> This is a description of my current best effort at a model of the multiverse
> and conscious entities considered as informational structures. It is based on
> ideas from Wei Dai, Jurgen Schmidhuber, and Max Tegmark, among others.
> 
> Basically it can be summed up very simply as: Universal Distribution (UD) plus
> ASSA (absolute self selection assumption).
> 
> 
> 
> 
> DEFINITIONS
> 
> Let me first define these terms. The UD is a probability distribution over
> information patterns. It is based on work by Solomonoff, Kolmogorov, and
> Chaitin. Under the UD, the measure of a bit string is the probability that a
> given Universal Turing Machine (an abstract computer) will output that bit
> string, when given a random program as input (probability taken over all
> possible input programs). It is related to the concept of Kolmogorov
> Complexity (KC), defined as the length of the shortest program that outputs
> the given bit string. Roughly, the measure of a bit string under the UD is 1/2
> to the power of its KC.
> 
> The ASSA is the Absolute Self Selection Assumption. It is a variant on the
> Self Selection Assumption (SSA) of Nick Bostrom. The SSA says that you should
> think of yourself as being a randomly selected conscious entity (aka
> "observer") from the universe. The Absolute SSA extends this concept to
> "observer moments" (OMs). An observer moment is one moment of existence of an
> observer's consciousness. If we think of conscious experience as a process,
> the OM is created by dividing this process up into small units of time such
> that no perceptible change occurs within that unit. The ASSA then says that
> you should think of the OM you are presently experiencing as being randomly
> selected from among all OMs in the universe.
> 
> 
> 
> --------------------------------------------------------------------------------
> 
> Traditional philosophy distinguished between ontology, the study of the nature
> of reality, and epistemology, which examines our relation to and understanding
> of the world. I can adopt this distinction and say that the UD is the
> ontology, and that the epistemology is roughly the ASSA.
> 
> 
> 
> 
> ONTOLOGY
> 
> For the ontology, the UD is a probability distribution over information
> objects (i.e. information patterns) which I assume is the fundamental system
> of measure in the multiverse. It is defined with respect to an arbitrary
> Universal Turing Machine (UTM) and basically is defined as the fraction of all
> possible input program strings that produce that information pattern as
> output.
> 
> I am therefore implicitly assuming that only information objects exist. Among
> the information objects are integers, universes, computer programs, program
> traces (records of executions), observers, and observer-moments.
> 
> The UD is an attractive choice because it is "dominant", meaning that it is
> asymptotically within a constant factor of any other distribution, including
> UD's defined by other UTMs. This is why it is called "universal". It is often
> considered the default probability distribution when no information is
> available. This makes it a natural choice, perhaps the only natural choice,
> for a distribution over information objects.
> 
> The UD defines a probability or "measure" for every information object. This
> is the basic ontology which I assume exists. It is the beginning and ending of
> my ontology.
> 
> A few additional points are worth making. Time does not play a significant
> role in this model. An information object may or may not include a time
> element. Time is merely a type of relationship which can exist among the parts
> of the information object, just as space is another type. In relativity
> theory, time is different from space in the sign (positive/negative) by which
> its effects are made known on the metric.
> 
> Among universes, some may have a time dimension, some may not; some may have
> more than one dimension of time. Similarly, they could have different
> dimensions of space, or perhaps fractal dimensions.
> 
> Observers are by definition information systems that are similar to us, and
> since time is intimately bound up in our perception of the world, observers
> will be information objects which do include a time element.
> 
> It is also worth noting that the UD measure is non-computable. However it can
> in practice be approximated, and that seems good enough for my purposes.
> 
> Another point relates to the question of copies. One way to interpret the UD
> is to imagine infinite numbers of UTMs operating on all possible programs. The
> measure of an object is the fraction of the UTMs which output that object.
> This inherently requires that "copies count", even exact copies. The more
> copies of an information object are created, the more measure it has.
> 
> A final point: I strongly suspect that the biggest contribution to the measure
> of observers (and observer-moments) like our own will arise from programs
> which conceptually have two parts. The first part creates a universe similar
> to the one we see where the observers evolve, and the second part selects the
> observer for output. I have argued elsewhere that each part can be relatively
> small compared to a program which was hard-wired to produce a specific
> observer and had all the information necessary to do so. Small programs have
> greater measure (occupy a greater fraction of possible input strings) hence
> this would be the main source of measure for observers like us.
> 
> 
> 
> 
> EPISTEMOLOGY
> 
> For the epistemology, we need some way to relate this definition of measure to
> our experience of the world. This is necessary to give the theory grounding
> and enable it to make predictions and explanations. What we want is to be able
> to explain things by arguing that they correspond to high-measure information
> patterns. We also want to be able to make predictions by saying that higher
> measure outcomes are more likely than lower measure ones. To achieve this I
> want to adopt a relatively vague statement like:
> 
> You are more likely to be a high measure information object.
> 
> Obviously this statement raises many questions. It seems to suggest that you
> might be a table, or the number 3. It also has problems with the passage of
> time. "When" are you a given information object? Are you first one and then
> another? If you start off as one, do you stay the same?
> 
> I am not aiming to fully explain and answer all of these questions in this
> document. At this point I am trying to keep to the big picture. Objects have
> measure, and for that to be meaningful, objects with higher measure have to be
> considered more prominent. We should expect the universe we observe to have
> relatively high measure. We should expect ourselves as observers, and as
> observer moments, to have relatively high measure. If we face alternatives of
> either a low measure or a high measure future, we should expect to experience
> the high measure one.
> 
> As far as the problem of "being" unconscious objects, I don't necessarily see
> that as contradictory. We all know what it is like to be unconscious. We
> become unconscious every day when we sleep. We also know through experience
> that there are many degrees and kinds of consciousness.
> 
> In practice, being a table or the number 3 is so different from what we think
> of as consciousness that we cannot relate to it as human beings. We need to
> restrict our attention to information objects that have a similar nature and
> complexity to our own. Among those objects, we can distinguish between ones
> with low and high measure. The theory predicts that we should find ourselves
> as entities with a relatively high measure, and explains those aspects of our
> existence which have a high measure.
> 
> The ASSA is well suited for this interpretation, because it relates measure of
> observer moments to subjective probability. The older SSA, which is observer
> based where the ASSA is observer-moment based, also can work reasonably well
> in this model for the same reason.
> 
> But the details of ASSA vs SSA vs other interpretations are not of fundamental
> importance in my view. The most important part is the UD. We then connect its
> definition of measure to subjective experience using the concept that higher
> measure states are more likely to be experienced. This is the basic principle
> from which we attempt to make our predictions and explanations.