Re: Algorithmic Revolution?
At 11/21/02, you wrote: The clockwork universe was shown to be wrong with Qunatum Mechanics. My gut feeling is that the computer universe will also be shown to be wrong. In my view there are two types of universes. Type 1 have internal rules of state succession that are like computers - UD's and the like could generate them. Type 2 have rules that have a degree of do not care in determining the valid next state and this do not care component is a channel to an external random oracle. However, I attempt to show in my approach that Type 1 are also subject to the external random oracle but the channel differs. This means that all universes have open logic systems and can have exploding cows and other white rabbit events. I believe ours to be a Type 2 universe with a rule set that allows few rabbit events of a macro nature and many of a micro nature. I suspect that in some aspects we agree. I also think that Bruno's UDA to the extent I think I understand it is a candidate for one of a Type 1 universe's channels to the external random oracle. I believe Juergen's work to be a candidate for the rule set of some Type 1 universes. However, I see no bias towards one type or the other in terms of quantity or in terms of any any other system wide measure. Hal
Re: Zuse's thesis web site
I agree as shown in a number of my posts that our universe is a CA [a 3d face centered cubic grid of regions containing points that can not leave that region is my best estimate so far], however one that is subject to an external random oracle. My model attempts to show that all universes are subject to this oracle. Such a CA is not closed so has no fixed map. The oracle effects the rules as well as the local cell update event so there would be no locality/non locality lack of ability to support issue as far as I can see. Hal
Re: My model presented more traditionally
Refinements to the next stages of my model. Proposal A type #2 universe can look and evolve like our universe. Justification: Stage 1 Designate the succession of states for universe j as Sj(i) and its representative binary bit string as Uj(i) where i runs over some range of integers from 1 to n. If we restrict the discussion to universes of type #2 as proposed and make the additional cut of restricting discussion to type #2 universes in which the true noise monotonically accumulates [i.e. make the Second Law of Thermodynamics an axiom for the universe globally, but not necessarily always so locally] then the complexity of Sj(i) and Uj(i) must monotonically increase as i counts up. If we measure the complexity of Uj(i) in the manner of Algorithmic Information Theory i.e by the length of the shortest self delimited program able to compute Uj(i) which generally increases in length as the degree of internal de-correlation and the length of string Uj(i) increase then: 1) To maintain a degree of internal correlation as its complexity increases Uj(i) must locally increase correlation while it is also locally de-correlating. 2) Finite strings can easily increase local correlation by appending or inserting finite correlated strings and they can also progressively internally de-correlate as information is added so they can satisfy the requirements for Uj(i) given in (1). Thus it may be simplest to represent states of some type #2 universes with finite strings Uj(i). Finite strings have limited resolution potential, but nevertheless can describe the location of discrete points within a 3D space on a grid with finite non zero pitch. An additional cut is now made to restrict examination to type #2 universes that can be modeled as finite face centered cubic 3D grid multi state cellular automata subject to true noise. Notice that an increase in length of Uj(i) can be identified as the addition of a new cell i.e. the expansion of the universe's space. Further if the rules of state succession for a universe have an appropriately constructed Do not care component then their repeated application to the data of each successive state will lead to an accelerating increase in the complexity of the finite Uj(i) [i.e. despite the true noise the rules are such that each successive shortest program Pj(i) that computes Uj(i) effectively contains the previous state's shortest program Pj(i -1) plus the noise as data plus the rules acting on the data plus its own delimiter] and so the length of Uj(i) must increase in an accelerating manner to contain this complexity increase i.e. the universe's space expands at an accelerating pace. Hal
Re: My model presented more traditionally
Further improvememts. Proposal: The concepts of Nothing and Everything [1def] are not antagonistic, but are actually synergistic and bootstrap existence. Justification: AXIOMS: Referring first to [1def] through [6def]: 1) A void consisting of the absence of factuals herein called the Nothing exists. 2) A collection of all complete sets of counterfactuals herein called the Everything exists. 3) There are no other existences at or above the level of the Everything and the Nothing. PROPOSITIONS: Proposition 1: The Everything and the Nothing are counterfactuals. Proof: The Everything is a parsing since it is a collection of a particular kind of factual. The Nothing is a parsing since it excludes all factuals from itself. These two parsings effect each other to some degree. The existence of the Everything would tend to put a factual in the void and thereby suppress the concept of the Nothing and the existence of the Nothing would tend to suppress the necessity for the Everything - no factuals equals no parsing potential. Thus Proposition 1 is true by [3def] and [4def] and Axioms 1 2. In addition to the suppression, The Everything and the Nothing also enhance each other to some degree as follows. Proposition 2: The Everything contains the Nothing. Proof: True by Proposition 1 and Axioms 1, 2, 3. Axiom 3 makes the Everything/Nothing pair a complete set of counterfactuals. Proposition 3: The Everything contains itself: Proof: True by Proposition 1 and Axioms 2 and 3. Proposition 4: The Everything is infinitely nested with itself and the Nothing. Proof: True by Propositions 2 and 3. Interpretation: The Everything and the Nothing form a synergistic pair - their simultaneous existence is easier than either existence by itself. Even more focused is to view the synergism as being the existence and Axioms 1, 2, and 3 continuously bootstrap each other to sustain it. The Everything/Nothing nesting is not considered as having dimensionality or of being in or on a dimension, but rather as an infinite entanglement of potential. Proposition 5: The nesting has a dynamic. Proof: A fixed parsing between the Nothing and the Everything would constitute the presence of an uneffected factual within the Everything contradicting Axiom 2. Possible interpretation: Proposition 5 can be realized if the Nothing/Everything parsing surface is composed of a dynamic mix of the surfaces of the counterfactuals constituting the Everything. The counterfactuals on this surface are - while so situated - slightly less effected than when they are remote from this surface. It is the patterns formed by the shifting mix of surface counterfactuals that are interpreted as universes. To support this interpretation the following axioms are incorporated into the model. Axiom 4: The members of a complete set of counterfactuals maintain the complete effectiveness only when uninterruptedly intertwined as in a foamy fractal . Axiom 5: Universes sustain themselves by finding a succeeding pattern on the Everything/Nothing surface that is consistent with their individual rules of state succession as their current pattern vanishes with the dynamic. Proposition 6: The dynamic of Proposition 5 is random. Proof: Same form of proof as for Proposition 5 but substituting A fixed evolution of the parsing between the Nothing and the Everything would. Proposition 7: There is no restriction on the structure of the various individual universe state succession rules. Proof: Same form of proof as for Proposition 5 but substituting Any such restriction would. Interpretative consequent: Some of the rules would have a Do not care component in terms of the selection of a succeeding pattern. This is the same as the rules of these universes allowing an external random oracle input or true noise [7def] into the state succession process for such universes. Proposition 8: All universes are subject to true noise. Proof: Same form of proof as for Proposition 5 but substituting By Proposition 7 at least some universes are subject to true noise by their own internal rules. If true noise susceptibility of universes is indeed restricted to some it would .. Interpretation: Even if their rules have no Do not care component such universes must nevertheless be subject to an external random oracle. There would be two general types of universes. Type #1 have internal rules that do not allow true noise as they evolve and type #2 have rules that do. Both are actually subject to true noise since the dynamic of the Everything/Nothing synergism is the apex of the overall system's hierarchical dynamic and dominates the internal dynamic rules of all interpretations within the synergism. There is also a bidirectional flow between type #1 and type #2 since the right dose of true noise will switch the type of any universe. NOTES [1def] Everything: Intended as a maximum expression of
Re: My model presented more traditionally
I post this again to fix a small but important error and to sustain a single thread title. Proposition 8: The dynamic of Proposition 5 is random. Proof: Same form of proof as for Proposition 5. Effect: I tried here to select a word that encompassed a sufficiently wide range of influences so that in the end the Everything/Nothing pair summed up to no net information. One type of influence between counterfactuals would be where the Everything contains two logic systems such that in one the statement A is true and in the other the statement Not A is true. I see this as too narrow. Noise: In the model, current states of universes are interpretations of the patterns of the counterfactuals that happen to be currently on the Everything/Nothing surface. The patterns shift randomly and a universe has to find a new compatible pattern to survive. A universe that has rules of state succession that allows for portions of the new pattern to be determined by the shifting dynamic - a Do not care content to the rules - rather than by the rules acting on the data of the current state is a universe whose succession of states is subject to the external random dynamic [external random oracle] to some degree. This is true noise injection into that universe. Nesting: I do not see the nesting I arrive at as having dimensionality or of being in or on a dimension. I see it as rather an infinite entanglement of potential. Hal
Proposition 8, effect, noise, nesting
Proposition 8: The dynamic of Proposition 5 is random. Proof: Same form of proof as for Proposition 5. Effect: I tried here to select a word that encompassed a sufficiently wide range of influences so that in the end the Everything summed up to no net information. One type of influence between counterfactuals would be where the Everything contains two logic systems such that in one the statement A is true and in the other the statement Not A is true. I see this as too narrow. Noise: In the model, current states of universes are interpretations of the patterns of the counterfactuals that happen to be currently on the Everything/Nothing surface. The patterns shift randomly and a universe has to find a new compatible pattern to survive. A universe that has rules of state succession that allows for portions of the new pattern to be determined by the shifting dynamic - a Do not care content to the rules - rather than by the rules acting on the data of the current state is a universe whose succession of states is subject to the external random dynamic [external random oracle] to some degree. This is true noise injection into that universe. Nesting: I do not see the nesting I arrive at as having dimensionality or of being in or on a dimension. I see it as rather an infinite entanglement of potential. Hal
My model presented more traditionally
The following is a new effort to present my model in a more traditional
way.
