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NOV JUN Jul 7 2011 2013 2014 3 captures 16 Nov 11 - 7 Jun 13 Close Help > 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.