The basic idea is that the concepts of nothing and everything [i.e. a
maximum expression of something] are not totally antagonistic but are
actually synergistic.
DEFINITIONS:
1) Information: The potential to parse [herein parse is used to mean to
divide as with a boundary].
2) Factual: A particular parsing. [like: {red, green, blue}]
3) Counterfactual: A factual [factual B] that to some degree effects the
parsing of another factual [factual A] {like: brown}. Note that a factual
that has a counterfactual is itself a counterfactual.
4) Complete set of counterfactuals: A set of counterfactuals that leaves no
member factual uneffected in any of its aspects. {like: gray}
AXIOMS:
1) A void consisting of the absence of factuals herein called the Nothing
exists.
2) A collection of all complete sets of counterfactuals herein called the
Everything exists.
3) There are no other existences at or above the level of the Everything
and the Nothing.
PROPOSITIONS:
Proposition 1: The Everything and the Nothing are counterfactuals.
Proof: The Everything is a parsing since it is a collection of a particular
kind of factual. The Nothing is a parsing since it excludes all factuals
from itself. These two parsings effect each other to some degree. The
existence of the Everything would tend to put a factual in the void and
thereby suppress the concept of the Nothing and the existence of the
Nothing would tend to suppress the necessity for the Everything - no
factuals equals no parsing potential. Thus Proposition 1 is true by
Definitions 2 3 and Axioms 1 2.
In addition to the suppression, The Everything and the Nothing also enhance
each other to some degree as follows.
Proposition 2: The Everything contains the Nothing.
Proof: True by Proposition 1 and Axioms 1, 2, 3. Axiom 3 makes the
Everything/Nothing pair a complete set of counterfactuals.
Proposition 3: The Everything contains itself:
Proof: True by Proposition 1 and Axioms 2 and 3.
Proposition 4: The Everything is infinitely nested with itself and the Nothing.
Proof: True by Propositions 2 and 3.
Interpretation: The Everything and the Nothing form a synergistic pair -
their simultaneous existence is easier than either existence by itself.
Proposition 5: The nesting has a dynamic.
Proof: A fixed parsing between the Nothing and the Everything would
constitute the presence of an uneffected factual within the Everything
contradicting Axiom 2.
Possible interpretation:
Proposition 5 can be realized if the Nothing/Everything parsing surface
is composed of a dynamic mix of the surfaces of the counterfactuals
constituting the Everything. The counterfactuals on this surface are -
while so situated - slightly less effected than when they are remote from
this surface. It is the patterns formed by the shifting mix of
surface counterfactuals that are interpreted as universes.
To support this interpretation the following axioms are incorporated into
the model.
Axiom 4: The members of a complete set of counterfactuals must be
intertwined as in a foamy fractal to sustain the effectiveness of the set.
Axiom 5: Universes sustain themselves by finding a succeeding pattern on
this surface that is consistent with their individual rules of state
succession as their current pattern vanishes with the dynamic.
Proposition 6: There is no restriction on the structure of the various
individual universe state succession rules.
Proof: Same form of proof as for Proposition 5.
Interpretative consequent: Some of the rules would have a Do not care
component in terms of the selection of a succeeding pattern. This is the
same as the rules of these universes allowing an external random oracle
input or true noise into the state succession process for such universes.
Proposition 7: All universes are subject to true noise.
Proof: Same form of proof as for Proposition 5.
Interpretation: Even if their rules have no Do not care component such
universes must nevertheless be subject to an external random oracle.
Hal
Re: Bruno's UDA argument
Dear John: I should be more careful when I describe my particular concept of the no information system. It is actually a system that contains the two possible expressions of no information the Nothing [no factuals of any sort] and the Everything [the ensemble of all counterfactuals]. The existence of either is information. However, they are mutually counterfactual so if they exist simultaneously they total to no information and this absent the need for any external referent. Since they are both counterfactuals they are both actually in the Everything. Thus the Everything is a member of itself infinitely and randomly nested with its counterfactual the Nothing and again no external referent is required so information vanishes. Of course one could initially parse the thing differently but in the end you still it seems to me wind up with an ensemble of all counterfactuals that is a member of itself. Hal At 7/23/02, you wrote: The statement it contains no information IS information. -- (In my Plenitude story the no info - infinite invariance total symmetry requires correction in this spirit. The infinite variety dose not fit: it intrinsically includes repetitions of similars (and that is a major point for generating universes) which (transitionally) falls out from both the infinite symmetry and the infinite invariance. Which is the fulguration for universe-formation, as observable complexity. Sorry for the digression: I am reworking my 2000 text in this sense. John Mikes [EMAIL PROTECTED] http://pages.prodigy.net/jamikes;
Re: Bruno's UDA argument
Dear Bruno: I remain confident that there is a link between what we both are saying. I think I must do my homework and closely study your argument. I hope circumstances will allow this. Yours Hal At 7/23/02, you wrote: At 22:11 -0700 22/07/2002, H J Ruhl wrote: Is it possible to sustain a no information Everything if there is a selection in which this latter ensemble is the only generators subject to such noise? The very concept of any selection within the Everything necessarily places information within the Everything and must thus be disallowed. It is here that the 1-3 distinction, or the comp 1- indeterminacy paves the way. (If I understand what you say). B.
Re: Bruno's UDA argument
Dear Hal: At 7/23/02, you wrote: The fact that this requires a relatively large program suggests that there is some substantial information content in the idea of running every program at once. Hal With that I have no issue but my view is that the Everything is an ensemble of counterfactuals that contains itself - see my other responses - therefore: If we allow the UD residence in the Everything which I do then it also needs to contain the full set of counterfactuals to the UD. Some if not all of these can be universe generators as well. In my view all of these generators share a susceptibility to noise of external origin but by different mechanisms. Some of these generators are simpler than the UD and I believe our universe is due to one of them not the UD. I believe this because I do not see the need for mathematics as the base for our universe, rather I see what we call mathematics as a macro approximation to the actual underlying rules that are of a complexity below that of any formal system. [IMO ours are a large look up table with built in susceptability to the external noise - extra columns.] I see no differential measure on the frequency of various generators due to the infinite nesting of the Everything and Nothing counterfactuals. Hal
Re: Bruno's UDA argument
Dear Hal: The idea that the Everything does not contain the UD appears self contradictory. That said the Everything as a system is generally thought of by some at least as containing no information. [Otherwise where did this information come from?] To sustain this requirement it must contain counterfactuals to the UD. Among these would be universe generators whose foundation is anything but the UD [or any ensemble of UDs]. Having reached that result, at least some of these generators would form an ensemble subject - by their internal structure - to the injection of external random noise originating in the remainder of the Everything. Is it possible to sustain a no information Everything if there is a selection in which this latter ensemble is the only generators subject to such noise? The very concept of any selection within the Everything necessarily places information within the Everything and must thus be disallowed. My conclusion is the all generators within the Everything are subject to such noise by some mechanism or another. Further I think that from this I would have to conclude that no differential measure of any sort [actually a selection result] between universes can arise over the ensemble of all universes. As to consciousness I do not believe a decent definition of it is extant but I do believe for obvious reasons that - whatever it is - it is only supported in a universe with noise of external origin there being no other kind of universe - IMO. All of this is OK as far as I can tell since one can see our universe inside the complete ensemble but I see it as being in the part of the ensemble that contains those universes that are subject to the noise by their internal structure as opposed to the UD type of generator which would be subject to this noise to avoid a selection. There is no reason that I can see why some of these universes subject to noise by their internal structure would not evolve in a way that appears [internally] to follow simple rules expressible in a mathematics. I also believe there are easy ways to demonstrate that features of our universe can be based on such a foundation. Further I do not see that universes evolving in a highly random way can not be an alternate base for a universe evolving by simple rather well behaved rules if we allow that intervening states inconsistent with such a view go unnoticed by an observer - whatever that is - that considers itself to be in the supposed well behaved universe. Hal
Re: JOINING posts
I am a licensed Professional Engineer.
BSEE The University of Illinois - Champaign/Urbana; 1966
MSEE Syracuse University; 1970
Tau Beta Pi, Eta Kappa Nu
A member of Mensa
From 1966 to about 1987 I worked in the power semiconductor/power
electronics industry. I published some papers on the subject such as in
the IEEE Transactions on Electron Devices.
Since 1987 I have been chief engineer at a medium size aerospace
company. My most recent publication [coauthored with my brother] is in the
Winter 1997 U. C. Davis Law Review and is an application of complex system
ideas to illuminating the effects of the burgeoning of the law.
My interest in material relevant to the list dates back a rather long
time. About 10 years ago this interest increased due to a general
dissatisfaction with the statistical approach to the founding of
thermodynamics during a dab at writing a social science fiction novel. The
intended moral is somewhat reflected in the title of Brian Czech's book:
Shoveling Fuel for a Runaway Train though I propose a purposely cyclic
economy/population since steady state seems an empty but dangerous quest
for so many reasons. [Growth is the derivative of size and when it comes
to an economy entrepreneurs can find fertile ground when it is either
positive or negative and the required rule set can have low complexity -
the latter seemingly coinciding with an interpretation of Joseph Tainter's
The collapse of Complex Societies. Being in the aerospace business I see
the negative marginal utility of new rules every day.] The social science
fiction approach to the moral seems a little bit like the possible
background driver for the book The Mote in God's Eye by Larry Niven and
Jerry Pournelle.
About four or five years ago this line of thought lead me to the idea that
our universe could be based on no net information. I was then pointed to
this list by participants on another list.
My current approach the issue of origins is to try to find our universe in
a zero information Everything type of ensemble. I am not looking for why
we are in our universe because I see any result - such as our universe and
its close relations form some major fraction of the population - as net
information in the Everything and therefore I reject such a search as a
departure from and incompatible with a zero information
foundation. Further I see machine based approaches such as a UD as also
requiring the Everything to have non zero information and so currently
reject them.
My current interests are to further refine my model based on the idea of a
zero information ensemble of counterfactuals, look for possible
observational evidence to support it, and see if I can make any predictions
with it. For example my discrete point space grid idea would be just a
ground condition - any number of excited conditions would be possible
including something a little like a gas of points. Thus I see no end to
the particles we will observe with ever higher energy machines, but I
currently see no place for an association of a particle and what we see
as gravity. I currently see no Free Will nor do I see a central [non
passive] role for an observer. The rules of evolution of a universe -
which I see as a large lookup table applied locally to each of the discrete
points rather like a cellular automaton - would be strictly followed unless
a state to state transition corresponded with the injection of true noise
from the dynamic of the ensemble.
I see lookup tables [all alphabet and {if - then}'s] as below formal
systems so I do not see formal system mathematics or any of its member
systems as pointers to the correct base model whatever it may be. However,
the extension of the base model to particular universes can make good use
of such systems to the extent that such systems of mathematics are large
scale [spanning many rows of the table and many state to state iterations
and many cells within the automaton] approximations to the lookup
tables. Further the arrival at such a lookup table base involves a logic
in the sense that the components of the Everything must form a complete and
thus zero information set of counterfactuals.
My ultimate interest is in life and its nature and behavior especially
its possible dependence on and response to true noise in its universe and
how to build reasonably robust social systems that would attract all
varieties of reasonable people.
I feel this list has an excellent chance of eventually arriving at what
seems to me to be the collective goal - a simple explanation for what I
believe to be my environment. I also think the list needs a FAQ like
document of a sort that suits it. I made an attempt to write one but ran
out of time for awhile.
As to my reading I own at least 150 books with relevant content that I have
read or browsed.
As to weather any of these seem to be an identifiable near precursor to my
current approach I do not
Re: decision theory papers
Dear Marcus: I have some basic issues with your post. The idea I use is that the basis of what we like to think of as our universe and all other universes is There is no information. This is not really an assumption in the sense that you can not extract anything from nothing as one usually extracts consequents [data snips] from the information in some assumption set. Rather it is more a principle that one attempts to sustain while building dynamic universes. To initiate this one can notice that no information has two simultaneous yet completely counterfactual expressions - all information and no information - and further that there must be a dynamic boundary between them - this latter part from the idea that no information requires no selection, that is both expressions must exist and the all information expression contains its counterpart in an infinite nesting with itself - this because it is the ensemble of all counterfactuals which must include both itself and the no information expression. One now simply explores the dynamic of this boundary [the dynamic comes from the need to avoid selection - no fixed boundary, and the dynamic is random for the same reason - no selected pattern] while sustaining the balance of counterfactuals. While this approach allows for no rationale for why we are in this particular universe why should there be one? Ours is just one of an uncountable set that contain large sub structures and can transition to a next state while sustaining most of them. In any event in my view your argument makes many assumptions - i.e. requires substantial information, isolates sub systems, and seems to allow many sub states between states of interest all of which are counter to my approach. Hal
Re: decision theory papers
Explorations of the definitional basis of a universe and its effect on the
idea of decisions:
First examine a deterministic universe j such that [using notation from a
post by Matthieu Walraet]:
TjTj Tj
Sj(0) Sj(1) Sj(2)
Sj(i)
An interpretation is that all the information needed to get from Sj(0) to
Sj(i) is contained in Sj(0) and the rules of state evolution for that
universe that is Tj.
I see a problem with this interpretation.
Suppose we write an expression for the shortest self delimiting program
able to compute Sj(i) as:
(1) Pj(i) = {Tj[Sj(i - 1)] + DLj(i)} computes Sj(i)
where DLj(i) is the self delimiter.
Compressing Sj(i - 1) it can be written as Pj(i - 1) and this short hand
substituted into (1) to yield:
(2) Pj(i) = {Tj[Pj(i - 1)] + DLj(i)} computes Sj(i)
Note that Pj(i) is always longer than Pj(i - 1) because it contains Pj(i -
1) plus the Tj plus the delimiter so Sj(i) contains more information [using
the program length definition of information] than Sj(i - 1) and thus more
information than Sj(0).
What kind of information is it? I see it as location record keeping
information. The universe is at state i of the recursion and this extra
information is the tag providing that location. The effect has several results:
1) This new information can never be removed from such a universe so its
local time has an arrow.
2) New information can manifest as either a decorrelation of the bit
pattern of and/or an increased length of the string representing Sj(i). The
length of the string is interpretable as space [a fixed number of bits
say x bits describe the configuration of a small region of that space and
there are y regions requiring description so an increase in length of the
string causes y to increase.]. Note that the effect increases as the
recursion progresses since DLj(i) increases monotonically with i. Thus such
a universe should see a long term acceleration in the rate of expansion of
its space.
3) So how do we define a universe? Suppose many universes are following
the same recursion some at earlier states and some at later states than
universe j. It seems best to define such universes by the state they are
in [which includes Tj and DLj(i)]. Where did the additional information
come from? The additional information is not that a universe can follow
the recursion but rather as stated above the location of a particular
universe in the recursion. Since this information is not in Sj(0) or Tj it
must have come from outside universe j.
Universes that are not deterministic but have rules that allow external
true to enter are easier to analyze in this regard since the current state
seems the only reasonable definition.
4) For a deterministic universe is the additional information true
noise? In at least one sense it is because a particular universe j is
defined by its current state it can not tell which state including the
current state was or is Sj(0) so there is no clue as to what the
information means or if it is somehow even additional or new or which
information is involved. This is the same as the situation for a universe
whose rules allow external origin true noise.
5) This would seem to enhance the case against the idea of decision since
noise [chance] of some sort seems to be everywhere.
6) Behavior similar to (2) is found in universes that are sufficiently well
behaved so that it is possible to propose a prior state such that the
universe's rules when stripped of their allowance for external true noise
can deterministicly arrive at the universe's current state. This proposed
prior state need not have been the actual prior state.
Hal
Re: decision theory papers
Dear Matthieu:
At 4/19/02, you wrote:
On 18 Apr 2002, at 20:03, H J Ruhl wrote:
5) I do not see universes as splitting by going to more than one next
state. This is not necessary to explain anything as far as I can see.
6) Universes that are in receipt of true noise as part of a state to state
transition are in effect destroyed on some scale in the sense the new state
can not fully determine the prior state.
The new state can not fully determine the prior state only means that the
application that give the next state from the prior state is not bijective.
I do not agree. You seem to have missed what I said. Post the true noise
event there is no T that can determine [deterministically extract] the
prior state from just the info in the current state [because the true noise
has no identifying tags].
Let's call S the set of all possible states of universes.
T is the application that give the next state from a prior state.
Without true noise T is an application from S to S
T
S S
prior state next state
If the application T is not bijective (There is no reason that it should
be) then the new state can not fully determine the prior state.
All that seems to say is that some computational universes are also severed
from their history when using a fixed T. Some other T may be able to make
that link.
Now with the mysterious true noise, the prior state alone can not
determine the next state. T is not an application from S to S.
T is an application from SxN to S.
T
S xN -- S
(prior state, noise)-- next state.
I see it as:
T + N
S(i) - S(i +1)
In your system universes are sequences s(t) defined by a given initial
state s(0) and a given application T. Without true noise the sequence
follows the rule: s(t+1) = T(s(t))
I usually write my Type 1 [no internal rules allowing external true noise]
more like T(i) acting on P(i) where P(i) is the shortest self delimiting
program that computes S(i) [not necessarily from S(i -1) in fact there may
be no S(i -1)]. This allows derivation of a cascade with naturally
increasing information in the P(i) as i counts up.
P(i + 1) always contains P(i) plus T(i) plus the self delimiter.
T(i) may change given the requirement for true noise regardless of the
nature of T
But with the true noise, s(t+1) = T( s(t), noise(t)).
I usually write my Type 2 [internal rules allow external true noise] as
T'(i) acting on P'(i) where P'(i) is the shortest self delimiting program
that computes S(i) from some S'(i - 1). S'(i - 1) is not necessarily the
actual S(i - 1) but can be deterministicly proposed from S(i) using some
deterministic T.
What is noise(t) ? Is it true random ? I would like to know your definition
of true random.
I suppose noise(t) is an arbitrary sequence in the N set.
I define it as new information from an external source [from the
Everything/Nothing boundary]. The closest model I can think of in our
universe is to attach a radiation counter to a computer input and use the
event data to create strings that are then used in the computer's
computations.
Why choosing an arbitrary sequence of noise ?
That is a little longer story and is addressed in my draft paper at:
http://home.mindspring.com/~hjr2/model01.html
I am still editing this work. The root reason is to avoid information
generating selection in the Everything.
I prefer to consider the application T' from S to the set of subset of S.
T'(s) is the union of { T(s,n) } for all n element of N.
T' is the application that give all possible next state for a given prior
state.
This means that when we consider a starting state s(0) there is not only a
sequence of successive states but a tree of all possible histories starting
from s(0).
In other words, true noise causes the universes to split.
As you can see I consider the process like one makes soup [the T'] and then
right at the end adds a random sprinkle of salt. The result is one
finished soup. No more is needed.
If you say your universes don't split and are affected by a true noise,
you are choosing an arbitrary sequence of noise.
Well what other kind of true noise is there?
This is a kind of physical
realism.
Actually I do not see a need for a physical reality. The S(i) strings
can have more than one interpretation but these interpretations need not be
physical
On this list, we are mathematic realist (some even think only algebra has
reality), and we think physical reality is a consequence of math reality.
In that sense I see no need for anything mathematic, just a lookup table
[a rather large but finite one in our case] active at each of a number of
discrete cells plus some degree of external noise in some of them [a
cellular automaton + some noise]. For example I suspect that our universe
Re: origin of notion of computable universes
Dear Juergen: I certainly currently agree with the idea that a particular universe is a cellular automaton but one that is subject to true noise from an external source. This does not preclude universes that are internally computational rather they are required to balance those that are not [no selection allowed]. Universes that are internally computational nevertheless are subject to true noise by the need to avoid an information selection within the everything. With either universe the true noise destroys the prior universe on some scale. Absent this true noise feature I do not see how one can have a zero information ensemble and I seem to be able to forge such an ensemble with it. I believe this idea of the universe being the result of chance plus necessity goes at least back to Democritus around 400 B.C. Then of course there is the Bible: I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor riches to men of understanding, nor yet favor to men of skill; but time and chance happeneth to them all. Ecclesiastes; 9:11-12 If I might be so bold: if my model is viable then it seems that here the Bible points to a zero information ensemble. The cellular automaton engine for any universe need be no more logical than a lookup table giving the next state of a central cell as a function of the current state of its neighbors, its own current state, plus true noise in some engines. Yours Hal At 4/15/02, you wrote: I am currently trying to understand the origins of the notion of computable universes. It seems that Konrad Zuse himself (the inventor of the computer who built the first digital machines in the 1930s and completed the first working programmable computer in 1941 and created the first higher-level programming language in 1945) was also the first to propose that the physical universe is just Computing Space (Rechnender Raum) implemented on a grid of computers, each communicating with its neighbors. Today this would be called a cellular automaton. The reference is: Zuse, Konrad: Rechnender Raum, Schriften zur Datenverarbeitung, Band 1. Friedrich Vieweg Sohn, Braunschweig (1969). I also found references to Fredkin's similar but more recent ideas.
Re: Optimal Prediction
I agree at this point that the AP by itself has no predictive power. My view is that a predictor that currently works in a given universe - say the AP plus other stuff - can not be considered to continue to work. Any universe is subject to true noise either because its rules allow it [type 2] or the Everything imposes it [type 1]. The effect of a true noise event is to replace the subject universe with a new one. Hal
Re: Optimal Prediction
At 3/26/02, you wrote: Normally we do not know the true conditional probability distribution p(next event | past). But assume we do know that p is in some set P of distributions. As I posted earlier my issue with this is how does one know p is in P unless one can compute p, i.e. check it? While I allow for such computable universes to exist [type 1] so too will non computable universes - those subject to true noise - exist [type 2]. Why? - The Everything can not contain just type 1 or type 2 universes since this is itself a selection i.e. information. Since the Everything can not contain any selection then all universes must be subject to true noise if any are. A way to resolve this apparent difficulty is a bidirectional flow between the two types of universes. A proper dose of true noise will convert type 2 into type 1 and the the need to eliminate selection which is the dominant dynamic driver of the Everything - will of necessity convert type 1 into type 2. Hal
Re: Draft Philosophy Paper
Dear Alastair: The infinite tape was just a way to show how your example actually has a most interesting behavior under an extension to more dimensions and to infinity. I believe you still miss what I am trying to say. The nested Everythings are not and can not be exact copies of each other. This would constitute an information generating selection. Rather they are each differently and dynamically parsed. The parsing is the venue for interpretations - universes. The idea that the Everything is dynamic is not new. After all many allow that there are all those UTMs - which I incorporate as a type #1 universe generating sub component of my model - running in there somewhere. To have an infinite number of copies of just one of these dynamics just begs the question: why that one? The picture in my approach is as follows: The Everything - the ensemble of all counterfactuals, and the Nothing - the absence of facts of any sort, are themselves mutual counterfactual. They must both be in the ensemble. Each Everything contains an infinite regression of Everything/Nothing counterfactual pairs and is itself a member of such a regression. There is an infinite and necessarily dynamic - again to avoid selection - boundary between the Everything and Nothing counterfactuals. The location of this boundary is different and dynamic at each level of the nesting [repeats are possible but this is not relevant]. Each different level is a different venue - different logical structures expressed. Thus within the Everything taken in total a universe based on any number of logical elements is accompanied by an infinite number of equally logically rich but logically different universes. So there is no numerical bias towards logically anemic universes. My only assumption is: There is no information. Even limiting the system to one level of Everything is an information generating selection. Yours Hal At 2/25/02, you wrote: You now appear to be talking about the indeterminate case (where effectively you can't fire individual random arrows), which is excluded on empirical grounds (see sect. 2 again). I repeat, the selective use of copies as given in the paper - *within* the context of states, and where relative frequencies match those of other states - will differ (as far as I can tell) from your 'nested everythings', which, if applicable, will be treated as a distinguishable state, and so amenable to an ordering process (under all possibilities). Thank you anyway for your comments which have definitely been helpful to me - I think we are bound to come up with different solutions if we have different starting assumptions.
Re: Draft Philosophy Paper
Dear Alastair: What I have is an infinite tape. [Each line one could draw in the x dimension is a different venue.] The entire tape from x = -1 to x = +10 and y = 0 to y = infinity is the target for each arrow launch. A random aim sample [a very large one - infinite actually] will produce a uniform density of hits over the entire area of the infinitely long and 11 unit wide tape. The generalized density units will be hits per square. The tape was parsed at x = 0 for your example. The tape area between x = -1 and x = 0 is identical to the area from x = 0 to x = +10. Multiplying the density of hits by either area - both infinite - produces the same number of hits - infinite - no bias as the sample size becomes infinite - the convergence you speak of goes to an equal number of positive and negative reals. This only works for an infinitely long tape but I have in my model enough venues - nested Everythings - to pave such a tape. Any finite length of this tape follows the biased convergence result of your original example. Of course any finite length of the tape has an infinite number of venues as well but if we made this restriction then we would have your information rich result and where did that information come from? Basically this would be sort of like restricting things to halting programs and why that? Some like to allow never halting programs and I like an infinitely long venue tape. Its origin is simple enough and uses the Everything and the Nothing as synergistic rather than antagonistic concepts. It also helps to eliminate information from the Everything. Hal At 2/23/02, you wrote: [I think the principle of the following comment also applies to your other post.] It is the x-coordinate that determines the state, in our analogy. Are you really saying that randomly shooting arrows into *any* finite segment (and therefore *all* finite segments) of your infinite tape will yield x-coordinates something like (rounded to one dec. place): -0.9, 3.1, 8.7, -0.1, -0.4, 1.8, -0.5, 3.0, ...? That does not seem very random to me. And what if I had wished to compare the chance of 'hitting' the first three states (-1 to 2.999...) with the last eight (3 to 9.999...)? Would that still be an equal chance of either? If so, that would require a different 'random' sequence - but they should be the same hits! - Original Message - From: H J Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: 23 February 2002 03:05 Subject: Re: Draft Philosophy Paper Dear Alastair: I think you still fail to see my point. So here I try to draw a picture. Original single venue system [V(0)]: V(0) x -- -1 - 0 -- + 10 Take a random sample into the line. The target size between x = -1 to x = 0 is clearly not equal to the target size between x = 0 to x = +10 therefore so to the resulting sample. My infinite venues system [V(0) to V(infinity)] y V(infinity) x -- -1 - 0 -- + 10 . . . V(2)x -- -1 - 0 -- + 10 V(1)x -- -1 - 0 -- + 10 V(0)x -- -1 - 0 -- + 10 Here, to be a random sample over the complete Everything - all venues - the sample is taken into the structure like shooting an arrow at random into an infinite piece of tape perpendicular to the surface of the tape over the whole tape strip bounded by -1 to + 10 on x and by y = 0 to y = infinity on y. The entire surface of the tape will have a uniform hit density - equal hits per square. Since the target area between x = -1 and x = 0 is now the same as the target area from x = 0 to x = +10 that is both have an infinite area - or the same number of squares - they will take the same number of hits and there will be no sign bias in the resulting sample. Any lengthwise parsing of the tape is not relevant.
Re: Draft Philosophy Paper
In an earlier post:
http://www.escribe.com/science/theory/m3532.html
I stated:
Can type #1 universes {those that do not allow true noise} become type #2
universes {Those that do allow true noise}. They must be able to or again
there would be a selection.
The rational is as follows:
xx
Bidirectional conversion of true noise not allowed and true noise allowed
to some degree types:
A proper dose of true noise can convert true noise allowed universes into
true noise not allowed universes. Whether or not true noise is allowed in
the determination of the next state for a particular universe is an aspect
of the current state of that universe. This intrinsic rule structure can
be overridden at any state to state transition by the dynamic of the
Everything itself. Thus conversions of true noise not allowed universes
into true noise
allowed universes is available.
Hal
Re: Draft Philosophy Paper
Dear Alastair: I think you still fail to see my point. So here I try to draw a picture. Original single venue system [V(0)]: V(0) x -- -1 - 0 -- + 10 Take a random sample into the line. The target size between x = -1 to x = 0 is clearly not equal to the target size between x = 0 to x = +10 therefore so to the resulting sample. My infinite venues system [V(0) to V(infinity)] y V(infinity) x -- -1 - 0 -- + 10 . . . V(2)x -- -1 - 0 -- + 10 V(1)x -- -1 - 0 -- + 10 V(0)x -- -1 - 0 -- + 10 Here, to be a random sample over the complete Everything - all venues - the sample is taken into the structure like shooting an arrow at random into an infinite piece of tape perpendicular to the surface of the tape over the whole tape strip bounded by -1 to + 10 on x and by y = 0 to y = infinity on y. The entire surface of the tape will have a uniform hit density - equal hits per square. Since the target area between x = -1 and x = 0 is now the same as the target area from x = 0 to x = +10 that is both have an infinite area - or the same number of squares - they will take the same number of hits and there will be no sign bias in the resulting sample. Any lengthwise parsing of the tape is not relevant. Your additional comment there is no more necessity to have no preponderance of any particular type of physical universe than to have no preponderance of a particular type of galaxy, or grain of sand. My reply With this I disagree when describing the Everything because on its face it attempts to extract information from an informationless source. Your example from within a particular universe [intrinsic information] is not applicable because here its any style you want. In the above reply I was merely stating that you could get any type of universe you wanted if sampled the Everything often enough. Your reply Certainly not - if anything, there will be all possible styles, but this would depend on what you mean by that word. I think you are just assuming a different starting point - for me it is all logically possible entities (not just universes), with no bias in favour of any one, as required by NAP. If there happened to be some resultant lack of bias (preponderance) at the level of physical universes (which would include those forming part of other entities), that would just be a coincidence. It is clear that I believe that a lack of preponderance of any type or sub group of types is not coincidence but necessary to yield no information in the Everything. Hal
Re: Draft Philosophy Paper
This is just an effort to get the diagram to post reasonably on the list archive. Original single venue system [V(0)]: V(0) x -1 - 0 --- + 10 My infinite venues system [V(0) to V(infinity)] y V(infinity) x -1 - 0 --- + 10 . . . V(2) x -1 - 0 --- + 10 V(1) x -1 - 0 --- + 10 V(0) x -1 - 0 --- + 10 Hal
Re: Draft Philosophy Paper
At 2/21/02, you wrote: If you are saying that it is the uncountability itself of copies that imparts indeterminacy, or changes the preponderancy, then effectively you are also saying that random selections from all the reals between -1 and +10 do not converge towards a ratio of 10:1 for positive to negative values - I can't see what other result is possible. That is you model and it is one dimensional [call it x] that is it has one venue. Now add a dimension call it y that is infinite and perpendicular to your example's x. This is an infinite number of venues. Now randomly sample on the xy plane. The area of the plane below zero on the x dimension is the same as the area above zero on the x dimension i.e. infinite = no bias as to sign mix of the resulting random sample of reals on x. snip there is no more necessity to have no preponderance of any particular type of physical universe than to have no preponderance of a particular type of galaxy, or grain of sand. With this I disagree when describing the Everything because on its face it attempts to extract information from an informationless source. Your example from within a particular universe [intrinsic information] is not applicable because here its any style you want. (Note also that copies in the sense referred to in the paper would not be produced by any 'nested Everything' (assuming they are a legitimate possibility) - With this I would agree, mine is not a one venue model. each different possible nested Everything would have to be a different state, for which there may or may not be copies, dependent on the correct interpretation of NAP.) What you seem to be saying re my approach using the above analysis of your example is that the boundaries of the plane in the y dimension may meander. With this I agree. Actually its essential. So what? The areas above and below the x = 0 line are still equal. Hal
Re: Draft Philosophy Paper
Dear Alastair:
An clarification of my analysis of your -1 to + 10 example:
That is your model and it is one dimensional [call it x] that is it has one
venue.
Now add a dimension call it y that is infinite and perpendicular to your
example's x. This is an infinite number of venues. Add the y boundaries
at x = -1 and x = +10. Now randomly sample on this bounded xy plane. The
area of the plane below zero on the x dimension is the same as the area
above zero on the x dimension i.e. infinite = no bias as to sign mix of the
resulting random sample of reals on x.
{near the end of my post a further clarification}
What you seem to be saying re my approach using the above analysis of your
example is that either of the boundaries of the above plane in the y
dimension may meander between x = -1 and x = + 1. With this I agree.
Actually its essential. So what? The areas above and below the x = 0 line
are still equal i.e. infinite so a random sample in the xy plane over this
structure still produces no bias as to sign mix of the resulting random
sample of reals on x.
Hal
Re: Draft Philosophy Paper
Dear Alastair: I think you still miss the thrust of my comment. As directly as I can say it: The Everything is the ensemble of all counterfactuals. The counterfactuals cancel out resulting in no information in the Everything. The Everything and the Nothing are cancelling counterfactuals and thus are in the ensemble. The Everything is a member of itself. So: The Everything contains infinitely many [uncountably so] nested copies of itself. Thus it contains an uncountable number of logical venues [its nested selves]. Therefore: All types of universes are present an uncountably infinite number of times in any of the nested Everythings. That is there is no preponderance [an extrinsic property of a universe] information in keeping with a definition of an Everything as information free. This seems to comply with NAP since the logical reason for the above is to maintain the zero information mantra. Either there is a reason why we are in this kind of universe beyond pure chance or there is not. If there is then where did that information come from if there is no information in the ensemble? Hal At 2/20/02, you wrote: The condition given at the start of the appendix is of one copy per (logically possible) unit combination. Section 2 of the paper deals with the various possible cases of copies. Alastair
Re: Draft Philosophy Paper
Dear Russell: As to any surprise that we are in the universe we are in I see none. It is just chance. My previous post did not go into the part of my approach as to why a universe should evolve. What drives this dynamic inside an Everything? The process I have currently set up for this happened to resemble when I was done the life process of survival of the fit. The universes themselves may qualify as life. It is then not surprising that some could for some set of sequential states support large internal structures that follow the same pattern. I currently have convinced myself that there is no observation process on the part of such structures. They simply are the sum total of past interactions with other structures in that universe across the boundary that defines their absence of isolation. The only influence such structures have on the embedding system is this interaction which is not observation but passive accommodation to state to state transition events at the boundary. I then base the rest i.e. predictions as to the nature of our universe on the ideas: 1) That some universes are sufficiently well behaved for some set of sequential states such that each state in the sequence has a deterministicly consistent prior state. This state is found using the rules of that universe absent any true noise component they may allow. This state need not be the actual prior state. 2) That the state for some universes is physically a pattern of discrete points in a space - in our case a three space. In the end, structures within a particular universe interact with their entire universe so their evolution may influence the survival of their universe. However, due to the nested nature of the Everything and the nature of the process driving the evolution of universes [basically an exercise in finding an allowed next pattern on a randomly shifting Nothing/Everything boundary] the extinction of one universe [a failure to find such a new pattern before the current pattern itself is disrupted by the boundary shifts] does not influence the success or failure of its copies to find an allowed next state. Hal At 2/21/02, you wrote: The information is contained within the Anthropic Principle itself. Resource constraints that any observer must have impose a bias towards simpler descriptions - that is the thrust of Alistair's and my argument. Without the AP, the Everything is indeed devoid of any structure whatsoever. I never understood why you persevere in denying a place for the AP. Cheers
Re: Draft Philosophy Paper
Dear Alastair: I believe I understood your appendix, but to clarify my question: You have a logical base of logical unit strength m. Call that a particular venue for all universes describable by some combination of one or more of the units in m. My original question was why have just one copy of this venue? The Everything surely has enough room for an infinite number of independent copies of m. So any universe describable in m is represented in the Everything by an infinite number of copies. This removes any preponderance of simple universes over complex ones. Further the venue m + 1 can support even more varieties of universes including all those in m and itself is repeated an infinite number of times in the Everything. So too for M + 2 and so on. This seems to completely remove the extrinsic property of preponderance and its associated information from the Everything. Hal At 2/19/02, you wrote: The intended implication is that the minimally represented versions of universes will predominate for all possible values of m (above n+d). Sorry if that wasn't clear. - Original Message - From: H J Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: 19 February 2002 04:50 Subject: Re: Draft Philosophy Paper Dear Alastair: In the appendix of your paper if we call m logical units a venue why do you have just one such venue? If there are an infinite number of venues of strength m in the Everything then any sub m sets in m appear an infinite number of times in the Everything. Hal
Re: Draft Philosophy Paper
Dear Alastair: I will read your paper, but it seems to me that the no information approach to formulating an Everything precludes selection. Selection assigns a property to a subset of the ensemble that the other members do not share. This destroys the ensemble. Prevalence being a property I would conclude from this that no allowed type of universe can be more prevalent than any other allowed type. Speculation: Is it possible to use this approach to exclude certain types of universes? First distinguish two types of evolving universes [universes that change state]: 1) Those that have rules of state succession that forbid a source of external information [true noise] 2) Those that have rules of state succession that allow a source of true noise [external information] to some degree [from zero true noise to nothing but true noise]. This distinction is already a selection so one or the other type must be absent from an informationless Everything. I think the first step to resolution is to notice that type #2 could include type #1 as an extreme lower limit case, but type #1 can not include type #2 at all. However, is the extreme lower limit case for #2 allowed to be zero true noise? Perhaps to resolve this ask whether either of these types is a larger set. Since type #2 is a continuum is also type #1? If an infinite rule set and/or data string is equivalent to number #2 then universes in #1 must have finite rule sets and finite data strings [finitely describable]. The number of such universes would be merely countable. At any non zero degree of true noise - say 2% or 20% etc. there would be an infinite number of ways to allow that percentage. The conclusion would be that universes with zero true noise would be extremely rare relative to any of those with a non zero degree of true noise and so such an information generating lower limit is excluded. The extreme lower limit for true noise in #2 must be greater than zero. However, this itself seems like a breach of the no information approach. This could be fixed if type #1 were reclassified as non evolving universes and a door is opened between the two types. A type #2 universe with the right dose of true noise can surely convert to a type #1. This would balance the quantity issue. Can type #1 universes become type #2 universes. They must be able to or again there would be a selection. It seems this is just a way of saying that universes do not have fixed rules of state succession. Hal At 2/17/02, you wrote: Thanks for your comments - the 'difficulty' that you refer to is none other than the White Rabbit problem, on which there has been much discussion in this forum. My own approach addresses the problem from the standpoint of all logical possibilities (rather than any particular model or set of rules), which can make the problem non-trivial to solve. Alastair
Re: Draft Philosophy Paper
I see no reason why any difficulty along this line arises in the first place. In my model all evolving universes have rules of state succession that allow some degree of true noise entering the universe at each transition. In this venue there would be an infinite number of universes that have rules with low randomness in large and medium [many many bits] events, substantial randomness in moderately small [moderate number of bits] events, and a sharp roll off in the number of the very smallest [one bit] events. This seems a decent description of universes like ours and there would be an infinite number of them. The same number as for any style of universe. Hal
Re: Mirror Symmetry
At 2/3/02, you wrote: It has been conventional wisdom that the fundamental laws of physics are not invariant under parity. Now, the computational complexity of a model that lacks mirror symmetry is much larger than a similar mirror symmetric model. It would thus be very strange if Nature is indeed not invariant under parity. I see no reason at this point to consider the evolution of a universe as ever being a complex algorithmic computational exercise. Using a different way of trying to explain my approach: In my approach the evolution is similar to a matching exercise between the possible next states of a universe as represented by finite bit strings and the current set of an endless series of randomly selected infinite bit strings presented by the underlying informationless system. The members of the set of currently presented infinite strings is in constant random flux. If a section of any of the current set of infinite bit strings presented by the system has a sub string that matches one of the possible next state bit strings of a universe then that universe has a next state. If not that universe is extinguished. Sort of a survival of the fit. To survive for many state transitions a universe has to allow the input of new information as true noise. The matching exercise is like a cellular automaton with true noise. Properly implemented cellular automata do their computation locally with just a few steps. Actually the computation in my approach is just working a lookup table. The evolution of a universe would always be as if run on an immense parallel computer of just the right configuration so as to precisely accommodate the current state of a universe plus noise. The new match would have to be made before the infinite string supporting the current match for that universe vanished from the set of presented strings. The arrangement of parallel table lookups in local cells and limited duration of the match search causes successful evolving universes to have at least a minimum amount of allowance for the input of true noise. Hal
my model
If anyone is interested a draft [which changes from time to time] of my model is at a new URL: http://home.mindspring.com/~hjr2/model01.html Hal
Observers
The reason I currently do not see observer or observation as necessary concepts is because there are no isolated systems within a universe. Rather sub systems of a universe are a summation of their prior interactions with the remainder of their universe via changes in the state of the surface that defines their absence of isolation. I see no communication between the evolution of universes. Hal
Histories and universes
Some ideas re histories and universes: 1) Definitions: Universe: A universe is defined by its current state. Identifiable past history: The prior state can be fully determined from the current state. Identifiable future history: The next state can be fully determined by the current state. 2) If a universe has an identifiable past history associated with it then there is a halting algorithm that allows that identification decision. This algorithm must be able to check that past history and to do so it must be able to compute that past history given the current state as data. 3) This same algorithm may or may not be able to compute the future history of such a universe because the universe's rules of state succession may change or acquire some degree of do not care i.e. develop a random content allowing in true noise as a result of the state shift. 4) If a universe does not have an identifiable past history but nevertheless has evolved then it has a past history but there is no algorithm that can compute it. Such a universe must currently have rules of state succession that allow in some degree of true noise. 5) There can at most be a countable infinity of universes with identifiable and thus computable past histories, future histories, or both because that is the limit on the number of halting algorithms. 6) On the other hand there can be an uncountable infinity of universes that have unidentifiable and thus uncomputable past and future histories. 7) Universes which always have identifiable past histories and/or future histories even if only countably infinite in number represent information in the Everything as they require it to contain a computer - a UTM - that has a parsed application - a selection. However the Everything has no information - no selection - so such universes are not present. The Everything can contain a UTM if universes with identifiable past histories act as seeds for universes that have unidentifiable past histories. In effect the UTM [or UD] spawns Big Bangs [in my model isomorphic links or interpretations] which then evolve with true noise input. This transition to having a true noise input converts their identifiable past history into an unidentifiable one and they thus join the uncountable number of universes with unidentifiable past and future histories - those whose rules of state succession require true noise input. Hal
Re: Juergen's paper
Dear Matthieu: Another correction to my post: I said: - I allow that the current state of a universe contains the information necessary to list all the possible future and prior states but not to determine the actual prior and future states. - However, a universe may have a rule that allows the rules to change. This if it happens would prevent a current state of a universe from having the information to list all the possible prior states. Hal
Re: Juergen's paper
Dear Matthieu: At 1/23/02, you wrote: An universe can be an oriented graph of states. Each state has no, one or more next states. It also has no, one or more previous states. While I allow that a universe can have more than one possible previous state or no previous state [when in the initial state] - in fact my model insists on it - I do not allow that there is more than one actual previous state for a particular universe. This universe may be computable. I allow that the current state of a universe contains the information necessary to list all the possible future and prior states but not to determine the actual prior and future states. This information is useless because to use it internally is itself a change of state. Further I do not agree that there is any external point of view or any observer with any point of view at all for that matter. That would just be excess entities [i.e. too complex a theory] To compute it doesn't means you start from an unique initial state and you go from it to the only next one and so on. The point I am exploring in these posts is that if one can associate a particular history with a particular universe [its current state defines a universe - see below] then that history must be computable or one could not make the association. In this case Juergen seems to make such an association and so the paper seems to assume that which was to be demonstrated. If the initial state of a universe is sufficient to establish it as a universe then it is not necessary for a universe to have a history. Each state of a universe can be an initial state in the sense that new information is introduced from an outside source at each transition. An evolving universe needs one extra property: the capability of finding a next state. This can be random choice or partly random choice but my model does not admit a choice via rules with no random content. If there is conscious beings in this universe. They will perceive the time flowing as they go from a state to a next one, and again. Not at all IMO. I can not demonstrate that my universe had a prior state. What may seem to be my history is just the current state of a part of a sub system of a universe. But from a third person point of view, this univers is a static (and so deterministic) mathematical object. Again I see observation of any sort as an unnecessary complication of a TOE. When for a given state there is more than one next state, it is for the concious being as if random rule their future. Again IMO observers are not necessary or even possible for that matter. My model does insist that for currently finite universes there will always be more than one possible next state but only one actual next state. They may think their universe is not deterministic, except for those who has an Everett-like theory. Multiple actually realized future states as opposed to multiple possible future states is also unnecessarily complex. When there is no next state, it's the end of times. There is indeed the possibility of no actual next state, but IMO there is always multiple possible next states for currently finite universes. This kind of universes doesn't have an history, but many histories. As I said my model insists that there are multiple possible prior and next states for finite universes but only one actual prior state and only one actually realized next state. Each way in the oriented graph is an history. I will suppose you mean over possible prior states. In my view each state has only one actual prior state but many possible prior states and the current state only has the information that could list the full set of possible prior states but there is never any information re the determination of the actual prior state. Even loops are possible. Yes this could happen for universes with rules of evolution that have a high random or do not care content. Many different histories can lead to a given state. IMO - as I have said - for any particular universe any state has multiple possible immediately prior states but only one actual prior state. If our universe is this kind of graph, the big-bang may not start from an inital eden state (which has no previous state) but from a set of states that can loop. After the big-bang I suppose there is no loop. I see this as too complex. My generating mechanism is very simple. Hal
Re: Juergen's paper
Dear Matthieu: I thought I had found all cases where I used future when I wanted to use next but a few escaped and are corrected below: xx I allow that the current state of a universe contains the information necessary to list all the possible next and prior states but not to determine the actual prior and next states. This information is useless because to use it internally is itself a change of state. Further I do not agree that there is any external point of view or any observer with any point of view at all for that matter. That would just be excess entities [i.e. too complex a theory] xx Multiple actually realized next states as opposed to multiple possible next states is also unnecessarily complex. Hal
Re: Kiln People
Dear Hal At 1/18/02, you wrote: snip I'm not convinced about the models of computation involving GTMs and such in Juergen Schmidhuber's paper. Basically these kinds of TMs can change their mind about the output, and the machine doesn't know when it is through changing its mind. So there is never any time you can point to the output or even a prefix and say that part is done. It is questionable to me whether this ought to count as computation. snip I am currently somewhat in accord with this view. My model of the ensemble of universes which is just approaching a finished condition is not a computational one. However, without regard to the application of computation to the comprehension of this ensemble I do not see an external difference between any of Juergen's machines and the usual UTM. Whenever a prefix is indeed done that is just the same as any external output of a UTM with the computation activity spread over a long section of tape internally IMO. snip As to the discussions of measure and probability re the likelihood of a particular sort of universe I do not see the point. The core idea for a founding postulate that seems most appealing is that no information exists. So the entire discussion re measure IMO is just an effort to extract a factual(s) from an ensemble of counterfactuals. Yours Hal Ruhl
Error in Refinements to my model
Sorry, I missed some editing errors in the lead in to the referenced post. I meant to say: I currently define information as fact(s) that are absent counter facts. Example of counter facts [sort of]: In our universe the rules dictate that any sufficiently large mass wants to assume a shape that is essentially a sphere. There are numerous other possibilities that could be the rule in some other universe. The ensemble of all these various rules is a complete set of counter facts that contains no information re this shape issue. Call facts that are absent counter facts factuals. Call counter facts counterfactuals A fact that has counterfactuals is itself a counterfactual. The objective is to model our universe using no information that is by using just complete sets of counterfactuals. First examine the following: The Everything which is defined as the ensemble of all counterfactuals exists. This existence by itself would be a factual and violate the objective. Now let us examine two counterfactuals. 1) The Everything which is the ensemble of all counterfactuals exists. 2) The Nothing which is the absence of all facts both counterfactual and factual exists. The Everything and the Nothing are antipodal representations of no information. The existence of either is the counterfactual to the existence of the other and so the dual existence is allowed under the objective since it represents no information. While the Nothing can not contain the Everything nor itself by definition and the Everything can not contain one or the other, can the Everything contain both? At the moment I think it can and this just produces an infinite nesting. That is the initial mathematical foundation. Next is the exploration of the manifestation of this foundation while defining physical universes as isomorphisms to this manifestation. At any nesting level if the manifestation was unchanging or structurally sequenced that would be a factual. If the manifestation at any given level is a random sequence of piece after piece of the Everything of that level each of which would be automatically accompanied by the counterfactual residual portion of the associated Nothing there would be no factual. Evolving universes must be isomorphic to a portion of each successive manifest counterfactual. The nesting would allow an infinite number of such universes. The rules of isomorphic shift [the laws of physics] for each such universe must have some random [true noise] content in order to sustain the succession of isomorphisms to the random sequence of counterfactuals. Hal
Provability, consistency, information, computability
The recent posts on Does provability matter prompt the following. If information can be defined as the single valued resolution of an issue then it would seem to me that information is actually consistency. The only way I can see for all information to equal no information is for there to be no consistency. The Everything then would be definable as the total absence of consistency. The first victim of this would be provability. The second victim would be computability - the first output to have a stable prefix would represent a consistency - thus no stable outputs possible even if given all opportunity to stabilize. This means no computers of any sort including the UD. This brings me to my point of view in which evolving universes must have a true noise content in the rules for selecting their next state and no histories - just isolated moments. What are the characteristics of an evolving universe that can support SAS? Universes that support SAS would seem to need a low level of true noise on the large event end of the scale and the rules of moment to moment succession required by this should impose a low level of one bit [small end of scale] events as well since few would fit the rules. The bit string descriptor of such a universe should need to have a decreasing internal correlation and an increasing length as the universe goes from moment to moment in order to have space for the accumulating results of the true noise thus a Second Law of Thermodynamics, an arrow to time, and a quantum mechanics coupled with a unifiable relativity. Hal
RE One page revisited again
Please allow me to try this one more time since I think I see why it did
not make it into the posted archive and I have a change to my additional
comment.
In #10 I discuss the length of the descriptive string. A better way to
state what is said there may be to indicate that I am only interested in
the structure of the finite prefix of what might be an infinite
string. The infinite tail if there is one is invaded for lack of a
better term as the length of the prefix increases until the prefix is
itself infinite.
This is an improved presentation of my current TOE model. Its a bit more
than one page.
I believe I see some shadow of both Juergen's approach and Bruno's approach
in it. The intermediate step has unfinished business and the lowest level
is a bit like a duplicator, transporter.
1) The single postulate is The total system contains no information.
2) Two distinct expressions of no information are recognized by the model:
a) The Nothing which is devoid of any information whatsoever.
b) The Everything which contains all information.
These are not identical. Rather they are antipodal in that neither
can contain the other because of a stability issue.
3) The stability issue is the unavoidable emergence of a question of the
stability of the manifestation of either of these expressions of no
information should either actually become manifest. This manifestation
must either be stable or not with respect to the alternate expressions of
no information. Thus the alternate expression must be separately
available for manifestation and the stability question must have a resolution.
4) If either expression of No information becomes manifest then the
resolution of the stability question represents information and violates
the postulate.
5) A way to make the total system comply with the postulate:
a) Both the Nothing and the Everything are in a simultaneous
partial manifestation.
b) To avoid any information including any permanent selection in this
system
and thus comply with the postulate the partial manifestation of
the Everything is realized by the actual but temporary
manifestation of randomly selected pieces of the Everything herein
called patterns each of which has a manifestation of random duration.
6) Evolving universes are successive isomorphisms to some portion of those
patterns with overlapping manifestations.
7) Enduring evolving universes with fully deterministic rules of
isomorphism succession find no home in this model because they would find
no sustainable state to state trajectory within the random nature of the
partial manifestation of the Everything. The rules of an enduring
universe must be partly true noise.
8) The cascade representation for state Sj(i + 1) of universe j while in
state Sj(i) is:
(1) P'j(i + 1) = {R'j(i)[Pj(i)]} determines the group of pairs:
{R'jk(i + 1),Sjk(i + 1)}; k = 1 to sj(i).
Where: Pj(i) is the shortest self delimiting program that computes Sj(i).
R'j(i) is the current full set of rules that act on the
current state
[represented in its compressed condition].
sj(i) is the number of acceptable successor {rule set, state}
pairs to
Sj(i) due to the true noise content of R'j(i).
Pj(i) contains Rj(i) which is a deterministic derivative of R'j(i - 1) used
only to allow the compression of the data in Sj(i) and a self delimiter DeL(i).
R'j(i) is the full and partially non deterministic true noise containing
successor to R'j(i - 1).
9) The first of the {R'jk(i + 1), Sjk(i + 1)} pairs to be represented in a
sub section of one of the manifest patterns becomes the next state and its
rules [isomorphic link] of universe j as the pattern supporting the current
link loses its own manifestation.
Once this happens the precursor program P'(i + 1) is replaced with Pj(i +
1) and the applicable Sjk(i + 1) becomes Sj(i + 1). So we get:
(2) Pj(i + 1) = {Rj(i + 1)[P(i)] + DeL(i + 1)} computes Sj(i + 1).
So operating on this with R'j(i + 1) in a manner similar to (1) gives the
next iteration to the cascade:
(3) P'j(i + 2) = {R'j(i + 1)[Pj(i + 1)} determines the group of
pairs
{R'jk(i + 2),Sjk(i + 2)}; k = 1 to sj(i + 1).
and so on.
10) The model's focus on the use of a discrete point space for a universe
is due to:
a) Notice that each successive Pj() is longer than its predecessor if
Rj() does
not decrease in length and ultimately any such shortening of Rj()
will be
swamped out. Over the long haul then Pj() increases in length.
b) As the length of Pj() increases the length of the string it
computes and
which represents Sj() must increase in length [perhaps not always
synchronized with length changes in Pj()] if it is to
